Traveltime inversion and error analysis for layered anisotropy

NASA Astrophysics Data System (ADS)

Jiang, Fan; Zhou, Hua-wei

2011-02-01

While tilted transverse isotropy (TTI) is a good approximation of the velocity structure for many dipping and fractured strata, it is still challenging to estimate anisotropic depth models even when the tilted angle is known. With the assumption of weak anisotropy, we present a TTI traveltime inversion approach for models consisting of several thickness-varying layers where the anisotropic parameters are constant for each layer. For each model layer the inversion variables consist of the anisotropic parameters ɛ and δ, the tilted angle φ of its symmetry axis, layer velocity along the symmetry axis, and thickness variation of the layer. Using this method and synthetic data, we evaluate the effects of errors in some of the model parameters on the inverted values of the other parameters in crosswell and Vertical Seismic Profile (VSP) acquisition geometry. The analyses show that the errors in the layer symmetry axes sensitively affect the inverted values of other parameters, especially δ. However, the impact of errors in δ on the inversion of other parameters is much less than the impact on δ from the errors in other parameters. Hence, a practical strategy is first to invert for the most error-tolerant parameter layer velocity, then progressively invert for ɛ in crosswell geometry or δ in VSP geometry.

Numerical Differentiation Methods for Computing Error Covariance Matrices in Item Response Theory Modeling: An Evaluation and a New Proposal

ERIC Educational Resources Information Center

Tian, Wei; Cai, Li; Thissen, David; Xin, Tao

2013-01-01

In item response theory (IRT) modeling, the item parameter error covariance matrix plays a critical role in statistical inference procedures. When item parameters are estimated using the EM algorithm, the parameter error covariance matrix is not an automatic by-product of item calibration. Cai proposed the use of Supplemented EM algorithm for…

Estimating standard errors in feature network models.

PubMed

Frank, Laurence E; Heiser, Willem J

2007-05-01

Feature network models are graphical structures that represent proximity data in a discrete space while using the same formalism that is the basis of least squares methods employed in multidimensional scaling. Existing methods to derive a network model from empirical data only give the best-fitting network and yield no standard errors for the parameter estimates. The additivity properties of networks make it possible to consider the model as a univariate (multiple) linear regression problem with positivity restrictions on the parameters. In the present study, both theoretical and empirical standard errors are obtained for the constrained regression parameters of a network model with known features. The performance of both types of standard error is evaluated using Monte Carlo techniques.

Incorporating measurement error in n = 1 psychological autoregressive modeling

PubMed Central

Schuurman, Noémi K.; Houtveen, Jan H.; Hamaker, Ellen L.

2015-01-01

Measurement error is omnipresent in psychological data. However, the vast majority of applications of autoregressive time series analyses in psychology do not take measurement error into account. Disregarding measurement error when it is present in the data results in a bias of the autoregressive parameters. We discuss two models that take measurement error into account: An autoregressive model with a white noise term (AR+WN), and an autoregressive moving average (ARMA) model. In a simulation study we compare the parameter recovery performance of these models, and compare this performance for both a Bayesian and frequentist approach. We find that overall, the AR+WN model performs better. Furthermore, we find that for realistic (i.e., small) sample sizes, psychological research would benefit from a Bayesian approach in fitting these models. Finally, we illustrate the effect of disregarding measurement error in an AR(1) model by means of an empirical application on mood data in women. We find that, depending on the person, approximately 30–50% of the total variance was due to measurement error, and that disregarding this measurement error results in a substantial underestimation of the autoregressive parameters. PMID:26283988

Parameter recovery, bias and standard errors in the linear ballistic accumulator model.

PubMed

Visser, Ingmar; Poessé, Rens

2017-05-01

The linear ballistic accumulator (LBA) model (Brown & Heathcote, , Cogn. Psychol., 57, 153) is increasingly popular in modelling response times from experimental data. An R package, glba, has been developed to fit the LBA model using maximum likelihood estimation which is validated by means of a parameter recovery study. At sufficient sample sizes parameter recovery is good, whereas at smaller sample sizes there can be large bias in parameters. In a second simulation study, two methods for computing parameter standard errors are compared. The Hessian-based method is found to be adequate and is (much) faster than the alternative bootstrap method. The use of parameter standard errors in model selection and inference is illustrated in an example using data from an implicit learning experiment (Visser et al., , Mem. Cogn., 35, 1502). It is shown that typical implicit learning effects are captured by different parameters of the LBA model. © 2017 The British Psychological Society.

An analysis of the least-squares problem for the DSN systematic pointing error model

NASA Technical Reports Server (NTRS)

Alvarez, L. S.

1991-01-01

A systematic pointing error model is used to calibrate antennas in the Deep Space Network. The least squares problem is described and analyzed along with the solution methods used to determine the model's parameters. Specifically studied are the rank degeneracy problems resulting from beam pointing error measurement sets that incorporate inadequate sky coverage. A least squares parameter subset selection method is described and its applicability to the systematic error modeling process is demonstrated on Voyager 2 measurement distribution.

A Novel Error Model of Optical Systems and an On-Orbit Calibration Method for Star Sensors.

PubMed

Wang, Shuang; Geng, Yunhai; Jin, Rongyu

2015-12-12

In order to improve the on-orbit measurement accuracy of star sensors, the effects of image-plane rotary error, image-plane tilt error and distortions of optical systems resulting from the on-orbit thermal environment were studied in this paper. Since these issues will affect the precision of star image point positions, in this paper, a novel measurement error model based on the traditional error model is explored. Due to the orthonormal characteristics of image-plane rotary-tilt errors and the strong nonlinearity among these error parameters, it is difficult to calibrate all the parameters simultaneously. To solve this difficulty, for the new error model, a modified two-step calibration method based on the Extended Kalman Filter (EKF) and Least Square Methods (LSM) is presented. The former one is used to calibrate the main point drift, focal length error and distortions of optical systems while the latter estimates the image-plane rotary-tilt errors. With this calibration method, the precision of star image point position influenced by the above errors is greatly improved from 15.42% to 1.389%. Finally, the simulation results demonstrate that the presented measurement error model for star sensors has higher precision. Moreover, the proposed two-step method can effectively calibrate model error parameters, and the calibration precision of on-orbit star sensors is also improved obviously.

Sensitivity of the model error parameter specification in weak-constraint four-dimensional variational data assimilation

NASA Astrophysics Data System (ADS)

Shaw, Jeremy A.; Daescu, Dacian N.

2017-08-01

This article presents the mathematical framework to evaluate the sensitivity of a forecast error aspect to the input parameters of a weak-constraint four-dimensional variational data assimilation system (w4D-Var DAS), extending the established theory from strong-constraint 4D-Var. Emphasis is placed on the derivation of the equations for evaluating the forecast sensitivity to parameters in the DAS representation of the model error statistics, including bias, standard deviation, and correlation structure. A novel adjoint-based procedure for adaptive tuning of the specified model error covariance matrix is introduced. Results from numerical convergence tests establish the validity of the model error sensitivity equations. Preliminary experiments providing a proof-of-concept are performed using the Lorenz multi-scale model to illustrate the theoretical concepts and potential benefits for practical applications.

Bayesian inversions of a dynamic vegetation model at four European grassland sites

NASA Astrophysics Data System (ADS)

Minet, J.; Laloy, E.; Tychon, B.; Francois, L.

2015-05-01

Eddy covariance data from four European grassland sites are used to probabilistically invert the CARAIB (CARbon Assimilation In the Biosphere) dynamic vegetation model (DVM) with 10 unknown parameters, using the DREAM(ZS) (DiffeRential Evolution Adaptive Metropolis) Markov chain Monte Carlo (MCMC) sampler. We focus on comparing model inversions, considering both homoscedastic and heteroscedastic eddy covariance residual errors, with variances either fixed a priori or jointly inferred together with the model parameters. Agreements between measured and simulated data during calibration are comparable with previous studies, with root mean square errors (RMSEs) of simulated daily gross primary productivity (GPP), ecosystem respiration (RECO) and evapotranspiration (ET) ranging from 1.73 to 2.19, 1.04 to 1.56 g C m-2 day-1 and 0.50 to 1.28 mm day-1, respectively. For the calibration period, using a homoscedastic eddy covariance residual error model resulted in a better agreement between measured and modelled data than using a heteroscedastic residual error model. However, a model validation experiment showed that CARAIB models calibrated considering heteroscedastic residual errors perform better. Posterior parameter distributions derived from using a heteroscedastic model of the residuals thus appear to be more robust. This is the case even though the classical linear heteroscedastic error model assumed herein did not fully remove heteroscedasticity of the GPP residuals. Despite the fact that the calibrated model is generally capable of fitting the data within measurement errors, systematic bias in the model simulations are observed. These are likely due to model inadequacies such as shortcomings in the photosynthesis modelling. Besides the residual error treatment, differences between model parameter posterior distributions among the four grassland sites are also investigated. It is shown that the marginal distributions of the specific leaf area and characteristic mortality time parameters can be explained by site-specific ecophysiological characteristics.

Semiparametric modeling: Correcting low-dimensional model error in parametric models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berry, Tyrus, E-mail: thb11@psu.edu; Harlim, John, E-mail: jharlim@psu.edu; Department of Meteorology, the Pennsylvania State University, 503 Walker Building, University Park, PA 16802-5013

2016-03-01

In this paper, a semiparametric modeling approach is introduced as a paradigm for addressing model error arising from unresolved physical phenomena. Our approach compensates for model error by learning an auxiliary dynamical model for the unknown parameters. Practically, the proposed approach consists of the following steps. Given a physics-based model and a noisy data set of historical observations, a Bayesian filtering algorithm is used to extract a time-series of the parameter values. Subsequently, the diffusion forecast algorithm is applied to the retrieved time-series in order to construct the auxiliary model for the time evolving parameters. The semiparametric forecasting algorithm consistsmore » of integrating the existing physics-based model with an ensemble of parameters sampled from the probability density function of the diffusion forecast. To specify initial conditions for the diffusion forecast, a Bayesian semiparametric filtering method that extends the Kalman-based filtering framework is introduced. In difficult test examples, which introduce chaotically and stochastically evolving hidden parameters into the Lorenz-96 model, we show that our approach can effectively compensate for model error, with forecasting skill comparable to that of the perfect model.« less

Utility of a novel error-stepping method to improve gradient-based parameter identification by increasing the smoothness of the local objective surface: a case-study of pulmonary mechanics.

PubMed

Docherty, Paul D; Schranz, Christoph; Chase, J Geoffrey; Chiew, Yeong Shiong; Möller, Knut

2014-05-01

Accurate model parameter identification relies on accurate forward model simulations to guide convergence. However, some forward simulation methodologies lack the precision required to properly define the local objective surface and can cause failed parameter identification. The role of objective surface smoothness in identification of a pulmonary mechanics model was assessed using forward simulation from a novel error-stepping method and a proprietary Runge-Kutta method. The objective surfaces were compared via the identified parameter discrepancy generated in a Monte Carlo simulation and the local smoothness of the objective surfaces they generate. The error-stepping method generated significantly smoother error surfaces in each of the cases tested (p<0.0001) and more accurate model parameter estimates than the Runge-Kutta method in three of the four cases tested (p<0.0001) despite a 75% reduction in computational cost. Of note, parameter discrepancy in most cases was limited to a particular oblique plane, indicating a non-intuitive multi-parameter trade-off was occurring. The error-stepping method consistently improved or equalled the outcomes of the Runge-Kutta time-integration method for forward simulations of the pulmonary mechanics model. This study indicates that accurate parameter identification relies on accurate definition of the local objective function, and that parameter trade-off can occur on oblique planes resulting prematurely halted parameter convergence. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Prediction-error variance in Bayesian model updating: a comparative study

NASA Astrophysics Data System (ADS)

Asadollahi, Parisa; Li, Jian; Huang, Yong

2017-04-01

In Bayesian model updating, the likelihood function is commonly formulated by stochastic embedding in which the maximum information entropy probability model of prediction error variances plays an important role and it is Gaussian distribution subject to the first two moments as constraints. The selection of prediction error variances can be formulated as a model class selection problem, which automatically involves a trade-off between the average data-fit of the model class and the information it extracts from the data. Therefore, it is critical for the robustness in the updating of the structural model especially in the presence of modeling errors. To date, three ways of considering prediction error variances have been seem in the literature: 1) setting constant values empirically, 2) estimating them based on the goodness-of-fit of the measured data, and 3) updating them as uncertain parameters by applying Bayes' Theorem at the model class level. In this paper, the effect of different strategies to deal with the prediction error variances on the model updating performance is investigated explicitly. A six-story shear building model with six uncertain stiffness parameters is employed as an illustrative example. Transitional Markov Chain Monte Carlo is used to draw samples of the posterior probability density function of the structure model parameters as well as the uncertain prediction variances. The different levels of modeling uncertainty and complexity are modeled through three FE models, including a true model, a model with more complexity, and a model with modeling error. Bayesian updating is performed for the three FE models considering the three aforementioned treatments of the prediction error variances. The effect of number of measurements on the model updating performance is also examined in the study. The results are compared based on model class assessment and indicate that updating the prediction error variances as uncertain parameters at the model class level produces more robust results especially when the number of measurement is small.

Improved parameter inference in catchment models: 1. Evaluating parameter uncertainty

NASA Astrophysics Data System (ADS)

Kuczera, George

1983-10-01

A Bayesian methodology is developed to evaluate parameter uncertainty in catchment models fitted to a hydrologic response such as runoff, the goal being to improve the chance of successful regionalization. The catchment model is posed as a nonlinear regression model with stochastic errors possibly being both autocorrelated and heteroscedastic. The end result of this methodology, which may use Box-Cox power transformations and ARMA error models, is the posterior distribution, which summarizes what is known about the catchment model parameters. This can be simplified to a multivariate normal provided a linearization in parameter space is acceptable; means of checking and improving this assumption are discussed. The posterior standard deviations give a direct measure of parameter uncertainty, and study of the posterior correlation matrix can indicate what kinds of data are required to improve the precision of poorly determined parameters. Finally, a case study involving a nine-parameter catchment model fitted to monthly runoff and soil moisture data is presented. It is shown that use of ordinary least squares when its underlying error assumptions are violated gives an erroneous description of parameter uncertainty.

A pharmacometric case study regarding the sensitivity of structural model parameter estimation to error in patient reported dosing times.

PubMed

Knights, Jonathan; Rohatagi, Shashank

2015-12-01

Although there is a body of literature focused on minimizing the effect of dosing inaccuracies on pharmacokinetic (PK) parameter estimation, most of the work centers on missing doses. No attempt has been made to specifically characterize the effect of error in reported dosing times. Additionally, existing work has largely dealt with cases in which the compound of interest is dosed at an interval no less than its terminal half-life. This work provides a case study investigating how error in patient reported dosing times might affect the accuracy of structural model parameter estimation under sparse sampling conditions when the dosing interval is less than the terminal half-life of the compound, and the underlying kinetics are monoexponential. Additional effects due to noncompliance with dosing events are not explored and it is assumed that the structural model and reasonable initial estimates of the model parameters are known. Under the conditions of our simulations, with structural model CV % ranging from ~20 to 60 %, parameter estimation inaccuracy derived from error in reported dosing times was largely controlled around 10 % on average. Given that no observed dosing was included in the design and sparse sampling was utilized, we believe these error results represent a practical ceiling given the variability and parameter estimates for the one-compartment model. The findings suggest additional investigations may be of interest and are noteworthy given the inability of current PK software platforms to accommodate error in dosing times.

An analysis of input errors in precipitation-runoff models using regression with errors in the independent variables

USGS Publications Warehouse

Troutman, Brent M.

1982-01-01

Errors in runoff prediction caused by input data errors are analyzed by treating precipitation-runoff models as regression (conditional expectation) models. Independent variables of the regression consist of precipitation and other input measurements; the dependent variable is runoff. In models using erroneous input data, prediction errors are inflated and estimates of expected storm runoff for given observed input variables are biased. This bias in expected runoff estimation results in biased parameter estimates if these parameter estimates are obtained by a least squares fit of predicted to observed runoff values. The problems of error inflation and bias are examined in detail for a simple linear regression of runoff on rainfall and for a nonlinear U.S. Geological Survey precipitation-runoff model. Some implications for flood frequency analysis are considered. A case study using a set of data from Turtle Creek near Dallas, Texas illustrates the problems of model input errors.

Carbon dioxide emission prediction using support vector machine

NASA Astrophysics Data System (ADS)

Saleh, Chairul; Rachman Dzakiyullah, Nur; Bayu Nugroho, Jonathan

2016-02-01

In this paper, the SVM model was proposed for predict expenditure of carbon (CO2) emission. The energy consumption such as electrical energy and burning coal is input variable that affect directly increasing of CO2 emissions were conducted to built the model. Our objective is to monitor the CO2 emission based on the electrical energy and burning coal used from the production process. The data electrical energy and burning coal used were obtained from Alcohol Industry in order to training and testing the models. It divided by cross-validation technique into 90% of training data and 10% of testing data. To find the optimal parameters of SVM model was used the trial and error approach on the experiment by adjusting C parameters and Epsilon. The result shows that the SVM model has an optimal parameter on C parameters 0.1 and 0 Epsilon. To measure the error of the model by using Root Mean Square Error (RMSE) with error value as 0.004. The smallest error of the model represents more accurately prediction. As a practice, this paper was contributing for an executive manager in making the effective decision for the business operation were monitoring expenditure of CO2 emission.

Difference-based ridge-type estimator of parameters in restricted partial linear model with correlated errors.

PubMed

Wu, Jibo

2016-01-01

In this article, a generalized difference-based ridge estimator is proposed for the vector parameter in a partial linear model when the errors are dependent. It is supposed that some additional linear constraints may hold to the whole parameter space. Its mean-squared error matrix is compared with the generalized restricted difference-based estimator. Finally, the performance of the new estimator is explained by a simulation study and a numerical example.

Unifying distance-based goodness-of-fit indicators for hydrologic model assessment

NASA Astrophysics Data System (ADS)

Cheng, Qinbo; Reinhardt-Imjela, Christian; Chen, Xi; Schulte, Achim

2014-05-01

The goodness-of-fit indicator, i.e. efficiency criterion, is very important for model calibration. However, recently the knowledge about the goodness-of-fit indicators is all empirical and lacks a theoretical support. Based on the likelihood theory, a unified distance-based goodness-of-fit indicator termed BC-GED model is proposed, which uses the Box-Cox (BC) transformation to remove the heteroscedasticity of model errors and the generalized error distribution (GED) with zero-mean to fit the distribution of model errors after BC. The BC-GED model can unify all recent distance-based goodness-of-fit indicators, and reveals the mean square error (MSE) and the mean absolute error (MAE) that are widely used goodness-of-fit indicators imply statistic assumptions that the model errors follow the Gaussian distribution and the Laplace distribution with zero-mean, respectively. The empirical knowledge about goodness-of-fit indicators can be also easily interpreted by BC-GED model, e.g. the sensitivity to high flow of the goodness-of-fit indicators with large power of model errors results from the low probability of large model error in the assumed distribution of these indicators. In order to assess the effect of the parameters (i.e. the BC transformation parameter λ and the GED kurtosis coefficient β also termed the power of model errors) of BC-GED model on hydrologic model calibration, six cases of BC-GED model were applied in Baocun watershed (East China) with SWAT-WB-VSA model. Comparison of the inferred model parameters and model simulation results among the six indicators demonstrates these indicators can be clearly separated two classes by the GED kurtosis β: β >1 and β ≤ 1. SWAT-WB-VSA calibrated by the class β >1 of distance-based goodness-of-fit indicators captures high flow very well and mimics the baseflow very badly, but it calibrated by the class β ≤ 1 mimics the baseflow very well, because first the larger value of β, the greater emphasis is put on high flow and second the derivative of GED probability density function at zero is zero as β >1, but discontinuous as β ≤ 1, and even infinity as β < 1 with which the maximum likelihood estimation can guarantee the model errors approach zero as well as possible. The BC-GED that estimates the parameters (i.e. λ and β) of BC-GED model as well as hydrologic model parameters is the best distance-based goodness-of-fit indicator because not only the model validation using groundwater levels is very good, but also the model errors fulfill the statistic assumption best. However, in some cases of model calibration with a few observations e.g. calibration of single-event model, for avoiding estimation of the parameters of BC-GED model the MAE i.e. the boundary indicator (β = 1) of the two classes, can replace the BC-GED, because the model validation of MAE is best.

Attitude error response of structures to actuator/sensor noise

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1991-01-01

Explicit closed-form formulas are presented for the RMS attitude-error response to sensor and actuator noise for co-located actuators/sensors as a function of both control-gain parameters and structure parameters. The main point of departure is the use of continuum models. In particular the anisotropic Timoshenko model is used for lattice trusses typified by the NASA EPS Structure Model and the Evolutionary Model. One conclusion is that the maximum attainable improvement in the attitude error varying either structure parameters or control gains is 3 dB for the axial and torsion modes, the bending being essentially insensitive. The results are similar whether the Bernoulli model or the anisotropic Timoshenko model is used.

Facial motion parameter estimation and error criteria in model-based image coding

NASA Astrophysics Data System (ADS)

Liu, Yunhai; Yu, Lu; Yao, Qingdong

2000-04-01

Model-based image coding has been given extensive attention due to its high subject image quality and low bit-rates. But the estimation of object motion parameter is still a difficult problem, and there is not a proper error criteria for the quality assessment that are consistent with visual properties. This paper presents an algorithm of the facial motion parameter estimation based on feature point correspondence and gives the motion parameter error criteria. The facial motion model comprises of three parts. The first part is the global 3-D rigid motion of the head, the second part is non-rigid translation motion in jaw area, and the third part consists of local non-rigid expression motion in eyes and mouth areas. The feature points are automatically selected by a function of edges, brightness and end-node outside the blocks of eyes and mouth. The numbers of feature point are adjusted adaptively. The jaw translation motion is tracked by the changes of the feature point position of jaw. The areas of non-rigid expression motion can be rebuilt by using block-pasting method. The estimation approach of motion parameter error based on the quality of reconstructed image is suggested, and area error function and the error function of contour transition-turn rate are used to be quality criteria. The criteria reflect the image geometric distortion caused by the error of estimated motion parameters properly.

Hydrological modelling of the Chaohe Basin in China: Statistical model formulation and Bayesian inference

NASA Astrophysics Data System (ADS)

Yang, Jing; Reichert, Peter; Abbaspour, Karim C.; Yang, Hong

2007-07-01

SummaryCalibration of hydrologic models is very difficult because of measurement errors in input and response, errors in model structure, and the large number of non-identifiable parameters of distributed models. The difficulties even increase in arid regions with high seasonal variation of precipitation, where the modelled residuals often exhibit high heteroscedasticity and autocorrelation. On the other hand, support of water management by hydrologic models is important in arid regions, particularly if there is increasing water demand due to urbanization. The use and assessment of model results for this purpose require a careful calibration and uncertainty analysis. Extending earlier work in this field, we developed a procedure to overcome (i) the problem of non-identifiability of distributed parameters by introducing aggregate parameters and using Bayesian inference, (ii) the problem of heteroscedasticity of errors by combining a Box-Cox transformation of results and data with seasonally dependent error variances, (iii) the problems of autocorrelated errors, missing data and outlier omission with a continuous-time autoregressive error model, and (iv) the problem of the seasonal variation of error correlations with seasonally dependent characteristic correlation times. The technique was tested with the calibration of the hydrologic sub-model of the Soil and Water Assessment Tool (SWAT) in the Chaohe Basin in North China. The results demonstrated the good performance of this approach to uncertainty analysis, particularly with respect to the fulfilment of statistical assumptions of the error model. A comparison with an independent error model and with error models that only considered a subset of the suggested techniques clearly showed the superiority of the approach based on all the features (i)-(iv) mentioned above.

The Limitations of Model-Based Experimental Design and Parameter Estimation in Sloppy Systems.

PubMed

White, Andrew; Tolman, Malachi; Thames, Howard D; Withers, Hubert Rodney; Mason, Kathy A; Transtrum, Mark K

2016-12-01

We explore the relationship among experimental design, parameter estimation, and systematic error in sloppy models. We show that the approximate nature of mathematical models poses challenges for experimental design in sloppy models. In many models of complex biological processes it is unknown what are the relevant physical mechanisms that must be included to explain system behaviors. As a consequence, models are often overly complex, with many practically unidentifiable parameters. Furthermore, which mechanisms are relevant/irrelevant vary among experiments. By selecting complementary experiments, experimental design may inadvertently make details that were ommitted from the model become relevant. When this occurs, the model will have a large systematic error and fail to give a good fit to the data. We use a simple hyper-model of model error to quantify a model's discrepancy and apply it to two models of complex biological processes (EGFR signaling and DNA repair) with optimally selected experiments. We find that although parameters may be accurately estimated, the discrepancy in the model renders it less predictive than it was in the sloppy regime where systematic error is small. We introduce the concept of a sloppy system-a sequence of models of increasing complexity that become sloppy in the limit of microscopic accuracy. We explore the limits of accurate parameter estimation in sloppy systems and argue that identifying underlying mechanisms controlling system behavior is better approached by considering a hierarchy of models of varying detail rather than focusing on parameter estimation in a single model.

Influence of conservative corrections on parameter estimation for extreme-mass-ratio inspirals

NASA Astrophysics Data System (ADS)

Huerta, E. A.; Gair, Jonathan R.

2009-04-01

We present an improved numerical kludge waveform model for circular, equatorial extreme-mass-ratio inspirals (EMRIs). The model is based on true Kerr geodesics, augmented by radiative self-force corrections derived from perturbative calculations, and in this paper for the first time we include conservative self-force corrections that we derive by comparison to post-Newtonian results. We present results of a Monte Carlo simulation of parameter estimation errors computed using the Fisher matrix and also assess the theoretical errors that would arise from omitting the conservative correction terms we include here. We present results for three different types of system, namely, the inspirals of black holes, neutron stars, or white dwarfs into a supermassive black hole (SMBH). The analysis shows that for a typical source (a 10M⊙ compact object captured by a 106M⊙ SMBH at a signal to noise ratio of 30) we expect to determine the two masses to within a fractional error of ˜10-4, measure the spin parameter q to ˜10-4.5, and determine the location of the source on the sky and the spin orientation to within 10-3 steradians. We show that, for this kludge model, omitting the conservative corrections leads to a small error over much of the parameter space, i.e., the ratio R of the theoretical model error to the Fisher matrix error is R<1 for all ten parameters in the model. For the few systems with larger errors typically R<3 and hence the conservative corrections can be marginally ignored. In addition, we use our model and first-order self-force results for Schwarzschild black holes to estimate the error that arises from omitting the second-order radiative piece of the self-force. This indicates that it may not be necessary to go beyond first order to recover accurate parameter estimates.

Parameter prediction based on Improved Process neural network and ARMA error compensation in Evaporation Process

NASA Astrophysics Data System (ADS)

Qian, Xiaoshan

2018-01-01

The traditional model of evaporation process parameters have continuity and cumulative characteristics of the prediction error larger issues, based on the basis of the process proposed an adaptive particle swarm neural network forecasting method parameters established on the autoregressive moving average (ARMA) error correction procedure compensated prediction model to predict the results of the neural network to improve prediction accuracy. Taking a alumina plant evaporation process to analyze production data validation, and compared with the traditional model, the new model prediction accuracy greatly improved, can be used to predict the dynamic process of evaporation of sodium aluminate solution components.

The Limitations of Model-Based Experimental Design and Parameter Estimation in Sloppy Systems

PubMed Central

Tolman, Malachi; Thames, Howard D.; Mason, Kathy A.

2016-01-01

We explore the relationship among experimental design, parameter estimation, and systematic error in sloppy models. We show that the approximate nature of mathematical models poses challenges for experimental design in sloppy models. In many models of complex biological processes it is unknown what are the relevant physical mechanisms that must be included to explain system behaviors. As a consequence, models are often overly complex, with many practically unidentifiable parameters. Furthermore, which mechanisms are relevant/irrelevant vary among experiments. By selecting complementary experiments, experimental design may inadvertently make details that were ommitted from the model become relevant. When this occurs, the model will have a large systematic error and fail to give a good fit to the data. We use a simple hyper-model of model error to quantify a model’s discrepancy and apply it to two models of complex biological processes (EGFR signaling and DNA repair) with optimally selected experiments. We find that although parameters may be accurately estimated, the discrepancy in the model renders it less predictive than it was in the sloppy regime where systematic error is small. We introduce the concept of a sloppy system–a sequence of models of increasing complexity that become sloppy in the limit of microscopic accuracy. We explore the limits of accurate parameter estimation in sloppy systems and argue that identifying underlying mechanisms controlling system behavior is better approached by considering a hierarchy of models of varying detail rather than focusing on parameter estimation in a single model. PMID:27923060

On-board adaptive model for state of charge estimation of lithium-ion batteries based on Kalman filter with proportional integral-based error adjustment

NASA Astrophysics Data System (ADS)

Wei, Jingwen; Dong, Guangzhong; Chen, Zonghai

2017-10-01

With the rapid development of battery-powered electric vehicles, the lithium-ion battery plays a critical role in the reliability of vehicle system. In order to provide timely management and protection for battery systems, it is necessary to develop a reliable battery model and accurate battery parameters estimation to describe battery dynamic behaviors. Therefore, this paper focuses on an on-board adaptive model for state-of-charge (SOC) estimation of lithium-ion batteries. Firstly, a first-order equivalent circuit battery model is employed to describe battery dynamic characteristics. Then, the recursive least square algorithm and the off-line identification method are used to provide good initial values of model parameters to ensure filter stability and reduce the convergence time. Thirdly, an extended-Kalman-filter (EKF) is applied to on-line estimate battery SOC and model parameters. Considering that the EKF is essentially a first-order Taylor approximation of battery model, which contains inevitable model errors, thus, a proportional integral-based error adjustment technique is employed to improve the performance of EKF method and correct model parameters. Finally, the experimental results on lithium-ion batteries indicate that the proposed EKF with proportional integral-based error adjustment method can provide robust and accurate battery model and on-line parameter estimation.

Control by model error estimation

NASA Technical Reports Server (NTRS)

Likins, P. W.; Skelton, R. E.

1976-01-01

Modern control theory relies upon the fidelity of the mathematical model of the system. Truncated modes, external disturbances, and parameter errors in linear system models are corrected by augmenting to the original system of equations an 'error system' which is designed to approximate the effects of such model errors. A Chebyshev error system is developed for application to the Large Space Telescope (LST).

Baseline Error Analysis and Experimental Validation for Height Measurement of Formation Insar Satellite

NASA Astrophysics Data System (ADS)

Gao, X.; Li, T.; Zhang, X.; Geng, X.

2018-04-01

In this paper, we proposed the stochastic model of InSAR height measurement by considering the interferometric geometry of InSAR height measurement. The model directly described the relationship between baseline error and height measurement error. Then the simulation analysis in combination with TanDEM-X parameters was implemented to quantitatively evaluate the influence of baseline error to height measurement. Furthermore, the whole emulation validation of InSAR stochastic model was performed on the basis of SRTM DEM and TanDEM-X parameters. The spatial distribution characteristics and error propagation rule of InSAR height measurement were fully evaluated.

The Impact of Model and Rainfall Forcing Errors on Characterizing Soil Moisture Uncertainty in Land Surface Modeling

NASA Technical Reports Server (NTRS)

Maggioni, V.; Anagnostou, E. N.; Reichle, R. H.

2013-01-01

The contribution of rainfall forcing errors relative to model (structural and parameter) uncertainty in the prediction of soil moisture is investigated by integrating the NASA Catchment Land Surface Model (CLSM), forced with hydro-meteorological data, in the Oklahoma region. Rainfall-forcing uncertainty is introduced using a stochastic error model that generates ensemble rainfall fields from satellite rainfall products. The ensemble satellite rain fields are propagated through CLSM to produce soil moisture ensembles. Errors in CLSM are modeled with two different approaches: either by perturbing model parameters (representing model parameter uncertainty) or by adding randomly generated noise (representing model structure and parameter uncertainty) to the model prognostic variables. Our findings highlight that the method currently used in the NASA GEOS-5 Land Data Assimilation System to perturb CLSM variables poorly describes the uncertainty in the predicted soil moisture, even when combined with rainfall model perturbations. On the other hand, by adding model parameter perturbations to rainfall forcing perturbations, a better characterization of uncertainty in soil moisture simulations is observed. Specifically, an analysis of the rank histograms shows that the most consistent ensemble of soil moisture is obtained by combining rainfall and model parameter perturbations. When rainfall forcing and model prognostic perturbations are added, the rank histogram shows a U-shape at the domain average scale, which corresponds to a lack of variability in the forecast ensemble. The more accurate estimation of the soil moisture prediction uncertainty obtained by combining rainfall and parameter perturbations is encouraging for the application of this approach in ensemble data assimilation systems.

Error analysis in inverse scatterometry. I. Modeling.

PubMed

Al-Assaad, Rayan M; Byrne, Dale M

2007-02-01

Scatterometry is an optical technique that has been studied and tested in recent years in semiconductor fabrication metrology for critical dimensions. Previous work presented an iterative linearized method to retrieve surface-relief profile parameters from reflectance measurements upon diffraction. With the iterative linear solution model in this work, rigorous models are developed to represent the random and deterministic or offset errors in scatterometric measurements. The propagation of different types of error from the measurement data to the profile parameter estimates is then presented. The improvement in solution accuracies is then demonstrated with theoretical and experimental data by adjusting for the offset errors. In a companion paper (in process) an improved optimization method is presented to account for unknown offset errors in the measurements based on the offset error model.

Calibration of a flexible measurement system based on industrial articulated robot and structured light sensor

NASA Astrophysics Data System (ADS)

Mu, Nan; Wang, Kun; Xie, Zexiao; Ren, Ping

2017-05-01

To realize online rapid measurement for complex workpieces, a flexible measurement system based on an articulated industrial robot with a structured light sensor mounted on the end-effector is developed. A method for calibrating the system parameters is proposed in which the hand-eye transformation parameters and the robot kinematic parameters are synthesized in the calibration process. An initial hand-eye calibration is first performed using a standard sphere as the calibration target. By applying the modified complete and parametrically continuous method, we establish a synthesized kinematic model that combines the initial hand-eye transformation and distal link parameters as a whole with the sensor coordinate system as the tool frame. According to the synthesized kinematic model, an error model is constructed based on spheres' center-to-center distance errors. Consequently, the error model parameters can be identified in a calibration experiment using a three-standard-sphere target. Furthermore, the redundancy of error model parameters is eliminated to ensure the accuracy and robustness of the parameter identification. Calibration and measurement experiments are carried out based on an ER3A-C60 robot. The experimental results show that the proposed calibration method enjoys high measurement accuracy, and this efficient and flexible system is suitable for online measurement in industrial scenes.

Toward On-line Parameter Estimation of Concentric Tube Robots Using a Mechanics-based Kinematic Model

PubMed Central

Jang, Cheongjae; Ha, Junhyoung; Dupont, Pierre E.; Park, Frank Chongwoo

2017-01-01

Although existing mechanics-based models of concentric tube robots have been experimentally demonstrated to approximate the actual kinematics, determining accurate estimates of model parameters remains difficult due to the complex relationship between the parameters and available measurements. Further, because the mechanics-based models neglect some phenomena like friction, nonlinear elasticity, and cross section deformation, it is also not clear if model error is due to model simplification or to parameter estimation errors. The parameters of the superelastic materials used in these robots can be slowly time-varying, necessitating periodic re-estimation. This paper proposes a method for estimating the mechanics-based model parameters using an extended Kalman filter as a step toward on-line parameter estimation. Our methodology is validated through both simulation and experiments. PMID:28717554

A Systematic Approach to Sensor Selection for Aircraft Engine Health Estimation

NASA Technical Reports Server (NTRS)

Simon, Donald L.; Garg, Sanjay

2009-01-01

A systematic approach for selecting an optimal suite of sensors for on-board aircraft gas turbine engine health estimation is presented. The methodology optimally chooses the engine sensor suite and the model tuning parameter vector to minimize the Kalman filter mean squared estimation error in the engine s health parameters or other unmeasured engine outputs. This technique specifically addresses the underdetermined estimation problem where there are more unknown system health parameters representing degradation than available sensor measurements. This paper presents the theoretical estimation error equations, and describes the optimization approach that is applied to select the sensors and model tuning parameters to minimize these errors. Two different model tuning parameter vector selection approaches are evaluated: the conventional approach of selecting a subset of health parameters to serve as the tuning parameters, and an alternative approach that selects tuning parameters as a linear combination of all health parameters. Results from the application of the technique to an aircraft engine simulation are presented, and compared to those from an alternative sensor selection strategy.

Impact of time-of-flight on indirect 3D and direct 4D parametric image reconstruction in the presence of inconsistent dynamic PET data.

PubMed

Kotasidis, F A; Mehranian, A; Zaidi, H

2016-05-07

Kinetic parameter estimation in dynamic PET suffers from reduced accuracy and precision when parametric maps are estimated using kinetic modelling following image reconstruction of the dynamic data. Direct approaches to parameter estimation attempt to directly estimate the kinetic parameters from the measured dynamic data within a unified framework. Such image reconstruction methods have been shown to generate parametric maps of improved precision and accuracy in dynamic PET. However, due to the interleaving between the tomographic and kinetic modelling steps, any tomographic or kinetic modelling errors in certain regions or frames, tend to spatially or temporally propagate. This results in biased kinetic parameters and thus limits the benefits of such direct methods. Kinetic modelling errors originate from the inability to construct a common single kinetic model for the entire field-of-view, and such errors in erroneously modelled regions could spatially propagate. Adaptive models have been used within 4D image reconstruction to mitigate the problem, though they are complex and difficult to optimize. Tomographic errors in dynamic imaging on the other hand, can originate from involuntary patient motion between dynamic frames, as well as from emission/transmission mismatch. Motion correction schemes can be used, however, if residual errors exist or motion correction is not included in the study protocol, errors in the affected dynamic frames could potentially propagate either temporally, to other frames during the kinetic modelling step or spatially, during the tomographic step. In this work, we demonstrate a new strategy to minimize such error propagation in direct 4D image reconstruction, focusing on the tomographic step rather than the kinetic modelling step, by incorporating time-of-flight (TOF) within a direct 4D reconstruction framework. Using ever improving TOF resolutions (580 ps, 440 ps, 300 ps and 160 ps), we demonstrate that direct 4D TOF image reconstruction can substantially prevent kinetic parameter error propagation either from erroneous kinetic modelling, inter-frame motion or emission/transmission mismatch. Furthermore, we demonstrate the benefits of TOF in parameter estimation when conventional post-reconstruction (3D) methods are used and compare the potential improvements to direct 4D methods. Further improvements could possibly be achieved in the future by combining TOF direct 4D image reconstruction with adaptive kinetic models and inter-frame motion correction schemes.

Impact of time-of-flight on indirect 3D and direct 4D parametric image reconstruction in the presence of inconsistent dynamic PET data

NASA Astrophysics Data System (ADS)

Kotasidis, F. A.; Mehranian, A.; Zaidi, H.

2016-05-01

Kinetic parameter estimation in dynamic PET suffers from reduced accuracy and precision when parametric maps are estimated using kinetic modelling following image reconstruction of the dynamic data. Direct approaches to parameter estimation attempt to directly estimate the kinetic parameters from the measured dynamic data within a unified framework. Such image reconstruction methods have been shown to generate parametric maps of improved precision and accuracy in dynamic PET. However, due to the interleaving between the tomographic and kinetic modelling steps, any tomographic or kinetic modelling errors in certain regions or frames, tend to spatially or temporally propagate. This results in biased kinetic parameters and thus limits the benefits of such direct methods. Kinetic modelling errors originate from the inability to construct a common single kinetic model for the entire field-of-view, and such errors in erroneously modelled regions could spatially propagate. Adaptive models have been used within 4D image reconstruction to mitigate the problem, though they are complex and difficult to optimize. Tomographic errors in dynamic imaging on the other hand, can originate from involuntary patient motion between dynamic frames, as well as from emission/transmission mismatch. Motion correction schemes can be used, however, if residual errors exist or motion correction is not included in the study protocol, errors in the affected dynamic frames could potentially propagate either temporally, to other frames during the kinetic modelling step or spatially, during the tomographic step. In this work, we demonstrate a new strategy to minimize such error propagation in direct 4D image reconstruction, focusing on the tomographic step rather than the kinetic modelling step, by incorporating time-of-flight (TOF) within a direct 4D reconstruction framework. Using ever improving TOF resolutions (580 ps, 440 ps, 300 ps and 160 ps), we demonstrate that direct 4D TOF image reconstruction can substantially prevent kinetic parameter error propagation either from erroneous kinetic modelling, inter-frame motion or emission/transmission mismatch. Furthermore, we demonstrate the benefits of TOF in parameter estimation when conventional post-reconstruction (3D) methods are used and compare the potential improvements to direct 4D methods. Further improvements could possibly be achieved in the future by combining TOF direct 4D image reconstruction with adaptive kinetic models and inter-frame motion correction schemes.

Gaussian copula as a likelihood function for environmental models

NASA Astrophysics Data System (ADS)

Wani, O.; Espadas, G.; Cecinati, F.; Rieckermann, J.

2017-12-01

Parameter estimation of environmental models always comes with uncertainty. To formally quantify this parametric uncertainty, a likelihood function needs to be formulated, which is defined as the probability of observations given fixed values of the parameter set. A likelihood function allows us to infer parameter values from observations using Bayes' theorem. The challenge is to formulate a likelihood function that reliably describes the error generating processes which lead to the observed monitoring data, such as rainfall and runoff. If the likelihood function is not representative of the error statistics, the parameter inference will give biased parameter values. Several uncertainty estimation methods that are currently being used employ Gaussian processes as a likelihood function, because of their favourable analytical properties. Box-Cox transformation is suggested to deal with non-symmetric and heteroscedastic errors e.g. for flow data which are typically more uncertain in high flows than in periods with low flows. Problem with transformations is that the results are conditional on hyper-parameters, for which it is difficult to formulate the analyst's belief a priori. In an attempt to address this problem, in this research work we suggest learning the nature of the error distribution from the errors made by the model in the "past" forecasts. We use a Gaussian copula to generate semiparametric error distributions . 1) We show that this copula can be then used as a likelihood function to infer parameters, breaking away from the practice of using multivariate normal distributions. Based on the results from a didactical example of predicting rainfall runoff, 2) we demonstrate that the copula captures the predictive uncertainty of the model. 3) Finally, we find that the properties of autocorrelation and heteroscedasticity of errors are captured well by the copula, eliminating the need to use transforms. In summary, our findings suggest that copulas are an interesting departure from the usage of fully parametric distributions as likelihood functions - and they could help us to better capture the statistical properties of errors and make more reliable predictions.

An error covariance model for sea surface topography and velocity derived from TOPEX/POSEIDON altimetry

NASA Technical Reports Server (NTRS)

Tsaoussi, Lucia S.; Koblinsky, Chester J.

1994-01-01

In order to facilitate the use of satellite-derived sea surface topography and velocity oceanographic models, methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from the TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10-day period is found tio be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm root mean square (RMS). This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions. For both variables the largest errors caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data.

Bootstrap Standard Errors for Maximum Likelihood Ability Estimates When Item Parameters Are Unknown

ERIC Educational Resources Information Center

Patton, Jeffrey M.; Cheng, Ying; Yuan, Ke-Hai; Diao, Qi

2014-01-01

When item parameter estimates are used to estimate the ability parameter in item response models, the standard error (SE) of the ability estimate must be corrected to reflect the error carried over from item calibration. For maximum likelihood (ML) ability estimates, a corrected asymptotic SE is available, but it requires a long test and the…

Theoretical study of the accuracy of the elution by characteristic points method for bi-langmuir isotherms.

PubMed

Ravald, L; Fornstedt, T

2001-01-26

The bi-Langmuir equation has recently been proven essential to describe chiral chromatographic surfaces and we therefore investigated the accuracy of the elution by characteristic points method (ECP) for estimation of bi-Langmuir isotherm parameters. The ECP calculations was done on elution profiles generated by the equilibrium-dispersive model of chromatography for five different sets of bi-Langmuir parameters. The ECP method generates two different errors; (i) the error of the ECP calculated isotherm and (ii) the model error of the fitting to the ECP isotherm. Both errors decreased with increasing column efficiency. Moreover, the model error was strongly affected by the weight of the bi-Langmuir function fitted. For some bi-Langmuir compositions the error of the ECP calculated isotherm is too large even at high column efficiencies. Guidelines will be given on surface types to be avoided and on column efficiencies and loading factors required for adequate parameter estimations with ECP.

Feasibility of Equivalent Dipole Models for Electroencephalogram-Based Brain Computer Interfaces.

PubMed

Schimpf, Paul H

2017-09-15

This article examines the localization errors of equivalent dipolar sources inverted from the surface electroencephalogram in order to determine the feasibility of using their location as classification parameters for non-invasive brain computer interfaces. Inverse localization errors are examined for two head models: a model represented by four concentric spheres and a realistic model based on medical imagery. It is shown that the spherical model results in localization ambiguity such that a number of dipolar sources, with different azimuths and varying orientations, provide a near match to the electroencephalogram of the best equivalent source. No such ambiguity exists for the elevation of inverted sources, indicating that for spherical head models, only the elevation of inverted sources (and not the azimuth) can be expected to provide meaningful classification parameters for brain-computer interfaces. In a realistic head model, all three parameters of the inverted source location are found to be reliable, providing a more robust set of parameters. In both cases, the residual error hypersurfaces demonstrate local minima, indicating that a search for the best-matching sources should be global. Source localization error vs. signal-to-noise ratio is also demonstrated for both head models.

Dependence of subject-specific parameters for a fast helical CT respiratory motion model on breathing rate: an animal study

NASA Astrophysics Data System (ADS)

O'Connell, Dylan; Thomas, David H.; Lamb, James M.; Lewis, John H.; Dou, Tai; Sieren, Jered P.; Saylor, Melissa; Hofmann, Christian; Hoffman, Eric A.; Lee, Percy P.; Low, Daniel A.

2018-02-01

To determine if the parameters relating lung tissue displacement to a breathing surrogate signal in a previously published respiratory motion model vary with the rate of breathing during image acquisition. An anesthetized pig was imaged using multiple fast helical scans to sample the breathing cycle with simultaneous surrogate monitoring. Three datasets were collected while the animal was mechanically ventilated with different respiratory rates: 12 bpm (breaths per minute), 17 bpm, and 24 bpm. Three sets of motion model parameters describing the correspondences between surrogate signals and tissue displacements were determined. The model error was calculated individually for each dataset, as well asfor pairs of parameters and surrogate signals from different experiments. The values of one model parameter, a vector field denoted α which related tissue displacement to surrogate amplitude, determined for each experiment were compared. The mean model error of the three datasets was 1.00  ±  0.36 mm with a 95th percentile value of 1.69 mm. The mean error computed from all combinations of parameters and surrogate signals from different datasets was 1.14  ±  0.42 mm with a 95th percentile of 1.95 mm. The mean difference in α over all pairs of experiments was 4.7%  ±  5.4%, and the 95th percentile was 16.8%. The mean angle between pairs of α was 5.0  ±  4.0 degrees, with a 95th percentile of 13.2 mm. The motion model parameters were largely unaffected by changes in the breathing rate during image acquisition. The mean error associated with mismatched sets of parameters and surrogate signals was 0.14 mm greater than the error achieved when using parameters and surrogate signals acquired with the same breathing rate, while maximum respiratory motion was 23.23 mm on average.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Irving, J.; Koepke, C.; Elsheikh, A. H.

2017-12-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward process model linking subsurface parameters to measured data, which is typically assumed to be known perfectly in the inversion procedure. However, in order to make the stochastic solution of the inverse problem computationally tractable using, for example, Markov-chain-Monte-Carlo (MCMC) methods, fast approximations of the forward model are commonly employed. This introduces model error into the problem, which has the potential to significantly bias posterior statistics and hamper data integration efforts if not properly accounted for. Here, we present a new methodology for addressing the issue of model error in Bayesian solutions to hydrogeophysical inverse problems that is geared towards the common case where these errors cannot be effectively characterized globally through some parametric statistical distribution or locally based on interpolation between a small number of computed realizations. Rather than focusing on the construction of a global or local error model, we instead work towards identification of the model-error component of the residual through a projection-based approach. In this regard, pairs of approximate and detailed model runs are stored in a dictionary that grows at a specified rate during the MCMC inversion procedure. At each iteration, a local model-error basis is constructed for the current test set of model parameters using the K-nearest neighbour entries in the dictionary, which is then used to separate the model error from the other error sources before computing the likelihood of the proposed set of model parameters. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar traveltime data for three different subsurface parameterizations of varying complexity. The synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed in the inversion procedure. In each case, the developed model-error approach enables to remove posterior bias and obtain a more realistic characterization of uncertainty.

Simultaneous treatment of unspecified heteroskedastic model error distribution and mismeasured covariates for restricted moment models.

PubMed

Garcia, Tanya P; Ma, Yanyuan

2017-10-01

We develop consistent and efficient estimation of parameters in general regression models with mismeasured covariates. We assume the model error and covariate distributions are unspecified, and the measurement error distribution is a general parametric distribution with unknown variance-covariance. We construct root- n consistent, asymptotically normal and locally efficient estimators using the semiparametric efficient score. We do not estimate any unknown distribution or model error heteroskedasticity. Instead, we form the estimator under possibly incorrect working distribution models for the model error, error-prone covariate, or both. Empirical results demonstrate robustness to different incorrect working models in homoscedastic and heteroskedastic models with error-prone covariates.

Statistical error model for a solar electric propulsion thrust subsystem

NASA Technical Reports Server (NTRS)

Bantell, M. H.

1973-01-01

The solar electric propulsion thrust subsystem statistical error model was developed as a tool for investigating the effects of thrust subsystem parameter uncertainties on navigation accuracy. The model is currently being used to evaluate the impact of electric engine parameter uncertainties on navigation system performance for a baseline mission to Encke's Comet in the 1980s. The data given represent the next generation in statistical error modeling for low-thrust applications. Principal improvements include the representation of thrust uncertainties and random process modeling in terms of random parametric variations in the thrust vector process for a multi-engine configuration.

CALCULATION OF NONLINEAR CONFIDENCE AND PREDICTION INTERVALS FOR GROUND-WATER FLOW MODELS.

USGS Publications Warehouse

Cooley, Richard L.; Vecchia, Aldo V.

1987-01-01

A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system. The method is applied to the problem of obtaining confidence and prediction intervals for manually-calibrated ground-water flow models. To obtain confidence and prediction intervals resulting from uncertainties in parameters, the calibrated model and information on extreme ranges and ordering of the model parameters within one or more independent groups are required. If random errors in the dependent variable are present in addition to uncertainties in parameters, then calculation of prediction intervals also requires information on the extreme range of error expected. A simple Monte Carlo method is used to compute the quantiles necessary to establish probability levels for the confidence and prediction intervals. Application of the method to a hypothetical example showed that inclusion of random errors in the dependent variable in addition to uncertainties in parameters can considerably widen the prediction intervals.

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Ping; Wang, Chenyu; Li, Mingjie

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) can not fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First,more » the modeling error PDF by the tradional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. Furthermore, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.« less

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Ping; Wang, Chenyu; Li, Mingjie

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) cannot fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, themore » modeling error PDF by the traditional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. However, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.« less

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

DOE PAGES

Zhou, Ping; Wang, Chenyu; Li, Mingjie; ...

2018-01-31

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) cannot fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, themore » modeling error PDF by the traditional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. However, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.« less

Model error estimation for distributed systems described by elliptic equations

NASA Technical Reports Server (NTRS)

Rodriguez, G.

1983-01-01

A function space approach is used to develop a theory for estimation of the errors inherent in an elliptic partial differential equation model for a distributed parameter system. By establishing knowledge of the inevitable deficiencies in the model, the error estimates provide a foundation for updating the model. The function space solution leads to a specification of a method for computation of the model error estimates and development of model error analysis techniques for comparison between actual and estimated errors. The paper summarizes the model error estimation approach as well as an application arising in the area of modeling for static shape determination of large flexible systems.

Efficient hierarchical trans-dimensional Bayesian inversion of magnetotelluric data

NASA Astrophysics Data System (ADS)

Xiang, Enming; Guo, Rongwen; Dosso, Stan E.; Liu, Jianxin; Dong, Hao; Ren, Zhengyong

2018-06-01

This paper develops an efficient hierarchical trans-dimensional (trans-D) Bayesian algorithm to invert magnetotelluric (MT) data for subsurface geoelectrical structure, with unknown geophysical model parameterization (the number of conductivity-layer interfaces) and data-error models parameterized by an auto-regressive (AR) process to account for potential error correlations. The reversible-jump Markov-chain Monte Carlo algorithm, which adds/removes interfaces and AR parameters in birth/death steps, is applied to sample the trans-D posterior probability density for model parameterization, model parameters, error variance and AR parameters, accounting for the uncertainties of model dimension and data-error statistics in the uncertainty estimates of the conductivity profile. To provide efficient sampling over the multiple subspaces of different dimensions, advanced proposal schemes are applied. Parameter perturbations are carried out in principal-component space, defined by eigen-decomposition of the unit-lag model covariance matrix, to minimize the effect of inter-parameter correlations and provide effective perturbation directions and length scales. Parameters of new layers in birth steps are proposed from the prior, instead of focused distributions centred at existing values, to improve birth acceptance rates. Parallel tempering, based on a series of parallel interacting Markov chains with successively relaxed likelihoods, is applied to improve chain mixing over model dimensions. The trans-D inversion is applied in a simulation study to examine the resolution of model structure according to the data information content. The inversion is also applied to a measured MT data set from south-central Australia.

Combined Uncertainty and A-Posteriori Error Bound Estimates for CFD Calculations: Theory and Implementation

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2014-01-01

Simulation codes often utilize finite-dimensional approximation resulting in numerical error. Some examples include, numerical methods utilizing grids and finite-dimensional basis functions, particle methods using a finite number of particles. These same simulation codes also often contain sources of uncertainty, for example, uncertain parameters and fields associated with the imposition of initial and boundary data,uncertain physical model parameters such as chemical reaction rates, mixture model parameters, material property parameters, etc.

Nonspinning numerical relativity waveform surrogates: assessing the model

NASA Astrophysics Data System (ADS)

Field, Scott; Blackman, Jonathan; Galley, Chad; Scheel, Mark; Szilagyi, Bela; Tiglio, Manuel

2015-04-01

Recently, multi-modal gravitational waveform surrogate models have been built directly from data numerically generated by the Spectral Einstein Code (SpEC). I will describe ways in which the surrogate model error can be quantified. This task, in turn, requires (i) characterizing differences between waveforms computed by SpEC with those predicted by the surrogate model and (ii) estimating errors associated with the SpEC waveforms from which the surrogate is built. Both pieces can have numerous sources of numerical and systematic errors. We make an attempt to study the most dominant error sources and, ultimately, the surrogate model's fidelity. These investigations yield information about the surrogate model's uncertainty as a function of time (or frequency) and parameter, and could be useful in parameter estimation studies which seek to incorporate model error. Finally, I will conclude by comparing the numerical relativity surrogate model to other inspiral-merger-ringdown models. A companion talk will cover the building of multi-modal surrogate models.

Optimum data weighting and error calibration for estimation of gravitational parameters

NASA Technical Reports Server (NTRS)

Lerch, Francis J.

1989-01-01

A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least-squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 Goddard Earth Model-T1 (GEM-T1) were employed toward application of this technique for gravity field parameters. Also GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized. The method employs subset solutions of the data associated with the complete solution to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.

A continuous optimization approach for inferring parameters in mathematical models of regulatory networks.

PubMed

Deng, Zhimin; Tian, Tianhai

2014-07-29

The advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging. To address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three models to examine the reliability of estimates. Simulation results show that the models with estimated parameters using continuous fitness functions have better robustness properties than those using the corresponding discrete fitness functions. The inference studies and robustness analysis suggest that the proposed continuous optimization criteria are effective and robust for estimating unknown parameters in mathematical models.

Numerical Error Estimation with UQ

NASA Astrophysics Data System (ADS)

Ackmann, Jan; Korn, Peter; Marotzke, Jochem

2014-05-01

Ocean models are still in need of means to quantify model errors, which are inevitably made when running numerical experiments. The total model error can formally be decomposed into two parts, the formulation error and the discretization error. The formulation error arises from the continuous formulation of the model not fully describing the studied physical process. The discretization error arises from having to solve a discretized model instead of the continuously formulated model. Our work on error estimation is concerned with the discretization error. Given a solution of a discretized model, our general problem statement is to find a way to quantify the uncertainties due to discretization in physical quantities of interest (diagnostics), which are frequently used in Geophysical Fluid Dynamics. The approach we use to tackle this problem is called the "Goal Error Ensemble method". The basic idea of the Goal Error Ensemble method is that errors in diagnostics can be translated into a weighted sum of local model errors, which makes it conceptually based on the Dual Weighted Residual method from Computational Fluid Dynamics. In contrast to the Dual Weighted Residual method these local model errors are not considered deterministically but interpreted as local model uncertainty and described stochastically by a random process. The parameters for the random process are tuned with high-resolution near-initial model information. However, the original Goal Error Ensemble method, introduced in [1], was successfully evaluated only in the case of inviscid flows without lateral boundaries in a shallow-water framework and is hence only of limited use in a numerical ocean model. Our work consists in extending the method to bounded, viscous flows in a shallow-water framework. As our numerical model, we use the ICON-Shallow-Water model. In viscous flows our high-resolution information is dependent on the viscosity parameter, making our uncertainty measures viscosity-dependent. We will show that we can choose a sensible parameter by using the Reynolds-number as a criteria. Another topic, we will discuss is the choice of the underlying distribution of the random process. This is especially of importance in the scope of lateral boundaries. We will present resulting error estimates for different height- and velocity-based diagnostics applied to the Munk gyre experiment. References [1] F. RAUSER: Error Estimation in Geophysical Fluid Dynamics through Learning; PhD Thesis, IMPRS-ESM, Hamburg, 2010 [2] F. RAUSER, J. MAROTZKE, P. KORN: Ensemble-type numerical uncertainty quantification from single model integrations; SIAM/ASA Journal on Uncertainty Quantification, submitted

Effects of waveform model systematics on the interpretation of GW150914

NASA Astrophysics Data System (ADS)

Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Aiello, L.; Ain, A.; Ajith, P.; Allen, B.; Allocca, A.; Altin, P. A.; Ananyeva, A.; Anderson, S. B.; Anderson, W. G.; Appert, S.; Arai, K.; Araya, M. C.; Areeda, J. S.; Arnaud, N.; Arun, K. G.; Ascenzi, S.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Avila-Alvarez, A.; Babak, S.; Bacon, P.; Bader, M. K. M.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; E Barclay, S.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bavigadda, V.; Bazzan, M.; Beer, C.; Bejger, M.; Belahcene, I.; Belgin, M.; Bell, A. S.; Berger, B. K.; Bergmann, G.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Billman, C. R.; Birch, J.; Birney, R.; Birnholtz, O.; Biscans, S.; Bisht, A.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blackman, J.; Blair, C. D.; Blair, D. G.; Blair, R. M.; Bloemen, S.; Bock, O.; Boer, M.; Bogaert, G.; Bohe, A.; Bondu, F.; Bonnand, R.; Boom, B. A.; Bork, R.; Boschi, V.; Bose, S.; Bouffanais, Y.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; E Brau, J.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; E Broida, J.; Brooks, A. F.; Brown, D. A.; Brown, D. D.; Brown, N. M.; Brunett, S.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cabero, M.; Cadonati, L.; Cagnoli, G.; Cahillane, C.; Calderón Bustillo, J.; Callister, T. A.; Calloni, E.; Camp, J. B.; Cannon, K. C.; Cao, H.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Casanueva Diaz, J.; Casentini, C.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C. B.; Cerboni Baiardi, L.; Cerretani, G.; Cesarini, E.; Chamberlin, S. J.; Chan, M.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Cheeseboro, B. D.; Chen, H. Y.; Chen, Y.; Cheng, H.-P.; Chincarini, A.; Chiummo, A.; Chmiel, T.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, A. J. K.; Chua, S.; Chung, S.; Ciani, G.; Clara, F.; Clark, J. A.; Cleva, F.; Cocchieri, C.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C. G.; Cominsky, L.; Constancio, M., Jr.; Conti, L.; Cooper, S. J.; Corbitt, T. R.; Cornish, N.; Corsi, A.; Cortese, S.; Costa, C. A.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Covas, P. B.; E Cowan, E.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; E Creighton, J. D.; Creighton, T. D.; Cripe, J.; Crowder, S. G.; Cullen, T. J.; Cumming, A.; Cunningham, L.; Cuoco, E.; Dal Canton, T.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Dasgupta, A.; Da Silva Costa, C. F.; Dattilo, V.; Dave, I.; Davier, M.; Davies, G. S.; Davis, D.; Daw, E. J.; Day, B.; Day, R.; De, S.; DeBra, D.; Debreczeni, G.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dergachev, V.; De Rosa, R.; DeRosa, R. T.; DeSalvo, R.; Devenson, J.; Devine, R. C.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Girolamo, T.; Di Lieto, A.; Di Pace, S.; Di Palma, I.; Di Virgilio, A.; Doctor, Z.; Dolique, V.; Donovan, F.; Dooley, K. L.; Doravari, S.; Dorrington, I.; Douglas, R.; Dovale Álvarez, M.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Ducrot, M.; E Dwyer, S.; Edo, T. B.; Edwards, M. C.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J.; Eikenberry, S. S.; Eisenstein, R. A.; Essick, R. C.; Etienne, Z.; Etzel, T.; Evans, M.; Evans, T. M.; Everett, R.; Factourovich, M.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, X.; Farinon, S.; Farr, B.; Farr, W. M.; Fauchon-Jones, E. J.; Favata, M.; Fays, M.; Fehrmann, H.; Fejer, M. M.; Fernández Galiana, A.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Fiori, I.; Fiorucci, D.; Fisher, R. P.; Flaminio, R.; Fletcher, M.; Fong, H.; Forsyth, S. S.; Fournier, J.-D.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Frey, V.; Fries, E. M.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H.; Gadre, B. U.; Gaebel, S. M.; Gair, J. R.; Gammaitoni, L.; Gaonkar, S. G.; Garufi, F.; Gaur, G.; Gayathri, V.; Gehrels, N.; Gemme, G.; Genin, E.; Gennai, A.; George, J.; Gergely, L.; Germain, V.; Ghonge, S.; Ghosh, Abhirup; Ghosh, Archisman; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, K.; Glaefke, A.; Goetz, E.; Goetz, R.; Gondan, L.; González, G.; Gonzalez Castro, J. M.; Gopakumar, A.; Gorodetsky, M. L.; E Gossan, S.; Gosselin, M.; Gouaty, R.; Grado, A.; Graef, C.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Green, A. C.; Groot, P.; Grote, H.; Grunewald, S.; Guidi, G. M.; Guo, X.; Gupta, A.; Gupta, M. K.; E Gushwa, K.; Gustafson, E. K.; Gustafson, R.; Hacker, J. J.; Hall, B. R.; Hall, E. D.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Hartman, M. T.; Haster, C.-J.; Haughian, K.; Healy, J.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Henry, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hoak, D.; Hofman, D.; Holt, K.; E Holz, D.; Hopkins, P.; Hough, J.; Houston, E. A.; Howell, E. J.; Hu, Y. M.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh-Dinh, T.; Indik, N.; Ingram, D. R.; Inta, R.; Isa, H. N.; Isac, J.-M.; Isi, M.; Isogai, T.; Iyer, B. R.; Izumi, K.; Jacqmin, T.; Jani, K.; Jaranowski, P.; Jawahar, S.; Jiménez-Forteza, F.; Johnson, W. W.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; Junker, J.; Kalaghatgi, C. V.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Karki, S.; Karvinen, K. S.; Kasprzack, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kaur, T.; Kawabe, K.; Kéfélian, F.; Keitel, D.; Kelley, D. B.; Kennedy, R.; Key, J. S.; Khalili, F. Y.; Khan, I.; Khan, S.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, Chunglee; Kim, J. C.; Kim, Whansun; Kim, W.; Kim, Y.-M.; Kimbrell, S. J.; King, E. J.; King, P. J.; Kirchhoff, R.; Kissel, J. S.; Klein, B.; Kleybolte, L.; Klimenko, S.; Koch, P.; Koehlenbeck, S. M.; Koley, S.; Kondrashov, V.; Kontos, A.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Krämer, C.; Kringel, V.; Krishnan, B.; Królak, A.; Kuehn, G.; Kumar, P.; Kumar, R.; Kuo, L.; Kutynia, A.; Lackey, B. D.; Landry, M.; Lang, R. N.; Lange, J.; Lantz, B.; Lanza, R. K.; Lartaux-Vollard, A.; Lasky, P. D.; Laxen, M.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lebigot, E. O.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, K.; Lehmann, J.; Lenon, A.; Leonardi, M.; Leong, J. R.; Leroy, N.; Letendre, N.; Levin, Y.; Li, T. G. F.; Libson, A.; Littenberg, T. B.; Liu, J.; Lockerbie, N. A.; Lombardi, A. L.; London, L. T.; E Lord, J.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lovelace, G.; Lück, H.; Lundgren, A. P.; Lynch, R.; Ma, Y.; Macfoy, S.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magaña-Sandoval, F.; Majorana, E.; Maksimovic, I.; Malvezzi, V.; Man, N.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markosyan, A. S.; Maros, E.; Martelli, F.; Martellini, L.; Martin, I. W.; Martynov, D. V.; Mason, K.; Masserot, A.; Massinger, T. J.; Masso-Reid, M.; Mastrogiovanni, S.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; McCarthy, R.; E McClelland, D.; McCormick, S.; McGrath, C.; McGuire, S. C.; McIntyre, G.; McIver, J.; McManus, D. J.; McRae, T.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Meidam, J.; Melatos, A.; Mendell, G.; Mendoza-Gandara, D.; Mercer, R. A.; Merilh, E. L.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Metzdorff, R.; Meyers, P. M.; Mezzani, F.; Miao, H.; Michel, C.; Middleton, H.; E Mikhailov, E.; Milano, L.; Miller, A. L.; Miller, A.; Miller, B. B.; Miller, J.; Millhouse, M.; Minenkov, Y.; Ming, J.; Mirshekari, S.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moggi, A.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, B. C.; Moore, C. J.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mours, B.; Mow-Lowry, C. M.; Mueller, G.; Muir, A. W.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, S.; Mukund, N.; Mullavey, A.; Munch, J.; Muniz, E. A. M.; Murray, P. G.; Mytidis, A.; Napier, K.; Nardecchia, I.; Naticchioni, L.; Nelemans, G.; Nelson, T. J. N.; Neri, M.; Nery, M.; Neunzert, A.; Newport, J. M.; Newton, G.; Nguyen, T. T.; Nielsen, A. B.; Nissanke, S.; Nitz, A.; Noack, A.; Nocera, F.; Nolting, D.; Normandin, M. E. N.; Nuttall, L. K.; Oberling, J.; Ochsner, E.; Oelker, E.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Oliver, M.; Oppermann, P.; Oram, Richard J.; O'Reilly, B.; O'Shaughnessy, R.; Ottaway, D. J.; Overmier, H.; Owen, B. J.; E Pace, A.; Page, J.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, H.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Paoli, A.; Papa, M. A.; Paris, H. R.; Parker, W.; Pascucci, D.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patricelli, B.; Pearlstone, B. L.; Pedraza, M.; Pedurand, R.; Pekowsky, L.; Pele, A.; Penn, S.; Perez, C. J.; Perreca, A.; Perri, L. M.; Pfeiffer, H. P.; Phelps, M.; Piccinni, O. J.; Pichot, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poe, M.; Poggiani, R.; Popolizio, P.; Post, A.; Powell, J.; Prasad, J.; Pratt, J. W. W.; Predoi, V.; Prestegard, T.; Prijatelj, M.; Principe, M.; Privitera, S.; Prodi, G. A.; Prokhorov, L. G.; Puncken, O.; Punturo, M.; Puppo, P.; Pürrer, M.; Qi, H.; Qin, J.; Qiu, S.; Quetschke, V.; Quintero, E. A.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Radkins, H.; Raffai, P.; Raja, S.; Rajan, C.; Rakhmanov, M.; Rapagnani, P.; Raymond, V.; Razzano, M.; Re, V.; Read, J.; Regimbau, T.; Rei, L.; Reid, S.; Reitze, D. H.; Rew, H.; Reyes, S. D.; Rhoades, E.; Ricci, F.; Riles, K.; Rizzo, M.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, J. D.; Romano, R.; Romie, J. H.; Rosińska, D.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Ryan, K.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Sakellariadou, M.; Salconi, L.; Saleem, M.; Salemi, F.; Samajdar, A.; Sammut, L.; Sampson, L. M.; Sanchez, E. J.; Sandberg, V.; Sanders, J. R.; Sassolas, B.; Sathyaprakash, B. S.; Saulson, P. R.; Sauter, O.; Savage, R. L.; Sawadsky, A.; Schale, P.; Scheuer, J.; Schmidt, E.; Schmidt, J.; Schmidt, P.; Schnabel, R.; Schofield, R. M. S.; Schönbeck, A.; Schreiber, E.; Schuette, D.; Schutz, B. F.; Schwalbe, S. G.; Scott, J.; Scott, S. M.; Sellers, D.; Sengupta, A. S.; Sentenac, D.; Sequino, V.; Sergeev, A.; Setyawati, Y.; Shaddock, D. A.; Shaffer, T. J.; Shahriar, M. S.; Shapiro, B.; Shawhan, P.; Sheperd, A.; Shoemaker, D. H.; Shoemaker, D. M.; Siellez, K.; Siemens, X.; Sieniawska, M.; Sigg, D.; Silva, A. D.; Singer, A.; Singer, L. P.; Singh, A.; Singh, R.; Singhal, A.; Sintes, A. M.; Slagmolen, B. J. J.; Smith, B.; Smith, J. R.; E Smith, R. J.; Son, E. J.; Sorazu, B.; Sorrentino, F.; Souradeep, T.; Spencer, A. P.; Srivastava, A. K.; Staley, A.; Steinke, M.; Steinlechner, J.; Steinlechner, S.; Steinmeyer, D.; Stephens, B. C.; Stevenson, S. P.; Stone, R.; Strain, K. A.; Straniero, N.; Stratta, G.; E Strigin, S.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Sun, L.; Sunil, S.; Sutton, P. J.; Swinkels, B. L.; Szczepańczyk, M. J.; Tacca, M.; Talukder, D.; Tanner, D. B.; Tápai, M.; Taracchini, A.; Taylor, R.; Theeg, T.; Thomas, E. G.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thrane, E.; Tippens, T.; Tiwari, S.; Tiwari, V.; Tokmakov, K. V.; Toland, K.; Tomlinson, C.; Tonelli, M.; Tornasi, Z.; Torrie, C. I.; Töyrä, D.; Travasso, F.; Traylor, G.; Trifirò, D.; Trinastic, J.; Tringali, M. C.; Trozzo, L.; Tse, M.; Tso, R.; Turconi, M.; Tuyenbayev, D.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Usman, S. A.; Vahlbruch, H.; Vajente, G.; Valdes, G.; van Bakel, N.; van Beuzekom, M.; van den Brand, J. F. J.; Van Den Broeck, C.; Vander-Hyde, D. C.; van der Schaaf, L.; van Heijningen, J. V.; van Veggel, A. A.; Vardaro, M.; Varma, V.; Vass, S.; Vasúth, M.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Venugopalan, G.; Verkindt, D.; Vetrano, F.; Viceré, A.; Viets, A. D.; Vinciguerra, S.; Vine, D. J.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Voss, D. V.; Vousden, W. D.; Vyatchanin, S. P.; Wade, A. R.; E Wade, L.; Wade, M.; Walker, M.; Wallace, L.; Walsh, S.; Wang, G.; Wang, H.; Wang, M.; Wang, Y.; Ward, R. L.; Warner, J.; Was, M.; Watchi, J.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Wen, L.; Weßels, P.; Westphal, T.; Wette, K.; Whelan, J. T.; Whiting, B. F.; Whittle, C.; Williams, D.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Woehler, J.; Worden, J.; Wright, J. L.; Wu, D. S.; Wu, G.; Yam, W.; Yamamoto, H.; Yancey, C. C.; Yap, M. J.; Yu, Hang; Yu, Haocun; Yvert, M.; Zadrożny, A.; Zangrando, L.; Zanolin, M.; Zendri, J.-P.; Zevin, M.; Zhang, L.; Zhang, M.; Zhang, T.; Zhang, Y.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, S. J.; Zhu, X. J.; E Zucker, M.; Zweizig, J.; LIGO Scientific Collaboration; Virgo Collaboration; Boyle, M.; Chu, T.; Hemberger, D.; Hinder, I.; E Kidder, L.; Ossokine, S.; Scheel, M.; Szilagyi, B.; Teukolsky, S.; Vano Vinuales, A.

2017-05-01

Parameter estimates of GW150914 were obtained using Bayesian inference, based on three semi-analytic waveform models for binary black hole coalescences. These waveform models differ from each other in their treatment of black hole spins, and all three models make some simplifying assumptions, notably to neglect sub-dominant waveform harmonic modes and orbital eccentricity. Furthermore, while the models are calibrated to agree with waveforms obtained by full numerical solutions of Einstein’s equations, any such calibration is accurate only to some non-zero tolerance and is limited by the accuracy of the underlying phenomenology, availability, quality, and parameter-space coverage of numerical simulations. This paper complements the original analyses of GW150914 with an investigation of the effects of possible systematic errors in the waveform models on estimates of its source parameters. To test for systematic errors we repeat the original Bayesian analysis on mock signals from numerical simulations of a series of binary configurations with parameters similar to those found for GW150914. Overall, we find no evidence for a systematic bias relative to the statistical error of the original parameter recovery of GW150914 due to modeling approximations or modeling inaccuracies. However, parameter biases are found to occur for some configurations disfavored by the data of GW150914: for binaries inclined edge-on to the detector over a small range of choices of polarization angles, and also for eccentricities greater than  ˜0.05. For signals with higher signal-to-noise ratio than GW150914, or in other regions of the binary parameter space (lower masses, larger mass ratios, or higher spins), we expect that systematic errors in current waveform models may impact gravitational-wave measurements, making more accurate models desirable for future observations.

Linear-quadratic-Gaussian synthesis with reduced parameter sensitivity

NASA Technical Reports Server (NTRS)

Lin, J. Y.; Mingori, D. L.

1992-01-01

We present a method for improving the tolerance of a conventional LQG controller to parameter errors in the plant model. The improvement is achieved by introducing additional terms reflecting the structure of the parameter errors into the LQR cost function, and also the process and measurement noise models. Adjusting the sizes of these additional terms permits a trade-off between robustness and nominal performance. Manipulation of some of the additional terms leads to high gain controllers while other terms lead to low gain controllers. Conditions are developed under which the high-gain approach asymptotically recovers the robustness of the corresponding full-state feedback design, and the low-gain approach makes the closed-loop poles asymptotically insensitive to parameter errors.

Exploring the impact of forcing error characteristics on physically based snow simulations within a global sensitivity analysis framework

NASA Astrophysics Data System (ADS)

Raleigh, M. S.; Lundquist, J. D.; Clark, M. P.

2015-07-01

Physically based models provide insights into key hydrologic processes but are associated with uncertainties due to deficiencies in forcing data, model parameters, and model structure. Forcing uncertainty is enhanced in snow-affected catchments, where weather stations are scarce and prone to measurement errors, and meteorological variables exhibit high variability. Hence, there is limited understanding of how forcing error characteristics affect simulations of cold region hydrology and which error characteristics are most important. Here we employ global sensitivity analysis to explore how (1) different error types (i.e., bias, random errors), (2) different error probability distributions, and (3) different error magnitudes influence physically based simulations of four snow variables (snow water equivalent, ablation rates, snow disappearance, and sublimation). We use the Sobol' global sensitivity analysis, which is typically used for model parameters but adapted here for testing model sensitivity to coexisting errors in all forcings. We quantify the Utah Energy Balance model's sensitivity to forcing errors with 1 840 000 Monte Carlo simulations across four sites and five different scenarios. Model outputs were (1) consistently more sensitive to forcing biases than random errors, (2) generally less sensitive to forcing error distributions, and (3) critically sensitive to different forcings depending on the relative magnitude of errors. For typical error magnitudes found in areas with drifting snow, precipitation bias was the most important factor for snow water equivalent, ablation rates, and snow disappearance timing, but other forcings had a more dominant impact when precipitation uncertainty was due solely to gauge undercatch. Additionally, the relative importance of forcing errors depended on the model output of interest. Sensitivity analysis can reveal which forcing error characteristics matter most for hydrologic modeling.

State estimation bias induced by optimization under uncertainty and error cost asymmetry is likely reflected in perception.

PubMed

Shimansky, Y P

2011-05-01

It is well known from numerous studies that perception can be significantly affected by intended action in many everyday situations, indicating that perception and related decision-making is not a simple, one-way sequence, but a complex iterative cognitive process. However, the underlying functional mechanisms are yet unclear. Based on an optimality approach, a quantitative computational model of one such mechanism has been developed in this study. It is assumed in the model that significant uncertainty about task-related parameters of the environment results in parameter estimation errors and an optimal control system should minimize the cost of such errors in terms of the optimality criterion. It is demonstrated that, if the cost of a parameter estimation error is significantly asymmetrical with respect to error direction, the tendency to minimize error cost creates a systematic deviation of the optimal parameter estimate from its maximum likelihood value. Consequently, optimization of parameter estimate and optimization of control action cannot be performed separately from each other under parameter uncertainty combined with asymmetry of estimation error cost, thus making the certainty equivalence principle non-applicable under those conditions. A hypothesis that not only the action, but also perception itself is biased by the above deviation of parameter estimate is supported by ample experimental evidence. The results provide important insights into the cognitive mechanisms of interaction between sensory perception and planning an action under realistic conditions. Implications for understanding related functional mechanisms of optimal control in the CNS are discussed.

Bayesian generalized least squares regression with application to log Pearson type 3 regional skew estimation

NASA Astrophysics Data System (ADS)

Reis, D. S.; Stedinger, J. R.; Martins, E. S.

2005-10-01

This paper develops a Bayesian approach to analysis of a generalized least squares (GLS) regression model for regional analyses of hydrologic data. The new approach allows computation of the posterior distributions of the parameters and the model error variance using a quasi-analytic approach. Two regional skew estimation studies illustrate the value of the Bayesian GLS approach for regional statistical analysis of a shape parameter and demonstrate that regional skew models can be relatively precise with effective record lengths in excess of 60 years. With Bayesian GLS the marginal posterior distribution of the model error variance and the corresponding mean and variance of the parameters can be computed directly, thereby providing a simple but important extension of the regional GLS regression procedures popularized by Tasker and Stedinger (1989), which is sensitive to the likely values of the model error variance when it is small relative to the sampling error in the at-site estimator.

Error Modeling of Multibaseline Optical Truss: Part 1: Modeling of System Level Performance

NASA Technical Reports Server (NTRS)

Milman, Mark H.; Korechoff, R. E.; Zhang, L. D.

2004-01-01

Global astrometry is the measurement of stellar positions and motions. These are typically characterized by five parameters, including two position parameters, two proper motion parameters, and parallax. The Space Interferometry Mission (SIM) will derive these parameters for a grid of approximately 1300 stars covering the celestial sphere to an accuracy of approximately 4uas, representing a two orders of magnitude improvement over the most precise current star catalogues. Narrow angle astrometry will be performed to a 1uas accuracy. A wealth of scientific information will be obtained from these accurate measurements encompassing many aspects of both galactic (and extragalactic science. SIM will be subject to a number of instrument errors that can potentially degrade performance. Many of these errors are systematic in that they are relatively static and repeatable with respect to the time frame and direction of the observation. This paper and its companion define the modeling of the, contributing factors to these errors and the analysis of how they impact SIM's ability to perform astrometric science.

Error analysis and system optimization of non-null aspheric testing system

NASA Astrophysics Data System (ADS)

Luo, Yongjie; Yang, Yongying; Liu, Dong; Tian, Chao; Zhuo, Yongmo

2010-10-01

A non-null aspheric testing system, which employs partial null lens (PNL for short) and reverse iterative optimization reconstruction (ROR for short) technique, is proposed in this paper. Based on system modeling in ray tracing software, the parameter of each optical element is optimized and this makes system modeling more precise. Systematic error of non-null aspheric testing system is analyzed and can be categorized into two types, the error due to surface parameters of PNL in the system modeling and the rest from non-null interferometer by the approach of error storage subtraction. Experimental results show that, after systematic error is removed from testing result of non-null aspheric testing system, the aspheric surface is precisely reconstructed by ROR technique and the consideration of systematic error greatly increase the test accuracy of non-null aspheric testing system.

Estimating population genetic parameters and comparing model goodness-of-fit using DNA sequences with error

PubMed Central

Liu, Xiaoming; Fu, Yun-Xin; Maxwell, Taylor J.; Boerwinkle, Eric

2010-01-01

It is known that sequencing error can bias estimation of evolutionary or population genetic parameters. This problem is more prominent in deep resequencing studies because of their large sample size n, and a higher probability of error at each nucleotide site. We propose a new method based on the composite likelihood of the observed SNP configurations to infer population mutation rate θ = 4Neμ, population exponential growth rate R, and error rate ɛ, simultaneously. Using simulation, we show the combined effects of the parameters, θ, n, ɛ, and R on the accuracy of parameter estimation. We compared our maximum composite likelihood estimator (MCLE) of θ with other θ estimators that take into account the error. The results show the MCLE performs well when the sample size is large or the error rate is high. Using parametric bootstrap, composite likelihood can also be used as a statistic for testing the model goodness-of-fit of the observed DNA sequences. The MCLE method is applied to sequence data on the ANGPTL4 gene in 1832 African American and 1045 European American individuals. PMID:19952140

Parameter de-correlation and model-identification in hybrid-style terrestrial laser scanner self-calibration

NASA Astrophysics Data System (ADS)

Lichti, Derek D.; Chow, Jacky; Lahamy, Hervé

One of the important systematic error parameters identified in terrestrial laser scanners is the collimation axis error, which models the non-orthogonality between two instrumental axes. The quality of this parameter determined by self-calibration, as measured by its estimated precision and its correlation with the tertiary rotation angle κ of the scanner exterior orientation, is strongly dependent on instrument architecture. While the quality is generally very high for panoramic-type scanners, it is comparably poor for hybrid-style instruments. Two methods for improving the quality of the collimation axis error in hybrid instrument self-calibration are proposed herein: (1) the inclusion of independent observations of the tertiary rotation angle κ; and (2) the use of a new collimation axis error model. Five real datasets were captured with two different hybrid-style scanners to test each method's efficacy. While the first method achieves the desired outcome of complete decoupling of the collimation axis error from κ, it is shown that the high correlation is simply transferred to other model variables. The second method achieves partial parameter de-correlation to acceptable levels. Importantly, it does so without any adverse, secondary correlations and is therefore the method recommended for future use. Finally, systematic error model identification has been greatly aided in previous studies by graphical analyses of self-calibration residuals. This paper presents results showing the architecture dependence of this technique, revealing its limitations for hybrid scanners.

Attitude control with realization of linear error dynamics

NASA Technical Reports Server (NTRS)

Paielli, Russell A.; Bach, Ralph E.

1993-01-01

An attitude control law is derived to realize linear unforced error dynamics with the attitude error defined in terms of rotation group algebra (rather than vector algebra). Euler parameters are used in the rotational dynamics model because they are globally nonsingular, but only the minimal three Euler parameters are used in the error dynamics model because they have no nonlinear mathematical constraints to prevent the realization of linear error dynamics. The control law is singular only when the attitude error angle is exactly pi rad about any eigenaxis, and a simple intuitive modification at the singularity allows the control law to be used globally. The forced error dynamics are nonlinear but stable. Numerical simulation tests show that the control law performs robustly for both initial attitude acquisition and attitude control.

Evaluation of seasonal and spatial variations of lumped water balance model sensitivity to precipitation data errors

NASA Astrophysics Data System (ADS)

Xu, Chong-yu; Tunemar, Liselotte; Chen, Yongqin David; Singh, V. P.

2006-06-01

Sensitivity of hydrological models to input data errors have been reported in the literature for particular models on a single or a few catchments. A more important issue, i.e. how model's response to input data error changes as the catchment conditions change has not been addressed previously. This study investigates the seasonal and spatial effects of precipitation data errors on the performance of conceptual hydrological models. For this study, a monthly conceptual water balance model, NOPEX-6, was applied to 26 catchments in the Mälaren basin in Central Sweden. Both systematic and random errors were considered. For the systematic errors, 5-15% of mean monthly precipitation values were added to the original precipitation to form the corrupted input scenarios. Random values were generated by Monte Carlo simulation and were assumed to be (1) independent between months, and (2) distributed according to a Gaussian law of zero mean and constant standard deviation that were taken as 5, 10, 15, 20, and 25% of the mean monthly standard deviation of precipitation. The results show that the response of the model parameters and model performance depends, among others, on the type of the error, the magnitude of the error, physical characteristics of the catchment, and the season of the year. In particular, the model appears less sensitive to the random error than to the systematic error. The catchments with smaller values of runoff coefficients were more influenced by input data errors than were the catchments with higher values. Dry months were more sensitive to precipitation errors than were wet months. Recalibration of the model with erroneous data compensated in part for the data errors by altering the model parameters.

Influence of precision of emission characteristic parameters on model prediction error of VOCs/formaldehyde from dry building material.

PubMed

Wei, Wenjuan; Xiong, Jianyin; Zhang, Yinping

2013-01-01

Mass transfer models are useful in predicting the emissions of volatile organic compounds (VOCs) and formaldehyde from building materials in indoor environments. They are also useful for human exposure evaluation and in sustainable building design. The measurement errors in the emission characteristic parameters in these mass transfer models, i.e., the initial emittable concentration (C 0), the diffusion coefficient (D), and the partition coefficient (K), can result in errors in predicting indoor VOC and formaldehyde concentrations. These errors have not yet been quantitatively well analyzed in the literature. This paper addresses this by using modelling to assess these errors for some typical building conditions. The error in C 0, as measured in environmental chambers and applied to a reference living room in Beijing, has the largest influence on the model prediction error in indoor VOC and formaldehyde concentration, while the error in K has the least effect. A correlation between the errors in D, K, and C 0 and the error in the indoor VOC and formaldehyde concentration prediction is then derived for engineering applications. In addition, the influence of temperature on the model prediction of emissions is investigated. It shows the impact of temperature fluctuations on the prediction errors in indoor VOC and formaldehyde concentrations to be less than 7% at 23±0.5°C and less than 30% at 23±2°C.

Accounting for measurement error in log regression models with applications to accelerated testing.

PubMed

Richardson, Robert; Tolley, H Dennis; Evenson, William E; Lunt, Barry M

2018-01-01

In regression settings, parameter estimates will be biased when the explanatory variables are measured with error. This bias can significantly affect modeling goals. In particular, accelerated lifetime testing involves an extrapolation of the fitted model, and a small amount of bias in parameter estimates may result in a significant increase in the bias of the extrapolated predictions. Additionally, bias may arise when the stochastic component of a log regression model is assumed to be multiplicative when the actual underlying stochastic component is additive. To account for these possible sources of bias, a log regression model with measurement error and additive error is approximated by a weighted regression model which can be estimated using Iteratively Re-weighted Least Squares. Using the reduced Eyring equation in an accelerated testing setting, the model is compared to previously accepted approaches to modeling accelerated testing data with both simulations and real data.

Parameter estimation for terrain modeling from gradient data. [navigation system for Martian rover

NASA Technical Reports Server (NTRS)

Dangelo, K. R.

1974-01-01

A method is developed for modeling terrain surfaces for use on an unmanned Martian roving vehicle. The modeling procedure employs a two-step process which uses gradient as well as height data in order to improve the accuracy of the model's gradient. Least square approximation is used in order to stochastically determine the parameters which describe the modeled surface. A complete error analysis of the modeling procedure is included which determines the effect of instrumental measurement errors on the model's accuracy. Computer simulation is used as a means of testing the entire modeling process which includes the acquisition of data points, the two-step modeling process and the error analysis. Finally, to illustrate the procedure, a numerical example is included.

The impact of experimental measurement errors on long-term viscoelastic predictions. [of structural materials

NASA Technical Reports Server (NTRS)

Tuttle, M. E.; Brinson, H. F.

1986-01-01

The impact of flight error in measured viscoelastic parameters on subsequent long-term viscoelastic predictions is numerically evaluated using the Schapery nonlinear viscoelastic model. Of the seven Schapery parameters, the results indicated that long-term predictions were most sensitive to errors in the power law parameter n. Although errors in the other parameters were significant as well, errors in n dominated all other factors at long times. The process of selecting an appropriate short-term test cycle so as to insure an accurate long-term prediction was considered, and a short-term test cycle was selected using material properties typical for T300/5208 graphite-epoxy at 149 C. The process of selection is described, and its individual steps are itemized.

Modeling Water Temperature in the Yakima River, Washington, from Roza Diversion Dam to Prosser Dam, 2005-06

USGS Publications Warehouse

Voss, Frank D.; Curran, Christopher A.; Mastin, Mark C.

2008-01-01

A mechanistic water-temperature model was constructed by the U.S. Geological Survey for use by the Bureau of Reclamation for studying the effect of potential water management decisions on water temperature in the Yakima River between Roza and Prosser, Washington. Flow and water temperature data for model input were obtained from the Bureau of Reclamation Hydromet database and from measurements collected by the U.S. Geological Survey during field trips in autumn 2005. Shading data for the model were collected by the U.S. Geological Survey in autumn 2006. The model was calibrated with data collected from April 1 through October 31, 2005, and tested with data collected from April 1 through October 31, 2006. Sensitivity analysis results showed that for the parameters tested, daily maximum water temperature was most sensitive to changes in air temperature and solar radiation. Root mean squared error for the five sites used for model calibration ranged from 1.3 to 1.9 degrees Celsius (?C) and mean error ranged from ?1.3 to 1.6?C. The root mean squared error for the five sites used for testing simulation ranged from 1.6 to 2.2?C and mean error ranged from 0.1 to 1.3?C. The accuracy of the stream temperatures estimated by the model is limited by four errors (model error, data error, parameter error, and user error).

Adaptive reduction of constitutive model-form error using a posteriori error estimation techniques

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bishop, Joseph E.; Brown, Judith Alice

In engineering practice, models are typically kept as simple as possible for ease of setup and use, computational efficiency, maintenance, and overall reduced complexity to achieve robustness. In solid mechanics, a simple and efficient constitutive model may be favored over one that is more predictive, but is difficult to parameterize, is computationally expensive, or is simply not available within a simulation tool. In order to quantify the modeling error due to the choice of a relatively simple and less predictive constitutive model, we adopt the use of a posteriori model-form error-estimation techniques. Based on local error indicators in the energymore » norm, an algorithm is developed for reducing the modeling error by spatially adapting the material parameters in the simpler constitutive model. The resulting material parameters are not material properties per se, but depend on the given boundary-value problem. As a first step to the more general nonlinear case, we focus here on linear elasticity in which the “complex” constitutive model is general anisotropic elasticity and the chosen simpler model is isotropic elasticity. As a result, the algorithm for adaptive error reduction is demonstrated using two examples: (1) A transversely-isotropic plate with hole subjected to tension, and (2) a transversely-isotropic tube with two side holes subjected to torsion.« less

Adaptive reduction of constitutive model-form error using a posteriori error estimation techniques

DOE PAGES

Bishop, Joseph E.; Brown, Judith Alice

2018-06-15

In engineering practice, models are typically kept as simple as possible for ease of setup and use, computational efficiency, maintenance, and overall reduced complexity to achieve robustness. In solid mechanics, a simple and efficient constitutive model may be favored over one that is more predictive, but is difficult to parameterize, is computationally expensive, or is simply not available within a simulation tool. In order to quantify the modeling error due to the choice of a relatively simple and less predictive constitutive model, we adopt the use of a posteriori model-form error-estimation techniques. Based on local error indicators in the energymore » norm, an algorithm is developed for reducing the modeling error by spatially adapting the material parameters in the simpler constitutive model. The resulting material parameters are not material properties per se, but depend on the given boundary-value problem. As a first step to the more general nonlinear case, we focus here on linear elasticity in which the “complex” constitutive model is general anisotropic elasticity and the chosen simpler model is isotropic elasticity. As a result, the algorithm for adaptive error reduction is demonstrated using two examples: (1) A transversely-isotropic plate with hole subjected to tension, and (2) a transversely-isotropic tube with two side holes subjected to torsion.« less

When to Make Mountains out of Molehills: The Pros and Cons of Simple and Complex Model Calibration Procedures

NASA Astrophysics Data System (ADS)

Smith, K. A.; Barker, L. J.; Harrigan, S.; Prudhomme, C.; Hannaford, J.; Tanguy, M.; Parry, S.

2017-12-01

Earth and environmental models are relied upon to investigate system responses that cannot otherwise be examined. In simulating physical processes, models have adjustable parameters which may, or may not, have a physical meaning. Determining the values to assign to these model parameters is an enduring challenge for earth and environmental modellers. Selecting different error metrics by which the models results are compared to observations will lead to different sets of calibrated model parameters, and thus different model results. Furthermore, models may exhibit `equifinal' behaviour, where multiple combinations of model parameters lead to equally acceptable model performance against observations. These decisions in model calibration introduce uncertainty that must be considered when model results are used to inform environmental decision-making. This presentation focusses on the uncertainties that derive from the calibration of a four parameter lumped catchment hydrological model (GR4J). The GR models contain an inbuilt automatic calibration algorithm that can satisfactorily calibrate against four error metrics in only a few seconds. However, a single, deterministic model result does not provide information on parameter uncertainty. Furthermore, a modeller interested in extreme events, such as droughts, may wish to calibrate against more low flows specific error metrics. In a comprehensive assessment, the GR4J model has been run with 500,000 Latin Hypercube Sampled parameter sets across 303 catchments in the United Kingdom. These parameter sets have been assessed against six error metrics, including two drought specific metrics. This presentation compares the two approaches, and demonstrates that the inbuilt automatic calibration can outperform the Latin Hypercube experiment approach in single metric assessed performance. However, it is also shown that there are many merits of the more comprehensive assessment, which allows for probabilistic model results, multi-objective optimisation, and better tailoring to calibrate the model for specific applications such as drought event characterisation. Modellers and decision-makers may be constrained in their choice of calibration method, so it is important that they recognise the strengths and limitations of their chosen approach.

A hybrid optimization approach to the estimation of distributed parameters in two-dimensional confined aquifers

USGS Publications Warehouse

Heidari, M.; Ranjithan, S.R.

1998-01-01

In using non-linear optimization techniques for estimation of parameters in a distributed ground water model, the initial values of the parameters and prior information about them play important roles. In this paper, the genetic algorithm (GA) is combined with the truncated-Newton search technique to estimate groundwater parameters for a confined steady-state ground water model. Use of prior information about the parameters is shown to be important in estimating correct or near-correct values of parameters on a regional scale. The amount of prior information needed for an accurate solution is estimated by evaluation of the sensitivity of the performance function to the parameters. For the example presented here, it is experimentally demonstrated that only one piece of prior information of the least sensitive parameter is sufficient to arrive at the global or near-global optimum solution. For hydraulic head data with measurement errors, the error in the estimation of parameters increases as the standard deviation of the errors increases. Results from our experiments show that, in general, the accuracy of the estimated parameters depends on the level of noise in the hydraulic head data and the initial values used in the truncated-Newton search technique.In using non-linear optimization techniques for estimation of parameters in a distributed ground water model, the initial values of the parameters and prior information about them play important roles. In this paper, the genetic algorithm (GA) is combined with the truncated-Newton search technique to estimate groundwater parameters for a confined steady-state ground water model. Use of prior information about the parameters is shown to be important in estimating correct or near-correct values of parameters on a regional scale. The amount of prior information needed for an accurate solution is estimated by evaluation of the sensitivity of the performance function to the parameters. For the example presented here, it is experimentally demonstrated that only one piece of prior information of the least sensitive parameter is sufficient to arrive at the global or near-global optimum solution. For hydraulic head data with measurement errors, the error in the estimation of parameters increases as the standard deviation of the errors increases. Results from our experiments show that, in general, the accuracy of the estimated parameters depends on the level of noise in the hydraulic head data and the initial values used in the truncated-Newton search technique.

Dynamic Modeling from Flight Data with Unknown Time Skews

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

2016-01-01

A method for estimating dynamic model parameters from flight data with unknown time skews is described and demonstrated. The method combines data reconstruction, nonlinear optimization, and equation-error parameter estimation in the frequency domain to accurately estimate both dynamic model parameters and the relative time skews in the data. Data from a nonlinear F-16 aircraft simulation with realistic noise, instrumentation errors, and arbitrary time skews were used to demonstrate the approach. The approach was further evaluated using flight data from a subscale jet transport aircraft, where the measured data were known to have relative time skews. Comparison of modeling results obtained from time-skewed and time-synchronized data showed that the method accurately estimates both dynamic model parameters and relative time skew parameters from flight data with unknown time skews.

Estimating Model Prediction Error: Should You Treat Predictions as Fixed or Random?

NASA Technical Reports Server (NTRS)

Wallach, Daniel; Thorburn, Peter; Asseng, Senthold; Challinor, Andrew J.; Ewert, Frank; Jones, James W.; Rotter, Reimund; Ruane, Alexander

2016-01-01

Crop models are important tools for impact assessment of climate change, as well as for exploring management options under current climate. It is essential to evaluate the uncertainty associated with predictions of these models. We compare two criteria of prediction error; MSEP fixed, which evaluates mean squared error of prediction for a model with fixed structure, parameters and inputs, and MSEP uncertain( X), which evaluates mean squared error averaged over the distributions of model structure, inputs and parameters. Comparison of model outputs with data can be used to estimate the former. The latter has a squared bias term, which can be estimated using hindcasts, and a model variance term, which can be estimated from a simulation experiment. The separate contributions to MSEP uncertain (X) can be estimated using a random effects ANOVA. It is argued that MSEP uncertain (X) is the more informative uncertainty criterion, because it is specific to each prediction situation.

Modeling uncertainties for tropospheric nitrogen dioxide columns affecting satellite-based inverse modeling of nitrogen oxides emissions

NASA Astrophysics Data System (ADS)

Lin, J.-T.; Liu, Z.; Zhang, Q.; Liu, H.; Mao, J.; Zhuang, G.

2012-12-01

Errors in chemical transport models (CTMs) interpreting the relation between space-retrieved tropospheric column densities of nitrogen dioxide (NO2) and emissions of nitrogen oxides (NOx) have important consequences on the inverse modeling. They are however difficult to quantify due to lack of adequate in situ measurements, particularly over China and other developing countries. This study proposes an alternate approach for model evaluation over East China, by analyzing the sensitivity of modeled NO2 columns to errors in meteorological and chemical parameters/processes important to the nitrogen abundance. As a demonstration, it evaluates the nested version of GEOS-Chem driven by the GEOS-5 meteorology and the INTEX-B anthropogenic emissions and used with retrievals from the Ozone Monitoring Instrument (OMI) to constrain emissions of NOx. The CTM has been used extensively for such applications. Errors are examined for a comprehensive set of meteorological and chemical parameters using measurements and/or uncertainty analysis based on current knowledge. Results are exploited then for sensitivity simulations perturbing the respective parameters, as the basis of the following post-model linearized and localized first-order modification. It is found that the model meteorology likely contains errors of various magnitudes in cloud optical depth, air temperature, water vapor, boundary layer height and many other parameters. Model errors also exist in gaseous and heterogeneous reactions, aerosol optical properties and emissions of non-nitrogen species affecting the nitrogen chemistry. Modifications accounting for quantified errors in 10 selected parameters increase the NO2 columns in most areas with an average positive impact of 18% in July and 8% in January, the most important factor being modified uptake of the hydroperoxyl radical (HO2) on aerosols. This suggests a possible systematic model bias such that the top-down emissions will be overestimated by the same magnitude if the model is used for emission inversion without corrections. The modifications however cannot eliminate the large model underestimates in cities and other extremely polluted areas (particularly in the north) as compared to satellite retrievals, likely pointing to underestimates of the a priori emission inventory in these places with important implications for understanding of atmospheric chemistry and air quality. Note that these modifications are simplified and should be interpreted with caution for error apportionment.

Examples of Nonconservatism in the CARE 3 Program

NASA Technical Reports Server (NTRS)

Dotson, Kelly J.

1988-01-01

This paper presents parameter regions in the CARE 3 (Computer-Aided Reliability Estimation version 3) computer program where the program overestimates the reliability of a modeled system without warning the user. Five simple models of fault-tolerant computer systems are analyzed; and, the parameter regions where reliability is overestimated are given. The source of the error in the reliability estimates for models which incorporate transient fault occurrences was not readily apparent. However, the source of much of the error for models with permanent and intermittent faults can be attributed to the choice of values for the run-time parameters of the program.

Real-Time Parameter Estimation in the Frequency Domain

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

2000-01-01

A method for real-time estimation of parameters in a linear dynamic state-space model was developed and studied. The application is aircraft dynamic model parameter estimation from measured data in flight. Equation error in the frequency domain was used with a recursive Fourier transform for the real-time data analysis. Linear and nonlinear simulation examples and flight test data from the F-18 High Alpha Research Vehicle were used to demonstrate that the technique produces accurate model parameter estimates with appropriate error bounds. Parameter estimates converged in less than one cycle of the dominant dynamic mode, using no a priori information, with control surface inputs measured in flight during ordinary piloted maneuvers. The real-time parameter estimation method has low computational requirements and could be implemented

An improved estimator for the hydration of fat-free mass from in vivo measurements subject to additive technical errors.

PubMed

Kinnamon, Daniel D; Lipsitz, Stuart R; Ludwig, David A; Lipshultz, Steven E; Miller, Tracie L

2010-04-01

The hydration of fat-free mass, or hydration fraction (HF), is often defined as a constant body composition parameter in a two-compartment model and then estimated from in vivo measurements. We showed that the widely used estimator for the HF parameter in this model, the mean of the ratios of measured total body water (TBW) to fat-free mass (FFM) in individual subjects, can be inaccurate in the presence of additive technical errors. We then proposed a new instrumental variables estimator that accurately estimates the HF parameter in the presence of such errors. In Monte Carlo simulations, the mean of the ratios of TBW to FFM was an inaccurate estimator of the HF parameter, and inferences based on it had actual type I error rates more than 13 times the nominal 0.05 level under certain conditions. The instrumental variables estimator was accurate and maintained an actual type I error rate close to the nominal level in all simulations. When estimating and performing inference on the HF parameter, the proposed instrumental variables estimator should yield accurate estimates and correct inferences in the presence of additive technical errors, but the mean of the ratios of TBW to FFM in individual subjects may not.

Data error and highly parameterized groundwater models

USGS Publications Warehouse

Hill, M.C.

2008-01-01

Strengths and weaknesses of highly parameterized models, in which the number of parameters exceeds the number of observations, are demonstrated using a synthetic test case. Results suggest that the approach can yield close matches to observations but also serious errors in system representation. It is proposed that avoiding the difficulties of highly parameterized models requires close evaluation of: (1) model fit, (2) performance of the regression, and (3) estimated parameter distributions. Comparisons to hydrogeologic information are expected to be critical to obtaining credible models. Copyright ?? 2008 IAHS Press.

Parameter Estimation for Thurstone Choice Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vojnovic, Milan; Yun, Seyoung

We consider the estimation accuracy of individual strength parameters of a Thurstone choice model when each input observation consists of a choice of one item from a set of two or more items (so called top-1 lists). This model accommodates the well-known choice models such as the Luce choice model for comparison sets of two or more items and the Bradley-Terry model for pair comparisons. We provide a tight characterization of the mean squared error of the maximum likelihood parameter estimator. We also provide similar characterizations for parameter estimators defined by a rank-breaking method, which amounts to deducing one ormore » more pair comparisons from a comparison of two or more items, assuming independence of these pair comparisons, and maximizing a likelihood function derived under these assumptions. We also consider a related binary classification problem where each individual parameter takes value from a set of two possible values and the goal is to correctly classify all items within a prescribed classification error. The results of this paper shed light on how the parameter estimation accuracy depends on given Thurstone choice model and the structure of comparison sets. In particular, we found that for unbiased input comparison sets of a given cardinality, when in expectation each comparison set of given cardinality occurs the same number of times, for a broad class of Thurstone choice models, the mean squared error decreases with the cardinality of comparison sets, but only marginally according to a diminishing returns relation. On the other hand, we found that there exist Thurstone choice models for which the mean squared error of the maximum likelihood parameter estimator can decrease much faster with the cardinality of comparison sets. We report empirical evaluation of some claims and key parameters revealed by theory using both synthetic and real-world input data from some popular sport competitions and online labor platforms.« less

Ensemble Solar Forecasting Statistical Quantification and Sensitivity Analysis: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheung, WanYin; Zhang, Jie; Florita, Anthony

2015-12-08

Uncertainties associated with solar forecasts present challenges to maintain grid reliability, especially at high solar penetrations. This study aims to quantify the errors associated with the day-ahead solar forecast parameters and the theoretical solar power output for a 51-kW solar power plant in a utility area in the state of Vermont, U.S. Forecasts were generated by three numerical weather prediction (NWP) models, including the Rapid Refresh, the High Resolution Rapid Refresh, and the North American Model, and a machine-learning ensemble model. A photovoltaic (PV) performance model was adopted to calculate theoretical solar power generation using the forecast parameters (e.g., irradiance,more » cell temperature, and wind speed). Errors of the power outputs were quantified using statistical moments and a suite of metrics, such as the normalized root mean squared error (NRMSE). In addition, the PV model's sensitivity to different forecast parameters was quantified and analyzed. Results showed that the ensemble model yielded forecasts in all parameters with the smallest NRMSE. The NRMSE of solar irradiance forecasts of the ensemble NWP model was reduced by 28.10% compared to the best of the three NWP models. Further, the sensitivity analysis indicated that the errors of the forecasted cell temperature attributed only approximately 0.12% to the NRMSE of the power output as opposed to 7.44% from the forecasted solar irradiance.« less

Error modeling for surrogates of dynamical systems using machine learning: Machine-learning-based error model for surrogates of dynamical systems

DOE PAGES

Trehan, Sumeet; Carlberg, Kevin T.; Durlofsky, Louis J.

2017-07-14

A machine learning–based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of high-dimensional regression techniques (eg, random forests, and LASSO) to map a large set of inexpensively computed “error indicators” (ie, features) produced by the surrogate model at a given time instance to a prediction of the surrogate-model error in a quantity of interest (QoI). This eliminates the need for the user to hand-select a small number of informative features. The methodology requires a training set of parameter instances at which the time-dependent surrogate-model error is computed bymore » simulating both the high-fidelity and surrogate models. Using these training data, the method first determines regression-model locality (via classification or clustering) and subsequently constructs a “local” regression model to predict the time-instantaneous error within each identified region of feature space. We consider 2 uses for the resulting error model: (1) as a correction to the surrogate-model QoI prediction at each time instance and (2) as a way to statistically model arbitrary functions of the time-dependent surrogate-model error (eg, time-integrated errors). We then apply the proposed framework to model errors in reduced-order models of nonlinear oil-water subsurface flow simulations, with time-varying well-control (bottom-hole pressure) parameters. The reduced-order models used in this work entail application of trajectory piecewise linearization in conjunction with proper orthogonal decomposition. Moreover, when the first use of the method is considered, numerical experiments demonstrate consistent improvement in accuracy in the time-instantaneous QoI prediction relative to the original surrogate model, across a large number of test cases. When the second use is considered, results show that the proposed method provides accurate statistical predictions of the time- and well-averaged errors.« less

Error modeling for surrogates of dynamical systems using machine learning: Machine-learning-based error model for surrogates of dynamical systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trehan, Sumeet; Carlberg, Kevin T.; Durlofsky, Louis J.

A machine learning–based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of high-dimensional regression techniques (eg, random forests, and LASSO) to map a large set of inexpensively computed “error indicators” (ie, features) produced by the surrogate model at a given time instance to a prediction of the surrogate-model error in a quantity of interest (QoI). This eliminates the need for the user to hand-select a small number of informative features. The methodology requires a training set of parameter instances at which the time-dependent surrogate-model error is computed bymore » simulating both the high-fidelity and surrogate models. Using these training data, the method first determines regression-model locality (via classification or clustering) and subsequently constructs a “local” regression model to predict the time-instantaneous error within each identified region of feature space. We consider 2 uses for the resulting error model: (1) as a correction to the surrogate-model QoI prediction at each time instance and (2) as a way to statistically model arbitrary functions of the time-dependent surrogate-model error (eg, time-integrated errors). We then apply the proposed framework to model errors in reduced-order models of nonlinear oil-water subsurface flow simulations, with time-varying well-control (bottom-hole pressure) parameters. The reduced-order models used in this work entail application of trajectory piecewise linearization in conjunction with proper orthogonal decomposition. Moreover, when the first use of the method is considered, numerical experiments demonstrate consistent improvement in accuracy in the time-instantaneous QoI prediction relative to the original surrogate model, across a large number of test cases. When the second use is considered, results show that the proposed method provides accurate statistical predictions of the time- and well-averaged errors.« less

Improvement and comparison of likelihood functions for model calibration and parameter uncertainty analysis within a Markov chain Monte Carlo scheme

NASA Astrophysics Data System (ADS)

Cheng, Qin-Bo; Chen, Xi; Xu, Chong-Yu; Reinhardt-Imjela, Christian; Schulte, Achim

2014-11-01

In this study, the likelihood functions for uncertainty analysis of hydrological models are compared and improved through the following steps: (1) the equivalent relationship between the Nash-Sutcliffe Efficiency coefficient (NSE) and the likelihood function with Gaussian independent and identically distributed residuals is proved; (2) a new estimation method of the Box-Cox transformation (BC) parameter is developed to improve the effective elimination of the heteroscedasticity of model residuals; and (3) three likelihood functions-NSE, Generalized Error Distribution with BC (BC-GED) and Skew Generalized Error Distribution with BC (BC-SGED)-are applied for SWAT-WB-VSA (Soil and Water Assessment Tool - Water Balance - Variable Source Area) model calibration in the Baocun watershed, Eastern China. Performances of calibrated models are compared using the observed river discharges and groundwater levels. The result shows that the minimum variance constraint can effectively estimate the BC parameter. The form of the likelihood function significantly impacts on the calibrated parameters and the simulated results of high and low flow components. SWAT-WB-VSA with the NSE approach simulates flood well, but baseflow badly owing to the assumption of Gaussian error distribution, where the probability of the large error is low, but the small error around zero approximates equiprobability. By contrast, SWAT-WB-VSA with the BC-GED or BC-SGED approach mimics baseflow well, which is proved in the groundwater level simulation. The assumption of skewness of the error distribution may be unnecessary, because all the results of the BC-SGED approach are nearly the same as those of the BC-GED approach.

A Sensor Dynamic Measurement Error Prediction Model Based on NAPSO-SVM.

PubMed

Jiang, Minlan; Jiang, Lan; Jiang, Dingde; Li, Fei; Song, Houbing

2018-01-15

Dynamic measurement error correction is an effective way to improve sensor precision. Dynamic measurement error prediction is an important part of error correction, and support vector machine (SVM) is often used for predicting the dynamic measurement errors of sensors. Traditionally, the SVM parameters were always set manually, which cannot ensure the model's performance. In this paper, a SVM method based on an improved particle swarm optimization (NAPSO) is proposed to predict the dynamic measurement errors of sensors. Natural selection and simulated annealing are added in the PSO to raise the ability to avoid local optima. To verify the performance of NAPSO-SVM, three types of algorithms are selected to optimize the SVM's parameters: the particle swarm optimization algorithm (PSO), the improved PSO optimization algorithm (NAPSO), and the glowworm swarm optimization (GSO). The dynamic measurement error data of two sensors are applied as the test data. The root mean squared error and mean absolute percentage error are employed to evaluate the prediction models' performances. The experimental results show that among the three tested algorithms the NAPSO-SVM method has a better prediction precision and a less prediction errors, and it is an effective method for predicting the dynamic measurement errors of sensors.

On parameters identification of computational models of vibrations during quiet standing of humans

NASA Astrophysics Data System (ADS)

Barauskas, R.; Krušinskienė, R.

2007-12-01

Vibration of the center of pressure (COP) of human body on the base of support during quiet standing is a very popular clinical research, which provides useful information about the physical and health condition of an individual. In this work, vibrations of COP of a human body in forward-backward direction during still standing are generated using controlled inverted pendulum (CIP) model with a single degree of freedom (dof) supplied with proportional, integral and differential (PID) controller, which represents the behavior of the central neural system of a human body and excited by cumulative disturbance vibration, generated within the body due to breathing or any other physical condition. The identification of the model and disturbance parameters is an important stage while creating a close-to-reality computational model able to evaluate features of disturbance. The aim of this study is to present the CIP model parameters identification approach based on the information captured by time series of the COP signal. The identification procedure is based on an error function minimization. Error function is formulated in terms of time laws of computed and experimentally measured COP vibrations. As an alternative, error function is formulated in terms of the stabilogram diffusion function (SDF). The minimization of error functions is carried out by employing methods based on sensitivity functions of the error with respect to model and excitation parameters. The sensitivity functions are obtained by using the variational techniques. The inverse dynamic problem approach has been employed in order to establish the properties of the disturbance time laws ensuring the satisfactory coincidence of measured and computed COP vibration laws. The main difficulty of the investigated problem is encountered during the model validation stage. Generally, neither the PID controller parameter set nor the disturbance time law are known in advance. In this work, an error function formulated in terms of time derivative of disturbance torque has been proposed in order to obtain PID controller parameters, as well as the reference time law of the disturbance. The disturbance torque is calculated from experimental data using the inverse dynamic approach. Experiments presented in this study revealed that vibrations of disturbance torque and PID controller parameters identified by the method may be qualified as feasible in humans. Presented approach may be easily extended to structural models with any number of dof or higher structural complexity.

Identifying Bearing Rotodynamic Coefficients Using an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Miller, Brad A.; Howard, Samuel A.

2008-01-01

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

Performance Metrics, Error Modeling, and Uncertainty Quantification

NASA Technical Reports Server (NTRS)

Tian, Yudong; Nearing, Grey S.; Peters-Lidard, Christa D.; Harrison, Kenneth W.; Tang, Ling

2016-01-01

A common set of statistical metrics has been used to summarize the performance of models or measurements-­ the most widely used ones being bias, mean square error, and linear correlation coefficient. They assume linear, additive, Gaussian errors, and they are interdependent, incomplete, and incapable of directly quantifying un­certainty. The authors demonstrate that these metrics can be directly derived from the parameters of the simple linear error model. Since a correct error model captures the full error information, it is argued that the specification of a parametric error model should be an alternative to the metrics-based approach. The error-modeling meth­odology is applicable to both linear and nonlinear errors, while the metrics are only meaningful for linear errors. In addition, the error model expresses the error structure more naturally, and directly quantifies uncertainty. This argument is further explained by highlighting the intrinsic connections between the performance metrics, the error model, and the joint distribution between the data and the reference.

Influence of Precision of Emission Characteristic Parameters on Model Prediction Error of VOCs/Formaldehyde from Dry Building Material

PubMed Central

Wei, Wenjuan; Xiong, Jianyin; Zhang, Yinping

2013-01-01

Mass transfer models are useful in predicting the emissions of volatile organic compounds (VOCs) and formaldehyde from building materials in indoor environments. They are also useful for human exposure evaluation and in sustainable building design. The measurement errors in the emission characteristic parameters in these mass transfer models, i.e., the initial emittable concentration (C 0), the diffusion coefficient (D), and the partition coefficient (K), can result in errors in predicting indoor VOC and formaldehyde concentrations. These errors have not yet been quantitatively well analyzed in the literature. This paper addresses this by using modelling to assess these errors for some typical building conditions. The error in C 0, as measured in environmental chambers and applied to a reference living room in Beijing, has the largest influence on the model prediction error in indoor VOC and formaldehyde concentration, while the error in K has the least effect. A correlation between the errors in D, K, and C 0 and the error in the indoor VOC and formaldehyde concentration prediction is then derived for engineering applications. In addition, the influence of temperature on the model prediction of emissions is investigated. It shows the impact of temperature fluctuations on the prediction errors in indoor VOC and formaldehyde concentrations to be less than 7% at 23±0.5°C and less than 30% at 23±2°C. PMID:24312497

Ensemble-Based Parameter Estimation in a Coupled General Circulation Model

DOE PAGES

Liu, Y.; Liu, Z.; Zhang, S.; ...

2014-09-10

Parameter estimation provides a potentially powerful approach to reduce model bias for complex climate models. Here, in a twin experiment framework, the authors perform the first parameter estimation in a fully coupled ocean–atmosphere general circulation model using an ensemble coupled data assimilation system facilitated with parameter estimation. The authors first perform single-parameter estimation and then multiple-parameter estimation. In the case of the single-parameter estimation, the error of the parameter [solar penetration depth (SPD)] is reduced by over 90% after ~40 years of assimilation of the conventional observations of monthly sea surface temperature (SST) and salinity (SSS). The results of multiple-parametermore » estimation are less reliable than those of single-parameter estimation when only the monthly SST and SSS are assimilated. Assimilating additional observations of atmospheric data of temperature and wind improves the reliability of multiple-parameter estimation. The errors of the parameters are reduced by 90% in ~8 years of assimilation. Finally, the improved parameters also improve the model climatology. With the optimized parameters, the bias of the climatology of SST is reduced by ~90%. Altogether, this study suggests the feasibility of ensemble-based parameter estimation in a fully coupled general circulation model.« less

Optimum data weighting and error calibration for estimation of gravitational parameters

NASA Technical Reports Server (NTRS)

Lerch, F. J.

1989-01-01

A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 (Goddard Earth Model, 36x36 spherical harmonic field) were employed toward application of this technique for gravity field parameters. Also, GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized here. The method employs subset solutions of the data associated with the complete solution and uses an algorithm to adjust the data weights by requiring the differences of parameters between solutions to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting as compared to the nominal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.

Accounting for nonsampling error in estimates of HIV epidemic trends from antenatal clinic sentinel surveillance

PubMed Central

Eaton, Jeffrey W.; Bao, Le

2017-01-01

Objectives The aim of the study was to propose and demonstrate an approach to allow additional nonsampling uncertainty about HIV prevalence measured at antenatal clinic sentinel surveillance (ANC-SS) in model-based inferences about trends in HIV incidence and prevalence. Design Mathematical model fitted to surveillance data with Bayesian inference. Methods We introduce a variance inflation parameter σinfl2 that accounts for the uncertainty of nonsampling errors in ANC-SS prevalence. It is additive to the sampling error variance. Three approaches are tested for estimating σinfl2 using ANC-SS and household survey data from 40 subnational regions in nine countries in sub-Saharan, as defined in UNAIDS 2016 estimates. Methods were compared using in-sample fit and out-of-sample prediction of ANC-SS data, fit to household survey prevalence data, and the computational implications. Results Introducing the additional variance parameter σinfl2 increased the error variance around ANC-SS prevalence observations by a median of 2.7 times (interquartile range 1.9–3.8). Using only sampling error in ANC-SS prevalence ( σinfl2=0), coverage of 95% prediction intervals was 69% in out-of-sample prediction tests. This increased to 90% after introducing the additional variance parameter σinfl2. The revised probabilistic model improved model fit to household survey prevalence and increased epidemic uncertainty intervals most during the early epidemic period before 2005. Estimating σinfl2 did not increase the computational cost of model fitting. Conclusions: We recommend estimating nonsampling error in ANC-SS as an additional parameter in Bayesian inference using the Estimation and Projection Package model. This approach may prove useful for incorporating other data sources such as routine prevalence from Prevention of mother-to-child transmission testing into future epidemic estimates. PMID:28296801

Application of Modified Particle Swarm Optimization Method for Parameter Extraction of 2-D TEC Mapping

NASA Astrophysics Data System (ADS)

Toker, C.; Gokdag, Y. E.; Arikan, F.; Arikan, O.

2012-04-01

Ionosphere is a very important part of Space Weather. Modeling and monitoring of ionospheric variability is a major part of satellite communication, navigation and positioning systems. Total Electron Content (TEC), which is defined as the line integral of the electron density along a ray path, is one of the parameters to investigate the ionospheric variability. Dual-frequency GPS receivers, with their world wide availability and efficiency in TEC estimation, have become a major source of global and regional TEC modeling. When Global Ionospheric Maps (GIM) of International GPS Service (IGS) centers (http://iono.jpl.nasa.gov/gim.html) are investigated, it can be observed that regional ionosphere along the midlatitude regions can be modeled as a constant, linear or a quadratic surface. Globally, especially around the magnetic equator, the TEC surfaces resemble twisted and dispersed single centered or double centered Gaussian functions. Particle Swarm Optimization (PSO) proved itself as a fast converging and an effective optimization tool in various diverse fields. Yet, in order to apply this optimization technique into TEC modeling, the method has to be modified for higher efficiency and accuracy in extraction of geophysical parameters such as model parameters of TEC surfaces. In this study, a modified PSO (mPSO) method is applied to regional and global synthetic TEC surfaces. The synthetic surfaces that represent the trend and small scale variability of various ionospheric states are necessary to compare the performance of mPSO over number of iterations, accuracy in parameter estimation and overall surface reconstruction. The Cramer-Rao bounds for each surface type and model are also investigated and performance of mPSO are tested with respect to these bounds. For global models, the sample points that are used in optimization are obtained using IGS receiver network. For regional TEC models, regional networks such as Turkish National Permanent GPS Network (TNPGN-Active) receiver sites are used. The regional TEC models are grouped into constant (one parameter), linear (two parameters), and quadratic (six parameters) surfaces which are functions of latitude and longitude. Global models require seven parameters for single centered Gaussian and 13 parameters for double centered Gaussian function. The error criterion is the normalized percentage error for both the surface and the parameters. It is observed that mPSO is very successful in parameter extraction of various regional and global models. The normalized reconstruction error varies from 10-4 for constant surfaces to 10-3 for quadratic surfaces in regional models, sampled with regional networks. Even for the cases of a severe geomagnetic storm that affects measurements globally, with IGS network, the reconstruction error is on the order of 10-1 even though individual parameters have higher normalized errors. The modified PSO technique proved itself to be a useful tool for parameter extraction of more complicated TEC models. This study is supported by TUBITAK EEEAG under Grant No: 109E055.

Trans-dimensional joint inversion of seabed scattering and reflection data.

PubMed

Steininger, Gavin; Dettmer, Jan; Dosso, Stan E; Holland, Charles W

2013-03-01

This paper examines joint inversion of acoustic scattering and reflection data to resolve seabed interface roughness parameters (spectral strength, exponent, and cutoff) and geoacoustic profiles. Trans-dimensional (trans-D) Bayesian sampling is applied with both the number of sediment layers and the order (zeroth or first) of auto-regressive parameters in the error model treated as unknowns. A prior distribution that allows fluid sediment layers over an elastic basement in a trans-D inversion is derived and implemented. Three cases are considered: Scattering-only inversion, joint scattering and reflection inversion, and joint inversion with the trans-D auto-regressive error model. Including reflection data improves the resolution of scattering and geoacoustic parameters. The trans-D auto-regressive model further improves scattering resolution and correctly differentiates between strongly and weakly correlated residual errors.

Model misspecification detection by means of multiple generator errors, using the observed potential map.

PubMed

Zhang, Z; Jewett, D L

1994-01-01

Due to model misspecification, currently-used Dipole Source Localization (DSL) methods may contain Multiple-Generator Errors (MulGenErrs) when fitting simultaneously-active dipoles. The size of the MulGenErr is a function of both the model used, and the dipole parameters, including the dipoles' waveforms (time-varying magnitudes). For a given fitting model, by examining the variation of the MulGenErrs (or the fit parameters) under different waveforms for the same generating-dipoles, the accuracy of the fitting model for this set of dipoles can be determined. This method of testing model misspecification can be applied to evoked potential maps even when the parameters of the generating-dipoles are unknown. The dipole parameters fitted in a model should only be accepted if the model can be shown to be sufficiently accurate.

Automation of workplace lifting hazard assessment for musculoskeletal injury prevention.

PubMed

Spector, June T; Lieblich, Max; Bao, Stephen; McQuade, Kevin; Hughes, Margaret

2014-01-01

Existing methods for practically evaluating musculoskeletal exposures such as posture and repetition in workplace settings have limitations. We aimed to automate the estimation of parameters in the revised United States National Institute for Occupational Safety and Health (NIOSH) lifting equation, a standard manual observational tool used to evaluate back injury risk related to lifting in workplace settings, using depth camera (Microsoft Kinect) and skeleton algorithm technology. A large dataset (approximately 22,000 frames, derived from six subjects) of simultaneous lifting and other motions recorded in a laboratory setting using the Kinect (Microsoft Corporation, Redmond, Washington, United States) and a standard optical motion capture system (Qualysis, Qualysis Motion Capture Systems, Qualysis AB, Sweden) was assembled. Error-correction regression models were developed to improve the accuracy of NIOSH lifting equation parameters estimated from the Kinect skeleton. Kinect-Qualysis errors were modelled using gradient boosted regression trees with a Huber loss function. Models were trained on data from all but one subject and tested on the excluded subject. Finally, models were tested on three lifting trials performed by subjects not involved in the generation of the model-building dataset. Error-correction appears to produce estimates for NIOSH lifting equation parameters that are more accurate than those derived from the Microsoft Kinect algorithm alone. Our error-correction models substantially decreased the variance of parameter errors. In general, the Kinect underestimated parameters, and modelling reduced this bias, particularly for more biased estimates. Use of the raw Kinect skeleton model tended to result in falsely high safe recommended weight limits of loads, whereas error-corrected models gave more conservative, protective estimates. Our results suggest that it may be possible to produce reasonable estimates of posture and temporal elements of tasks such as task frequency in an automated fashion, although these findings should be confirmed in a larger study. Further work is needed to incorporate force assessments and address workplace feasibility challenges. We anticipate that this approach could ultimately be used to perform large-scale musculoskeletal exposure assessment not only for research but also to provide real-time feedback to workers and employers during work method improvement activities and employee training.

Full-envelope aerodynamic modeling of the Harrier aircraft

NASA Technical Reports Server (NTRS)

Mcnally, B. David

1986-01-01

A project to identify a full-envelope model of the YAV-8B Harrier using flight-test and parameter identification techniques is described. As part of the research in advanced control and display concepts for V/STOL aircraft, a full-envelope aerodynamic model of the Harrier is identified, using mathematical model structures and parameter identification methods. A global-polynomial model structure is also used as a basis for the identification of the YAV-8B aerodynamic model. State estimation methods are used to ensure flight data consistency prior to parameter identification.Equation-error methods are used to identify model parameters. A fixed-base simulator is used extensively to develop flight test procedures and to validate parameter identification software. Using simple flight maneuvers, a simulated data set was created covering the YAV-8B flight envelope from about 0.3 to 0.7 Mach and about -5 to 15 deg angle of attack. A singular value decomposition implementation of the equation-error approach produced good parameter estimates based on this simulated data set.

Error Analysis and Validation for Insar Height Measurement Induced by Slant Range

NASA Astrophysics Data System (ADS)

Zhang, X.; Li, T.; Fan, W.; Geng, X.

2018-04-01

InSAR technique is an important method for large area DEM extraction. Several factors have significant influence on the accuracy of height measurement. In this research, the effect of slant range measurement for InSAR height measurement was analysis and discussed. Based on the theory of InSAR height measurement, the error propagation model was derived assuming no coupling among different factors, which directly characterise the relationship between slant range error and height measurement error. Then the theoretical-based analysis in combination with TanDEM-X parameters was implemented to quantitatively evaluate the influence of slant range error to height measurement. In addition, the simulation validation of InSAR error model induced by slant range was performed on the basis of SRTM DEM and TanDEM-X parameters. The spatial distribution characteristics and error propagation rule of InSAR height measurement were further discussed and evaluated.

Dependence of Dynamic Modeling Accuracy on Sensor Measurements, Mass Properties, and Aircraft Geometry

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2013-01-01

The NASA Generic Transport Model (GTM) nonlinear simulation was used to investigate the effects of errors in sensor measurements, mass properties, and aircraft geometry on the accuracy of identified parameters in mathematical models describing the flight dynamics and determined from flight data. Measurements from a typical flight condition and system identification maneuver were systematically and progressively deteriorated by introducing noise, resolution errors, and bias errors. The data were then used to estimate nondimensional stability and control derivatives within a Monte Carlo simulation. Based on these results, recommendations are provided for maximum allowable errors in sensor measurements, mass properties, and aircraft geometry to achieve desired levels of dynamic modeling accuracy. Results using additional flight conditions and parameter estimation methods, as well as a nonlinear flight simulation of the General Dynamics F-16 aircraft, were compared with these recommendations

Model error in covariance structure models: Some implications for power and Type I error

PubMed Central

Coffman, Donna L.

2010-01-01

The present study investigated the degree to which violation of the parameter drift assumption affects the Type I error rate for the test of close fit and power analysis procedures proposed by MacCallum, Browne, and Sugawara (1996) for both the test of close fit and the test of exact fit. The parameter drift assumption states that as sample size increases both sampling error and model error (i.e. the degree to which the model is an approximation in the population) decrease. Model error was introduced using a procedure proposed by Cudeck and Browne (1992). The empirical power for both the test of close fit, in which the null hypothesis specifies that the Root Mean Square Error of Approximation (RMSEA) ≤ .05, and the test of exact fit, in which the null hypothesis specifies that RMSEA = 0, is compared with the theoretical power computed using the MacCallum et al. (1996) procedure. The empirical power and theoretical power for both the test of close fit and the test of exact fit are nearly identical under violations of the assumption. The results also indicated that the test of close fit maintains the nominal Type I error rate under violations of the assumption. PMID:21331302

Financial model calibration using consistency hints.

PubMed

Abu-Mostafa, Y S

2001-01-01

We introduce a technique for forcing the calibration of a financial model to produce valid parameters. The technique is based on learning from hints. It converts simple curve fitting into genuine calibration, where broad conclusions can be inferred from parameter values. The technique augments the error function of curve fitting with consistency hint error functions based on the Kullback-Leibler distance. We introduce an efficient EM-type optimization algorithm tailored to this technique. We also introduce other consistency hints, and balance their weights using canonical errors. We calibrate the correlated multifactor Vasicek model of interest rates, and apply it successfully to Japanese Yen swaps market and US dollar yield market.

Optimal Tuner Selection for Kalman-Filter-Based Aircraft Engine Performance Estimation

NASA Technical Reports Server (NTRS)

Simon, Donald L.; Garg, Sanjay

2011-01-01

An emerging approach in the field of aircraft engine controls and system health management is the inclusion of real-time, onboard models for the inflight estimation of engine performance variations. This technology, typically based on Kalman-filter concepts, enables the estimation of unmeasured engine performance parameters that can be directly utilized by controls, prognostics, and health-management applications. A challenge that complicates this practice is the fact that an aircraft engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters such as efficiencies and flow capacities related to each major engine module. Through Kalman-filter-based estimation techniques, the level of engine performance degradation can be estimated, given that there are at least as many sensors as health parameters to be estimated. However, in an aircraft engine, the number of sensors available is typically less than the number of health parameters, presenting an under-determined estimation problem. A common approach to address this shortcoming is to estimate a subset of the health parameters, referred to as model tuning parameters. The problem/objective is to optimally select the model tuning parameters to minimize Kalman-filterbased estimation error. A tuner selection technique has been developed that specifically addresses the under-determined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine that seeks to minimize the theoretical mean-squared estimation error of the Kalman filter. This approach can significantly reduce the error in onboard aircraft engine parameter estimation applications such as model-based diagnostic, controls, and life usage calculations. The advantage of the innovation is the significant reduction in estimation errors that it can provide relative to the conventional approach of selecting a subset of health parameters to serve as the model tuning parameter vector. Because this technique needs only to be performed during the system design process, it places no additional computation burden on the onboard Kalman filter implementation. The technique has been developed for aircraft engine onboard estimation applications, as this application typically presents an under-determined estimation problem. However, this generic technique could be applied to other industries using gas turbine engine technology.

Quality Control Analysis of Selected Aspects of Programs Administered by the Bureau of Student Financial Assistance. Task 1 and Quality Control Sample; Error-Prone Modeling Analysis Plan.

ERIC Educational Resources Information Center

Saavedra, Pedro; And Others

Parameters and procedures for developing an error-prone model (EPM) to predict financial aid applicants who are likely to misreport on Basic Educational Opportunity Grant (BEOG) applications are introduced. Specifications to adapt these general parameters to secondary data analysis of the Validation, Edits, and Applications Processing Systems…

Addressing the impact of environmental uncertainty in plankton model calibration with a dedicated software system: the Marine Model Optimization Testbed (MarMOT 1.1 alpha)

NASA Astrophysics Data System (ADS)

Hemmings, J. C. P.; Challenor, P. G.

2012-04-01

A wide variety of different plankton system models have been coupled with ocean circulation models, with the aim of understanding and predicting aspects of environmental change. However, an ability to make reliable inferences about real-world processes from the model behaviour demands a quantitative understanding of model error that remains elusive. Assessment of coupled model output is inhibited by relatively limited observing system coverage of biogeochemical components. Any direct assessment of the plankton model is further inhibited by uncertainty in the physical state. Furthermore, comparative evaluation of plankton models on the basis of their design is inhibited by the sensitivity of their dynamics to many adjustable parameters. Parameter uncertainty has been widely addressed by calibrating models at data-rich ocean sites. However, relatively little attention has been given to quantifying uncertainty in the physical fields required by the plankton models at these sites, and tendencies in the biogeochemical properties due to the effects of horizontal processes are often neglected. Here we use model twin experiments, in which synthetic data are assimilated to estimate a system's known "true" parameters, to investigate the impact of error in a plankton model's environmental input data. The experiments are supported by a new software tool, the Marine Model Optimization Testbed, designed for rigorous analysis of plankton models in a multi-site 1-D framework. Simulated errors are derived from statistical characterizations of the mixed layer depth, the horizontal flux divergence tendencies of the biogeochemical tracers and the initial state. Plausible patterns of uncertainty in these data are shown to produce strong temporal and spatial variability in the expected simulation error variance over an annual cycle, indicating variation in the significance attributable to individual model-data differences. An inverse scheme using ensemble-based estimates of the simulation error variance to allow for this environment error performs well compared with weighting schemes used in previous calibration studies, giving improved estimates of the known parameters. The efficacy of the new scheme in real-world applications will depend on the quality of statistical characterizations of the input data. Practical approaches towards developing reliable characterizations are discussed.

System identification for modeling for control of flexible structures

NASA Technical Reports Server (NTRS)

Mettler, Edward; Milman, Mark

1986-01-01

The major components of a design and operational flight strategy for flexible structure control systems are presented. In this strategy an initial distributed parameter control design is developed and implemented from available ground test data and on-orbit identification using sophisticated modeling and synthesis techniques. The reliability of this high performance controller is directly linked to the accuracy of the parameters on which the design is based. Because uncertainties inevitably grow without system monitoring, maintaining the control system requires an active on-line system identification function to supply parameter updates and covariance information. Control laws can then be modified to improve performance when the error envelopes are decreased. In terms of system safety and stability the covariance information is of equal importance as the parameter values themselves. If the on-line system ID function detects an increase in parameter error covariances, then corresponding adjustments must be made in the control laws to increase robustness. If the error covariances exceed some threshold, an autonomous calibration sequence could be initiated to restore the error enveloped to an acceptable level.

Dynamic imaging model and parameter optimization for a star tracker.

PubMed

Yan, Jinyun; Jiang, Jie; Zhang, Guangjun

2016-03-21

Under dynamic conditions, star spots move across the image plane of a star tracker and form a smeared star image. This smearing effect increases errors in star position estimation and degrades attitude accuracy. First, an analytical energy distribution model of a smeared star spot is established based on a line segment spread function because the dynamic imaging process of a star tracker is equivalent to the static imaging process of linear light sources. The proposed model, which has a clear physical meaning, explicitly reflects the key parameters of the imaging process, including incident flux, exposure time, velocity of a star spot in an image plane, and Gaussian radius. Furthermore, an analytical expression of the centroiding error of the smeared star spot is derived using the proposed model. An accurate and comprehensive evaluation of centroiding accuracy is obtained based on the expression. Moreover, analytical solutions of the optimal parameters are derived to achieve the best performance in centroid estimation. Finally, we perform numerical simulations and a night sky experiment to validate the correctness of the dynamic imaging model, the centroiding error expression, and the optimal parameters.

Model identification using stochastic differential equation grey-box models in diabetes.

PubMed

Duun-Henriksen, Anne Katrine; Schmidt, Signe; Røge, Rikke Meldgaard; Møller, Jonas Bech; Nørgaard, Kirsten; Jørgensen, John Bagterp; Madsen, Henrik

2013-03-01

The acceptance of virtual preclinical testing of control algorithms is growing and thus also the need for robust and reliable models. Models based on ordinary differential equations (ODEs) can rarely be validated with standard statistical tools. Stochastic differential equations (SDEs) offer the possibility of building models that can be validated statistically and that are capable of predicting not only a realistic trajectory, but also the uncertainty of the prediction. In an SDE, the prediction error is split into two noise terms. This separation ensures that the errors are uncorrelated and provides the possibility to pinpoint model deficiencies. An identifiable model of the glucoregulatory system in a type 1 diabetes mellitus (T1DM) patient is used as the basis for development of a stochastic-differential-equation-based grey-box model (SDE-GB). The parameters are estimated on clinical data from four T1DM patients. The optimal SDE-GB is determined from likelihood-ratio tests. Finally, parameter tracking is used to track the variation in the "time to peak of meal response" parameter. We found that the transformation of the ODE model into an SDE-GB resulted in a significant improvement in the prediction and uncorrelated errors. Tracking of the "peak time of meal absorption" parameter showed that the absorption rate varied according to meal type. This study shows the potential of using SDE-GBs in diabetes modeling. Improved model predictions were obtained due to the separation of the prediction error. SDE-GBs offer a solid framework for using statistical tools for model validation and model development. © 2013 Diabetes Technology Society.

Control of Systems With Slow Actuators Using Time Scale Separation

NASA Technical Reports Server (NTRS)

Stepanyan, Vehram; Nguyen, Nhan

2009-01-01

This paper addresses the problem of controlling a nonlinear plant with a slow actuator using singular perturbation method. For the known plant-actuator cascaded system the proposed scheme achieves tracking of a given reference model with considerably less control demand than would otherwise result when using conventional design techniques. This is the consequence of excluding the small parameter from the actuator dynamics via time scale separation. The resulting tracking error is within the order of this small parameter. For the unknown system the adaptive counterpart is developed based on the prediction model, which is driven towards the reference model by the control design. It is proven that the prediction model tracks the reference model with an error proportional to the small parameter, while the prediction error converges to zero. The resulting closed-loop system with all prediction models and adaptive laws remains stable. The benefits of the approach are demonstrated in simulation studies and compared to conventional control approaches.

Effect of Dipolar Cross Correlation on Model-Free Motional Parameters Obtained from 13C Relaxation in AX 2 Systems

NASA Astrophysics Data System (ADS)

Zhu, L. Y.; Kemple, M. D.; Landy, S. B.; Buckley, P.

The importance of dipolar cross correlation in 13C relaxation studies of molecular motion in AX 2 spin systems (A = 13C, X = 1H) was examined. Several different models for the internal motion, including two restricted-diffusion, and two-site jump models, the Kinosita model [K. Kinosita, Jr., S. Kawato, and A. Ikegami, Biophys. J.20, 289 (1977)], and an axially symmetric model, were applied through the Lipari and Szabo [ J. Am. Chem. Soc.104, 4546 (1982)] formalism to calculate errors in 13C T1, obtained from inversion-recovery measurements under proton saturation, and NOE when dipolar cross correlation is neglected. Motional parameters in the Lipari and Szabo formalism, τ m, S2, and τ e, were then determined from T1 and NOE (including the errors) and compared with parameters initially used to simulate the relaxation data. The resulting differences in the motional parameters, while model dependent, were generally small for plausible motions. At larger S2 values (≥ 0.6), the errors in both τ m and S2 were <5%. Errors in τ e increased with S2 but were usually less than 10%. Larger errors in the parameters were found for an axially symmetric model, but with τ m fixed even those were >5% only for the τ m = 1 ns, τ e = 10 ps case. Furthermore, it was observed that deviations in a given motional parameter were mostly of the same sign, which allows bounds to be set on experimentally derived parameters. Relaxation data for the peptide melittin synthesized with gly enriched with 13C at the backbone cu position and with lys enriched with 13C in the side chain were examined in light of the results of the simulations. All in all, it appears that neglect of dipolar cross correlation in 13C T1 (With proton saturation) and NOE measurements in AX 2 systems does not lead to major problems in interpretation of the results in terms of molecular motion.

Combined proportional and additive residual error models in population pharmacokinetic modelling.

PubMed

Proost, Johannes H

2017-11-15

In pharmacokinetic modelling, a combined proportional and additive residual error model is often preferred over a proportional or additive residual error model. Different approaches have been proposed, but a comparison between approaches is still lacking. The theoretical background of the methods is described. Method VAR assumes that the variance of the residual error is the sum of the statistically independent proportional and additive components; this method can be coded in three ways. Method SD assumes that the standard deviation of the residual error is the sum of the proportional and additive components. Using datasets from literature and simulations based on these datasets, the methods are compared using NONMEM. The different coding of methods VAR yield identical results. Using method SD, the values of the parameters describing residual error are lower than for method VAR, but the values of the structural parameters and their inter-individual variability are hardly affected by the choice of the method. Both methods are valid approaches in combined proportional and additive residual error modelling, and selection may be based on OFV. When the result of an analysis is used for simulation purposes, it is essential that the simulation tool uses the same method as used during analysis. Copyright © 2017 Elsevier B.V. All rights reserved.

Estimation of the sea surface's two-scale backscatter parameters

NASA Technical Reports Server (NTRS)

Wentz, F. J.

1978-01-01

The relationship between the sea-surface normalized radar cross section and the friction velocity vector is determined using a parametric two-scale scattering model. The model parameters are found from a nonlinear maximum likelihood estimation. The estimation is based on aircraft scatterometer measurements and the sea-surface anemometer measurements collected during the JONSWAP '75 experiment. The estimates of the ten model parameters converge to realistic values that are in good agreement with the available oceanographic data. The rms discrepancy between the model and the cross section measurements is 0.7 db, which is the rms sum of a 0.3 db average measurement error and a 0.6 db modeling error.

Optimizing the learning rate for adaptive estimation of neural encoding models

PubMed Central

2018-01-01

Closed-loop neurotechnologies often need to adaptively learn an encoding model that relates the neural activity to the brain state, and is used for brain state decoding. The speed and accuracy of adaptive learning algorithms are critically affected by the learning rate, which dictates how fast model parameters are updated based on new observations. Despite the importance of the learning rate, currently an analytical approach for its selection is largely lacking and existing signal processing methods vastly tune it empirically or heuristically. Here, we develop a novel analytical calibration algorithm for optimal selection of the learning rate in adaptive Bayesian filters. We formulate the problem through a fundamental trade-off that learning rate introduces between the steady-state error and the convergence time of the estimated model parameters. We derive explicit functions that predict the effect of learning rate on error and convergence time. Using these functions, our calibration algorithm can keep the steady-state parameter error covariance smaller than a desired upper-bound while minimizing the convergence time, or keep the convergence time faster than a desired value while minimizing the error. We derive the algorithm both for discrete-valued spikes modeled as point processes nonlinearly dependent on the brain state, and for continuous-valued neural recordings modeled as Gaussian processes linearly dependent on the brain state. Using extensive closed-loop simulations, we show that the analytical solution of the calibration algorithm accurately predicts the effect of learning rate on parameter error and convergence time. Moreover, the calibration algorithm allows for fast and accurate learning of the encoding model and for fast convergence of decoding to accurate performance. Finally, larger learning rates result in inaccurate encoding models and decoders, and smaller learning rates delay their convergence. The calibration algorithm provides a novel analytical approach to predictably achieve a desired level of error and convergence time in adaptive learning, with application to closed-loop neurotechnologies and other signal processing domains. PMID:29813069

Optimizing the learning rate for adaptive estimation of neural encoding models.

PubMed

Hsieh, Han-Lin; Shanechi, Maryam M

2018-05-01

Closed-loop neurotechnologies often need to adaptively learn an encoding model that relates the neural activity to the brain state, and is used for brain state decoding. The speed and accuracy of adaptive learning algorithms are critically affected by the learning rate, which dictates how fast model parameters are updated based on new observations. Despite the importance of the learning rate, currently an analytical approach for its selection is largely lacking and existing signal processing methods vastly tune it empirically or heuristically. Here, we develop a novel analytical calibration algorithm for optimal selection of the learning rate in adaptive Bayesian filters. We formulate the problem through a fundamental trade-off that learning rate introduces between the steady-state error and the convergence time of the estimated model parameters. We derive explicit functions that predict the effect of learning rate on error and convergence time. Using these functions, our calibration algorithm can keep the steady-state parameter error covariance smaller than a desired upper-bound while minimizing the convergence time, or keep the convergence time faster than a desired value while minimizing the error. We derive the algorithm both for discrete-valued spikes modeled as point processes nonlinearly dependent on the brain state, and for continuous-valued neural recordings modeled as Gaussian processes linearly dependent on the brain state. Using extensive closed-loop simulations, we show that the analytical solution of the calibration algorithm accurately predicts the effect of learning rate on parameter error and convergence time. Moreover, the calibration algorithm allows for fast and accurate learning of the encoding model and for fast convergence of decoding to accurate performance. Finally, larger learning rates result in inaccurate encoding models and decoders, and smaller learning rates delay their convergence. The calibration algorithm provides a novel analytical approach to predictably achieve a desired level of error and convergence time in adaptive learning, with application to closed-loop neurotechnologies and other signal processing domains.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Y.; Liu, Z.; Zhang, S.

Parameter estimation provides a potentially powerful approach to reduce model bias for complex climate models. Here, in a twin experiment framework, the authors perform the first parameter estimation in a fully coupled ocean–atmosphere general circulation model using an ensemble coupled data assimilation system facilitated with parameter estimation. The authors first perform single-parameter estimation and then multiple-parameter estimation. In the case of the single-parameter estimation, the error of the parameter [solar penetration depth (SPD)] is reduced by over 90% after ~40 years of assimilation of the conventional observations of monthly sea surface temperature (SST) and salinity (SSS). The results of multiple-parametermore » estimation are less reliable than those of single-parameter estimation when only the monthly SST and SSS are assimilated. Assimilating additional observations of atmospheric data of temperature and wind improves the reliability of multiple-parameter estimation. The errors of the parameters are reduced by 90% in ~8 years of assimilation. Finally, the improved parameters also improve the model climatology. With the optimized parameters, the bias of the climatology of SST is reduced by ~90%. Altogether, this study suggests the feasibility of ensemble-based parameter estimation in a fully coupled general circulation model.« less

Constitutive Modeling of Porcine Liver in Indentation Using 3D Ultrasound Imaging

PubMed Central

Jordan, P.; Socrate, S.; Zickler, T.E.; Howe, R.D.

2009-01-01

In this work we present an inverse finite-element modeling framework for constitutive modeling and parameter estimation of soft tissues using full-field volumetric deformation data obtained from 3D ultrasound. The finite-element model is coupled to full-field visual measurements by regularization springs attached at nodal locations. The free ends of the springs are displaced according to the locally estimated tissue motion and the normalized potential energy stored in all springs serves as a measure of model-experiment agreement for material parameter optimization. We demonstrate good accuracy of estimated parameters and consistent convergence properties on synthetically generated data. We present constitutive model selection and parameter estimation for perfused porcine liver in indentation and demonstrate that a quasilinear viscoelastic model with shear modulus relaxation offers good model-experiment agreement in terms of indenter displacement (0.19 mm RMS error) and tissue displacement field (0.97 mm RMS error). PMID:19627823

Error reduction and representation in stages (ERRIS) in hydrological modelling for ensemble streamflow forecasting

NASA Astrophysics Data System (ADS)

Li, Ming; Wang, Q. J.; Bennett, James C.; Robertson, David E.

2016-09-01

This study develops a new error modelling method for ensemble short-term and real-time streamflow forecasting, called error reduction and representation in stages (ERRIS). The novelty of ERRIS is that it does not rely on a single complex error model but runs a sequence of simple error models through four stages. At each stage, an error model attempts to incrementally improve over the previous stage. Stage 1 establishes parameters of a hydrological model and parameters of a transformation function for data normalization, Stage 2 applies a bias correction, Stage 3 applies autoregressive (AR) updating, and Stage 4 applies a Gaussian mixture distribution to represent model residuals. In a case study, we apply ERRIS for one-step-ahead forecasting at a range of catchments. The forecasts at the end of Stage 4 are shown to be much more accurate than at Stage 1 and to be highly reliable in representing forecast uncertainty. Specifically, the forecasts become more accurate by applying the AR updating at Stage 3, and more reliable in uncertainty spread by using a mixture of two Gaussian distributions to represent the residuals at Stage 4. ERRIS can be applied to any existing calibrated hydrological models, including those calibrated to deterministic (e.g. least-squares) objectives.

Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

NASA Astrophysics Data System (ADS)

Lu, Dan; Ricciuto, Daniel; Walker, Anthony; Safta, Cosmin; Munger, William

2017-09-01

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results in a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. The result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.

Orbit/attitude estimation with LANDSAT Landmark data

NASA Technical Reports Server (NTRS)

Hall, D. L.; Waligora, S.

1979-01-01

The use of LANDSAT landmark data for orbit/attitude and camera bias estimation was studied. The preliminary results of these investigations are presented. The Goddard Trajectory Determination System (GTDS) error analysis capability was used to perform error analysis studies. A number of questions were addressed including parameter observability and sensitivity, effects on the solve-for parameter errors of data span, density, and distribution an a priori covariance weighting. The use of the GTDS differential correction capability with acutal landmark data was examined. The rms line and element observation residuals were studied as a function of the solve-for parameter set, a priori covariance weighting, force model, attitude model and data characteristics. Sample results are presented. Finally, verfication and preliminary system evaluation of the LANDSAT NAVPAK system for sequential (extended Kalman Filter) estimation of orbit, and camera bias parameters is given.

Novel Calibration Algorithm for a Three-Axis Strapdown Magnetometer

PubMed Central

Liu, Yan Xia; Li, Xi Sheng; Zhang, Xiao Juan; Feng, Yi Bo

2014-01-01

A complete error calibration model with 12 independent parameters is established by analyzing the three-axis magnetometer error mechanism. The said model conforms to an ellipsoid restriction, the parameters of the ellipsoid equation are estimated, and the ellipsoid coefficient matrix is derived. However, the calibration matrix cannot be determined completely, as there are fewer ellipsoid parameters than calibration model parameters. Mathematically, the calibration matrix derived from the ellipsoid coefficient matrix by a different matrix decomposition method is not unique, and there exists an unknown rotation matrix R between them. This paper puts forward a constant intersection angle method (angles between the geomagnetic field and gravitational field are fixed) to estimate R. The Tikhonov method is adopted to solve the problem that rounding errors or other errors may seriously affect the calculation results of R when the condition number of the matrix is very large. The geomagnetic field vector and heading error are further corrected by R. The constant intersection angle method is convenient and practical, as it is free from any additional calibration procedure or coordinate transformation. In addition, the simulation experiment indicates that the heading error declines from ±1° calibrated by classical ellipsoid fitting to ±0.2° calibrated by a constant intersection angle method, and the signal-to-noise ratio is 50 dB. The actual experiment exhibits that the heading error is further corrected from ±0.8° calibrated by the classical ellipsoid fitting to ±0.3° calibrated by a constant intersection angle method. PMID:24831110

A Vision-Based Self-Calibration Method for Robotic Visual Inspection Systems

PubMed Central

Yin, Shibin; Ren, Yongjie; Zhu, Jigui; Yang, Shourui; Ye, Shenghua

2013-01-01

A vision-based robot self-calibration method is proposed in this paper to evaluate the kinematic parameter errors of a robot using a visual sensor mounted on its end-effector. This approach could be performed in the industrial field without external, expensive apparatus or an elaborate setup. A robot Tool Center Point (TCP) is defined in the structural model of a line-structured laser sensor, and aligned to a reference point fixed in the robot workspace. A mathematical model is established to formulate the misalignment errors with kinematic parameter errors and TCP position errors. Based on the fixed point constraints, the kinematic parameter errors and TCP position errors are identified with an iterative algorithm. Compared to the conventional methods, this proposed method eliminates the need for a robot-based-frame and hand-to-eye calibrations, shortens the error propagation chain, and makes the calibration process more accurate and convenient. A validation experiment is performed on an ABB IRB2400 robot. An optimal configuration on the number and distribution of fixed points in the robot workspace is obtained based on the experimental results. Comparative experiments reveal that there is a significant improvement of the measuring accuracy of the robotic visual inspection system. PMID:24300597

The predictive consequences of parameterization

NASA Astrophysics Data System (ADS)

White, J.; Hughes, J. D.; Doherty, J. E.

2013-12-01

In numerical groundwater modeling, parameterization is the process of selecting the aspects of a computer model that will be allowed to vary during history matching. This selection process is dependent on professional judgment and is, therefore, inherently subjective. Ideally, a robust parameterization should be commensurate with the spatial and temporal resolution of the model and should include all uncertain aspects of the model. Limited computing resources typically require reducing the number of adjustable parameters so that only a subset of the uncertain model aspects are treated as estimable parameters; the remaining aspects are treated as fixed parameters during history matching. We use linear subspace theory to develop expressions for the predictive error incurred by fixing parameters. The predictive error is comprised of two terms. The first term arises directly from the sensitivity of a prediction to fixed parameters. The second term arises from prediction-sensitive adjustable parameters that are forced to compensate for fixed parameters during history matching. The compensation is accompanied by inappropriate adjustment of otherwise uninformed, null-space parameter components. Unwarranted adjustment of null-space components away from prior maximum likelihood values may produce bias if a prediction is sensitive to those components. The potential for subjective parameterization choices to corrupt predictions is examined using a synthetic model. Several strategies are evaluated, including use of piecewise constant zones, use of pilot points with Tikhonov regularization and use of the Karhunen-Loeve transformation. The best choice of parameterization (as defined by minimum error variance) is strongly dependent on the types of predictions to be made by the model.

Edge Modeling by Two Blur Parameters in Varying Contrasts.

PubMed

Seo, Suyoung

2018-06-01

This paper presents a method of modeling edge profiles with two blur parameters, and estimating and predicting those edge parameters with varying brightness combinations and camera-to-object distances (COD). First, the validity of the edge model is proven mathematically. Then, it is proven experimentally with edges from a set of images captured for specifically designed target sheets and with edges from natural images. Estimation of the two blur parameters for each observed edge profile is performed with a brute-force method to find parameters that produce global minimum errors. Then, using the estimated blur parameters, actual blur parameters of edges with arbitrary brightness combinations are predicted using a surface interpolation method (i.e., kriging). The predicted surfaces show that the two blur parameters of the proposed edge model depend on both dark-side edge brightness and light-side edge brightness following a certain global trend. This is similar across varying CODs. The proposed edge model is compared with a one-blur parameter edge model using experiments of the root mean squared error for fitting the edge models to each observed edge profile. The comparison results suggest that the proposed edge model has superiority over the one-blur parameter edge model in most cases where edges have varying brightness combinations.

Real­-Time Ensemble Forecasting of Coronal Mass Ejections Using the Wsa-Enlil+Cone Model

NASA Astrophysics Data System (ADS)

Mays, M. L.; Taktakishvili, A.; Pulkkinen, A. A.; Odstrcil, D.; MacNeice, P. J.; Rastaetter, L.; LaSota, J. A.

2014-12-01

Ensemble forecasting of coronal mass ejections (CMEs) provides significant information in that it provides an estimation of the spread or uncertainty in CME arrival time predictions. Real-time ensemble modeling of CME propagation is performed by forecasters at the Space Weather Research Center (SWRC) using the WSA-ENLIL+cone model available at the Community Coordinated Modeling Center (CCMC). To estimate the effect of uncertainties in determining CME input parameters on arrival time predictions, a distribution of n (routinely n=48) CME input parameter sets are generated using the CCMC Stereo CME Analysis Tool (StereoCAT) which employs geometrical triangulation techniques. These input parameters are used to perform n different simulations yielding an ensemble of solar wind parameters at various locations of interest, including a probability distribution of CME arrival times (for hits), and geomagnetic storm strength (for Earth-directed hits). We present the results of ensemble simulations for a total of 38 CME events in 2013-2014. For 28 of the ensemble runs containing hits, the observed CME arrival was within the range of ensemble arrival time predictions for 14 runs (half). The average arrival time prediction was computed for each of the 28 ensembles predicting hits and using the actual arrival time, an average absolute error of 10.0 hours (RMSE=11.4 hours) was found for all 28 ensembles, which is comparable to current forecasting errors. Some considerations for the accuracy of ensemble CME arrival time predictions include the importance of the initial distribution of CME input parameters, particularly the mean and spread. When the observed arrivals are not within the predicted range, this still allows the ruling out of prediction errors caused by tested CME input parameters. Prediction errors can also arise from ambient model parameters such as the accuracy of the solar wind background, and other limitations. Additionally the ensemble modeling sysem was used to complete a parametric event case study of the sensitivity of the CME arrival time prediction to free parameters for ambient solar wind model and CME. The parameter sensitivity study suggests future directions for the system, such as running ensembles using various magnetogram inputs to the WSA model.

Multiplicity Control in Structural Equation Modeling

ERIC Educational Resources Information Center

Cribbie, Robert A.

2007-01-01

Researchers conducting structural equation modeling analyses rarely, if ever, control for the inflated probability of Type I errors when evaluating the statistical significance of multiple parameters in a model. In this study, the Type I error control, power and true model rates of famsilywise and false discovery rate controlling procedures were…

Probabilistic parameter estimation in a 2-step chemical kinetics model for n-dodecane jet autoignition

NASA Astrophysics Data System (ADS)

Hakim, Layal; Lacaze, Guilhem; Khalil, Mohammad; Sargsyan, Khachik; Najm, Habib; Oefelein, Joseph

2018-05-01

This paper demonstrates the development of a simple chemical kinetics model designed for autoignition of n-dodecane in air using Bayesian inference with a model-error representation. The model error, i.e. intrinsic discrepancy from a high-fidelity benchmark model, is represented by allowing additional variability in selected parameters. Subsequently, we quantify predictive uncertainties in the results of autoignition simulations of homogeneous reactors at realistic diesel engine conditions. We demonstrate that these predictive error bars capture model error as well. The uncertainty propagation is performed using non-intrusive spectral projection that can also be used in principle with larger scale computations, such as large eddy simulation. While the present calibration is performed to match a skeletal mechanism, it can be done with equal success using experimental data only (e.g. shock-tube measurements). Since our method captures the error associated with structural model simplifications, we believe that the optimised model could then lead to better qualified predictions of autoignition delay time in high-fidelity large eddy simulations than the existing detailed mechanisms. This methodology provides a way to reduce the cost of reaction kinetics in simulations systematically, while quantifying the accuracy of predictions of important target quantities.

Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Miller, Brad A.; Howard, Samuel A.

2008-01-01

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

Analytical performance evaluation of SAR ATR with inaccurate or estimated models

NASA Astrophysics Data System (ADS)

DeVore, Michael D.

2004-09-01

Hypothesis testing algorithms for automatic target recognition (ATR) are often formulated in terms of some assumed distribution family. The parameter values corresponding to a particular target class together with the distribution family constitute a model for the target's signature. In practice such models exhibit inaccuracy because of incorrect assumptions about the distribution family and/or because of errors in the assumed parameter values, which are often determined experimentally. Model inaccuracy can have a significant impact on performance predictions for target recognition systems. Such inaccuracy often causes model-based predictions that ignore the difference between assumed and actual distributions to be overly optimistic. This paper reports on research to quantify the effect of inaccurate models on performance prediction and to estimate the effect using only trained parameters. We demonstrate that for large observation vectors the class-conditional probabilities of error can be expressed as a simple function of the difference between two relative entropies. These relative entropies quantify the discrepancies between the actual and assumed distributions and can be used to express the difference between actual and predicted error rates. Focusing on the problem of ATR from synthetic aperture radar (SAR) imagery, we present estimators of the probabilities of error in both ideal and plug-in tests expressed in terms of the trained model parameters. These estimators are defined in terms of unbiased estimates for the first two moments of the sample statistic. We present an analytical treatment of these results and include demonstrations from simulated radar data.

High dimensional linear regression models under long memory dependence and measurement error

NASA Astrophysics Data System (ADS)

Kaul, Abhishek

This dissertation consists of three chapters. The first chapter introduces the models under consideration and motivates problems of interest. A brief literature review is also provided in this chapter. The second chapter investigates the properties of Lasso under long range dependent model errors. Lasso is a computationally efficient approach to model selection and estimation, and its properties are well studied when the regression errors are independent and identically distributed. We study the case, where the regression errors form a long memory moving average process. We establish a finite sample oracle inequality for the Lasso solution. We then show the asymptotic sign consistency in this setup. These results are established in the high dimensional setup (p> n) where p can be increasing exponentially with n. Finally, we show the consistency, n½ --d-consistency of Lasso, along with the oracle property of adaptive Lasso, in the case where p is fixed. Here d is the memory parameter of the stationary error sequence. The performance of Lasso is also analysed in the present setup with a simulation study. The third chapter proposes and investigates the properties of a penalized quantile based estimator for measurement error models. Standard formulations of prediction problems in high dimension regression models assume the availability of fully observed covariates and sub-Gaussian and homogeneous model errors. This makes these methods inapplicable to measurement errors models where covariates are unobservable and observations are possibly non sub-Gaussian and heterogeneous. We propose weighted penalized corrected quantile estimators for the regression parameter vector in linear regression models with additive measurement errors, where unobservable covariates are nonrandom. The proposed estimators forgo the need for the above mentioned model assumptions. We study these estimators in both the fixed dimension and high dimensional sparse setups, in the latter setup, the dimensionality can grow exponentially with the sample size. In the fixed dimensional setting we provide the oracle properties associated with the proposed estimators. In the high dimensional setting, we provide bounds for the statistical error associated with the estimation, that hold with asymptotic probability 1, thereby providing the ℓ1-consistency of the proposed estimator. We also establish the model selection consistency in terms of the correctly estimated zero components of the parameter vector. A simulation study that investigates the finite sample accuracy of the proposed estimator is also included in this chapter.

A comparison between a new model and current models for estimating trunk segment inertial parameters.

PubMed

Wicke, Jason; Dumas, Genevieve A; Costigan, Patrick A

2009-01-05

Modeling of the body segments to estimate segment inertial parameters is required in the kinetic analysis of human motion. A new geometric model for the trunk has been developed that uses various cross-sectional shapes to estimate segment volume and adopts a non-uniform density function that is gender-specific. The goal of this study was to test the accuracy of the new model for estimating the trunk's inertial parameters by comparing it to the more current models used in biomechanical research. Trunk inertial parameters estimated from dual X-ray absorptiometry (DXA) were used as the standard. Twenty-five female and 24 male college-aged participants were recruited for the study. Comparisons of the new model to the accepted models were accomplished by determining the error between the models' trunk inertial estimates and that from DXA. Results showed that the new model was more accurate across all inertial estimates than the other models. The new model had errors within 6.0% for both genders, whereas the other models had higher average errors ranging from 10% to over 50% and were much more inconsistent between the genders. In addition, there was little consistency in the level of accuracy for the other models when estimating the different inertial parameters. These results suggest that the new model provides more accurate and consistent trunk inertial estimates than the other models for both female and male college-aged individuals. However, similar studies need to be performed using other populations, such as elderly or individuals from a distinct morphology (e.g. obese). In addition, the effect of using different models on the outcome of kinetic parameters, such as joint moments and forces needs to be assessed.

Water quality management using statistical analysis and time-series prediction model

NASA Astrophysics Data System (ADS)

Parmar, Kulwinder Singh; Bhardwaj, Rashmi

2014-12-01

This paper deals with water quality management using statistical analysis and time-series prediction model. The monthly variation of water quality standards has been used to compare statistical mean, median, mode, standard deviation, kurtosis, skewness, coefficient of variation at Yamuna River. Model validated using R-squared, root mean square error, mean absolute percentage error, maximum absolute percentage error, mean absolute error, maximum absolute error, normalized Bayesian information criterion, Ljung-Box analysis, predicted value and confidence limits. Using auto regressive integrated moving average model, future water quality parameters values have been estimated. It is observed that predictive model is useful at 95 % confidence limits and curve is platykurtic for potential of hydrogen (pH), free ammonia, total Kjeldahl nitrogen, dissolved oxygen, water temperature (WT); leptokurtic for chemical oxygen demand, biochemical oxygen demand. Also, it is observed that predicted series is close to the original series which provides a perfect fit. All parameters except pH and WT cross the prescribed limits of the World Health Organization /United States Environmental Protection Agency, and thus water is not fit for drinking, agriculture and industrial use.

Balancing the stochastic description of uncertainties as a function of hydrologic model complexity

NASA Astrophysics Data System (ADS)

Del Giudice, D.; Reichert, P.; Albert, C.; Kalcic, M.; Logsdon Muenich, R.; Scavia, D.; Bosch, N. S.; Michalak, A. M.

2016-12-01

Uncertainty analysis is becoming an important component of forecasting water and pollutant fluxes in urban and rural environments. Properly accounting for errors in the modeling process can help to robustly assess the uncertainties associated with the inputs (e.g. precipitation) and outputs (e.g. runoff) of hydrological models. In recent years we have investigated several Bayesian methods to infer the parameters of a mechanistic hydrological model along with those of the stochastic error component. The latter describes the uncertainties of model outputs and possibly inputs. We have adapted our framework to a variety of applications, ranging from predicting floods in small stormwater systems to nutrient loads in large agricultural watersheds. Given practical constraints, we discuss how in general the number of quantities to infer probabilistically varies inversely with the complexity of the mechanistic model. Most often, when evaluating a hydrological model of intermediate complexity, we can infer the parameters of the model as well as of the output error model. Describing the output errors as a first order autoregressive process can realistically capture the "downstream" effect of inaccurate inputs and structure. With simpler runoff models we can additionally quantify input uncertainty by using a stochastic rainfall process. For complex hydrologic transport models, instead, we show that keeping model parameters fixed and just estimating time-dependent output uncertainties could be a viable option. The common goal across all these applications is to create time-dependent prediction intervals which are both reliable (cover the nominal amount of validation data) and precise (are as narrow as possible). In conclusion, we recommend focusing both on the choice of the hydrological model and of the probabilistic error description. The latter can include output uncertainty only, if the model is computationally-expensive, or, with simpler models, it can separately account for different sources of errors like in the inputs and the structure of the model.

Optimized tuner selection for engine performance estimation

NASA Technical Reports Server (NTRS)

Simon, Donald L. (Inventor); Garg, Sanjay (Inventor)

2013-01-01

A methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented. This technique specifically addresses the underdetermined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine which seeks to minimize the theoretical mean-squared estimation error. Theoretical Kalman filter estimation error bias and variance values are derived at steady-state operating conditions, and the tuner selection routine is applied to minimize these values. The new methodology yields an improvement in on-line engine performance estimation accuracy.

Offline modeling for product quality prediction of mineral processing using modeling error PDF shaping and entropy minimization.

PubMed

Ding, Jinliang; Chai, Tianyou; Wang, Hong

2011-03-01

This paper presents a novel offline modeling for product quality prediction of mineral processing which consists of a number of unit processes in series. The prediction of the product quality of the whole mineral process (i.e., the mixed concentrate grade) plays an important role and the establishment of its predictive model is a key issue for the plantwide optimization. For this purpose, a hybrid modeling approach of the mixed concentrate grade prediction is proposed, which consists of a linear model and a nonlinear model. The least-squares support vector machine is adopted to establish the nonlinear model. The inputs of the predictive model are the performance indices of each unit process, while the output is the mixed concentrate grade. In this paper, the model parameter selection is transformed into the shape control of the probability density function (PDF) of the modeling error. In this context, both the PDF-control-based and minimum-entropy-based model parameter selection approaches are proposed. Indeed, this is the first time that the PDF shape control idea is used to deal with system modeling, where the key idea is to turn model parameters so that either the modeling error PDF is controlled to follow a target PDF or the modeling error entropy is minimized. The experimental results using the real plant data and the comparison of the two approaches are discussed. The results show the effectiveness of the proposed approaches.

Mesh refinement and numerical sensitivity analysis for parameter calibration of partial differential equations

NASA Astrophysics Data System (ADS)

Becker, Roland; Vexler, Boris

2005-06-01

We consider the calibration of parameters in physical models described by partial differential equations. This task is formulated as a constrained optimization problem with a cost functional of least squares type using information obtained from measurements. An important issue in the numerical solution of this type of problem is the control of the errors introduced, first, by discretization of the equations describing the physical model, and second, by measurement errors or other perturbations. Our strategy is as follows: we suppose that the user defines an interest functional I, which might depend on both the state variable and the parameters and which represents the goal of the computation. First, we propose an a posteriori error estimator which measures the error with respect to this functional. This error estimator is used in an adaptive algorithm to construct economic meshes by local mesh refinement. The proposed estimator requires the solution of an auxiliary linear equation. Second, we address the question of sensitivity. Applying similar techniques as before, we derive quantities which describe the influence of small changes in the measurements on the value of the interest functional. These numbers, which we call relative condition numbers, give additional information on the problem under consideration. They can be computed by means of the solution of the auxiliary problem determined before. Finally, we demonstrate our approach at hand of a parameter calibration problem for a model flow problem.

System Identification Applied to Dynamic CFD Simulation and Wind Tunnel Data

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.; Klein, Vladislav; Frink, Neal T.; Vicroy, Dan D.

2011-01-01

Demanding aerodynamic modeling requirements for military and civilian aircraft have provided impetus for researchers to improve computational and experimental techniques. Model validation is a key component for these research endeavors so this study is an initial effort to extend conventional time history comparisons by comparing model parameter estimates and their standard errors using system identification methods. An aerodynamic model of an aircraft performing one-degree-of-freedom roll oscillatory motion about its body axes is developed. The model includes linear aerodynamics and deficiency function parameters characterizing an unsteady effect. For estimation of unknown parameters two techniques, harmonic analysis and two-step linear regression, were applied to roll-oscillatory wind tunnel data and to computational fluid dynamics (CFD) simulated data. The model used for this study is a highly swept wing unmanned aerial combat vehicle. Differences in response prediction, parameters estimates, and standard errors are compared and discussed

Calibration and compensation method of three-axis geomagnetic sensor based on pre-processing total least square iteration

NASA Astrophysics Data System (ADS)

Zhou, Y.; Zhang, X.; Xiao, W.

2018-04-01

As the geomagnetic sensor is susceptible to interference, a pre-processing total least square iteration method is proposed for calibration compensation. Firstly, the error model of the geomagnetic sensor is analyzed and the correction model is proposed, then the characteristics of the model are analyzed and converted into nine parameters. The geomagnetic data is processed by Hilbert transform (HHT) to improve the signal-to-noise ratio, and the nine parameters are calculated by using the combination of Newton iteration method and the least squares estimation method. The sifter algorithm is used to filter the initial value of the iteration to ensure that the initial error is as small as possible. The experimental results show that this method does not need additional equipment and devices, can continuously update the calibration parameters, and better than the two-step estimation method, it can compensate geomagnetic sensor error well.

Accounting for uncertainty in pedotransfer functions in vulnerability assessments of pesticide leaching to groundwater.

PubMed

Stenemo, Fredrik; Jarvis, Nicholas

2007-09-01

A simulation tool for site-specific vulnerability assessments of pesticide leaching to groundwater was developed, based on the pesticide fate and transport model MACRO, parameterized using pedotransfer functions and reasonable worst-case parameter values. The effects of uncertainty in the pedotransfer functions on simulation results were examined for 48 combinations of soils, pesticides and application timings, by sampling pedotransfer function regression errors and propagating them through the simulation model in a Monte Carlo analysis. An uncertainty factor, f(u), was derived, defined as the ratio between the concentration simulated with no errors, c(sim), and the 80th percentile concentration for the scenario. The pedotransfer function errors caused a large variation in simulation results, with f(u) ranging from 1.14 to 1440, with a median of 2.8. A non-linear relationship was found between f(u) and c(sim), which can be used to account for parameter uncertainty by correcting the simulated concentration, c(sim), to an estimated 80th percentile value. For fine-textured soils, the predictions were most sensitive to errors in the pedotransfer functions for two parameters regulating macropore flow (the saturated matrix hydraulic conductivity, K(b), and the effective diffusion pathlength, d) and two water retention function parameters (van Genuchten's N and alpha parameters). For coarse-textured soils, the model was also sensitive to errors in the exponent in the degradation water response function and the dispersivity, in addition to K(b), but showed little sensitivity to d. To reduce uncertainty in model predictions, improved pedotransfer functions for K(b), d, N and alpha would therefore be most useful. 2007 Society of Chemical Industry

Modeling and Development of INS-Aided PLLs in a GNSS/INS Deeply-Coupled Hardware Prototype for Dynamic Applications

PubMed Central

Zhang, Tisheng; Niu, Xiaoji; Ban, Yalong; Zhang, Hongping; Shi, Chuang; Liu, Jingnan

2015-01-01

A GNSS/INS deeply-coupled system can improve the satellite signals tracking performance by INS aiding tracking loops under dynamics. However, there was no literature available on the complete modeling of the INS branch in the INS-aided tracking loop, which caused the lack of a theoretical tool to guide the selections of inertial sensors, parameter optimization and quantitative analysis of INS-aided PLLs. This paper makes an effort on the INS branch in modeling and parameter optimization of phase-locked loops (PLLs) based on the scalar-based GNSS/INS deeply-coupled system. It establishes the transfer function between all known error sources and the PLL tracking error, which can be used to quantitatively evaluate the candidate inertial measurement unit (IMU) affecting the carrier phase tracking error. Based on that, a steady-state error model is proposed to design INS-aided PLLs and to analyze their tracking performance. Based on the modeling and error analysis, an integrated deeply-coupled hardware prototype is developed, with the optimization of the aiding information. Finally, the performance of the INS-aided PLLs designed based on the proposed steady-state error model is evaluated through the simulation and road tests of the hardware prototype. PMID:25569751

Data assimilation with soil water content sensors and pedotransfer functions in soil water flow modeling

USDA-ARS?s Scientific Manuscript database

Soil water flow models are based on a set of simplified assumptions about the mechanisms, processes, and parameters of water retention and flow. That causes errors in soil water flow model predictions. Soil water content monitoring data can be used to reduce the errors in models. Data assimilation (...

Optimization of processing parameters of UAV integral structural components based on yield response

NASA Astrophysics Data System (ADS)

Chen, Yunsheng

2018-05-01

In order to improve the overall strength of unmanned aerial vehicle (UAV), it is necessary to optimize the processing parameters of UAV structural components, which is affected by initial residual stress in the process of UAV structural components processing. Because machining errors are easy to occur, an optimization model for machining parameters of UAV integral structural components based on yield response is proposed. The finite element method is used to simulate the machining parameters of UAV integral structural components. The prediction model of workpiece surface machining error is established, and the influence of the path of walking knife on residual stress of UAV integral structure is studied, according to the stress of UAV integral component. The yield response of the time-varying stiffness is analyzed, and the yield response and the stress evolution mechanism of the UAV integral structure are analyzed. The simulation results show that this method is used to optimize the machining parameters of UAV integral structural components and improve the precision of UAV milling processing. The machining error is reduced, and the deformation prediction and error compensation of UAV integral structural parts are realized, thus improving the quality of machining.

Rank score and permutation testing alternatives for regression quantile estimates

USGS Publications Warehouse

Cade, B.S.; Richards, J.D.; Mielke, P.W.

2006-01-01

Performance of quantile rank score tests used for hypothesis testing and constructing confidence intervals for linear quantile regression estimates (0 ≤ τ ≤ 1) were evaluated by simulation for models with p = 2 and 6 predictors, moderate collinearity among predictors, homogeneous and hetero-geneous errors, small to moderate samples (n = 20–300), and central to upper quantiles (0.50–0.99). Test statistics evaluated were the conventional quantile rank score T statistic distributed as χ2 random variable with q degrees of freedom (where q parameters are constrained by H 0:) and an F statistic with its sampling distribution approximated by permutation. The permutation F-test maintained better Type I errors than the T-test for homogeneous error models with smaller n and more extreme quantiles τ. An F distributional approximation of the F statistic provided some improvements in Type I errors over the T-test for models with > 2 parameters, smaller n, and more extreme quantiles but not as much improvement as the permutation approximation. Both rank score tests required weighting to maintain correct Type I errors when heterogeneity under the alternative model increased to 5 standard deviations across the domain of X. A double permutation procedure was developed to provide valid Type I errors for the permutation F-test when null models were forced through the origin. Power was similar for conditions where both T- and F-tests maintained correct Type I errors but the F-test provided some power at smaller n and extreme quantiles when the T-test had no power because of excessively conservative Type I errors. When the double permutation scheme was required for the permutation F-test to maintain valid Type I errors, power was less than for the T-test with decreasing sample size and increasing quantiles. Confidence intervals on parameters and tolerance intervals for future predictions were constructed based on test inversion for an example application relating trout densities to stream channel width:depth.

Improving the twilight model for polar cap absorption nowcasts

NASA Astrophysics Data System (ADS)

Rogers, N. C.; Kero, A.; Honary, F.; Verronen, P. T.; Warrington, E. M.; Danskin, D. W.

2016-11-01

During solar proton events (SPE), energetic protons ionize the polar mesosphere causing HF radio wave attenuation, more strongly on the dayside where the effective recombination coefficient, αeff, is low. Polar cap absorption models predict the 30 MHz cosmic noise absorption, A, measured by riometers, based on real-time measurements of the integrated proton flux-energy spectrum, J. However, empirical models in common use cannot account for regional and day-to-day variations in the daytime and nighttime profiles of αeff(z) or the related sensitivity parameter, m=A>/&sqrt;J. Large prediction errors occur during twilight when m changes rapidly, and due to errors locating the rigidity cutoff latitude. Modeling the twilight change in m as a linear or Gauss error-function transition over a range of solar-zenith angles (χl < χ < χu) provides a better fit to measurements than selecting day or night αeff profiles based on the Earth-shadow height. Optimal model parameters were determined for several polar cap riometers for large SPEs in 1998-2005. The optimal χl parameter was found to be most variable, with smaller values (as low as 60°) postsunrise compared with presunset and with positive correlation between riometers over a wide area. Day and night values of m exhibited higher correlation for closely spaced riometers. A nowcast simulation is presented in which rigidity boundary latitude and twilight model parameters are optimized by assimilating age-weighted measurements from 25 riometers. The technique reduces model bias, and root-mean-square errors are reduced by up to 30% compared with a model employing no riometer data assimilation.

Sample Size Limits for Estimating Upper Level Mediation Models Using Multilevel SEM

ERIC Educational Resources Information Center

Li, Xin; Beretvas, S. Natasha

2013-01-01

This simulation study investigated use of the multilevel structural equation model (MLSEM) for handling measurement error in both mediator and outcome variables ("M" and "Y") in an upper level multilevel mediation model. Mediation and outcome variable indicators were generated with measurement error. Parameter and standard…

Use of Numerical Groundwater Model and Analytical Empirical Orthogonal Function for Calibrating Spatiotemporal pattern of Pumpage, Recharge and Parameter

NASA Astrophysics Data System (ADS)

Huang, C. L.; Hsu, N. S.; Hsu, F. C.; Liu, H. J.

2016-12-01

This study develops a novel methodology for the spatiotemporal groundwater calibration of mega-quantitative recharge and parameters by coupling a specialized numerical model and analytical empirical orthogonal function (EOF). The actual spatiotemporal patterns of groundwater pumpage are estimated by an originally developed back propagation neural network-based response matrix with the electrical consumption analysis. The spatiotemporal patterns of the recharge from surface water and hydrogeological parameters (i.e. horizontal hydraulic conductivity and vertical leakance) are calibrated by EOF with the simulated error hydrograph of groundwater storage, in order to qualify the multiple error sources and quantify the revised volume. The objective function of the optimization model is minimizing the root mean square error of the simulated storage error percentage across multiple aquifers, meanwhile subject to mass balance of groundwater budget and the governing equation in transient state. The established method was applied on the groundwater system of Chou-Shui River Alluvial Fan. The simulated period is from January 2012 to December 2014. The total numbers of hydraulic conductivity, vertical leakance and recharge from surface water among four aquifers are 126, 96 and 1080, respectively. Results showed that the RMSE during the calibration process was decreased dramatically and can quickly converse within 6th iteration, because of efficient filtration of the transmission induced by the estimated error and recharge across the boundary. Moreover, the average simulated error percentage according to groundwater level corresponding to the calibrated budget variables and parameters of aquifer one is as small as 0.11%. It represent that the developed methodology not only can effectively detect the flow tendency and error source in all aquifers to achieve accurately spatiotemporal calibration, but also can capture the peak and fluctuation of groundwater level in shallow aquifer.

Parameter optimization in biased decoy-state quantum key distribution with both source errors and statistical fluctuations

NASA Astrophysics Data System (ADS)

Zhu, Jian-Rong; Li, Jian; Zhang, Chun-Mei; Wang, Qin

2017-10-01

The decoy-state method has been widely used in commercial quantum key distribution (QKD) systems. In view of the practical decoy-state QKD with both source errors and statistical fluctuations, we propose a universal model of full parameter optimization in biased decoy-state QKD with phase-randomized sources. Besides, we adopt this model to carry out simulations of two widely used sources: weak coherent source (WCS) and heralded single-photon source (HSPS). Results show that full parameter optimization can significantly improve not only the secure transmission distance but also the final key generation rate. And when taking source errors and statistical fluctuations into account, the performance of decoy-state QKD using HSPS suffered less than that of decoy-state QKD using WCS.

Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Dan; Ricciuto, Daniel M.; Walker, Anthony P.

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results inmore » a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. Here, the result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.« less

Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

DOE PAGES

Lu, Dan; Ricciuto, Daniel M.; Walker, Anthony P.; ...

2017-09-27

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results inmore » a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. Here, the result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.« less

Model parameter estimation approach based on incremental analysis for lithium-ion batteries without using open circuit voltage

NASA Astrophysics Data System (ADS)

Wu, Hongjie; Yuan, Shifei; Zhang, Xi; Yin, Chengliang; Ma, Xuerui

2015-08-01

To improve the suitability of lithium-ion battery model under varying scenarios, such as fluctuating temperature and SoC variation, dynamic model with parameters updated realtime should be developed. In this paper, an incremental analysis-based auto regressive exogenous (I-ARX) modeling method is proposed to eliminate the modeling error caused by the OCV effect and improve the accuracy of parameter estimation. Then, its numerical stability, modeling error, and parametric sensitivity are analyzed at different sampling rates (0.02, 0.1, 0.5 and 1 s). To identify the model parameters recursively, a bias-correction recursive least squares (CRLS) algorithm is applied. Finally, the pseudo random binary sequence (PRBS) and urban dynamic driving sequences (UDDSs) profiles are performed to verify the realtime performance and robustness of the newly proposed model and algorithm. Different sampling rates (1 Hz and 10 Hz) and multiple temperature points (5, 25, and 45 °C) are covered in our experiments. The experimental and simulation results indicate that the proposed I-ARX model can present high accuracy and suitability for parameter identification without using open circuit voltage.

Optical System Error Analysis and Calibration Method of High-Accuracy Star Trackers

PubMed Central

Sun, Ting; Xing, Fei; You, Zheng

2013-01-01

The star tracker is a high-accuracy attitude measurement device widely used in spacecraft. Its performance depends largely on the precision of the optical system parameters. Therefore, the analysis of the optical system parameter errors and a precise calibration model are crucial to the accuracy of the star tracker. Research in this field is relatively lacking a systematic and universal analysis up to now. This paper proposes in detail an approach for the synthetic error analysis of the star tracker, without the complicated theoretical derivation. This approach can determine the error propagation relationship of the star tracker, and can build intuitively and systematically an error model. The analysis results can be used as a foundation and a guide for the optical design, calibration, and compensation of the star tracker. A calibration experiment is designed and conducted. Excellent calibration results are achieved based on the calibration model. To summarize, the error analysis approach and the calibration method are proved to be adequate and precise, and could provide an important guarantee for the design, manufacture, and measurement of high-accuracy star trackers. PMID:23567527

Bayesian calibration of the Community Land Model using surrogates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi

2014-02-01

We present results from the Bayesian calibration of hydrological parameters of the Community Land Model (CLM), which is often used in climate simulations and Earth system models. A statistical inverse problem is formulated for three hydrological parameters, conditional on observations of latent heat surface fluxes over 48 months. Our calibration method uses polynomial and Gaussian process surrogates of the CLM, and solves the parameter estimation problem using a Markov chain Monte Carlo sampler. Posterior probability densities for the parameters are developed for two sites with different soil and vegetation covers. Our method also allows us to examine the structural errormore » in CLM under two error models. We find that surrogate models can be created for CLM in most cases. The posterior distributions are more predictive than the default parameter values in CLM. Climatologically averaging the observations does not modify the parameters' distributions significantly. The structural error model reveals a correlation time-scale which can be used to identify the physical process that could be contributing to it. While the calibrated CLM has a higher predictive skill, the calibration is under-dispersive.« less

Development of uncertainty-based work injury model using Bayesian structural equation modelling.

PubMed

Chatterjee, Snehamoy

2014-01-01

This paper proposed a Bayesian method-based structural equation model (SEM) of miners' work injury for an underground coal mine in India. The environmental and behavioural variables for work injury were identified and causal relationships were developed. For Bayesian modelling, prior distributions of SEM parameters are necessary to develop the model. In this paper, two approaches were adopted to obtain prior distribution for factor loading parameters and structural parameters of SEM. In the first approach, the prior distributions were considered as a fixed distribution function with specific parameter values, whereas, in the second approach, prior distributions of the parameters were generated from experts' opinions. The posterior distributions of these parameters were obtained by applying Bayesian rule. The Markov Chain Monte Carlo sampling in the form Gibbs sampling was applied for sampling from the posterior distribution. The results revealed that all coefficients of structural and measurement model parameters are statistically significant in experts' opinion-based priors, whereas, two coefficients are not statistically significant when fixed prior-based distributions are applied. The error statistics reveals that Bayesian structural model provides reasonably good fit of work injury with high coefficient of determination (0.91) and less mean squared error as compared to traditional SEM.

Artificial Vector Calibration Method for Differencing Magnetic Gradient Tensor Systems

PubMed Central

Li, Zhining; Zhang, Yingtang; Yin, Gang

2018-01-01

The measurement error of the differencing (i.e., using two homogenous field sensors at a known baseline distance) magnetic gradient tensor system includes the biases, scale factors, nonorthogonality of the single magnetic sensor, and the misalignment error between the sensor arrays, all of which can severely affect the measurement accuracy. In this paper, we propose a low-cost artificial vector calibration method for the tensor system. Firstly, the error parameter linear equations are constructed based on the single-sensor’s system error model to obtain the artificial ideal vector output of the platform, with the total magnetic intensity (TMI) scalar as a reference by two nonlinear conversions, without any mathematical simplification. Secondly, the Levenberg–Marquardt algorithm is used to compute the integrated model of the 12 error parameters by nonlinear least-squares fitting method with the artificial vector output as a reference, and a total of 48 parameters of the system is estimated simultaneously. The calibrated system outputs along the reference platform-orthogonal coordinate system. The analysis results show that the artificial vector calibrated output can track the orientation fluctuations of TMI accurately, effectively avoiding the “overcalibration” problem. The accuracy of the error parameters’ estimation in the simulation is close to 100%. The experimental root-mean-square error (RMSE) of the TMI and tensor components is less than 3 nT and 20 nT/m, respectively, and the estimation of the parameters is highly robust. PMID:29373544

Numerical relativity waveform surrogate model for generically precessing binary black hole mergers

NASA Astrophysics Data System (ADS)

Blackman, Jonathan; Field, Scott E.; Scheel, Mark A.; Galley, Chad R.; Ott, Christian D.; Boyle, Michael; Kidder, Lawrence E.; Pfeiffer, Harald P.; Szilágyi, Béla

2017-07-01

A generic, noneccentric binary black hole (BBH) system emits gravitational waves (GWs) that are completely described by seven intrinsic parameters: the black hole spin vectors and the ratio of their masses. Simulating a BBH coalescence by solving Einstein's equations numerically is computationally expensive, requiring days to months of computing resources for a single set of parameter values. Since theoretical predictions of the GWs are often needed for many different source parameters, a fast and accurate model is essential. We present the first surrogate model for GWs from the coalescence of BBHs including all seven dimensions of the intrinsic noneccentric parameter space. The surrogate model, which we call NRSur7dq2, is built from the results of 744 numerical relativity simulations. NRSur7dq2 covers spin magnitudes up to 0.8 and mass ratios up to 2, includes all ℓ≤4 modes, begins about 20 orbits before merger, and can be evaluated in ˜50 ms . We find the largest NRSur7dq2 errors to be comparable to the largest errors in the numerical relativity simulations, and more than an order of magnitude smaller than the errors of other waveform models. Our model, and more broadly the methods developed here, will enable studies that were not previously possible when using highly accurate waveforms, such as parameter inference and tests of general relativity with GW observations.

Reference-free error estimation for multiple measurement methods.

PubMed

Madan, Hennadii; Pernuš, Franjo; Špiclin, Žiga

2018-01-01

We present a computational framework to select the most accurate and precise method of measurement of a certain quantity, when there is no access to the true value of the measurand. A typical use case is when several image analysis methods are applied to measure the value of a particular quantitative imaging biomarker from the same images. The accuracy of each measurement method is characterized by systematic error (bias), which is modeled as a polynomial in true values of measurand, and the precision as random error modeled with a Gaussian random variable. In contrast to previous works, the random errors are modeled jointly across all methods, thereby enabling the framework to analyze measurement methods based on similar principles, which may have correlated random errors. Furthermore, the posterior distribution of the error model parameters is estimated from samples obtained by Markov chain Monte-Carlo and analyzed to estimate the parameter values and the unknown true values of the measurand. The framework was validated on six synthetic and one clinical dataset containing measurements of total lesion load, a biomarker of neurodegenerative diseases, which was obtained with four automatic methods by analyzing brain magnetic resonance images. The estimates of bias and random error were in a good agreement with the corresponding least squares regression estimates against a reference.

Modeling of mouse eye and errors in ocular parameters affecting refractive state

NASA Astrophysics Data System (ADS)

Bawa, Gurinder

Rodents eye are particularly used to study refractive error state of an eye and development of refractive eye. Genetic organization of rodents is similar to that of humans, which makes them interesting candidates to be researched upon. From rodents family mice models are encouraged over rats because of availability of genetically engineered models. Despite of extensive work that has been performed on mice and rat models, still no one is able to quantify an optical model, due to variability in the reported ocular parameters. In this Dissertation, we have extracted ocular parameters and generated schematics of eye from the raw data from School of Medicine, Detroit. In order to see how the rays would travel through an eye and the defects associated with an eye; ray tracing has been performed using ocular parameters. Finally we have systematically evaluated the contribution of various ocular parameters, such as radii of curvature of ocular surfaces, thicknesses of ocular components, and refractive indices of ocular refractive media, using variational analysis and a computational model of the rodent eye. Variational analysis revealed that variation in all the ocular parameters does affect the refractive status of the eye, but depending upon the magnitude of the impact those parameters are listed as critical or non critical. Variation in the depth of the vitreous chamber, thickness of the lens, radius of the anterior surface of the cornea, radius of the anterior surface of the lens, as well as refractive indices for the lens and vitreous, appears to have the largest impact on the refractive error and thus are categorized as critical ocular parameters. The radii of the posterior surfaces of the cornea and lens have much smaller contributions to the refractive state, while the radii of the anterior and posterior surfaces of the retina have no effect on the refractive error. These data provide the framework for further refinement of the optical models of the rat and mouse eye and suggest that extra efforts should be directed towards increasing the linear resolution of the rodent eye biometry and obtaining more accurate data for the refractive indices of the lens and vitreous.

Practical identifiability analysis of a minimal cardiovascular system model.

PubMed

Pironet, Antoine; Docherty, Paul D; Dauby, Pierre C; Chase, J Geoffrey; Desaive, Thomas

2017-01-17

Parameters of mathematical models of the cardiovascular system can be used to monitor cardiovascular state, such as total stressed blood volume status, vessel elastance and resistance. To do so, the model parameters have to be estimated from data collected at the patient's bedside. This work considers a seven-parameter model of the cardiovascular system and investigates whether these parameters can be uniquely determined using indices derived from measurements of arterial and venous pressures, and stroke volume. An error vector defined the residuals between the simulated and reference values of the seven clinically available haemodynamic indices. The sensitivity of this error vector to each model parameter was analysed, as well as the collinearity between parameters. To assess practical identifiability of the model parameters, profile-likelihood curves were constructed for each parameter. Four of the seven model parameters were found to be practically identifiable from the selected data. The remaining three parameters were practically non-identifiable. Among these non-identifiable parameters, one could be decreased as much as possible. The other two non-identifiable parameters were inversely correlated, which prevented their precise estimation. This work presented the practical identifiability analysis of a seven-parameter cardiovascular system model, from limited clinical data. The analysis showed that three of the seven parameters were practically non-identifiable, thus limiting the use of the model as a monitoring tool. Slight changes in the time-varying function modeling cardiac contraction and use of larger values for the reference range of venous pressure made the model fully practically identifiable. Copyright © 2017. Published by Elsevier B.V.

Enhanced orbit determination filter: Inclusion of ground system errors as filter parameters

NASA Technical Reports Server (NTRS)

Masters, W. C.; Scheeres, D. J.; Thurman, S. W.

1994-01-01

The theoretical aspects of an orbit determination filter that incorporates ground-system error sources as model parameters for use in interplanetary navigation are presented in this article. This filter, which is derived from sequential filtering theory, allows a systematic treatment of errors in calibrations of transmission media, station locations, and earth orientation models associated with ground-based radio metric data, in addition to the modeling of the spacecraft dynamics. The discussion includes a mathematical description of the filter and an analytical comparison of its characteristics with more traditional filtering techniques used in this application. The analysis in this article shows that this filter has the potential to generate navigation products of substantially greater accuracy than more traditional filtering procedures.

VLBI-derived troposphere parameters during CONT08

NASA Astrophysics Data System (ADS)

Heinkelmann, R.; Böhm, J.; Bolotin, S.; Engelhardt, G.; Haas, R.; Lanotte, R.; MacMillan, D. S.; Negusini, M.; Skurikhina, E.; Titov, O.; Schuh, H.

2011-07-01

Time-series of zenith wet and total troposphere delays as well as north and east gradients are compared, and zenith total delays ( ZTD) are combined on the level of parameter estimates. Input data sets are provided by ten Analysis Centers (ACs) of the International VLBI Service for Geodesy and Astrometry (IVS) for the CONT08 campaign (12-26 August 2008). The inconsistent usage of meteorological data and models, such as mapping functions, causes systematics among the ACs, and differing parameterizations and constraints add noise to the troposphere parameter estimates. The empirical standard deviation of ZTD among the ACs with regard to an unweighted mean is 4.6 mm. The ratio of the analysis noise to the observation noise assessed by the operator/software impact (OSI) model is about 2.5. These and other effects have to be accounted for to improve the intra-technique combination of VLBI-derived troposphere parameters. While the largest systematics caused by inconsistent usage of meteorological data can be avoided and the application of different mapping functions can be considered by applying empirical corrections, the noise has to be modeled in the stochastic model of intra-technique combination. The application of different stochastic models shows no significant effects on the combined parameters but results in different mean formal errors: the mean formal errors of the combined ZTD are 2.3 mm (unweighted), 4.4 mm (diagonal), 8.6 mm [variance component (VC) estimation], and 8.6 mm (operator/software impact, OSI). On the one hand, the OSI model, i.e. the inclusion of off-diagonal elements in the cofactor-matrix, considers the reapplication of observations yielding a factor of about two for mean formal errors as compared to the diagonal approach. On the other hand, the combination based on VC estimation shows large differences among the VCs and exhibits a comparable scaling of formal errors. Thus, for the combination of troposphere parameters a combination of the two extensions of the stochastic model is recommended.

Error analysis of mechanical system and wavelength calibration of monochromator

NASA Astrophysics Data System (ADS)

Zhang, Fudong; Chen, Chen; Liu, Jie; Wang, Zhihong

2018-02-01

This study focuses on improving the accuracy of a grating monochromator on the basis of the grating diffraction equation in combination with an analysis of the mechanical transmission relationship between the grating, the sine bar, and the screw of the scanning mechanism. First, the relationship between the mechanical error in the monochromator with the sine drive and the wavelength error is analyzed. Second, a mathematical model of the wavelength error and mechanical error is developed, and an accurate wavelength calibration method based on the sine bar's length adjustment and error compensation is proposed. Based on the mathematical model and calibration method, experiments using a standard light source with known spectral lines and a pre-adjusted sine bar length are conducted. The model parameter equations are solved, and subsequent parameter optimization simulations are performed to determine the optimal length ratio. Lastly, the length of the sine bar is adjusted. The experimental results indicate that the wavelength accuracy is ±0.3 nm, which is better than the original accuracy of ±2.6 nm. The results confirm the validity of the error analysis of the mechanical system of the monochromator as well as the validity of the calibration method.

Investigation of Primary Mirror Segment's Residual Errors for the Thirty Meter Telescope

NASA Technical Reports Server (NTRS)

Seo, Byoung-Joon; Nissly, Carl; Angeli, George; MacMynowski, Doug; Sigrist, Norbert; Troy, Mitchell; Williams, Eric

2009-01-01

The primary mirror segment aberrations after shape corrections with warping harness have been identified as the single largest error term in the Thirty Meter Telescope (TMT) image quality error budget. In order to better understand the likely errors and how they will impact the telescope performance we have performed detailed simulations. We first generated unwarped primary mirror segment surface shapes that met TMT specifications. Then we used the predicted warping harness influence functions and a Shack-Hartmann wavefront sensor model to determine estimates for the 492 corrected segment surfaces that make up the TMT primary mirror. Surface and control parameters, as well as the number of subapertures were varied to explore the parameter space. The corrected segment shapes were then passed to an optical TMT model built using the Jet Propulsion Laboratory (JPL) developed Modeling and Analysis for Controlled Optical Systems (MACOS) ray-trace simulator. The generated exit pupil wavefront error maps provided RMS wavefront error and image-plane characteristics like the Normalized Point Source Sensitivity (PSSN). The results have been used to optimize the segment shape correction and wavefront sensor designs as well as provide input to the TMT systems engineering error budgets.

Identification method of laser gyro error model under changing physical field

NASA Astrophysics Data System (ADS)

Wang, Qingqing; Niu, Zhenzhong

2018-04-01

In this paper, the influence mechanism of temperature, temperature changing rate and temperature gradient on the inertial devices is studied. The two-order model of zero bias and the three-order model of the calibration factor of lster gyro under temperature variation are deduced. The calibration scheme of temperature error is designed, and the experiment is carried out. Two methods of stepwise regression analysis and BP neural network are used to identify the parameters of the temperature error model, and the effectiveness of the two methods is proved by the temperature error compensation.

Model parameter-related optimal perturbations and their contributions to El Niño prediction errors

NASA Astrophysics Data System (ADS)

Tao, Ling-Jiang; Gao, Chuan; Zhang, Rong-Hua

2018-04-01

Errors in initial conditions and model parameters (MPs) are the main sources that limit the accuracy of ENSO predictions. In addition to exploring the initial error-induced prediction errors, model errors are equally important in determining prediction performance. In this paper, the MP-related optimal errors that can cause prominent error growth in ENSO predictions are investigated using an intermediate coupled model (ICM) and a conditional nonlinear optimal perturbation (CNOP) approach. Two MPs related to the Bjerknes feedback are considered in the CNOP analysis: one involves the SST-surface wind coupling ({α _τ } ), and the other involves the thermocline effect on the SST ({α _{Te}} ). The MP-related optimal perturbations (denoted as CNOP-P) are found uniformly positive and restrained in a small region: the {α _τ } component is mainly concentrated in the central equatorial Pacific, and the {α _{Te}} component is mainly located in the eastern cold tongue region. This kind of CNOP-P enhances the strength of the Bjerknes feedback and induces an El Niño- or La Niña-like error evolution, resulting in an El Niño-like systematic bias in this model. The CNOP-P is also found to play a role in the spring predictability barrier (SPB) for ENSO predictions. Evidently, such error growth is primarily attributed to MP errors in small areas based on the localized distribution of CNOP-P. Further sensitivity experiments firmly indicate that ENSO simulations are sensitive to the representation of SST-surface wind coupling in the central Pacific and to the thermocline effect in the eastern Pacific in the ICM. These results provide guidance and theoretical support for the future improvement in numerical models to reduce the systematic bias and SPB phenomenon in ENSO predictions.

Error modeling for differential GPS. M.S. Thesis - MIT, 12 May 1995

NASA Technical Reports Server (NTRS)

Blerman, Gregory S.

1995-01-01

Differential Global Positioning System (DGPS) positioning is used to accurately locate a GPS receiver based upon the well-known position of a reference site. In utilizing this technique, several error sources contribute to position inaccuracy. This thesis investigates the error in DGPS operation and attempts to develop a statistical model for the behavior of this error. The model for DGPS error is developed using GPS data collected by Draper Laboratory. The Marquardt method for nonlinear curve-fitting is used to find the parameters of a first order Markov process that models the average errors from the collected data. The results show that a first order Markov process can be used to model the DGPS error as a function of baseline distance and time delay. The model's time correlation constant is 3847.1 seconds (1.07 hours) for the mean square error. The distance correlation constant is 122.8 kilometers. The total process variance for the DGPS model is 3.73 sq meters.

Bayesian Treatment of Uncertainty in Environmental Modeling: Optimization, Sampling and Data Assimilation Using the DREAM Software Package

NASA Astrophysics Data System (ADS)

Vrugt, J. A.

2012-12-01

In the past decade much progress has been made in the treatment of uncertainty in earth systems modeling. Whereas initial approaches has focused mostly on quantification of parameter and predictive uncertainty, recent methods attempt to disentangle the effects of parameter, forcing (input) data, model structural and calibration data errors. In this talk I will highlight some of our recent work involving theory, concepts and applications of Bayesian parameter and/or state estimation. In particular, new methods for sequential Monte Carlo (SMC) and Markov Chain Monte Carlo (MCMC) simulation will be presented with emphasis on massively parallel distributed computing and quantification of model structural errors. The theoretical and numerical developments will be illustrated using model-data synthesis problems in hydrology, hydrogeology and geophysics.

Comparison of Optimal Design Methods in Inverse Problems

PubMed Central

Banks, H. T.; Holm, Kathleen; Kappel, Franz

2011-01-01

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix (FIM). A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criteria with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29]. PMID:21857762

Analyzing Multilevel Data: An Empirical Comparison of Parameter Estimates of Hierarchical Linear Modeling and Ordinary Least Squares Regression

ERIC Educational Resources Information Center

Rocconi, Louis M.

2011-01-01

Hierarchical linear models (HLM) solve the problems associated with the unit of analysis problem such as misestimated standard errors, heterogeneity of regression and aggregation bias by modeling all levels of interest simultaneously. Hierarchical linear modeling resolves the problem of misestimated standard errors by incorporating a unique random…

Bayesian design criteria: computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model.

PubMed

Merlé, Y; Mentré, F

1995-02-01

In this paper 3 criteria to design experiments for Bayesian estimation of the parameters of nonlinear models with respect to their parameters, when a prior distribution is available, are presented: the determinant of the Bayesian information matrix, the determinant of the pre-posterior covariance matrix, and the expected information provided by an experiment. A procedure to simplify the computation of these criteria is proposed in the case of continuous prior distributions and is compared with the criterion obtained from a linearization of the model about the mean of the prior distribution for the parameters. This procedure is applied to two models commonly encountered in the area of pharmacokinetics and pharmacodynamics: the one-compartment open model with bolus intravenous single-dose injection and the Emax model. They both involve two parameters. Additive as well as multiplicative gaussian measurement errors are considered with normal prior distributions. Various combinations of the variances of the prior distribution and of the measurement error are studied. Our attention is restricted to designs with limited numbers of measurements (1 or 2 measurements). This situation often occurs in practice when Bayesian estimation is performed. The optimal Bayesian designs that result vary with the variances of the parameter distribution and with the measurement error. The two-point optimal designs sometimes differ from the D-optimal designs for the mean of the prior distribution and may consist of replicating measurements. For the studied cases, the determinant of the Bayesian information matrix and its linearized form lead to the same optimal designs. In some cases, the pre-posterior covariance matrix can be far from its lower bound, namely, the inverse of the Bayesian information matrix, especially for the Emax model and a multiplicative measurement error. The expected information provided by the experiment and the determinant of the pre-posterior covariance matrix generally lead to the same designs except for the Emax model and the multiplicative measurement error. Results show that these criteria can be easily computed and that they could be incorporated in modules for designing experiments.

Worst-error analysis of batch filter and sequential filter in navigation problems. [in spacecraft trajectory estimation

NASA Technical Reports Server (NTRS)

Nishimura, T.

1975-01-01

This paper proposes a worst-error analysis for dealing with problems of estimation of spacecraft trajectories in deep space missions. Navigation filters in use assume either constant or stochastic (Markov) models for their estimated parameters. When the actual behavior of these parameters does not follow the pattern of the assumed model, the filters sometimes result in very poor performance. To prepare for such pathological cases, the worst errors of both batch and sequential filters are investigated based on the incremental sensitivity studies of these filters. By finding critical switching instances of non-gravitational accelerations, intensive tracking can be carried out around those instances. Also the worst errors in the target plane provide a measure in assignment of the propellant budget for trajectory corrections. Thus the worst-error study presents useful information as well as practical criteria in establishing the maneuver and tracking strategy of spacecraft's missions.

Two statistics for evaluating parameter identifiability and error reduction

USGS Publications Warehouse

Doherty, John; Hunt, Randall J.

2009-01-01

Two statistics are presented that can be used to rank input parameters utilized by a model in terms of their relative identifiability based on a given or possible future calibration dataset. Identifiability is defined here as the capability of model calibration to constrain parameters used by a model. Both statistics require that the sensitivity of each model parameter be calculated for each model output for which there are actual or presumed field measurements. Singular value decomposition (SVD) of the weighted sensitivity matrix is then undertaken to quantify the relation between the parameters and observations that, in turn, allows selection of calibration solution and null spaces spanned by unit orthogonal vectors. The first statistic presented, "parameter identifiability", is quantitatively defined as the direction cosine between a parameter and its projection onto the calibration solution space. This varies between zero and one, with zero indicating complete non-identifiability and one indicating complete identifiability. The second statistic, "relative error reduction", indicates the extent to which the calibration process reduces error in estimation of a parameter from its pre-calibration level where its value must be assigned purely on the basis of prior expert knowledge. This is more sophisticated than identifiability, in that it takes greater account of the noise associated with the calibration dataset. Like identifiability, it has a maximum value of one (which can only be achieved if there is no measurement noise). Conceptually it can fall to zero; and even below zero if a calibration problem is poorly posed. An example, based on a coupled groundwater/surface-water model, is included that demonstrates the utility of the statistics. ?? 2009 Elsevier B.V.

Experiences in multiyear combined state-parameter estimation with an ecosystem model of the North Atlantic and Arctic Oceans using the Ensemble Kalman Filter

NASA Astrophysics Data System (ADS)

Simon, Ehouarn; Samuelsen, Annette; Bertino, Laurent; Mouysset, Sandrine

2015-12-01

A sequence of one-year combined state-parameter estimation experiments has been conducted in a North Atlantic and Arctic Ocean configuration of the coupled physical-biogeochemical model HYCOM-NORWECOM over the period 2007-2010. The aim is to evaluate the ability of an ensemble-based data assimilation method to calibrate ecosystem model parameters in a pre-operational setting, namely the production of the MyOcean pilot reanalysis of the Arctic biology. For that purpose, four biological parameters (two phyto- and two zooplankton mortality rates) are estimated by assimilating weekly data such as, satellite-derived Sea Surface Temperature, along-track Sea Level Anomalies, ice concentrations and chlorophyll-a concentrations with an Ensemble Kalman Filter. The set of optimized parameters locally exhibits seasonal variations suggesting that time-dependent parameters should be used in ocean ecosystem models. A clustering analysis of the optimized parameters is performed in order to identify consistent ecosystem regions. In the north part of the domain, where the ecosystem model is the most reliable, most of them can be associated with Longhurst provinces and new provinces emerge in the Arctic Ocean. However, the clusters do not coincide anymore with the Longhurst provinces in the Tropics due to large model errors. Regarding the ecosystem state variables, the assimilation of satellite-derived chlorophyll concentration leads to significant reduction of the RMS errors in the observed variables during the first year, i.e. 2008, compared to a free run simulation. However, local filter divergences of the parameter component occur in 2009 and result in an increase in the RMS error at the time of the spring bloom.

Optimal error functional for parameter identification in anisotropic finite strain elasto-plasticity

NASA Astrophysics Data System (ADS)

Shutov, A. V.; Kaygorodtseva, A. A.; Dranishnikov, N. S.

2017-10-01

A problem of parameter identification for a model of finite strain elasto-plasticity is discussed. The utilized phenomenological material model accounts for nonlinear isotropic and kinematic hardening; the model kinematics is described by a nested multiplicative split of the deformation gradient. A hierarchy of optimization problems is considered. First, following the standard procedure, the material parameters are identified through minimization of a certain least square error functional. Next, the focus is placed on finding optimal weighting coefficients which enter the error functional. Toward that end, a stochastic noise with systematic and non-systematic components is introduced to the available measurement results; a superordinate optimization problem seeks to minimize the sensitivity of the resulting material parameters to the introduced noise. The advantage of this approach is that no additional experiments are required; it also provides an insight into the robustness of the identification procedure. As an example, experimental data for the steel 42CrMo4 are considered and a set of weighting coefficients is found, which is optimal in a certain class.

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

NASA Astrophysics Data System (ADS)

Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur

2018-03-01

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

Using Bayesian hierarchical models to better understand nitrate sources and sinks in agricultural watersheds.

PubMed

Xia, Yongqiu; Weller, Donald E; Williams, Meghan N; Jordan, Thomas E; Yan, Xiaoyuan

2016-11-15

Export coefficient models (ECMs) are often used to predict nutrient sources and sinks in watersheds because ECMs can flexibly incorporate processes and have minimal data requirements. However, ECMs do not quantify uncertainties in model structure, parameters, or predictions; nor do they account for spatial and temporal variability in land characteristics, weather, and management practices. We applied Bayesian hierarchical methods to address these problems in ECMs used to predict nitrate concentration in streams. We compared four model formulations, a basic ECM and three models with additional terms to represent competing hypotheses about the sources of error in ECMs and about spatial and temporal variability of coefficients: an ADditive Error Model (ADEM), a SpatioTemporal Parameter Model (STPM), and a Dynamic Parameter Model (DPM). The DPM incorporates a first-order random walk to represent spatial correlation among parameters and a dynamic linear model to accommodate temporal correlation. We tested the modeling approach in a proof of concept using watershed characteristics and nitrate export measurements from watersheds in the Coastal Plain physiographic province of the Chesapeake Bay drainage. Among the four models, the DPM was the best--it had the lowest mean error, explained the most variability (R 2  = 0.99), had the narrowest prediction intervals, and provided the most effective tradeoff between fit complexity (its deviance information criterion, DIC, was 45.6 units lower than any other model, indicating overwhelming support for the DPM). The superiority of the DPM supports its underlying hypothesis that the main source of error in ECMs is their failure to account for parameter variability rather than structural error. Analysis of the fitted DPM coefficients for cropland export and instream retention revealed some of the factors controlling nitrate concentration: cropland nitrate exports were positively related to stream flow and watershed average slope, while instream nitrate retention was positively correlated with nitrate concentration. By quantifying spatial and temporal variability in sources and sinks, the DPM provides new information to better target management actions to the most effective times and places. Given the wide use of ECMs as research and management tools, our approach can be broadly applied in other watersheds and to other materials. Copyright © 2016 Elsevier Ltd. All rights reserved.

An AI-based approach to structural damage identification by modal analysis

NASA Technical Reports Server (NTRS)

Glass, B. J.; Hanagud, S.

1990-01-01

Flexible-structure damage is presently addressed by a combined model- and parameter-identification approach which employs the AI methodologies of classification, heuristic search, and object-oriented model knowledge representation. The conditions for model-space search convergence to the best model are discussed in terms of search-tree organization and initial model parameter error. In the illustrative example of a truss structure presented, the use of both model and parameter identification is shown to lead to smaller parameter corrections than would be required by parameter identification alone.

The Consequences of Ignoring Item Parameter Drift in Longitudinal Item Response Models

ERIC Educational Resources Information Center

Lee, Wooyeol; Cho, Sun-Joo

2017-01-01

Utilizing a longitudinal item response model, this study investigated the effect of item parameter drift (IPD) on item parameters and person scores via a Monte Carlo study. Item parameter recovery was investigated for various IPD patterns in terms of bias and root mean-square error (RMSE), and percentage of time the 95% confidence interval covered…

Improving the Non-Hydrostatic Numerical Dust Model by Integrating Soil Moisture and Greenness Vegetation Fraction Data with Different Spatiotemporal Resolutions.

PubMed

Yu, Manzhu; Yang, Chaowei

2016-01-01

Dust storms are devastating natural disasters that cost billions of dollars and many human lives every year. Using the Non-Hydrostatic Mesoscale Dust Model (NMM-dust), this research studies how different spatiotemporal resolutions of two input parameters (soil moisture and greenness vegetation fraction) impact the sensitivity and accuracy of a dust model. Experiments are conducted by simulating dust concentration during July 1-7, 2014, for the target area covering part of Arizona and California (31, 37, -118, -112), with a resolution of ~ 3 km. Using ground-based and satellite observations, this research validates the temporal evolution and spatial distribution of dust storm output from the NMM-dust, and quantifies model error using measurements of four evaluation metrics (mean bias error, root mean square error, correlation coefficient and fractional gross error). Results showed that the default configuration of NMM-dust (with a low spatiotemporal resolution of both input parameters) generates an overestimation of Aerosol Optical Depth (AOD). Although it is able to qualitatively reproduce the temporal trend of the dust event, the default configuration of NMM-dust cannot fully capture its actual spatial distribution. Adjusting the spatiotemporal resolution of soil moisture and vegetation cover datasets showed that the model is sensitive to both parameters. Increasing the spatiotemporal resolution of soil moisture effectively reduces model's overestimation of AOD, while increasing the spatiotemporal resolution of vegetation cover changes the spatial distribution of reproduced dust storm. The adjustment of both parameters enables NMM-dust to capture the spatial distribution of dust storms, as well as reproducing more accurate dust concentration.

Forecasting impact injuries of unrestrained occupants in railway vehicle passenger compartments.

PubMed

Xie, Suchao; Zhou, Hui

2014-01-01

In order to predict the injury parameters of the occupants corresponding to different experimental parameters and to determine impact injury indices conveniently and efficiently, a model forecasting occupant impact injury was established in this work. The work was based on finite experimental observation values obtained by numerical simulation. First, the various factors influencing the impact injuries caused by the interaction between unrestrained occupants and the compartment's internal structures were collated and the most vulnerable regions of the occupant's body were analyzed. Then, the forecast model was set up based on a genetic algorithm-back propagation (GA-BP) hybrid algorithm, which unified the individual characteristics of the back propagation-artificial neural network (BP-ANN) model and the genetic algorithm (GA). The model was well suited to studies of occupant impact injuries and allowed multiple-parameter forecasts of the occupant impact injuries to be realized assuming values for various influencing factors. Finally, the forecast results for three types of secondary collision were analyzed using forecasting accuracy evaluation methods. All of the results showed the ideal accuracy of the forecast model. When an occupant faced a table, the relative errors between the predicted and experimental values of the respective injury parameters were kept within ± 6.0 percent and the average relative error (ARE) values did not exceed 3.0 percent. When an occupant faced a seat, the relative errors between the predicted and experimental values of the respective injury parameters were kept within ± 5.2 percent and the ARE values did not exceed 3.1 percent. When the occupant faced another occupant, the relative errors between the predicted and experimental values of the respective injury parameters were kept within ± 6.3 percent and the ARE values did not exceed 3.8 percent. The injury forecast model established in this article reduced repeat experiment times and improved the design efficiency of the internal compartment's structure parameters, and it provided a new way for assessing the safety performance of the interior structural parameters in existing, and newly designed, railway vehicle compartments.

Determination of heat capacity of ionic liquid based nanofluids using group method of data handling technique

NASA Astrophysics Data System (ADS)

Sadi, Maryam

2018-01-01

In this study a group method of data handling model has been successfully developed to predict heat capacity of ionic liquid based nanofluids by considering reduced temperature, acentric factor and molecular weight of ionic liquids, and nanoparticle concentration as input parameters. In order to accomplish modeling, 528 experimental data points extracted from the literature have been divided into training and testing subsets. The training set has been used to predict model coefficients and the testing set has been applied for model validation. The ability and accuracy of developed model, has been evaluated by comparison of model predictions with experimental values using different statistical parameters such as coefficient of determination, mean square error and mean absolute percentage error. The mean absolute percentage error of developed model for training and testing sets are 1.38% and 1.66%, respectively, which indicate excellent agreement between model predictions and experimental data. Also, the results estimated by the developed GMDH model exhibit a higher accuracy when compared to the available theoretical correlations.

Bayesian analysis of stochastic volatility-in-mean model with leverage and asymmetrically heavy-tailed error using generalized hyperbolic skew Student’s t-distribution*

PubMed Central

Leão, William L.; Chen, Ming-Hui

2017-01-01

A stochastic volatility-in-mean model with correlated errors using the generalized hyperbolic skew Student-t (GHST) distribution provides a robust alternative to the parameter estimation for daily stock returns in the absence of normality. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for parameter estimation. The deviance information, the Bayesian predictive information and the log-predictive score criterion are used to assess the fit of the proposed model. The proposed method is applied to an analysis of the daily stock return data from the Standard & Poor’s 500 index (S&P 500). The empirical results reveal that the stochastic volatility-in-mean model with correlated errors and GH-ST distribution leads to a significant improvement in the goodness-of-fit for the S&P 500 index returns dataset over the usual normal model. PMID:29333210

Bayesian analysis of stochastic volatility-in-mean model with leverage and asymmetrically heavy-tailed error using generalized hyperbolic skew Student's t-distribution.

PubMed

Leão, William L; Abanto-Valle, Carlos A; Chen, Ming-Hui

2017-01-01

A stochastic volatility-in-mean model with correlated errors using the generalized hyperbolic skew Student-t (GHST) distribution provides a robust alternative to the parameter estimation for daily stock returns in the absence of normality. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for parameter estimation. The deviance information, the Bayesian predictive information and the log-predictive score criterion are used to assess the fit of the proposed model. The proposed method is applied to an analysis of the daily stock return data from the Standard & Poor's 500 index (S&P 500). The empirical results reveal that the stochastic volatility-in-mean model with correlated errors and GH-ST distribution leads to a significant improvement in the goodness-of-fit for the S&P 500 index returns dataset over the usual normal model.

Experiences from the testing of a theory for modelling groundwater flow in heterogeneous media

USGS Publications Warehouse

Christensen, S.; Cooley, R.L.

2002-01-01

Usually, small-scale model error is present in groundwater modelling because the model only represents average system characteristics having the same form as the drift and small-scale variability is neglected. These errors cause the true errors of a regression model to be correlated. Theory and an example show that the errors also contribute to bias in the estimates of model parameters. This bias originates from model nonlinearity. In spite of this bias, predictions of hydraulic head are nearly unbiased if the model intrinsic nonlinearity is small. Individual confidence and prediction intervals are accurate if the t-statistic is multiplied by a correction factor. The correction factor can be computed from the true error second moment matrix, which can be determined when the stochastic properties of the system characteristics are known.

Experience gained in testing a theory for modelling groundwater flow in heterogeneous media

USGS Publications Warehouse

Christensen, S.; Cooley, R.L.

2002-01-01

Usually, small-scale model error is present in groundwater modelling because the model only represents average system characteristics having the same form as the drift, and small-scale variability is neglected. These errors cause the true errors of a regression model to be correlated. Theory and an example show that the errors also contribute to bias in the estimates of model parameters. This bias originates from model nonlinearity. In spite of this bias, predictions of hydraulic head are nearly unbiased if the model intrinsic nonlinearity is small. Individual confidence and prediction intervals are accurate if the t-statistic is multiplied by a correction factor. The correction factor can be computed from the true error second moment matrix, which can be determined when the stochastic properties of the system characteristics are known.

Modeling Infrared Signal Reflections to Characterize Indoor Multipath Propagation

PubMed Central

De-La-Llana-Calvo, Álvaro; Lázaro-Galilea, José Luis; Gardel-Vicente, Alfredo; Rodríguez-Navarro, David; Bravo-Muñoz, Ignacio; Tsirigotis, Georgios; Iglesias-Miguel, Juan

2017-01-01

In this paper, we propose a model to characterize Infrared (IR) signal reflections on any kind of surface material, together with a simplified procedure to compute the model parameters. The model works within the framework of Local Positioning Systems (LPS) based on IR signals (IR-LPS) to evaluate the behavior of transmitted signal Multipaths (MP), which are the main cause of error in IR-LPS, and makes several contributions to mitigation methods. Current methods are based on physics, optics, geometry and empirical methods, but these do not meet our requirements because of the need to apply several different restrictions and employ complex tools. We propose a simplified model based on only two reflection components, together with a method for determining the model parameters based on 12 empirical measurements that are easily performed in the real environment where the IR-LPS is being applied. Our experimental results show that the model provides a comprehensive solution to the real behavior of IR MP, yielding small errors when comparing real and modeled data (the mean error ranges from 1% to 4% depending on the environment surface materials). Other state-of-the-art methods yielded mean errors ranging from 15% to 40% in test measurements. PMID:28406436

Determining geometric error model parameters of a terrestrial laser scanner through Two-face, Length-consistency, and Network methods

PubMed Central

Wang, Ling; Muralikrishnan, Bala; Rachakonda, Prem; Sawyer, Daniel

2017-01-01

Terrestrial laser scanners (TLS) are increasingly used in large-scale manufacturing and assembly where required measurement uncertainties are on the order of few tenths of a millimeter or smaller. In order to meet these stringent requirements, systematic errors within a TLS are compensated in-situ through self-calibration. In the Network method of self-calibration, numerous targets distributed in the work-volume are measured from multiple locations with the TLS to determine parameters of the TLS error model. In this paper, we propose two new self-calibration methods, the Two-face method and the Length-consistency method. The Length-consistency method is proposed as a more efficient way of realizing the Network method where the length between any pair of targets from multiple TLS positions are compared to determine TLS model parameters. The Two-face method is a two-step process. In the first step, many model parameters are determined directly from the difference between front-face and back-face measurements of targets distributed in the work volume. In the second step, all remaining model parameters are determined through the Length-consistency method. We compare the Two-face method, the Length-consistency method, and the Network method in terms of the uncertainties in the model parameters, and demonstrate the validity of our techniques using a calibrated scale bar and front-face back-face target measurements. The clear advantage of these self-calibration methods is that a reference instrument or calibrated artifacts are not required, thus significantly lowering the cost involved in the calibration process. PMID:28890607

On the Statistical Errors of RADAR Location Sensor Networks with Built-In Wi-Fi Gaussian Linear Fingerprints

PubMed Central

Zhou, Mu; Xu, Yu Bin; Ma, Lin; Tian, Shuo

2012-01-01

The expected errors of RADAR sensor networks with linear probabilistic location fingerprints inside buildings with varying Wi-Fi Gaussian strength are discussed. As far as we know, the statistical errors of equal and unequal-weighted RADAR networks have been suggested as a better way to evaluate the behavior of different system parameters and the deployment of reference points (RPs). However, up to now, there is still not enough related work on the relations between the statistical errors, system parameters, number and interval of the RPs, let alone calculating the correlated analytical expressions of concern. Therefore, in response to this compelling problem, under a simple linear distribution model, much attention will be paid to the mathematical relations of the linear expected errors, number of neighbors, number and interval of RPs, parameters in logarithmic attenuation model and variations of radio signal strength (RSS) at the test point (TP) with the purpose of constructing more practical and reliable RADAR location sensor networks (RLSNs) and also guaranteeing the accuracy requirements for the location based services in future ubiquitous context-awareness environments. Moreover, the numerical results and some real experimental evaluations of the error theories addressed in this paper will also be presented for our future extended analysis. PMID:22737027

On the statistical errors of RADAR location sensor networks with built-in Wi-Fi Gaussian linear fingerprints.

PubMed

Zhou, Mu; Xu, Yu Bin; Ma, Lin; Tian, Shuo

2012-01-01

The expected errors of RADAR sensor networks with linear probabilistic location fingerprints inside buildings with varying Wi-Fi Gaussian strength are discussed. As far as we know, the statistical errors of equal and unequal-weighted RADAR networks have been suggested as a better way to evaluate the behavior of different system parameters and the deployment of reference points (RPs). However, up to now, there is still not enough related work on the relations between the statistical errors, system parameters, number and interval of the RPs, let alone calculating the correlated analytical expressions of concern. Therefore, in response to this compelling problem, under a simple linear distribution model, much attention will be paid to the mathematical relations of the linear expected errors, number of neighbors, number and interval of RPs, parameters in logarithmic attenuation model and variations of radio signal strength (RSS) at the test point (TP) with the purpose of constructing more practical and reliable RADAR location sensor networks (RLSNs) and also guaranteeing the accuracy requirements for the location based services in future ubiquitous context-awareness environments. Moreover, the numerical results and some real experimental evaluations of the error theories addressed in this paper will also be presented for our future extended analysis.

LATERAL CONTROL IN A DRIVING SIMULATOR: CORRELATIONS WITH NEUROPSYCHOLOGICAL TESTS AND ON-ROAD SAFETY ERRORS

PubMed Central

Johnson, Amy; Dawson, Jeffrey; Rizzo, Matthew

2012-01-01

Summary Driving simulators provide precise information on vehicular position at high capture rates. To analyze such data, we have previously proposed a time series model that reduces lateral position data into several parameters for measuring lateral control, and have shown that these parameters can detect differences between neurologically impaired and healthy drivers (Dawson et al, 2010a). In this paper, we focus on the “re-centering” parameter of this model, and test whether the parameter estimates are associated with off-road neuropsychological tests and/or with on-road safety errors. We assessed such correlations in 127 neurologically healthy drivers, ages 40 to 89. We found that our re-centering parameter had significant correlations with five neuropsychological tests: Judgment of Line Orientation (r = 0.38), Block Design (r = 0.27), Contrast Sensitivity (r = 0.31), Near Visual Acuity (r = -0.26), and Grooved Pegboard (r = -0.25). We also found that our re-centering parameter was associated with on-road safety errors at stop signs (r = -0.34) and on-road safety errors during turns (r = -0.22). These results suggest that our re-centering parameter may be a useful tool for measuring and monitoring ability to maintain vehicular lateral control. As GPS-based technology continues to improve in precision and reliability to measure vehicular positioning, our time-series model may potentially be applied as an automated index of driver performance in real world settings that is sensitive to cognitive decline. This work was supported by NIH/NIA awards AG17177, AG15071, and NS044930, and by a scholarship from Nissan Motor Company. PMID:24273756

A Note on the Specification of Error Structures in Latent Interaction Models

ERIC Educational Resources Information Center

Mao, Xiulin; Harring, Jeffrey R.; Hancock, Gregory R.

2015-01-01

Latent interaction models have motivated a great deal of methodological research, mainly in the area of estimating such models. Product-indicator methods have been shown to be competitive with other methods of estimation in terms of parameter bias and standard error accuracy, and their continued popularity in empirical studies is due, in part, to…

The Relationship between Root Mean Square Error of Approximation and Model Misspecification in Confirmatory Factor Analysis Models

ERIC Educational Resources Information Center

Savalei, Victoria

2012-01-01

The fit index root mean square error of approximation (RMSEA) is extremely popular in structural equation modeling. However, its behavior under different scenarios remains poorly understood. The present study generates continuous curves where possible to capture the full relationship between RMSEA and various "incidental parameters," such as…

On the biosorption, by brown seaweed, Lobophora variegata, of Ni(II) from aqueous solutions: equilibrium and thermodynamic studies.

PubMed

Basha, Shaik; Jaiswar, Santlal; Jha, Bhavanath

2010-09-01

The biosorption equilibrium isotherms of Ni(II) onto marine brown algae Lobophora variegata, which was chemically-modified by CaCl(2) were studied and modeled. To predict the biosorption isotherms and to determine the characteristic parameters for process design, twenty-three one-, two-, three-, four- and five-parameter isotherm models were applied to experimental data. The interaction among biosorbed molecules is attractive and biosorption is carried out on energetically different sites and is an endothermic process. The five-parameter Fritz-Schluender model gives the most accurate fit with high regression coefficient, R (2) (0.9911-0.9975) and F-ratio (118.03-179.96), and low standard error, SE (0.0902-0.0.1556) and the residual or sum of square error, SSE (0.0012-0.1789) values to all experimental data in comparison to other models. The biosorption isotherm models fitted the experimental data in the order: Fritz-Schluender (five-parameter) > Freundlich (two-parameter) > Langmuir (two-parameter) > Khan (three-parameter) > Fritz-Schluender (four-parameter). The thermodynamic parameters such as DeltaG (0), DeltaH (0) and DeltaS (0) have been determined, which indicates the sorption of Ni(II) onto L. variegata was spontaneous and endothermic in nature.

Error sensitivity analysis in 10-30-day extended range forecasting by using a nonlinear cross-prediction error model

NASA Astrophysics Data System (ADS)

Xia, Zhiye; Xu, Lisheng; Chen, Hongbin; Wang, Yongqian; Liu, Jinbao; Feng, Wenlan

2017-06-01

Extended range forecasting of 10-30 days, which lies between medium-term and climate prediction in terms of timescale, plays a significant role in decision-making processes for the prevention and mitigation of disastrous meteorological events. The sensitivity of initial error, model parameter error, and random error in a nonlinear crossprediction error (NCPE) model, and their stability in the prediction validity period in 10-30-day extended range forecasting, are analyzed quantitatively. The associated sensitivity of precipitable water, temperature, and geopotential height during cases of heavy rain and hurricane is also discussed. The results are summarized as follows. First, the initial error and random error interact. When the ratio of random error to initial error is small (10-6-10-2), minor variation in random error cannot significantly change the dynamic features of a chaotic system, and therefore random error has minimal effect on the prediction. When the ratio is in the range of 10-1-2 (i.e., random error dominates), attention should be paid to the random error instead of only the initial error. When the ratio is around 10-2-10-1, both influences must be considered. Their mutual effects may bring considerable uncertainty to extended range forecasting, and de-noising is therefore necessary. Second, in terms of model parameter error, the embedding dimension m should be determined by the factual nonlinear time series. The dynamic features of a chaotic system cannot be depicted because of the incomplete structure of the attractor when m is small. When m is large, prediction indicators can vanish because of the scarcity of phase points in phase space. A method for overcoming the cut-off effect ( m > 4) is proposed. Third, for heavy rains, precipitable water is more sensitive to the prediction validity period than temperature or geopotential height; however, for hurricanes, geopotential height is most sensitive, followed by precipitable water.

Real-time Ensemble Forecasting of Coronal Mass Ejections using the WSA-ENLIL+Cone Model

NASA Astrophysics Data System (ADS)

Mays, M. L.; Taktakishvili, A.; Pulkkinen, A. A.; MacNeice, P. J.; Rastaetter, L.; Kuznetsova, M. M.; Odstrcil, D.

2013-12-01

Ensemble forecasting of coronal mass ejections (CMEs) provides significant information in that it provides an estimation of the spread or uncertainty in CME arrival time predictions due to uncertainties in determining CME input parameters. Ensemble modeling of CME propagation in the heliosphere is performed by forecasters at the Space Weather Research Center (SWRC) using the WSA-ENLIL cone model available at the Community Coordinated Modeling Center (CCMC). SWRC is an in-house research-based operations team at the CCMC which provides interplanetary space weather forecasting for NASA's robotic missions and performs real-time model validation. A distribution of n (routinely n=48) CME input parameters are generated using the CCMC Stereo CME Analysis Tool (StereoCAT) which employs geometrical triangulation techniques. These input parameters are used to perform n different simulations yielding an ensemble of solar wind parameters at various locations of interest (satellites or planets), including a probability distribution of CME shock arrival times (for hits), and geomagnetic storm strength (for Earth-directed hits). Ensemble simulations have been performed experimentally in real-time at the CCMC since January 2013. We present the results of ensemble simulations for a total of 15 CME events, 10 of which were performed in real-time. The observed CME arrival was within the range of ensemble arrival time predictions for 5 out of the 12 ensemble runs containing hits. The average arrival time prediction was computed for each of the twelve ensembles predicting hits and using the actual arrival time an average absolute error of 8.20 hours was found for all twelve ensembles, which is comparable to current forecasting errors. Some considerations for the accuracy of ensemble CME arrival time predictions include the importance of the initial distribution of CME input parameters, particularly the mean and spread. When the observed arrivals are not within the predicted range, this still allows the ruling out of prediction errors caused by tested CME input parameters. Prediction errors can also arise from ambient model parameters such as the accuracy of the solar wind background, and other limitations. Additionally the ensemble modeling setup was used to complete a parametric event case study of the sensitivity of the CME arrival time prediction to free parameters for ambient solar wind model and CME.

Determinants of Standard Errors of MLEs in Confirmatory Factor Analysis

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Cheng, Ying; Zhang, Wei

2010-01-01

This paper studies changes of standard errors (SE) of the normal-distribution-based maximum likelihood estimates (MLE) for confirmatory factor models as model parameters vary. Using logical analysis, simplified formulas and numerical verification, monotonic relationships between SEs and factor loadings as well as unique variances are found.…

Real-Time Parameter Estimation Using Output Error

NASA Technical Reports Server (NTRS)

Grauer, Jared A.

2014-01-01

Output-error parameter estimation, normally a post- ight batch technique, was applied to real-time dynamic modeling problems. Variations on the traditional algorithm were investigated with the goal of making the method suitable for operation in real time. Im- plementation recommendations are given that are dependent on the modeling problem of interest. Application to ight test data showed that accurate parameter estimates and un- certainties for the short-period dynamics model were available every 2 s using time domain data, or every 3 s using frequency domain data. The data compatibility problem was also solved in real time, providing corrected sensor measurements every 4 s. If uncertainty corrections for colored residuals are omitted, this rate can be increased to every 0.5 s.

Aerial robot intelligent control method based on back-stepping

NASA Astrophysics Data System (ADS)

Zhou, Jian; Xue, Qian

2018-05-01

The aerial robot is characterized as strong nonlinearity, high coupling and parameter uncertainty, a self-adaptive back-stepping control method based on neural network is proposed in this paper. The uncertain part of the aerial robot model is compensated online by the neural network of Cerebellum Model Articulation Controller and robust control items are designed to overcome the uncertainty error of the system during online learning. At the same time, particle swarm algorithm is used to optimize and fix parameters so as to improve the dynamic performance, and control law is obtained by the recursion of back-stepping regression. Simulation results show that the designed control law has desired attitude tracking performance and good robustness in case of uncertainties and large errors in the model parameters.

A new approach to identify the sensitivity and importance of physical parameters combination within numerical models using the Lund-Potsdam-Jena (LPJ) model as an example

NASA Astrophysics Data System (ADS)

Sun, Guodong; Mu, Mu

2017-05-01

An important source of uncertainty, which causes further uncertainty in numerical simulations, is that residing in the parameters describing physical processes in numerical models. Therefore, finding a subset among numerous physical parameters in numerical models in the atmospheric and oceanic sciences, which are relatively more sensitive and important parameters, and reducing the errors in the physical parameters in this subset would be a far more efficient way to reduce the uncertainties involved in simulations. In this context, we present a new approach based on the conditional nonlinear optimal perturbation related to parameter (CNOP-P) method. The approach provides a framework to ascertain the subset of those relatively more sensitive and important parameters among the physical parameters. The Lund-Potsdam-Jena (LPJ) dynamical global vegetation model was utilized to test the validity of the new approach in China. The results imply that nonlinear interactions among parameters play a key role in the identification of sensitive parameters in arid and semi-arid regions of China compared to those in northern, northeastern, and southern China. The uncertainties in the numerical simulations were reduced considerably by reducing the errors of the subset of relatively more sensitive and important parameters. The results demonstrate that our approach not only offers a new route to identify relatively more sensitive and important physical parameters but also that it is viable to then apply "target observations" to reduce the uncertainties in model parameters.

Application of a Combined Model with Autoregressive Integrated Moving Average (ARIMA) and Generalized Regression Neural Network (GRNN) in Forecasting Hepatitis Incidence in Heng County, China

PubMed Central

Liang, Hao; Gao, Lian; Liang, Bingyu; Huang, Jiegang; Zang, Ning; Liao, Yanyan; Yu, Jun; Lai, Jingzhen; Qin, Fengxiang; Su, Jinming; Ye, Li; Chen, Hui

2016-01-01

Background Hepatitis is a serious public health problem with increasing cases and property damage in Heng County. It is necessary to develop a model to predict the hepatitis epidemic that could be useful for preventing this disease. Methods The autoregressive integrated moving average (ARIMA) model and the generalized regression neural network (GRNN) model were used to fit the incidence data from the Heng County CDC (Center for Disease Control and Prevention) from January 2005 to December 2012. Then, the ARIMA-GRNN hybrid model was developed. The incidence data from January 2013 to December 2013 were used to validate the models. Several parameters, including mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE) and mean square error (MSE), were used to compare the performance among the three models. Results The morbidity of hepatitis from Jan 2005 to Dec 2012 has seasonal variation and slightly rising trend. The ARIMA(0,1,2)(1,1,1)12 model was the most appropriate one with the residual test showing a white noise sequence. The smoothing factor of the basic GRNN model and the combined model was 1.8 and 0.07, respectively. The four parameters of the hybrid model were lower than those of the two single models in the validation. The parameters values of the GRNN model were the lowest in the fitting of the three models. Conclusions The hybrid ARIMA-GRNN model showed better hepatitis incidence forecasting in Heng County than the single ARIMA model and the basic GRNN model. It is a potential decision-supportive tool for controlling hepatitis in Heng County. PMID:27258555

Bias in error estimation when using cross-validation for model selection.

PubMed

Varma, Sudhir; Simon, Richard

2006-02-23

Cross-validation (CV) is an effective method for estimating the prediction error of a classifier. Some recent articles have proposed methods for optimizing classifiers by choosing classifier parameter values that minimize the CV error estimate. We have evaluated the validity of using the CV error estimate of the optimized classifier as an estimate of the true error expected on independent data. We used CV to optimize the classification parameters for two kinds of classifiers; Shrunken Centroids and Support Vector Machines (SVM). Random training datasets were created, with no difference in the distribution of the features between the two classes. Using these "null" datasets, we selected classifier parameter values that minimized the CV error estimate. 10-fold CV was used for Shrunken Centroids while Leave-One-Out-CV (LOOCV) was used for the SVM. Independent test data was created to estimate the true error. With "null" and "non null" (with differential expression between the classes) data, we also tested a nested CV procedure, where an inner CV loop is used to perform the tuning of the parameters while an outer CV is used to compute an estimate of the error. The CV error estimate for the classifier with the optimal parameters was found to be a substantially biased estimate of the true error that the classifier would incur on independent data. Even though there is no real difference between the two classes for the "null" datasets, the CV error estimate for the Shrunken Centroid with the optimal parameters was less than 30% on 18.5% of simulated training data-sets. For SVM with optimal parameters the estimated error rate was less than 30% on 38% of "null" data-sets. Performance of the optimized classifiers on the independent test set was no better than chance. The nested CV procedure reduces the bias considerably and gives an estimate of the error that is very close to that obtained on the independent testing set for both Shrunken Centroids and SVM classifiers for "null" and "non-null" data distributions. We show that using CV to compute an error estimate for a classifier that has itself been tuned using CV gives a significantly biased estimate of the true error. Proper use of CV for estimating true error of a classifier developed using a well defined algorithm requires that all steps of the algorithm, including classifier parameter tuning, be repeated in each CV loop. A nested CV procedure provides an almost unbiased estimate of the true error.

Uncertainty analysis of the Operational Simplified Surface Energy Balance (SSEBop) model at multiple flux tower sites

USGS Publications Warehouse

Chen, Mingshi; Senay, Gabriel B.; Singh, Ramesh K.; Verdin, James P.

2016-01-01

Evapotranspiration (ET) is an important component of the water cycle – ET from the land surface returns approximately 60% of the global precipitation back to the atmosphere. ET also plays an important role in energy transport among the biosphere, atmosphere, and hydrosphere. Current regional to global and daily to annual ET estimation relies mainly on surface energy balance (SEB) ET models or statistical and empirical methods driven by remote sensing data and various climatological databases. These models have uncertainties due to inevitable input errors, poorly defined parameters, and inadequate model structures. The eddy covariance measurements on water, energy, and carbon fluxes at the AmeriFlux tower sites provide an opportunity to assess the ET modeling uncertainties. In this study, we focused on uncertainty analysis of the Operational Simplified Surface Energy Balance (SSEBop) model for ET estimation at multiple AmeriFlux tower sites with diverse land cover characteristics and climatic conditions. The 8-day composite 1-km MODerate resolution Imaging Spectroradiometer (MODIS) land surface temperature (LST) was used as input land surface temperature for the SSEBop algorithms. The other input data were taken from the AmeriFlux database. Results of statistical analysis indicated that the SSEBop model performed well in estimating ET with an R2 of 0.86 between estimated ET and eddy covariance measurements at 42 AmeriFlux tower sites during 2001–2007. It was encouraging to see that the best performance was observed for croplands, where R2 was 0.92 with a root mean square error of 13 mm/month. The uncertainties or random errors from input variables and parameters of the SSEBop model led to monthly ET estimates with relative errors less than 20% across multiple flux tower sites distributed across different biomes. This uncertainty of the SSEBop model lies within the error range of other SEB models, suggesting systematic error or bias of the SSEBop model is within the normal range. This finding implies that the simplified parameterization of the SSEBop model did not significantly affect the accuracy of the ET estimate while increasing the ease of model setup for operational applications. The sensitivity analysis indicated that the SSEBop model is most sensitive to input variables, land surface temperature (LST) and reference ET (ETo); and parameters, differential temperature (dT), and maximum ET scalar (Kmax), particularly during the non-growing season and in dry areas. In summary, the uncertainty assessment verifies that the SSEBop model is a reliable and robust method for large-area ET estimation. The SSEBop model estimates can be further improved by reducing errors in two input variables (ETo and LST) and two key parameters (Kmax and dT).

An LPV Adaptive Observer for Updating a Map Applied to an MAF Sensor in a Diesel Engine.

PubMed

Liu, Zhiyuan; Wang, Changhui

2015-10-23

In this paper, a new method for mass air flow (MAF) sensor error compensation and an online updating error map (or lookup table) due to installation and aging in a diesel engine is developed. Since the MAF sensor error is dependent on the engine operating point, the error model is represented as a two-dimensional (2D) map with two inputs, fuel mass injection quantity and engine speed. Meanwhile, the 2D map representing the MAF sensor error is described as a piecewise bilinear interpolation model, which can be written as a dot product between the regression vector and parameter vector using a membership function. With the combination of the 2D map regression model and the diesel engine air path system, an LPV adaptive observer with low computational load is designed to estimate states and parameters jointly. The convergence of the proposed algorithm is proven under the conditions of persistent excitation and given inequalities. The observer is validated against the simulation data from engine software enDYNA provided by Tesis. The results demonstrate that the operating point-dependent error of the MAF sensor can be approximated acceptably by the 2D map from the proposed method.

A Formal Approach to Empirical Dynamic Model Optimization and Validation

NASA Technical Reports Server (NTRS)

Crespo, Luis G; Morelli, Eugene A.; Kenny, Sean P.; Giesy, Daniel P.

2014-01-01

A framework was developed for the optimization and validation of empirical dynamic models subject to an arbitrary set of validation criteria. The validation requirements imposed upon the model, which may involve several sets of input-output data and arbitrary specifications in time and frequency domains, are used to determine if model predictions are within admissible error limits. The parameters of the empirical model are estimated by finding the parameter realization for which the smallest of the margins of requirement compliance is as large as possible. The uncertainty in the value of this estimate is characterized by studying the set of model parameters yielding predictions that comply with all the requirements. Strategies are presented for bounding this set, studying its dependence on admissible prediction error set by the analyst, and evaluating the sensitivity of the model predictions to parameter variations. This information is instrumental in characterizing uncertainty models used for evaluating the dynamic model at operating conditions differing from those used for its identification and validation. A practical example based on the short period dynamics of the F-16 is used for illustration.

Ancient numerical daemons of conceptual hydrological modeling: 1. Fidelity and efficiency of time stepping schemes

NASA Astrophysics Data System (ADS)

Clark, Martyn P.; Kavetski, Dmitri

2010-10-01

A major neglected weakness of many current hydrological models is the numerical method used to solve the governing model equations. This paper thoroughly evaluates several classes of time stepping schemes in terms of numerical reliability and computational efficiency in the context of conceptual hydrological modeling. Numerical experiments are carried out using 8 distinct time stepping algorithms and 6 different conceptual rainfall-runoff models, applied in a densely gauged experimental catchment, as well as in 12 basins with diverse physical and hydroclimatic characteristics. Results show that, over vast regions of the parameter space, the numerical errors of fixed-step explicit schemes commonly used in hydrology routinely dwarf the structural errors of the model conceptualization. This substantially degrades model predictions, but also, disturbingly, generates fortuitously adequate performance for parameter sets where numerical errors compensate for model structural errors. Simply running fixed-step explicit schemes with shorter time steps provides a poor balance between accuracy and efficiency: in some cases daily-step adaptive explicit schemes with moderate error tolerances achieved comparable or higher accuracy than 15 min fixed-step explicit approximations but were nearly 10 times more efficient. From the range of simple time stepping schemes investigated in this work, the fixed-step implicit Euler method and the adaptive explicit Heun method emerge as good practical choices for the majority of simulation scenarios. In combination with the companion paper, where impacts on model analysis, interpretation, and prediction are assessed, this two-part study vividly highlights the impact of numerical errors on critical performance aspects of conceptual hydrological models and provides practical guidelines for robust numerical implementation.

New error calibration tests for gravity models using subset solutions and independent data - Applied to GEM-T3

NASA Technical Reports Server (NTRS)

Lerch, F. J.; Nerem, R. S.; Chinn, D. S.; Chan, J. C.; Patel, G. B.; Klosko, S. M.

1993-01-01

A new method has been developed to provide a direct test of the error calibrations of gravity models based on actual satellite observations. The basic approach projects the error estimates of the gravity model parameters onto satellite observations, and the results of these projections are then compared with data residual computed from the orbital fits. To allow specific testing of the gravity error calibrations, subset solutions are computed based on the data set and data weighting of the gravity model. The approach is demonstrated using GEM-T3 to show that the gravity error estimates are well calibrated and that reliable predictions of orbit accuracies can be achieved for independent orbits.

A provisional effective evaluation when errors are present in independent variables

NASA Technical Reports Server (NTRS)

Gurin, L. S.

1983-01-01

Algorithms are examined for evaluating the parameters of a regression model when there are errors in the independent variables. The algorithms are fast and the estimates they yield are stable with respect to the correlation of errors and measurements of both the dependent variable and the independent variables.

Standard Errors and Confidence Intervals from Bootstrapping for Ramsay-Curve Item Response Theory Model Item Parameters

ERIC Educational Resources Information Center

Gu, Fei; Skorupski, William P.; Hoyle, Larry; Kingston, Neal M.

2011-01-01

Ramsay-curve item response theory (RC-IRT) is a nonparametric procedure that estimates the latent trait using splines, and no distributional assumption about the latent trait is required. For item parameters of the two-parameter logistic (2-PL), three-parameter logistic (3-PL), and polytomous IRT models, RC-IRT can provide more accurate estimates…

Correcting for Measurement Error in Time-Varying Covariates in Marginal Structural Models.

PubMed

Kyle, Ryan P; Moodie, Erica E M; Klein, Marina B; Abrahamowicz, Michał

2016-08-01

Unbiased estimation of causal parameters from marginal structural models (MSMs) requires a fundamental assumption of no unmeasured confounding. Unfortunately, the time-varying covariates used to obtain inverse probability weights are often error-prone. Although substantial measurement error in important confounders is known to undermine control of confounders in conventional unweighted regression models, this issue has received comparatively limited attention in the MSM literature. Here we propose a novel application of the simulation-extrapolation (SIMEX) procedure to address measurement error in time-varying covariates, and we compare 2 approaches. The direct approach to SIMEX-based correction targets outcome model parameters, while the indirect approach corrects the weights estimated using the exposure model. We assess the performance of the proposed methods in simulations under different clinically plausible assumptions. The simulations demonstrate that measurement errors in time-dependent covariates may induce substantial bias in MSM estimators of causal effects of time-varying exposures, and that both proposed SIMEX approaches yield practically unbiased estimates in scenarios featuring low-to-moderate degrees of error. We illustrate the proposed approach in a simple analysis of the relationship between sustained virological response and liver fibrosis progression among persons infected with hepatitis C virus, while accounting for measurement error in γ-glutamyltransferase, using data collected in the Canadian Co-infection Cohort Study from 2003 to 2014. © The Author 2016. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Minimization of model representativity errors in identification of point source emission from atmospheric concentration measurements

NASA Astrophysics Data System (ADS)

Sharan, Maithili; Singh, Amit Kumar; Singh, Sarvesh Kumar

2017-11-01

Estimation of an unknown atmospheric release from a finite set of concentration measurements is considered an ill-posed inverse problem. Besides ill-posedness, the estimation process is influenced by the instrumental errors in the measured concentrations and model representativity errors. The study highlights the effect of minimizing model representativity errors on the source estimation. This is described in an adjoint modelling framework and followed in three steps. First, an estimation of point source parameters (location and intensity) is carried out using an inversion technique. Second, a linear regression relationship is established between the measured concentrations and corresponding predicted using the retrieved source parameters. Third, this relationship is utilized to modify the adjoint functions. Further, source estimation is carried out using these modified adjoint functions to analyse the effect of such modifications. The process is tested for two well known inversion techniques, called renormalization and least-square. The proposed methodology and inversion techniques are evaluated for a real scenario by using concentrations measurements from the Idaho diffusion experiment in low wind stable conditions. With both the inversion techniques, a significant improvement is observed in the retrieval of source estimation after minimizing the representativity errors.

Using model order tests to determine sensory inputs in a motion study

NASA Technical Reports Server (NTRS)

Repperger, D. W.; Junker, A. M.

1977-01-01

In the study of motion effects on tracking performance, a problem of interest is the determination of what sensory inputs a human uses in controlling his tracking task. In the approach presented here a simple canonical model (FID or a proportional, integral, derivative structure) is used to model the human's input-output time series. A study of significant changes in reduction of the output error loss functional is conducted as different permutations of parameters are considered. Since this canonical model includes parameters which are related to inputs to the human (such as the error signal, its derivatives and integration), the study of model order is equivalent to the study of which sensory inputs are being used by the tracker. The parameters are obtained which have the greatest effect on reducing the loss function significantly. In this manner the identification procedure converts the problem of testing for model order into the problem of determining sensory inputs.

Added-value joint source modelling of seismic and geodetic data

NASA Astrophysics Data System (ADS)

Sudhaus, Henriette; Heimann, Sebastian; Walter, Thomas R.; Krueger, Frank

2013-04-01

In tectonically active regions earthquake source studies strongly support the analysis of the current faulting processes as they reveal the location and geometry of active faults, the average slip released or more. For source modelling of shallow, moderate to large earthquakes often a combination of geodetic (GPS, InSAR) and seismic data is used. A truly joint use of these data, however, usually takes place only on a higher modelling level, where some of the first-order characteristics (time, centroid location, fault orientation, moment) have been fixed already. These required basis model parameters have to be given, assumed or inferred in a previous, separate and highly non-linear modelling step using one of the these data sets alone. We present a new earthquake rupture model implementation that realizes a fully combined data integration of surface displacement measurements and seismic data in a non-linear optimization of simple but extended planar ruptures. The model implementation allows for fast forward calculations of full seismograms and surface deformation and therefore enables us to use Monte Carlo global search algorithms. Furthermore, we benefit from the complementary character of seismic and geodetic data, e. g. the high definition of the source location from geodetic data and the sensitivity of the resolution of the seismic data on moment releases at larger depth. These increased constraints from the combined dataset make optimizations efficient, even for larger model parameter spaces and with a very limited amount of a priori assumption on the source. A vital part of our approach is rigorous data weighting based on the empirically estimated data errors. We construct full data error variance-covariance matrices for geodetic data to account for correlated data noise and also weight the seismic data based on their signal-to-noise ratio. The estimation of the data errors and the fast forward modelling opens the door for Bayesian inferences of the source model parameters. The source model product then features parameter uncertainty estimates and reveals parameter trade-offs that arise from imperfect data coverage and data errors. We applied our new source modelling approach to the 2010 Haiti earthquake for which a number of apparently different seismic, geodetic and joint source models has been reported already - mostly without any model parameter estimations. We here show that the variability of all these source models seems to arise from inherent model parameter trade-offs and mostly has little statistical significance, e.g. even using a large dataset comprising seismic and geodetic data the confidence interval of the fault dip remains as wide as about 20 degrees.

Cross Validation Through Two-Dimensional Solution Surface for Cost-Sensitive SVM.

PubMed

Gu, Bin; Sheng, Victor S; Tay, Keng Yeow; Romano, Walter; Li, Shuo

2017-06-01

Model selection plays an important role in cost-sensitive SVM (CS-SVM). It has been proven that the global minimum cross validation (CV) error can be efficiently computed based on the solution path for one parameter learning problems. However, it is a challenge to obtain the global minimum CV error for CS-SVM based on one-dimensional solution path and traditional grid search, because CS-SVM is with two regularization parameters. In this paper, we propose a solution and error surfaces based CV approach (CV-SES). More specifically, we first compute a two-dimensional solution surface for CS-SVM based on a bi-parameter space partition algorithm, which can fit solutions of CS-SVM for all values of both regularization parameters. Then, we compute a two-dimensional validation error surface for each CV fold, which can fit validation errors of CS-SVM for all values of both regularization parameters. Finally, we obtain the CV error surface by superposing K validation error surfaces, which can find the global minimum CV error of CS-SVM. Experiments are conducted on seven datasets for cost sensitive learning and on four datasets for imbalanced learning. Experimental results not only show that our proposed CV-SES has a better generalization ability than CS-SVM with various hybrids between grid search and solution path methods, and than recent proposed cost-sensitive hinge loss SVM with three-dimensional grid search, but also show that CV-SES uses less running time.

Design of a Two-Step Calibration Method of Kinematic Parameters for Serial Robots

NASA Astrophysics Data System (ADS)

WANG, Wei; WANG, Lei; YUN, Chao

2017-03-01

Serial robots are used to handle workpieces with large dimensions, and calibrating kinematic parameters is one of the most efficient ways to upgrade their accuracy. Many models are set up to investigate how many kinematic parameters can be identified to meet the minimal principle, but the base frame and the kinematic parameter are indistinctly calibrated in a one-step way. A two-step method of calibrating kinematic parameters is proposed to improve the accuracy of the robot's base frame and kinematic parameters. The forward kinematics described with respect to the measuring coordinate frame are established based on the product-of-exponential (POE) formula. In the first step the robot's base coordinate frame is calibrated by the unit quaternion form. The errors of both the robot's reference configuration and the base coordinate frame's pose are equivalently transformed to the zero-position errors of the robot's joints. The simplified model of the robot's positioning error is established in second-power explicit expressions. Then the identification model is finished by the least square method, requiring measuring position coordinates only. The complete subtasks of calibrating the robot's 39 kinematic parameters are finished in the second step. It's proved by a group of calibration experiments that by the proposed two-step calibration method the average absolute accuracy of industrial robots is updated to 0.23 mm. This paper presents that the robot's base frame should be calibrated before its kinematic parameters in order to upgrade its absolute positioning accuracy.

Multielevation calibration of frequency-domain electromagnetic data

USGS Publications Warehouse

Minsley, Burke J.; Kass, M. Andy; Hodges, Greg; Smith, Bruce D.

2014-01-01

Systematic calibration errors must be taken into account because they can substantially impact the accuracy of inverted subsurface resistivity models derived from frequency-domain electromagnetic data, resulting in potentially misleading interpretations. We have developed an approach that uses data acquired at multiple elevations over the same location to assess calibration errors. A significant advantage is that this method does not require prior knowledge of subsurface properties from borehole or ground geophysical data (though these can be readily incorporated if available), and is, therefore, well suited to remote areas. The multielevation data were used to solve for calibration parameters and a single subsurface resistivity model that are self consistent over all elevations. The deterministic and Bayesian formulations of the multielevation approach illustrate parameter sensitivity and uncertainty using synthetic- and field-data examples. Multiplicative calibration errors (gain and phase) were found to be better resolved at high frequencies and when data were acquired over a relatively conductive area, whereas additive errors (bias) were reasonably resolved over conductive and resistive areas at all frequencies. The Bayesian approach outperformed the deterministic approach when estimating calibration parameters using multielevation data at a single location; however, joint analysis of multielevation data at multiple locations using the deterministic algorithm yielded the most accurate estimates of calibration parameters. Inversion results using calibration-corrected data revealed marked improvement in misfit, lending added confidence to the interpretation of these models.

Error Consistency Analysis Scheme for Infrared Ultraspectral Sounding Retrieval Error Budget Estimation

NASA Technical Reports Server (NTRS)

Zhou, Daniel K.; Larar, Allen M.; Liu, Xu; Smith, William L.; Strow, Larry, L.

2013-01-01

Great effort has been devoted towards validating geophysical parameters retrieved from ultraspectral infrared radiances obtained from satellite remote sensors. An error consistency analysis scheme (ECAS), utilizing fast radiative transfer model (RTM) forward and inverse calculations, has been developed to estimate the error budget in terms of mean difference and standard deviation of error in both spectral radiance and retrieval domains. The retrieval error is assessed through ECAS without relying on other independent measurements such as radiosonde data. ECAS establishes a link between the accuracies of radiances and retrieved geophysical parameters. ECAS can be applied to measurements from any ultraspectral instrument and any retrieval scheme with its associated RTM. In this manuscript, ECAS is described and demonstrated with measurements from the MetOp-A satellite Infrared Atmospheric Sounding Interferometer (IASI). This scheme can be used together with other validation methodologies to give a more definitive characterization of the error and/or uncertainty of geophysical parameters retrieved from ultraspectral radiances observed from current and future satellite remote sensors such as IASI, the Atmospheric Infrared Sounder (AIRS), and the Cross-track Infrared Sounder (CrIS).

Pharmacokinetic design optimization in children and estimation of maturation parameters: example of cytochrome P450 3A4.

PubMed

Bouillon-Pichault, Marion; Jullien, Vincent; Bazzoli, Caroline; Pons, Gérard; Tod, Michel

2011-02-01

The aim of this work was to determine whether optimizing the study design in terms of ages and sampling times for a drug eliminated solely via cytochrome P450 3A4 (CYP3A4) would allow us to accurately estimate the pharmacokinetic parameters throughout the entire childhood timespan, while taking into account age- and weight-related changes. A linear monocompartmental model with first-order absorption was used successively with three different residual error models and previously published pharmacokinetic parameters ("true values"). The optimal ages were established by D-optimization using the CYP3A4 maturation function to create "optimized demographic databases." The post-dose times for each previously selected age were determined by D-optimization using the pharmacokinetic model to create "optimized sparse sampling databases." We simulated concentrations by applying the population pharmacokinetic model to the optimized sparse sampling databases to create optimized concentration databases. The latter were modeled to estimate population pharmacokinetic parameters. We then compared true and estimated parameter values. The established optimal design comprised four age ranges: 0.008 years old (i.e., around 3 days), 0.192 years old (i.e., around 2 months), 1.325 years old, and adults, with the same number of subjects per group and three or four samples per subject, in accordance with the error model. The population pharmacokinetic parameters that we estimated with this design were precise and unbiased (root mean square error [RMSE] and mean prediction error [MPE] less than 11% for clearance and distribution volume and less than 18% for k(a)), whereas the maturation parameters were unbiased but less precise (MPE < 6% and RMSE < 37%). Based on our results, taking growth and maturation into account a priori in a pediatric pharmacokinetic study is theoretically feasible. However, it requires that very early ages be included in studies, which may present an obstacle to the use of this approach. First-pass effects, alternative elimination routes, and combined elimination pathways should also be investigated.

Improved Analysis of GW150914 Using a Fully Spin-Precessing Waveform Model

NASA Astrophysics Data System (ADS)

Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Aiello, L.; Ain, A.; Ajith, P.; Allen, B.; Allocca, A.; Altin, P. A.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Araya, M. C.; Arceneaux, C. C.; Areeda, J. S.; Arnaud, N.; Arun, K. G.; Ascenzi, S.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Babak, S.; Bacon, P.; Bader, M. K. M.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bavigadda, V.; Bazzan, M.; Bejger, M.; Bell, A. S.; Berger, B. K.; Bergmann, G.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Birney, R.; Birnholtz, O.; Biscans, S.; Bisht, A.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blair, C. D.; Blair, D. G.; Blair, R. M.; Bloemen, S.; Bock, O.; Boer, M.; Bogaert, G.; Bogan, C.; Bohe, A.; Bond, C.; Bondu, F.; Bonnand, R.; Boom, B. A.; Bork, R.; Boschi, V.; Bose, S.; Bouffanais, Y.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Broida, J. E.; Brooks, A. F.; Brown, D. A.; Brown, D. D.; Brown, N. M.; Brunett, S.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cabero, M.; Cadonati, L.; Cagnoli, G.; Cahillane, C.; Calderón Bustillo, J.; Callister, T.; Calloni, E.; Camp, J. B.; Cannon, K. C.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Casanueva Diaz, C.; Casentini, J.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C. B.; Cerboni Baiardi, L.; Cerretani, G.; Cesarini, E.; Chamberlin, S. J.; Chan, M.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Cheeseboro, B. D.; Chen, H. Y.; Chen, Y.; Cheng, C.; Chincarini, A.; Chiummo, A.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, S.; Chung, S.; Ciani, G.; Clara, F.; Clark, J. A.; Cleva, F.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C. G.; Cominsky, L.; Constancio, M.; Conte, A.; Conti, L.; Cook, D.; Corbitt, T. R.; Cornish, N.; Corsi, A.; Cortese, S.; Costa, C. A.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Cowan, E. E.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Craig, K.; Creighton, J. D. E.; Cripe, J.; Crowder, S. G.; Cumming, A.; Cunningham, L.; Cuoco, E.; Dal Canton, T.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Darman, N. S.; Dasgupta, A.; Da Silva Costa, C. F.; Dattilo, V.; Dave, I.; Davier, M.; Davies, G. S.; Daw, E. J.; Day, R.; De, S.; DeBra, D.; Debreczeni, G.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dergachev, V.; De Rosa, R.; DeRosa, R. T.; DeSalvo, R.; Devine, R. C.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Girolamo, T.; Di Lieto, A.; Di Pace, S.; Di Palma, I.; Di Virgilio, A.; Dolique, V.; Donovan, F.; Dooley, K. L.; Doravari, S.; Douglas, R.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Ducrot, M.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J.; Eikenberry, S. S.; Engels, W.; Essick, R. C.; Etienne, Z.; Etzel, T.; Evans, M.; Evans, T. M.; Everett, R.; Factourovich, M.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, X.; Fang, Q.; Farinon, S.; Farr, B.; Farr, W. M.; Fauchon-Jones, E.; Favata, M.; Fays, M.; Fehrmann, H.; Fejer, M. M.; Fenyvesi, E.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Fiori, I.; Fiorucci, D.; Fisher, R. P.; Flaminio, R.; Fletcher, M.; Fournier, J.-D.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Frey, V.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H. A. G.; Gaebel, S.; Gair, J. R.; Gammaitoni, L.; Gaonkar, S. G.; Garufi, F.; Gaur, G.; Gehrels, N.; Gemme, G.; Geng, P.; Genin, E.; Gennai, A.; George, J.; Gergely, L.; Germain, V.; Ghosh, Abhirup; Ghosh, Archisman; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, K.; Glaefke, A.; Goetz, E.; Goetz, R.; Gondan, L.; González, G.; Gonzalez Castro, J. M.; Gopakumar, A.; Gordon, N. A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Gouaty, R.; Grado, A.; Graef, C.; Graff, P. B.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Green, A. C.; Groot, P.; Grote, H.; Grunewald, S.; Guidi, G. M.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Hacker, J. J.; Hall, B. R.; Hall, E. D.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Hartman, M. T.; Haster, C.-J.; Haughian, K.; Healy, J.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Henry, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hoak, D.; Hofman, D.; Holt, K.; Holz, D. E.; Hopkins, P.; Hough, J.; Houston, E. A.; Howell, E. J.; Hu, Y. M.; Huang, S.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh-Dinh, T.; Indik, N.; Ingram, D. R.; Inta, R.; Isa, H. N.; Isac, J.-M.; Isi, M.; Isogai, T.; Iyer, B. R.; Izumi, K.; Jacqmin, T.; Jang, H.; Jani, K.; Jaranowski, P.; Jawahar, S.; Jian, L.; Jiménez-Forteza, F.; Johnson, W. W.; Johnson-McDaniel, N. K.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; K, Haris; Kalaghatgi, C. V.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Kapadia, S. J.; Karki, S.; Karvinen, K. S.; Kasprzack, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kaur, T.; Kawabe, K.; Kéfélian, F.; Kehl, M. S.; Keitel, D.; Kelley, D. B.; Kells, W.; Kennedy, R.; Key, J. S.; Khalili, F. Y.; Khan, I.; Khan, S.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, Chi-Woong; Kim, Chunglee; Kim, J.; Kim, K.; Kim, N.; Kim, W.; Kim, Y.-M.; Kimbrell, S. J.; King, E. J.; King, P. J.; Kissel, J. S.; Klein, B.; Kleybolte, L.; Klimenko, S.; Koehlenbeck, S. M.; Koley, S.; Kondrashov, V.; Kontos, A.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Kringel, V.; Królak, A.; Krueger, C.; Kuehn, G.; Kumar, P.; Kumar, R.; Kuo, L.; Kutynia, A.; Lackey, B. D.; Landry, M.; Lange, J.; Lantz, B.; Lasky, P. D.; Laxen, M.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lebigot, E. O.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, K.; Lenon, A.; Leonardi, M.; Leong, J. R.; Leroy, N.; Letendre, N.; Levin, Y.; Lewis, J. B.; Li, T. G. F.; Libson, A.; Littenberg, T. B.; Lockerbie, N. A.; Lombardi, A. L.; London, L. T.; Lord, J. E.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lousto, C. O.; Lovelace, G.; Lück, H.; Lundgren, A. P.; Lynch, R.; Ma, Y.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magaña-Sandoval, F.; Magaña Zertuche, L.; Magee, R. M.; Majorana, E.; Maksimovic, I.; Malvezzi, V.; Man, N.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markosyan, A. S.; Maros, E.; Martelli, F.; Martellini, L.; Martin, I. W.; Martynov, D. V.; Marx, J. N.; Mason, K.; Masserot, A.; Massinger, T. J.; Masso-Reid, M.; Mastrogiovanni, S.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McGuire, S. C.; McIntyre, G.; McIver, J.; McManus, D. J.; McRae, T.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Meidam, J.; Melatos, A.; Mendell, G.; Mercer, R. A.; Merilh, E. L.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Metzdorff, R.; Meyers, P. M.; Mezzani, F.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, A. L.; Miller, A.; Miller, B. B.; Miller, J.; Millhouse, M.; Minenkov, Y.; Ming, J.; Mirshekari, S.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moggi, A.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, B. C.; Moore, C. J.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mossavi, K.; Mours, B.; Mow-Lowry, C. M.; Mueller, G.; Muir, A. W.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, S.; Mukund, N.; Mullavey, A.; Munch, J.; Murphy, D. J.; Murray, P. G.; Mytidis, A.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Nedkova, K.; Nelemans, G.; Nelson, T. J. N.; Neri, M.; Neunzert, A.; Newton, G.; Nguyen, T. T.; Nielsen, A. B.; Nissanke, S.; Nitz, A.; Nocera, F.; Nolting, D.; Normandin, M. E. N.; Nuttall, L. K.; Oberling, J.; Ochsner, E.; O'Dell, J.; Oelker, E.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Oliver, M.; Oppermann, P.; Oram, Richard J.; O'Reilly, B.; O'Shaughnessy, R.; Ottaway, D. J.; Overmier, H.; Owen, B. J.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, H.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Paoli, A.; Papa, M. A.; Paris, H. R.; Parker, W.; Pascucci, D.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patricelli, B.; Patrick, Z.; Pearlstone, B. L.; Pedraza, M.; Pedurand, R.; Pekowsky, L.; Pele, A.; Penn, S.; Perreca, A.; Perri, L. M.; Pfeiffer, H. P.; Phelps, M.; Piccinni, O. J.; Pichot, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poe, M.; Poggiani, R.; Popolizio, P.; Post, A.; Powell, J.; Prasad, J.; Predoi, V.; Prestegard, T.; Price, L. R.; Prijatelj, M.; Principe, M.; Privitera, S.; Prix, R.; Prodi, G. A.; Prokhorov, L.; Puncken, O.; Punturo, M.; Puppo, P.; Pürrer, M.; Qi, H.; Qin, J.; Qiu, S.; Quetschke, V.; Quintero, E. A.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Radkins, H.; Raffai, P.; Raja, S.; Rajan, C.; Rakhmanov, M.; Rapagnani, P.; Raymond, V.; Razzano, M.; Re, V.; Read, J.; Reed, C. M.; Regimbau, T.; Rei, L.; Reid, S.; Reitze, D. H.; Rew, H.; Reyes, S. D.; Ricci, F.; Riles, K.; Rizzo, M.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, R.; Romanov, G.; Romie, J. H.; Rosińska, D.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Ryan, K.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Sakellariadou, M.; Salconi, L.; Saleem, M.; Salemi, F.; Samajdar, A.; Sammut, L.; Sanchez, E. J.; Sandberg, V.; Sandeen, B.; Sanders, J. R.; Sassolas, B.; Sathyaprakash, B. S.; Saulson, P. R.; Sauter, O. E. S.; Savage, R. L.; Sawadsky, A.; Schale, P.; Schilling, R.; Schmidt, J.; Schmidt, P.; Schnabel, R.; Schofield, R. M. S.; Schönbeck, A.; Schreiber, E.; Schuette, D.; Schutz, B. F.; Scott, J.; Scott, S. M.; Sellers, D.; Sengupta, A. S.; Sentenac, D.; Sequino, V.; Sergeev, A.; Setyawati, Y.; Shaddock, D. A.; Shaffer, T.; Shahriar, M. S.; Shaltev, M.; Shapiro, B.; Shawhan, P.; Sheperd, A.; Shoemaker, D. H.; Shoemaker, D. M.; Siellez, K.; Siemens, X.; Sieniawska, M.; Sigg, D.; Silva, A. D.; Singer, A.; Singer, L. P.; Singh, A.; Singh, R.; Singhal, A.; Sintes, A. M.; Slagmolen, B. J. J.; Smith, J. R.; Smith, N. D.; Smith, R. J. E.; Son, E. J.; Sorazu, B.; Sorrentino, F.; Souradeep, T.; Srivastava, A. K.; Staley, A.; Steinke, M.; Steinlechner, J.; Steinlechner, S.; Steinmeyer, D.; Stephens, B. C.; Stevenson, S. P.; Stone, R.; Strain, K. A.; Straniero, N.; Stratta, G.; Strauss, N. A.; Strigin, S.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Sun, L.; Sunil, S.; Sutton, P. J.; Swinkels, B. L.; Szczepańczyk, M. J.; Tacca, M.; Talukder, D.; Tanner, D. B.; Tápai, M.; Tarabrin, S. P.; Taracchini, A.; Taylor, R.; Theeg, T.; Thirugnanasambandam, M. P.; Thomas, E. G.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thorne, K. S.; Thrane, E.; Tiwari, S.; Tiwari, V.; Tokmakov, K. V.; Toland, K.; Tomlinson, C.; Tonelli, M.; Tornasi, Z.; Torres, C. V.; Torrie, C. I.; Töyrä, D.; Travasso, F.; Traylor, G.; Trifirò, D.; Tringali, M. C.; Trozzo, L.; Tse, M.; Turconi, M.; Tuyenbayev, D.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Usman, S. A.; Vahlbruch, H.; Vajente, G.; Valdes, G.; Vallisneri, M.; van Bakel, N.; van Beuzekom, M.; van den Brand, J. F. J.; Van Den Broeck, C.; Vander-Hyde, D. C.; van der Schaaf, L.; van der Sluys, M. V.; van Heijningen, J. V.; Vano-Vinuales, A.; van Veggel, A. A.; Vardaro, M.; Vass, S.; Vasúth, M.; Vaulin, R.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Verkindt, D.; Vetrano, F.; Viceré, A.; Vinciguerra, S.; Vine, D. J.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Voss, D. V.; Vousden, W. D.; Vyatchanin, S. P.; Wade, A. R.; Wade, L. E.; Wade, M.; Walker, M.; Wallace, L.; Walsh, S.; Wang, G.; Wang, H.; Wang, M.; Wang, X.; Wang, Y.; Ward, R. L.; Warner, J.; Was, M.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Wen, L.; Weßels, P.; Westphal, T.; Wette, K.; Whelan, J. T.; Whiting, B. F.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Woehler, J.; Worden, J.; Wright, J. L.; Wu, D. S.; Wu, G.; Yablon, J.; Yam, W.; Yamamoto, H.; Yancey, C. C.; Yu, H.; Yvert, M.; ZadroŻny, A.; Zangrando, L.; Zanolin, M.; Zendri, J.-P.; Zevin, M.; Zhang, L.; Zhang, M.; Zhang, Y.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, X. J.; Zucker, M. E.; Zuraw, S. E.; Zweizig, J.; Boyle, M.; Brügmann, B.; Campanelli, M.; Chu, T.; Clark, M.; Haas, R.; Hemberger, D.; Hinder, I.; Kidder, L. E.; Kinsey, M.; Laguna, P.; Ossokine, S.; Pan, Y.; Röver, C.; Scheel, M.; Szilagyi, B.; Teukolsky, S.; Zlochower, Y.; LIGO Scientific Collaboration; Virgo Collaboration

2016-10-01

This paper presents updated estimates of source parameters for GW150914, a binary black-hole coalescence event detected by the Laser Interferometer Gravitational-wave Observatory (LIGO) in 2015 [Abbott et al. Phys. Rev. Lett. 116, 061102 (2016).]. Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016).] presented parameter estimation of the source using a 13-dimensional, phenomenological precessing-spin model (precessing IMRPhenom) and an 11-dimensional nonprecessing effective-one-body (EOB) model calibrated to numerical-relativity simulations, which forces spin alignment (nonprecessing EOBNR). Here, we present new results that include a 15-dimensional precessing-spin waveform model (precessing EOBNR) developed within the EOB formalism. We find good agreement with the parameters estimated previously [Abbott et al. Phys. Rev. Lett. 116, 241102 (2016).], and we quote updated component masses of 35-3+5 M⊙ and 3 0-4+3 M⊙ (where errors correspond to 90% symmetric credible intervals). We also present slightly tighter constraints on the dimensionless spin magnitudes of the two black holes, with a primary spin estimate <0.65 and a secondary spin estimate <0.75 at 90% probability. Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016).] estimated the systematic parameter-extraction errors due to waveform-model uncertainty by combining the posterior probability densities of precessing IMRPhenom and nonprecessing EOBNR. Here, we find that the two precessing-spin models are in closer agreement, suggesting that these systematic errors are smaller than previously quoted.

Improvements in GRACE Gravity Field Determination through Stochastic Observation Modeling

NASA Astrophysics Data System (ADS)

McCullough, C.; Bettadpur, S. V.

2016-12-01

Current unconstrained Release 05 GRACE gravity field solutions from the Center for Space Research (CSR RL05) assume random observation errors following an independent multivariate Gaussian distribution. This modeling of observations, a simplifying assumption, fails to account for long period, correlated errors arising from inadequacies in the background force models. Fully modeling the errors inherent in the observation equations, through the use of a full observation covariance (modeling colored noise), enables optimal combination of GPS and inter-satellite range-rate data and obviates the need for estimating kinematic empirical parameters during the solution process. Most importantly, fully modeling the observation errors drastically improves formal error estimates of the spherical harmonic coefficients, potentially enabling improved uncertainty quantification of scientific results derived from GRACE and optimizing combinations of GRACE with independent data sets and a priori constraints.

Void Growth and Coalescence Simulations

DTIC Science & Technology

2013-08-01

distortion and damage, minimum time step, and appropriate material model parameters. Further, a temporal and spatial convergence study was used to...estimate errors, thus, this study helps to provide guidelines for modeling of materials with voids. Finally, we use a Gurson model with Johnson-Cook...spatial convergence study was used to estimate errors, thus, this study helps to provide guidelines for modeling of materials with voids. Finally, we

Stratospheric Assimilation of Chemical Tracer Observations Using a Kalman Filter. Pt. 2; Chi-Square Validated Results and Analysis of Variance and Correlation Dynamics

NASA Technical Reports Server (NTRS)

Menard, Richard; Chang, Lang-Ping

1998-01-01

A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I (Menard et al. 1998) The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board of the Upper Atmosphere Research Satellite are described in this paper. A robust (chi)(sup 2) criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only three days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. We further found that the model error due to numerical discretization as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave-breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, we have conducted an analysis of the variance and correlation dynamics to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.

Tuning a climate model using nudging to reanalysis.

NASA Astrophysics Data System (ADS)

Cheedela, S. K.; Mapes, B. E.

2014-12-01

Tuning a atmospheric general circulation model involves a daunting task of adjusting non-observable parameters to adjust the mean climate. These parameters arise from necessity to describe unresolved flow through parametrizations. Tuning a climate model is often done with certain set of priorities, such as global mean temperature, net top of the atmosphere radiation. These priorities are hard enough to reach let alone reducing systematic biases in the models. The goal of currently study is to explore alternate ways to tune a climate model to reduce some systematic biases that can be used in synergy with existing efforts. Nudging a climate model to a known state is a poor man's inverse of tuning process described above. Our approach involves nudging the atmospheric model to state of art reanalysis fields thereby providing a balanced state with respect to the global mean temperature and winds. The tendencies derived from nudging are negative of errors from physical parametrizations as the errors from dynamical core would be small. Patterns of nudging are compared to the patterns of different physical parametrizations to decipher the cause for certain biases in relation to tuning parameters. This approach might also help in understanding certain compensating errors that arise from tuning process. ECHAM6 is a comprehensive general model, also used in recent Coupled Model Intercomparision Project(CMIP5). The approach used to tune it and effect of certain parameters that effect its mean climate are reported clearly, hence it serves as a benchmark for our approach. Our planned experiments include nudging ECHAM6 atmospheric model to European Center Reanalysis (ERA-Interim) and reanalysis from National Center for Environmental Prediction (NCEP) and decipher choice of certain parameters that lead to systematic biases in its simulations. Of particular interest are reducing long standing biases related to simulation of Asian summer monsoon.

External Evaluation of Two Fluconazole Infant Population Pharmacokinetic Models

PubMed Central

Hwang, Michael F.; Beechinor, Ryan J.; Wade, Kelly C.; Benjamin, Daniel K.; Smith, P. Brian; Hornik, Christoph P.; Capparelli, Edmund V.; Duara, Shahnaz; Kennedy, Kathleen A.; Cohen-Wolkowiez, Michael

2017-01-01

ABSTRACT Fluconazole is an antifungal agent used for the treatment of invasive candidiasis, a leading cause of morbidity and mortality in premature infants. Population pharmacokinetic (PK) models of fluconazole in infants have been previously published by Wade et al. (Antimicrob Agents Chemother 52:4043–4049, 2008, https://doi.org/10.1128/AAC.00569-08) and Momper et al. (Antimicrob Agents Chemother 60:5539–5545, 2016, https://doi.org/10.1128/AAC.00963-16). Here we report the results of the first external evaluation of the predictive performance of both models. We used patient-level data from both studies to externally evaluate both PK models. The predictive performance of each model was evaluated using the model prediction error (PE), mean prediction error (MPE), mean absolute prediction error (MAPE), prediction-corrected visual predictive check (pcVPC), and normalized prediction distribution errors (NPDE). The values of the parameters of each model were reestimated using both the external and merged data sets. When evaluated with the external data set, the model proposed by Wade et al. showed lower median PE, MPE, and MAPE (0.429 μg/ml, 41.9%, and 57.6%, respectively) than the model proposed by Momper et al. (2.45 μg/ml, 188%, and 195%, respectively). The values of the majority of reestimated parameters were within 20% of their respective original parameter values for all model evaluations. Our analysis determined that though both models are robust, the model proposed by Wade et al. had greater accuracy and precision than the model proposed by Momper et al., likely because it was derived from a patient population with a wider age range. This study highlights the importance of the external evaluation of infant population PK models. PMID:28893774

Multiplicity Control in Structural Equation Modeling: Incorporating Parameter Dependencies

ERIC Educational Resources Information Center

Smith, Carrie E.; Cribbie, Robert A.

2013-01-01

When structural equation modeling (SEM) analyses are conducted, significance tests for all important model relationships (parameters including factor loadings, covariances, etc.) are typically conducted at a specified nominal Type I error rate ([alpha]). Despite the fact that many significance tests are often conducted in SEM, rarely is…

Validation of Real-time Modeling of Coronal Mass Ejections Using the WSA-ENLIL+Cone Heliospheric Model

NASA Astrophysics Data System (ADS)

Romano, M.; Mays, M. L.; Taktakishvili, A.; MacNeice, P. J.; Zheng, Y.; Pulkkinen, A. A.; Kuznetsova, M. M.; Odstrcil, D.

2013-12-01

Modeling coronal mass ejections (CMEs) is of great interest to the space weather research and forecasting communities. We present recent validation work of real-time CME arrival time predictions at different satellites using the WSA-ENLIL+Cone three-dimensional MHD heliospheric model available at the Community Coordinated Modeling Center (CCMC) and performed by the Space Weather Research Center (SWRC). SWRC is an in-house research-based operations team at the CCMC which provides interplanetary space weather forecasting for NASA's robotic missions and performs real-time model validation. The quality of model operation is evaluated by comparing its output to a measurable parameter of interest such as the CME arrival time and geomagnetic storm strength. The Kp index is calculated from the relation given in Newell et al. (2007), using solar wind parameters predicted by the WSA-ENLIL+Cone model at Earth. The CME arrival time error is defined as the difference between the predicted arrival time and the observed in-situ CME shock arrival time at the ACE, STEREO A, or STEREO B spacecraft. This study includes all real-time WSA-ENLIL+Cone model simulations performed between June 2011-2013 (over 400 runs) at the CCMC/SWRC. We report hit, miss, false alarm, and correct rejection statistics for all three spacecraft. For hits we show the average absolute CME arrival time error, and the dependence of this error on CME input parameters such as speed, width, and direction. We also present the predicted geomagnetic storm strength (using the Kp index) error for Earth-directed CMEs.

Volumetric error modeling, identification and compensation based on screw theory for a large multi-axis propeller-measuring machine

NASA Astrophysics Data System (ADS)

Zhong, Xuemin; Liu, Hongqi; Mao, Xinyong; Li, Bin; He, Songping; Peng, Fangyu

2018-05-01

Large multi-axis propeller-measuring machines have two types of geometric error, position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs), which both have significant effects on the volumetric error of the measuring tool relative to the worktable. This paper focuses on modeling, identifying and compensating for the volumetric error of the measuring machine. A volumetric error model in the base coordinate system is established based on screw theory considering all the geometric errors. In order to fully identify all the geometric error parameters, a new method for systematic measurement and identification is proposed. All the PIGEs of adjacent axes and the six PDGEs of the linear axes are identified with a laser tracker using the proposed model. Finally, a volumetric error compensation strategy is presented and an inverse kinematic solution for compensation is proposed. The final measuring and compensation experiments have further verified the efficiency and effectiveness of the measuring and identification method, indicating that the method can be used in volumetric error compensation for large machine tools.

Improving Empirical Magnetic Field Models by Fitting to In Situ Data Using an Optimized Parameter Approach

DOE PAGES

Brito, Thiago V.; Morley, Steven K.

2017-10-25

A method for comparing and optimizing the accuracy of empirical magnetic field models using in situ magnetic field measurements is presented in this paper. The optimization method minimizes a cost function—τ—that explicitly includes both a magnitude and an angular term. A time span of 21 days, including periods of mild and intense geomagnetic activity, was used for this analysis. A comparison between five magnetic field models (T96, T01S, T02, TS04, and TS07) widely used by the community demonstrated that the T02 model was, on average, the most accurate when driven by the standard model input parameters. The optimization procedure, performedmore » in all models except TS07, generally improved the results when compared to unoptimized versions of the models. Additionally, using more satellites in the optimization procedure produces more accurate results. This procedure reduces the number of large errors in the model, that is, it reduces the number of outliers in the error distribution. The TS04 model shows the most accurate results after the optimization in terms of both the magnitude and direction, when using at least six satellites in the fitting. It gave a smaller error than its unoptimized counterpart 57.3% of the time and outperformed the best unoptimized model (T02) 56.2% of the time. Its median percentage error in |B| was reduced from 4.54% to 3.84%. Finally, the difference among the models analyzed, when compared in terms of the median of the error distributions, is not very large. However, the unoptimized models can have very large errors, which are much reduced after the optimization.« less

Improving Empirical Magnetic Field Models by Fitting to In Situ Data Using an Optimized Parameter Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brito, Thiago V.; Morley, Steven K.

A method for comparing and optimizing the accuracy of empirical magnetic field models using in situ magnetic field measurements is presented in this paper. The optimization method minimizes a cost function—τ—that explicitly includes both a magnitude and an angular term. A time span of 21 days, including periods of mild and intense geomagnetic activity, was used for this analysis. A comparison between five magnetic field models (T96, T01S, T02, TS04, and TS07) widely used by the community demonstrated that the T02 model was, on average, the most accurate when driven by the standard model input parameters. The optimization procedure, performedmore » in all models except TS07, generally improved the results when compared to unoptimized versions of the models. Additionally, using more satellites in the optimization procedure produces more accurate results. This procedure reduces the number of large errors in the model, that is, it reduces the number of outliers in the error distribution. The TS04 model shows the most accurate results after the optimization in terms of both the magnitude and direction, when using at least six satellites in the fitting. It gave a smaller error than its unoptimized counterpart 57.3% of the time and outperformed the best unoptimized model (T02) 56.2% of the time. Its median percentage error in |B| was reduced from 4.54% to 3.84%. Finally, the difference among the models analyzed, when compared in terms of the median of the error distributions, is not very large. However, the unoptimized models can have very large errors, which are much reduced after the optimization.« less

The effect of the dynamic wet troposphere on radio interferometric measurements

NASA Technical Reports Server (NTRS)

Treuhaft, R. N.; Lanyi, G. E.

1987-01-01

A statistical model of water vapor fluctuations is used to describe the effect of the dynamic wet troposphere on radio interferometric measurements. It is assumed that the spatial structure of refractivity is approximated by Kolmogorov turbulence theory, and that the temporal fluctuations are caused by spatial patterns moved over a site by the wind, and these assumptions are examined for the VLBI delay and delay rate observables. The results suggest that the delay rate measurement error is usually dominated by water vapor fluctuations, and water vapor induced VLBI parameter errors and correlations are determined as a function of the delay observable errors. A method is proposed for including the water vapor fluctuations in the parameter estimation method to obtain improved parameter estimates and parameter covariances.

Parameter estimation of kinetic models from metabolic profiles: two-phase dynamic decoupling method.

PubMed

Jia, Gengjie; Stephanopoulos, Gregory N; Gunawan, Rudiyanto

2011-07-15

Time-series measurements of metabolite concentration have become increasingly more common, providing data for building kinetic models of metabolic networks using ordinary differential equations (ODEs). In practice, however, such time-course data are usually incomplete and noisy, and the estimation of kinetic parameters from these data is challenging. Practical limitations due to data and computational aspects, such as solving stiff ODEs and finding global optimal solution to the estimation problem, give motivations to develop a new estimation procedure that can circumvent some of these constraints. In this work, an incremental and iterative parameter estimation method is proposed that combines and iterates between two estimation phases. One phase involves a decoupling method, in which a subset of model parameters that are associated with measured metabolites, are estimated using the minimization of slope errors. Another phase follows, in which the ODE model is solved one equation at a time and the remaining model parameters are obtained by minimizing concentration errors. The performance of this two-phase method was tested on a generic branched metabolic pathway and the glycolytic pathway of Lactococcus lactis. The results showed that the method is efficient in getting accurate parameter estimates, even when some information is missing.

A novel auto-tuning PID control mechanism for nonlinear systems.

PubMed

Cetin, Meric; Iplikci, Serdar

2015-09-01

In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

The use of error-category mapping in pharmacokinetic model analysis of dynamic contrast-enhanced MRI data.

PubMed

Gill, Andrew B; Anandappa, Gayathri; Patterson, Andrew J; Priest, Andrew N; Graves, Martin J; Janowitz, Tobias; Jodrell, Duncan I; Eisen, Tim; Lomas, David J

2015-02-01

This study introduces the use of 'error-category mapping' in the interpretation of pharmacokinetic (PK) model parameter results derived from dynamic contrast-enhanced (DCE-) MRI data. Eleven patients with metastatic renal cell carcinoma were enrolled in a multiparametric study of the treatment effects of bevacizumab. For the purposes of the present analysis, DCE-MRI data from two identical pre-treatment examinations were analysed by application of the extended Tofts model (eTM), using in turn a model arterial input function (AIF), an individually-measured AIF and a sample-average AIF. PK model parameter maps were calculated. Errors in the signal-to-gadolinium concentration ([Gd]) conversion process and the model-fitting process itself were assigned to category codes on a voxel-by-voxel basis, thereby forming a colour-coded 'error-category map' for each imaged slice. These maps were found to be repeatable between patient visits and showed that the eTM converged adequately in the majority of voxels in all the tumours studied. However, the maps also clearly indicated sub-regions of low Gd uptake and of non-convergence of the model in nearly all tumours. The non-physical condition ve ≥ 1 was the most frequently indicated error category and appeared sensitive to the form of AIF used. This simple method for visualisation of errors in DCE-MRI could be used as a routine quality-control technique and also has the potential to reveal otherwise hidden patterns of failure in PK model applications. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

The Effects of Measurement Error on Statistical Models for Analyzing Change. Final Report.

ERIC Educational Resources Information Center

Dunivant, Noel

The results of six major projects are discussed including a comprehensive mathematical and statistical analysis of the problems caused by errors of measurement in linear models for assessing change. In a general matrix representation of the problem, several new analytic results are proved concerning the parameters which affect bias in…

Effects of OCR Errors on Ranking and Feedback Using the Vector Space Model.

ERIC Educational Resources Information Center

Taghva, Kazem; And Others

1996-01-01

Reports on the performance of the vector space model in the presence of OCR (optical character recognition) errors in information retrieval. Highlights include precision and recall, a full-text test collection, smart vector representation, impact of weighting parameters, ranking variability, and the effect of relevance feedback. (Author/LRW)

Taking error into account when fitting models using Approximate Bayesian Computation.

PubMed

van der Vaart, Elske; Prangle, Dennis; Sibly, Richard M

2018-03-01

Stochastic computer simulations are often the only practical way of answering questions relating to ecological management. However, due to their complexity, such models are difficult to calibrate and evaluate. Approximate Bayesian Computation (ABC) offers an increasingly popular approach to this problem, widely applied across a variety of fields. However, ensuring the accuracy of ABC's estimates has been difficult. Here, we obtain more accurate estimates by incorporating estimation of error into the ABC protocol. We show how this can be done where the data consist of repeated measures of the same quantity and errors may be assumed to be normally distributed and independent. We then derive the correct acceptance probabilities for a probabilistic ABC algorithm, and update the coverage test with which accuracy is assessed. We apply this method, which we call error-calibrated ABC, to a toy example and a realistic 14-parameter simulation model of earthworms that is used in environmental risk assessment. A comparison with exact methods and the diagnostic coverage test show that our approach improves estimation of parameter values and their credible intervals for both models. © 2017 by the Ecological Society of America.

Ensemble-based simultaneous state and parameter estimation for treatment of mesoscale model error: A real-data study

NASA Astrophysics Data System (ADS)

Hu, Xiao-Ming; Zhang, Fuqing; Nielsen-Gammon, John W.

2010-04-01

This study explores the treatment of model error and uncertainties through simultaneous state and parameter estimation (SSPE) with an ensemble Kalman filter (EnKF) in the simulation of a 2006 air pollution event over the greater Houston area during the Second Texas Air Quality Study (TexAQS-II). Two parameters in the atmospheric boundary layer parameterization associated with large model sensitivities are combined with standard prognostic variables in an augmented state vector to be continuously updated through assimilation of wind profiler observations. It is found that forecasts of the atmosphere with EnKF/SSPE are markedly improved over experiments with no state and/or parameter estimation. More specifically, the EnKF/SSPE is shown to help alleviate a near-surface cold bias and to alter the momentum mixing in the boundary layer to produce more realistic wind profiles.

Convergence in parameters and predictions using computational experimental design.

PubMed

Hagen, David R; White, Jacob K; Tidor, Bruce

2013-08-06

Typically, biological models fitted to experimental data suffer from significant parameter uncertainty, which can lead to inaccurate or uncertain predictions. One school of thought holds that accurate estimation of the true parameters of a biological system is inherently problematic. Recent work, however, suggests that optimal experimental design techniques can select sets of experiments whose members probe complementary aspects of a biochemical network that together can account for its full behaviour. Here, we implemented an experimental design approach for selecting sets of experiments that constrain parameter uncertainty. We demonstrated with a model of the epidermal growth factor-nerve growth factor pathway that, after synthetically performing a handful of optimal experiments, the uncertainty in all 48 parameters converged below 10 per cent. Furthermore, the fitted parameters converged to their true values with a small error consistent with the residual uncertainty. When untested experimental conditions were simulated with the fitted models, the predicted species concentrations converged to their true values with errors that were consistent with the residual uncertainty. This paper suggests that accurate parameter estimation is achievable with complementary experiments specifically designed for the task, and that the resulting parametrized models are capable of accurate predictions.

Fast maximum likelihood estimation using continuous-time neural point process models.

PubMed

Lepage, Kyle Q; MacDonald, Christopher J

2015-06-01

A recent report estimates that the number of simultaneously recorded neurons is growing exponentially. A commonly employed statistical paradigm using discrete-time point process models of neural activity involves the computation of a maximum-likelihood estimate. The time to computate this estimate, per neuron, is proportional to the number of bins in a finely spaced discretization of time. By using continuous-time models of neural activity and the optimally efficient Gaussian quadrature, memory requirements and computation times are dramatically decreased in the commonly encountered situation where the number of parameters p is much less than the number of time-bins n. In this regime, with q equal to the quadrature order, memory requirements are decreased from O(np) to O(qp), and the number of floating-point operations are decreased from O(np(2)) to O(qp(2)). Accuracy of the proposed estimates is assessed based upon physiological consideration, error bounds, and mathematical results describing the relation between numerical integration error and numerical error affecting both parameter estimates and the observed Fisher information. A check is provided which is used to adapt the order of numerical integration. The procedure is verified in simulation and for hippocampal recordings. It is found that in 95 % of hippocampal recordings a q of 60 yields numerical error negligible with respect to parameter estimate standard error. Statistical inference using the proposed methodology is a fast and convenient alternative to statistical inference performed using a discrete-time point process model of neural activity. It enables the employment of the statistical methodology available with discrete-time inference, but is faster, uses less memory, and avoids any error due to discretization.

Closed-loop stability of linear quadratic optimal systems in the presence of modeling errors

NASA Technical Reports Server (NTRS)

Toda, M.; Patel, R.; Sridhar, B.

1976-01-01

The well-known stabilizing property of linear quadratic state feedback design is utilized to evaluate the robustness of a linear quadratic feedback design in the presence of modeling errors. Two general conditions are obtained for allowable modeling errors such that the resulting closed-loop system remains stable. One of these conditions is applied to obtain two more particular conditions which are readily applicable to practical situations where a designer has information on the bounds of modeling errors. Relations are established between the allowable parameter uncertainty and the weighting matrices of the quadratic performance index, thereby enabling the designer to select appropriate weighting matrices to attain a robust feedback design.

Three-parameter error analysis method based on rotating coordinates in rotating birefringent polarizer system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cao, Junjie; Jia, Hongzhi, E-mail: hzjia@usst.edu.cn

2015-11-15

We propose error analysis using a rotating coordinate system with three parameters of linearly polarized light—incidence angle, azimuth angle on the front surface, and angle between the incidence and vibration planes—and demonstrate the method on a rotating birefringent prism system. The transmittance and angles are calculated plane-by-plane using a birefringence ellipsoid model and the final transmitted intensity equation is deduced. The effects of oblique incidence, light interference, beam convergence, and misalignment of the rotation and prism axes are discussed. We simulate the entire error model using MATLAB and conduct experiments based on a built polarimeter. The simulation and experimental resultsmore » are consistent and demonstrate the rationality and validity of this method.« less

Quantifying Adventitious Error in a Covariance Structure as a Random Effect

PubMed Central

Wu, Hao; Browne, Michael W.

2017-01-01

We present an approach to quantifying errors in covariance structures in which adventitious error, identified as the process underlying the discrepancy between the population and the structured model, is explicitly modeled as a random effect with a distribution, and the dispersion parameter of this distribution to be estimated gives a measure of misspecification. Analytical properties of the resultant procedure are investigated and the measure of misspecification is found to be related to the RMSEA. An algorithm is developed for numerical implementation of the procedure. The consistency and asymptotic sampling distributions of the estimators are established under a new asymptotic paradigm and an assumption weaker than the standard Pitman drift assumption. Simulations validate the asymptotic sampling distributions and demonstrate the importance of accounting for the variations in the parameter estimates due to adventitious error. Two examples are also given as illustrations. PMID:25813463

Precision modelling of M dwarf stars: the magnetic components of CM Draconis

NASA Astrophysics Data System (ADS)

MacDonald, J.; Mullan, D. J.

2012-04-01

The eclipsing binary CM Draconis (CM Dra) contains two nearly identical red dwarfs of spectral class dM4.5. The masses and radii of the two components have been reported with unprecedentedly small statistical errors: for M, these errors are 1 part in 260, while for R, the errors reported by Morales et al. are 1 part in 130. When compared with standard stellar models with appropriate mass and age (≈4 Gyr), the empirical results indicate that both components are discrepant from the models in the following sense: the observed stars are larger in R ('bloated'), by several standard deviations, than the models predict. The observed luminosities are also lower than the models predict. Here, we attempt at first to model the two components of CM Dra in the context of standard (non-magnetic) stellar models using a systematic array of different assumptions about helium abundances (Y), heavy element abundances (Z), opacities and mixing length parameter (α). We find no 4-Gyr-old models with plausible values of these four parameters that fit the observed L and R within the reported statistical error bars. However, CM Dra is known to contain magnetic fields, as evidenced by the occurrence of star-spots and flares. Here we ask: can inclusion of magnetic effects into stellar evolution models lead to fits of L and R within the error bars? Morales et al. have reported that the presence of polar spots results in a systematic overestimate of R by a few per cent when eclipses are interpreted with a standard code. In a star where spots cover a fraction f of the surface area, we find that the revised R and L for CM Dra A can be fitted within the error bars by varying the parameter α. The latter is often assumed to be reduced by the presence of magnetic fields, although the reduction in α as a function of B is difficult to quantify. An alternative magnetic effect, namely inhibition of the onset of convection, can be readily quantified in terms of a magnetic parameter δ≈B2/4πγpgas (where B is the strength of the local vertical magnetic field). In the context of δ models in which B is not allowed to exceed a 'ceiling' of 106 G, we find that the revised R and L can also be fitted, within the error bars, in a finite region of the f-δ plane. The permitted values of δ near the surface leads us to estimate that the vertical field strength on the surface of CM Dra A is about 500 G, in good agreement with independent observational evidence for similar low-mass stars. Recent results for another binary with parameters close to those of CM Dra suggest that metallicity differences cannot be the dominant explanation for the bloating of the two components of CM Dra.

Inverse problem of HIV cell dynamics using Genetic Algorithms

NASA Astrophysics Data System (ADS)

González, J. A.; Guzmán, F. S.

2017-01-01

In order to describe the cell dynamics of T-cells in a patient infected with HIV, we use a flavour of Perelson's model. This is a non-linear system of Ordinary Differential Equations that describes the evolution of healthy, latently infected, infected T-cell concentrations and the free viral cells. Different parameters in the equations give different dynamics. Considering the concentration of these types of cells is known for a particular patient, the inverse problem consists in estimating the parameters in the model. We solve this inverse problem using a Genetic Algorithm (GA) that minimizes the error between the solutions of the model and the data from the patient. These errors depend on the parameters of the GA, like mutation rate and population, although a detailed analysis of this dependence will be described elsewhere.

Development of advanced techniques for rotorcraft state estimation and parameter identification

NASA Technical Reports Server (NTRS)

Hall, W. E., Jr.; Bohn, J. G.; Vincent, J. H.

1980-01-01

An integrated methodology for rotorcraft system identification consists of rotorcraft mathematical modeling, three distinct data processing steps, and a technique for designing inputs to improve the identifiability of the data. These elements are as follows: (1) a Kalman filter smoother algorithm which estimates states and sensor errors from error corrupted data. Gust time histories and statistics may also be estimated; (2) a model structure estimation algorithm for isolating a model which adequately explains the data; (3) a maximum likelihood algorithm for estimating the parameters and estimates for the variance of these estimates; and (4) an input design algorithm, based on a maximum likelihood approach, which provides inputs to improve the accuracy of parameter estimates. Each step is discussed with examples to both flight and simulated data cases.

Bayesian parameter estimation of a k-ε model for accurate jet-in-crossflow simulations

DOE PAGES

Ray, Jaideep; Lefantzi, Sophia; Arunajatesan, Srinivasan; ...

2016-05-31

Reynolds-averaged Navier–Stokes models are not very accurate for high-Reynolds-number compressible jet-in-crossflow interactions. The inaccuracy arises from the use of inappropriate model parameters and model-form errors in the Reynolds-averaged Navier–Stokes model. In this study, the hypothesis is pursued that Reynolds-averaged Navier–Stokes predictions can be significantly improved by using parameters inferred from experimental measurements of a supersonic jet interacting with a transonic crossflow.

Incorporation of prior information on parameters into nonlinear regression groundwater flow models: 2. Applications

USGS Publications Warehouse

Cooley, Richard L.

1983-01-01

This paper investigates factors influencing the degree of improvement in estimates of parameters of a nonlinear regression groundwater flow model by incorporating prior information of unknown reliability. Consideration of expected behavior of the regression solutions and results of a hypothetical modeling problem lead to several general conclusions. First, if the parameters are properly scaled, linearized expressions for the mean square error (MSE) in parameter estimates of a nonlinear model will often behave very nearly as if the model were linear. Second, by using prior information, the MSE in properly scaled parameters can be reduced greatly over the MSE of ordinary least squares estimates of parameters. Third, plots of estimated MSE and the estimated standard deviation of MSE versus an auxiliary parameter (the ridge parameter) specifying the degree of influence of the prior information on regression results can help determine the potential for improvement of parameter estimates. Fourth, proposed criteria can be used to make appropriate choices for the ridge parameter and another parameter expressing degree of overall bias in the prior information. Results of a case study of Truckee Meadows, Reno-Sparks area, Washoe County, Nevada, conform closely to the results of the hypothetical problem. In the Truckee Meadows case, incorporation of prior information did not greatly change the parameter estimates from those obtained by ordinary least squares. However, the analysis showed that both sets of estimates are more reliable than suggested by the standard errors from ordinary least squares.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaczmarski, Krzysztof; Guiochon, Georges A

The adsorption isotherms of selected compounds are our main source of information on the mechanisms of adsorption processes. Thus, the selection of the methods used to determine adsorption isotherm data and to evaluate the errors made is critical. Three chromatographic methods were evaluated, frontal analysis (FA), frontal analysis by characteristic point (FACP), and the pulse or perturbation method (PM), and their accuracies were compared. Using the equilibrium-dispersive (ED) model of chromatography, breakthrough curves of single components were generated corresponding to three different adsorption isotherm models: the Langmuir, the bi-Langmuir, and the Moreau isotherms. For each breakthrough curve, the best conventionalmore » procedures of each method (FA, FACP, PM) were used to calculate the corresponding data point, using typical values of the parameters of each isotherm model, for four different values of the column efficiency (N = 500, 1000, 2000, and 10,000). Then, the data points were fitted to each isotherm model and the corresponding isotherm parameters were compared to those of the initial isotherm model. When isotherm data are derived with a chromatographic method, they may suffer from two types of errors: (1) the errors made in deriving the experimental data points from the chromatographic records; (2) the errors made in selecting an incorrect isotherm model and fitting to it the experimental data. Both errors decrease significantly with increasing column efficiency with FA and FACP, but not with PM.« less

Mathematical models and photogrammetric exploitation of image sensing

NASA Astrophysics Data System (ADS)

Puatanachokchai, Chokchai

Mathematical models of image sensing are generally categorized into physical/geometrical sensor models and replacement sensor models. While the former is determined from image sensing geometry, the latter is based on knowledge of the physical/geometric sensor models and on using such models for its implementation. The main thrust of this research is in replacement sensor models which have three important characteristics: (1) Highly accurate ground-to-image functions; (2) Rigorous error propagation that is essentially of the same accuracy as the physical model; and, (3) Adjustability, or the ability to upgrade the replacement sensor model parameters when additional control information becomes available after the replacement sensor model has replaced the physical model. In this research, such replacement sensor models are considered as True Replacement Models or TRMs. TRMs provide a significant advantage of universality, particularly for image exploitation functions. There have been several writings about replacement sensor models, and except for the so called RSM (Replacement Sensor Model as a product described in the Manual of Photogrammetry), almost all of them pay very little or no attention to errors and their propagation. This is because, it is suspected, the few physical sensor parameters are usually replaced by many more parameters, thus presenting a potential error estimation difficulty. The third characteristic, adjustability, is perhaps the most demanding. It provides an equivalent flexibility to that of triangulation using the physical model. Primary contributions of this thesis include not only "the eigen-approach", a novel means of replacing the original sensor parameter covariance matrices at the time of estimating the TRM, but also the implementation of the hybrid approach that combines the eigen-approach with the added parameters approach used in the RSM. Using either the eigen-approach or the hybrid approach, rigorous error propagation can be performed during image exploitation. Further, adjustability can be performed when additional control information becomes available after the TRM has been implemented. The TRM is shown to apply to imagery from sensors having different geometries, including an aerial frame camera, a spaceborne linear array sensor, an airborne pushbroom sensor, and an airborne whiskbroom sensor. TRM results show essentially negligible differences as compared to those from rigorous physical sensor models, both for geopositioning from single and overlapping images. Simulated as well as real image data are used to address all three characteristics of the TRM.

Research on On-Line Modeling of Fed-Batch Fermentation Process Based on v-SVR

NASA Astrophysics Data System (ADS)

Ma, Yongjun

The fermentation process is very complex and non-linear, many parameters are not easy to measure directly on line, soft sensor modeling is a good solution. This paper introduces v-support vector regression (v-SVR) for soft sensor modeling of fed-batch fermentation process. v-SVR is a novel type of learning machine. It can control the accuracy of fitness and prediction error by adjusting the parameter v. An on-line training algorithm is discussed in detail to reduce the training complexity of v-SVR. The experimental results show that v-SVR has low error rate and better generalization with appropriate v.

Using state-space models to predict the abundance of juvenile and adult sea lice on Atlantic salmon.

PubMed

Elghafghuf, Adel; Vanderstichel, Raphael; St-Hilaire, Sophie; Stryhn, Henrik

2018-04-11

Sea lice are marine parasites affecting salmon farms, and are considered one of the most costly pests of the salmon aquaculture industry. Infestations of sea lice on farms significantly increase opportunities for the parasite to spread in the surrounding ecosystem, making control of this pest a challenging issue for salmon producers. The complexity of controlling sea lice on salmon farms requires frequent monitoring of the abundance of different sea lice stages over time. Industry-based data sets of counts of lice are amenable to multivariate time-series data analyses. In this study, two sets of multivariate autoregressive state-space models were applied to Chilean sea lice data from six Atlantic salmon production cycles on five isolated farms (at least 20 km seaway distance away from other known active farms), to evaluate the utility of these models for predicting sea lice abundance over time on farms. The models were constructed with different parameter configurations, and the analysis demonstrated large heterogeneity between production cycles for the autoregressive parameter, the effects of chemotherapeutant bath treatments, and the process-error variance. A model allowing for different parameters across production cycles had the best fit and the smallest overall prediction errors. However, pooling information across cycles for the drift and observation error parameters did not substantially affect model performance, thus reducing the number of necessary parameters in the model. Bath treatments had strong but variable effects for reducing sea lice burdens, and these effects were stronger for adult lice than juvenile lice. Our multivariate state-space models were able to handle different sea lice stages and provide predictions for sea lice abundance with reasonable accuracy up to five weeks out. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.

Mammalian cell culture process for monoclonal antibody production: nonlinear modelling and parameter estimation.

PubMed

Selişteanu, Dan; Șendrescu, Dorin; Georgeanu, Vlad; Roman, Monica

2015-01-01

Monoclonal antibodies (mAbs) are at present one of the fastest growing products of pharmaceutical industry, with widespread applications in biochemistry, biology, and medicine. The operation of mAbs production processes is predominantly based on empirical knowledge, the improvements being achieved by using trial-and-error experiments and precedent practices. The nonlinearity of these processes and the absence of suitable instrumentation require an enhanced modelling effort and modern kinetic parameter estimation strategies. The present work is dedicated to nonlinear dynamic modelling and parameter estimation for a mammalian cell culture process used for mAb production. By using a dynamical model of such kind of processes, an optimization-based technique for estimation of kinetic parameters in the model of mammalian cell culture process is developed. The estimation is achieved as a result of minimizing an error function by a particle swarm optimization (PSO) algorithm. The proposed estimation approach is analyzed in this work by using a particular model of mammalian cell culture, as a case study, but is generic for this class of bioprocesses. The presented case study shows that the proposed parameter estimation technique provides a more accurate simulation of the experimentally observed process behaviour than reported in previous studies.

Mammalian Cell Culture Process for Monoclonal Antibody Production: Nonlinear Modelling and Parameter Estimation

PubMed Central

Selişteanu, Dan; Șendrescu, Dorin; Georgeanu, Vlad

2015-01-01

Monoclonal antibodies (mAbs) are at present one of the fastest growing products of pharmaceutical industry, with widespread applications in biochemistry, biology, and medicine. The operation of mAbs production processes is predominantly based on empirical knowledge, the improvements being achieved by using trial-and-error experiments and precedent practices. The nonlinearity of these processes and the absence of suitable instrumentation require an enhanced modelling effort and modern kinetic parameter estimation strategies. The present work is dedicated to nonlinear dynamic modelling and parameter estimation for a mammalian cell culture process used for mAb production. By using a dynamical model of such kind of processes, an optimization-based technique for estimation of kinetic parameters in the model of mammalian cell culture process is developed. The estimation is achieved as a result of minimizing an error function by a particle swarm optimization (PSO) algorithm. The proposed estimation approach is analyzed in this work by using a particular model of mammalian cell culture, as a case study, but is generic for this class of bioprocesses. The presented case study shows that the proposed parameter estimation technique provides a more accurate simulation of the experimentally observed process behaviour than reported in previous studies. PMID:25685797

SEPARABLE FACTOR ANALYSIS WITH APPLICATIONS TO MORTALITY DATA

PubMed Central

Fosdick, Bailey K.; Hoff, Peter D.

2014-01-01

Human mortality data sets can be expressed as multiway data arrays, the dimensions of which correspond to categories by which mortality rates are reported, such as age, sex, country and year. Regression models for such data typically assume an independent error distribution or an error model that allows for dependence along at most one or two dimensions of the data array. However, failing to account for other dependencies can lead to inefficient estimates of regression parameters, inaccurate standard errors and poor predictions. An alternative to assuming independent errors is to allow for dependence along each dimension of the array using a separable covariance model. However, the number of parameters in this model increases rapidly with the dimensions of the array and, for many arrays, maximum likelihood estimates of the covariance parameters do not exist. In this paper, we propose a submodel of the separable covariance model that estimates the covariance matrix for each dimension as having factor analytic structure. This model can be viewed as an extension of factor analysis to array-valued data, as it uses a factor model to estimate the covariance along each dimension of the array. We discuss properties of this model as they relate to ordinary factor analysis, describe maximum likelihood and Bayesian estimation methods, and provide a likelihood ratio testing procedure for selecting the factor model ranks. We apply this methodology to the analysis of data from the Human Mortality Database, and show in a cross-validation experiment how it outperforms simpler methods. Additionally, we use this model to impute mortality rates for countries that have no mortality data for several years. Unlike other approaches, our methodology is able to estimate similarities between the mortality rates of countries, time periods and sexes, and use this information to assist with the imputations. PMID:25489353

Comparison of the CME-associated shock arrival times at the earth using the WSA-ENLIL model with three cone models

NASA Astrophysics Data System (ADS)

Jang, S.; Moon, Y.; Na, H.

2012-12-01

We have made a comparison of CME-associated shock arrival times at the earth based on the WSA-ENLIL model with three cone models using 29 halo CMEs from 2001 to 2002. These halo CMEs have cone model parameters from Michalek et al. (2007) as well as their associated interplanetary (IP) shocks. For this study we consider three different cone models (an asymmetric cone model, an ice-cream cone model and an elliptical cone model) to determine CME cone parameters (radial velocity, angular width and source location), which are used for input parameters of the WSA-ENLIL model. The mean absolute error (MAE) of the arrival times for the elliptical cone model is 10 hours, which is about 2 hours smaller than those of the other models. However, this value is still larger than that (8.7 hours) of an empirical model by Kim et al. (2007). We are investigating several possibilities on relatively large errors of the WSA-ENLIL cone model, which may be caused by CME-CME interaction, background solar wind speed, and/or CME density enhancement.

A heteroskedastic error covariance matrix estimator using a first-order conditional autoregressive Markov simulation for deriving asympotical efficient estimates from ecological sampled Anopheles arabiensis aquatic habitat covariates

PubMed Central

Jacob, Benjamin G; Griffith, Daniel A; Muturi, Ephantus J; Caamano, Erick X; Githure, John I; Novak, Robert J

2009-01-01

Background Autoregressive regression coefficients for Anopheles arabiensis aquatic habitat models are usually assessed using global error techniques and are reported as error covariance matrices. A global statistic, however, will summarize error estimates from multiple habitat locations. This makes it difficult to identify where there are clusters of An. arabiensis aquatic habitats of acceptable prediction. It is therefore useful to conduct some form of spatial error analysis to detect clusters of An. arabiensis aquatic habitats based on uncertainty residuals from individual sampled habitats. In this research, a method of error estimation for spatial simulation models was demonstrated using autocorrelation indices and eigenfunction spatial filters to distinguish among the effects of parameter uncertainty on a stochastic simulation of ecological sampled Anopheles aquatic habitat covariates. A test for diagnostic checking error residuals in an An. arabiensis aquatic habitat model may enable intervention efforts targeting productive habitats clusters, based on larval/pupal productivity, by using the asymptotic distribution of parameter estimates from a residual autocovariance matrix. The models considered in this research extends a normal regression analysis previously considered in the literature. Methods Field and remote-sampled data were collected during July 2006 to December 2007 in Karima rice-village complex in Mwea, Kenya. SAS 9.1.4® was used to explore univariate statistics, correlations, distributions, and to generate global autocorrelation statistics from the ecological sampled datasets. A local autocorrelation index was also generated using spatial covariance parameters (i.e., Moran's Indices) in a SAS/GIS® database. The Moran's statistic was decomposed into orthogonal and uncorrelated synthetic map pattern components using a Poisson model with a gamma-distributed mean (i.e. negative binomial regression). The eigenfunction values from the spatial configuration matrices were then used to define expectations for prior distributions using a Markov chain Monte Carlo (MCMC) algorithm. A set of posterior means were defined in WinBUGS 1.4.3®. After the model had converged, samples from the conditional distributions were used to summarize the posterior distribution of the parameters. Thereafter, a spatial residual trend analyses was used to evaluate variance uncertainty propagation in the model using an autocovariance error matrix. Results By specifying coefficient estimates in a Bayesian framework, the covariate number of tillers was found to be a significant predictor, positively associated with An. arabiensis aquatic habitats. The spatial filter models accounted for approximately 19% redundant locational information in the ecological sampled An. arabiensis aquatic habitat data. In the residual error estimation model there was significant positive autocorrelation (i.e., clustering of habitats in geographic space) based on log-transformed larval/pupal data and the sampled covariate depth of habitat. Conclusion An autocorrelation error covariance matrix and a spatial filter analyses can prioritize mosquito control strategies by providing a computationally attractive and feasible description of variance uncertainty estimates for correctly identifying clusters of prolific An. arabiensis aquatic habitats based on larval/pupal productivity. PMID:19772590

Analysis of the effects of Eye-Tracker performance on the pulse positioning errors during refractive surgery☆

PubMed Central

Arba-Mosquera, Samuel; Aslanides, Ioannis M.

2012-01-01

Purpose To analyze the effects of Eye-Tracker performance on the pulse positioning errors during refractive surgery. Methods A comprehensive model, which directly considers eye movements, including saccades, vestibular, optokinetic, vergence, and miniature, as well as, eye-tracker acquisition rate, eye-tracker latency time, scanner positioning time, laser firing rate, and laser trigger delay have been developed. Results Eye-tracker acquisition rates below 100 Hz correspond to pulse positioning errors above 1.5 mm. Eye-tracker latency times to about 15 ms correspond to pulse positioning errors of up to 3.5 mm. Scanner positioning times to about 9 ms correspond to pulse positioning errors of up to 2 mm. Laser firing rates faster than eye-tracker acquisition rates basically duplicate pulse-positioning errors. Laser trigger delays to about 300 μs have minor to no impact on pulse-positioning errors. Conclusions The proposed model can be used for comparison of laser systems used for ablation processes. Due to the pseudo-random nature of eye movements, positioning errors of single pulses are much larger than observed decentrations in the clinical settings. There is no single parameter that ‘alone’ minimizes the positioning error. It is the optimal combination of the several parameters that minimizes the error. The results of this analysis are important to understand the limitations of correcting very irregular ablation patterns.

A Comparison of Pseudo-Maximum Likelihood and Asymptotically Distribution-Free Dynamic Factor Analysis Parameter Estimation in Fitting Covariance Structure Models to Block-Toeplitz Matrices Representing Single-Subject Multivariate Time-Series.

ERIC Educational Resources Information Center

Molenaar, Peter C. M.; Nesselroade, John R.

1998-01-01

Pseudo-Maximum Likelihood (p-ML) and Asymptotically Distribution Free (ADF) estimation methods for estimating dynamic factor model parameters within a covariance structure framework were compared through a Monte Carlo simulation. Both methods appear to give consistent model parameter estimates, but only ADF gives standard errors and chi-square…

Identification of time-varying structural dynamic systems - An artificial intelligence approach

NASA Technical Reports Server (NTRS)

Glass, B. J.; Hanagud, S.

1992-01-01

An application of the artificial intelligence-derived methodologies of heuristic search and object-oriented programming to the problem of identifying the form of the model and the associated parameters of a time-varying structural dynamic system is presented in this paper. Possible model variations due to changes in boundary conditions or configurations of a structure are organized into a taxonomy of models, and a variant of best-first search is used to identify the model whose simulated response best matches that of the current physical structure. Simulated model responses are verified experimentally. An output-error approach is used in a discontinuous model space, and an equation-error approach is used in the parameter space. The advantages of the AI methods used, compared with conventional programming techniques for implementing knowledge structuring and inheritance, are discussed. Convergence conditions and example problems have been discussed. In the example problem, both the time-varying model and its new parameters have been identified when changes occur.

An LPV Adaptive Observer for Updating a Map Applied to an MAF Sensor in a Diesel Engine

PubMed Central

Liu, Zhiyuan; Wang, Changhui

2015-01-01

In this paper, a new method for mass air flow (MAF) sensor error compensation and an online updating error map (or lookup table) due to installation and aging in a diesel engine is developed. Since the MAF sensor error is dependent on the engine operating point, the error model is represented as a two-dimensional (2D) map with two inputs, fuel mass injection quantity and engine speed. Meanwhile, the 2D map representing the MAF sensor error is described as a piecewise bilinear interpolation model, which can be written as a dot product between the regression vector and parameter vector using a membership function. With the combination of the 2D map regression model and the diesel engine air path system, an LPV adaptive observer with low computational load is designed to estimate states and parameters jointly. The convergence of the proposed algorithm is proven under the conditions of persistent excitation and given inequalities. The observer is validated against the simulation data from engine software enDYNA provided by Tesis. The results demonstrate that the operating point-dependent error of the MAF sensor can be approximated acceptably by the 2D map from the proposed method. PMID:26512675

Computer-Controlled Cylindrical Polishing Process for Large X-Ray Mirror Mandrels

NASA Technical Reports Server (NTRS)

Khan, Gufran S.; Gubarev, Mikhail; Speegle, Chet; Ramsey, Brian

2010-01-01

We are developing high-energy grazing incidence shell optics for hard-x-ray telescopes. The resolution of a mirror shells depends on the quality of cylindrical mandrel from which they are being replicated. Mid-spatial-frequency axial figure error is a dominant contributor in the error budget of the mandrel. This paper presents our efforts to develop a deterministic cylindrical polishing process in order to keep the mid-spatial-frequency axial figure errors to a minimum. Simulation software is developed to model the residual surface figure errors of a mandrel due to the polishing process parameters and the tools used, as well as to compute the optical performance of the optics. The study carried out using the developed software was focused on establishing a relationship between the polishing process parameters and the mid-spatial-frequency error generation. The process parameters modeled are the speeds of the lap and the mandrel, the tool s influence function, the contour path (dwell) of the tools, their shape and the distribution of the tools on the polishing lap. Using the inputs from the mathematical model, a mandrel having conical approximated Wolter-1 geometry, has been polished on a newly developed computer-controlled cylindrical polishing machine. The preliminary results of a series of polishing experiments demonstrate a qualitative agreement with the developed model. We report our first experimental results and discuss plans for further improvements in the polishing process. The ability to simulate the polishing process is critical to optimize the polishing process, improve the mandrel quality and significantly reduce the cost of mandrel production

Hydrologic Model Development and Calibration: Contrasting a Single- and Multi-Objective Approach for Comparing Model Performance

NASA Astrophysics Data System (ADS)

Asadzadeh, M.; Maclean, A.; Tolson, B. A.; Burn, D. H.

2009-05-01

Hydrologic model calibration aims to find a set of parameters that adequately simulates observations of watershed behavior, such as streamflow, or a state variable, such as snow water equivalent (SWE). There are different metrics for evaluating calibration effectiveness that involve quantifying prediction errors, such as the Nash-Sutcliffe (NS) coefficient and bias evaluated for the entire calibration period, on a seasonal basis, for low flows, or for high flows. Many of these metrics are conflicting such that the set of parameters that maximizes the high flow NS differs from the set of parameters that maximizes the low flow NS. Conflicting objectives are very likely when different calibration objectives are based on different fluxes and/or state variables (e.g., NS based on streamflow versus SWE). One of the most popular ways to balance different metrics is to aggregate them based on their importance and find the set of parameters that optimizes a weighted sum of the efficiency metrics. Comparing alternative hydrologic models (e.g., assessing model improvement when a process or more detail is added to the model) based on the aggregated objective might be misleading since it represents one point on the tradeoff of desired error metrics. To derive a more comprehensive model comparison, we solved a bi-objective calibration problem to estimate the tradeoff between two error metrics for each model. Although this approach is computationally more expensive than the aggregation approach, it results in a better understanding of the effectiveness of selected models at each level of every error metric and therefore provides a better rationale for judging relative model quality. The two alternative models used in this study are two MESH hydrologic models (version 1.2) of the Wolf Creek Research basin that differ in their watershed spatial discretization (a single Grouped Response Unit, GRU, versus multiple GRUs). The MESH model, currently under development by Environment Canada, is a coupled land-surface and hydrologic model. Results will demonstrate the conclusions a modeller might make regarding the value of additional watershed spatial discretization under both an aggregated (single-objective) and multi-objective model comparison framework.

Inverse modeling for seawater intrusion in coastal aquifers: Insights about parameter sensitivities, variances, correlations and estimation procedures derived from the Henry problem

USGS Publications Warehouse

Sanz, E.; Voss, C.I.

2006-01-01

Inverse modeling studies employing data collected from the classic Henry seawater intrusion problem give insight into several important aspects of inverse modeling of seawater intrusion problems and effective measurement strategies for estimation of parameters for seawater intrusion. Despite the simplicity of the Henry problem, it embodies the behavior of a typical seawater intrusion situation in a single aquifer. Data collected from the numerical problem solution are employed without added noise in order to focus on the aspects of inverse modeling strategies dictated by the physics of variable-density flow and solute transport during seawater intrusion. Covariances of model parameters that can be estimated are strongly dependent on the physics. The insights gained from this type of analysis may be directly applied to field problems in the presence of data errors, using standard inverse modeling approaches to deal with uncertainty in data. Covariance analysis of the Henry problem indicates that in order to generally reduce variance of parameter estimates, the ideal places to measure pressure are as far away from the coast as possible, at any depth, and the ideal places to measure concentration are near the bottom of the aquifer between the center of the transition zone and its inland fringe. These observations are located in and near high-sensitivity regions of system parameters, which may be identified in a sensitivity analysis with respect to several parameters. However, both the form of error distribution in the observations and the observation weights impact the spatial sensitivity distributions, and different choices for error distributions or weights can result in significantly different regions of high sensitivity. Thus, in order to design effective sampling networks, the error form and weights must be carefully considered. For the Henry problem, permeability and freshwater inflow can be estimated with low estimation variance from only pressure or only concentration observations. Permeability, freshwater inflow, solute molecular diffusivity, and porosity can be estimated with roughly equivalent confidence using observations of only the logarithm of concentration. Furthermore, covariance analysis allows a logical reduction of the number of estimated parameters for ill-posed inverse seawater intrusion problems. Ill-posed problems may exhibit poor estimation convergence, have a non-unique solution, have multiple minima, or require excessive computational effort, and the condition often occurs when estimating too many or co-dependent parameters. For the Henry problem, such analysis allows selection of the two parameters that control system physics from among all possible system parameters. ?? 2005 Elsevier Ltd. All rights reserved.

Estimating the Uncertainty In Diameter Growth Model Predictions and Its Effects On The Uncertainty of Annual Inventory Estimates

Treesearch

Ronald E. McRoberts; Veronica C. Lessard

2001-01-01

Uncertainty in diameter growth predictions is attributed to three general sources: measurement error or sampling variability in predictor variables, parameter covariances, and residual or unexplained variation around model expectations. Using measurement error and sampling variability distributions obtained from the literature and Monte Carlo simulation methods, the...

Modeling human tracking error in several different anti-tank systems

NASA Technical Reports Server (NTRS)

Kleinman, D. L.

1981-01-01

An optimal control model for generating time histories of human tracking errors in antitank systems is outlined. Monte Carlo simulations of human operator responses for three Army antitank systems are compared. System/manipulator dependent data comparisons reflecting human operator limitations in perceiving displayed quantities and executing intended control motions are presented. Motor noise parameters are also discussed.

Argo Development Program.

DTIC Science & Technology

1986-06-01

nonlinear form and account for uncertainties in model parameters, structural simplifications of the model, and disturbances. This technique summarizes...SHARPS system. *The take into account the coupling between axes two curves are nearly identical, except that the without becoming unwieldy. The low...are mainly caused by errors and control errors and accounts for the bandwidth limitations and the simulated current. observed offsets. The overshoot

A Systematic Approach for Identifying Level-1 Error Covariance Structures in Latent Growth Modeling

ERIC Educational Resources Information Center

Ding, Cherng G.; Jane, Ten-Der; Wu, Chiu-Hui; Lin, Hang-Rung; Shen, Chih-Kang

2017-01-01

It has been pointed out in the literature that misspecification of the level-1 error covariance structure in latent growth modeling (LGM) has detrimental impacts on the inferences about growth parameters. Since correct covariance structure is difficult to specify by theory, the identification needs to rely on a specification search, which,…

Building on crossvalidation for increasing the quality of geostatistical modeling

USGS Publications Warehouse

Olea, R.A.

2012-01-01

The random function is a mathematical model commonly used in the assessment of uncertainty associated with a spatially correlated attribute that has been partially sampled. There are multiple algorithms for modeling such random functions, all sharing the requirement of specifying various parameters that have critical influence on the results. The importance of finding ways to compare the methods and setting parameters to obtain results that better model uncertainty has increased as these algorithms have grown in number and complexity. Crossvalidation has been used in spatial statistics, mostly in kriging, for the analysis of mean square errors. An appeal of this approach is its ability to work with the same empirical sample available for running the algorithms. This paper goes beyond checking estimates by formulating a function sensitive to conditional bias. Under ideal conditions, such function turns into a straight line, which can be used as a reference for preparing measures of performance. Applied to kriging, deviations from the ideal line provide sensitivity to the semivariogram lacking in crossvalidation of kriging errors and are more sensitive to conditional bias than analyses of errors. In terms of stochastic simulation, in addition to finding better parameters, the deviations allow comparison of the realizations resulting from the applications of different methods. Examples show improvements of about 30% in the deviations and approximately 10% in the square root of mean square errors between reasonable starting modelling and the solutions according to the new criteria. ?? 2011 US Government.

Groundwater Pollution Source Identification using Linked ANN-Optimization Model

NASA Astrophysics Data System (ADS)

Ayaz, Md; Srivastava, Rajesh; Jain, Ashu

2014-05-01

Groundwater is the principal source of drinking water in several parts of the world. Contamination of groundwater has become a serious health and environmental problem today. Human activities including industrial and agricultural activities are generally responsible for this contamination. Identification of groundwater pollution source is a major step in groundwater pollution remediation. Complete knowledge of pollution source in terms of its source characteristics is essential to adopt an effective remediation strategy. Groundwater pollution source is said to be identified completely when the source characteristics - location, strength and release period - are known. Identification of unknown groundwater pollution source is an ill-posed inverse problem. It becomes more difficult for real field conditions, when the lag time between the first reading at observation well and the time at which the source becomes active is not known. We developed a linked ANN-Optimization model for complete identification of an unknown groundwater pollution source. The model comprises two parts- an optimization model and an ANN model. Decision variables of linked ANN-Optimization model contain source location and release period of pollution source. An objective function is formulated using the spatial and temporal data of observed and simulated concentrations, and then minimized to identify the pollution source parameters. In the formulation of the objective function, we require the lag time which is not known. An ANN model with one hidden layer is trained using Levenberg-Marquardt algorithm to find the lag time. Different combinations of source locations and release periods are used as inputs and lag time is obtained as the output. Performance of the proposed model is evaluated for two and three dimensional case with error-free and erroneous data. Erroneous data was generated by adding uniformly distributed random error (error level 0-10%) to the analytically computed concentration values. The main advantage of the proposed model is that it requires only upper half of the breakthrough curve and is capable of predicting source parameters when the lag time is not known. Linking of ANN model with proposed optimization model reduces the dimensionality of the decision variables of the optimization model by one and hence complexity of optimization model is reduced. The results show that our proposed linked ANN-Optimization model is able to predict the source parameters for the error-free data accurately. The proposed model was run several times to obtain the mean, standard deviation and interval estimate of the predicted parameters for observations with random measurement errors. It was observed that mean values as predicted by the model were quite close to the exact values. An increasing trend was observed in the standard deviation of the predicted values with increasing level of measurement error. The model appears to be robust and may be efficiently utilized to solve the inverse pollution source identification problem.

Using Least Squares for Error Propagation

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2015-01-01

The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…

Generalized background error covariance matrix model (GEN_BE v2.0)

NASA Astrophysics Data System (ADS)

Descombes, G.; Auligné, T.; Vandenberghe, F.; Barker, D. M.; Barré, J.

2015-03-01

The specification of state background error statistics is a key component of data assimilation since it affects the impact observations will have on the analysis. In the variational data assimilation approach, applied in geophysical sciences, the dimensions of the background error covariance matrix (B) are usually too large to be explicitly determined and B needs to be modeled. Recent efforts to include new variables in the analysis such as cloud parameters and chemical species have required the development of the code to GENerate the Background Errors (GEN_BE) version 2.0 for the Weather Research and Forecasting (WRF) community model. GEN_BE allows for a simpler, flexible, robust, and community-oriented framework that gathers methods used by some meteorological operational centers and researchers. We present the advantages of this new design for the data assimilation community by performing benchmarks of different modeling of B and showing some of the new features in data assimilation test cases. As data assimilation for clouds remains a challenge, we present a multivariate approach that includes hydrometeors in the control variables and new correlated errors. In addition, the GEN_BE v2.0 code is employed to diagnose error parameter statistics for chemical species, which shows that it is a tool flexible enough to implement new control variables. While the generation of the background errors statistics code was first developed for atmospheric research, the new version (GEN_BE v2.0) can be easily applied to other domains of science and chosen to diagnose and model B. Initially developed for variational data assimilation, the model of the B matrix may be useful for variational ensemble hybrid methods as well.

Improved Analysis of GW150914 Using a Fully Spin-Precessing Waveform Model

NASA Technical Reports Server (NTRS)

Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Camp, J. B.;

Modeling Input Errors to Improve Uncertainty Estimates for Sediment Transport Model Predictions

NASA Astrophysics Data System (ADS)

Jung, J. Y.; Niemann, J. D.; Greimann, B. P.

2016-12-01

Bayesian methods using Markov chain Monte Carlo algorithms have recently been applied to sediment transport models to assess the uncertainty in the model predictions due to the parameter values. Unfortunately, the existing approaches can only attribute overall uncertainty to the parameters. This limitation is critical because no model can produce accurate forecasts if forced with inaccurate input data, even if the model is well founded in physical theory. In this research, an existing Bayesian method is modified to consider the potential errors in input data during the uncertainty evaluation process. The input error is modeled using Gaussian distributions, and the means and standard deviations are treated as uncertain parameters. The proposed approach is tested by coupling it to the Sedimentation and River Hydraulics - One Dimension (SRH-1D) model and simulating a 23-km reach of the Tachia River in Taiwan. The Wu equation in SRH-1D is used for computing the transport capacity for a bed material load of non-cohesive material. Three types of input data are considered uncertain: (1) the input flowrate at the upstream boundary, (2) the water surface elevation at the downstream boundary, and (3) the water surface elevation at a hydraulic structure in the middle of the reach. The benefits of modeling the input errors in the uncertainty analysis are evaluated by comparing the accuracy of the most likely forecast and the coverage of the observed data by the credible intervals to those of the existing method. The results indicate that the internal boundary condition has the largest uncertainty among those considered. Overall, the uncertainty estimates from the new method are notably different from those of the existing method for both the calibration and forecast periods.

Exploratory Analyses To Improve Model Fit: Errors Due to Misspecification and a Strategy To Reduce Their Occurrence.

ERIC Educational Resources Information Center

Green, Samuel B.; Thompson, Marilyn S.; Poirier, Jennifer

1999-01-01

The use of Lagrange multiplier (LM) tests in specification searches and the efforts that involve the addition of extraneous parameters to models are discussed. Presented are a rationale and strategy for conducting specification searches in two stages that involve adding parameters to LM tests to maximize fit and then deleting parameters not needed…

An Improved Fast Self-Calibration Method for Hybrid Inertial Navigation System under Stationary Condition

PubMed Central

Liu, Bingqi; Wei, Shihui; Su, Guohua; Wang, Jiping; Lu, Jiazhen

2018-01-01

The navigation accuracy of the inertial navigation system (INS) can be greatly improved when the inertial measurement unit (IMU) is effectively calibrated and compensated, such as gyro drifts and accelerometer biases. To reduce the requirement for turntable precision in the classical calibration method, a continuous dynamic self-calibration method based on a three-axis rotating frame for the hybrid inertial navigation system is presented. First, by selecting a suitable IMU frame, the error models of accelerometers and gyros are established. Then, by taking the navigation errors during rolling as the observations, the overall twenty-one error parameters of hybrid inertial navigation system (HINS) are identified based on the calculation of the intermediate parameter. The actual experiment verifies that the method can identify all error parameters of HINS and this method has equivalent accuracy to the classical calibration on a high-precision turntable. In addition, this method is rapid, simple and feasible. PMID:29695041

An Improved Fast Self-Calibration Method for Hybrid Inertial Navigation System under Stationary Condition.

PubMed

Liu, Bingqi; Wei, Shihui; Su, Guohua; Wang, Jiping; Lu, Jiazhen

2018-04-24

The navigation accuracy of the inertial navigation system (INS) can be greatly improved when the inertial measurement unit (IMU) is effectively calibrated and compensated, such as gyro drifts and accelerometer biases. To reduce the requirement for turntable precision in the classical calibration method, a continuous dynamic self-calibration method based on a three-axis rotating frame for the hybrid inertial navigation system is presented. First, by selecting a suitable IMU frame, the error models of accelerometers and gyros are established. Then, by taking the navigation errors during rolling as the observations, the overall twenty-one error parameters of hybrid inertial navigation system (HINS) are identified based on the calculation of the intermediate parameter. The actual experiment verifies that the method can identify all error parameters of HINS and this method has equivalent accuracy to the classical calibration on a high-precision turntable. In addition, this method is rapid, simple and feasible.

Accuracy and sensitivity analysis on seismic anisotropy parameter estimation

NASA Astrophysics Data System (ADS)

Yan, Fuyong; Han, De-Hua

2018-04-01

There is significant uncertainty in measuring the Thomsen’s parameter δ in laboratory even though the dimensions and orientations of the rock samples are known. It is expected that more challenges will be encountered in the estimating of the seismic anisotropy parameters from field seismic data. Based on Monte Carlo simulation of vertical transversely isotropic layer cake model using the database of laboratory anisotropy measurement from the literature, we apply the commonly used quartic non-hyperbolic reflection moveout equation to estimate the seismic anisotropy parameters and test its accuracy and sensitivities to the source-receive offset, vertical interval velocity error and time picking error. The testing results show that the methodology works perfectly for noise-free synthetic data with short spread length. However, this method is extremely sensitive to the time picking error caused by mild random noises, and it requires the spread length to be greater than the depth of the reflection event. The uncertainties increase rapidly for the deeper layers and the estimated anisotropy parameters can be very unreliable for a layer with more than five overlain layers. It is possible that an isotropic formation can be misinterpreted as a strong anisotropic formation. The sensitivity analysis should provide useful guidance on how to group the reflection events and build a suitable geological model for anisotropy parameter inversion.

Bayesian analysis of input uncertainty in hydrological modeling: 2. Application

NASA Astrophysics Data System (ADS)

Kavetski, Dmitri; Kuczera, George; Franks, Stewart W.

2006-03-01

The Bayesian total error analysis (BATEA) methodology directly addresses both input and output errors in hydrological modeling, requiring the modeler to make explicit, rather than implicit, assumptions about the likely extent of data uncertainty. This study considers a BATEA assessment of two North American catchments: (1) French Broad River and (2) Potomac basins. It assesses the performance of the conceptual Variable Infiltration Capacity (VIC) model with and without accounting for input (precipitation) uncertainty. The results show the considerable effects of precipitation errors on the predicted hydrographs (especially the prediction limits) and on the calibrated parameters. In addition, the performance of BATEA in the presence of severe model errors is analyzed. While BATEA allows a very direct treatment of input uncertainty and yields some limited insight into model errors, it requires the specification of valid error models, which are currently poorly understood and require further work. Moreover, it leads to computationally challenging highly dimensional problems. For some types of models, including the VIC implemented using robust numerical methods, the computational cost of BATEA can be reduced using Newton-type methods.

State-space models’ dirty little secrets: even simple linear Gaussian models can have estimation problems

NASA Astrophysics Data System (ADS)

Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M.; Derocher, Andrew E.; Lewis, Mark A.; Jonsen, Ian D.; Mills Flemming, Joanna

2016-05-01

State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results.

Understanding and comparisons of different sampling approaches for the Fourier Amplitudes Sensitivity Test (FAST)

PubMed Central

Xu, Chonggang; Gertner, George

2013-01-01

Fourier Amplitude Sensitivity Test (FAST) is one of the most popular uncertainty and sensitivity analysis techniques. It uses a periodic sampling approach and a Fourier transformation to decompose the variance of a model output into partial variances contributed by different model parameters. Until now, the FAST analysis is mainly confined to the estimation of partial variances contributed by the main effects of model parameters, but does not allow for those contributed by specific interactions among parameters. In this paper, we theoretically show that FAST analysis can be used to estimate partial variances contributed by both main effects and interaction effects of model parameters using different sampling approaches (i.e., traditional search-curve based sampling, simple random sampling and random balance design sampling). We also analytically calculate the potential errors and biases in the estimation of partial variances. Hypothesis tests are constructed to reduce the effect of sampling errors on the estimation of partial variances. Our results show that compared to simple random sampling and random balance design sampling, sensitivity indices (ratios of partial variances to variance of a specific model output) estimated by search-curve based sampling generally have higher precision but larger underestimations. Compared to simple random sampling, random balance design sampling generally provides higher estimation precision for partial variances contributed by the main effects of parameters. The theoretical derivation of partial variances contributed by higher-order interactions and the calculation of their corresponding estimation errors in different sampling schemes can help us better understand the FAST method and provide a fundamental basis for FAST applications and further improvements. PMID:24143037

Understanding and comparisons of different sampling approaches for the Fourier Amplitudes Sensitivity Test (FAST).

PubMed

Xu, Chonggang; Gertner, George

2011-01-01

Fourier Amplitude Sensitivity Test (FAST) is one of the most popular uncertainty and sensitivity analysis techniques. It uses a periodic sampling approach and a Fourier transformation to decompose the variance of a model output into partial variances contributed by different model parameters. Until now, the FAST analysis is mainly confined to the estimation of partial variances contributed by the main effects of model parameters, but does not allow for those contributed by specific interactions among parameters. In this paper, we theoretically show that FAST analysis can be used to estimate partial variances contributed by both main effects and interaction effects of model parameters using different sampling approaches (i.e., traditional search-curve based sampling, simple random sampling and random balance design sampling). We also analytically calculate the potential errors and biases in the estimation of partial variances. Hypothesis tests are constructed to reduce the effect of sampling errors on the estimation of partial variances. Our results show that compared to simple random sampling and random balance design sampling, sensitivity indices (ratios of partial variances to variance of a specific model output) estimated by search-curve based sampling generally have higher precision but larger underestimations. Compared to simple random sampling, random balance design sampling generally provides higher estimation precision for partial variances contributed by the main effects of parameters. The theoretical derivation of partial variances contributed by higher-order interactions and the calculation of their corresponding estimation errors in different sampling schemes can help us better understand the FAST method and provide a fundamental basis for FAST applications and further improvements.

DC servomechanism parameter identification: a Closed Loop Input Error approach.

PubMed

Garrido, Ruben; Miranda, Roger

2012-01-01

This paper presents a Closed Loop Input Error (CLIE) approach for on-line parametric estimation of a continuous-time model of a DC servomechanism functioning in closed loop. A standard Proportional Derivative (PD) position controller stabilizes the loop without requiring knowledge on the servomechanism parameters. The analysis of the identification algorithm takes into account the control law employed for closing the loop. The model contains four parameters that depend on the servo inertia, viscous, and Coulomb friction as well as on a constant disturbance. Lyapunov stability theory permits assessing boundedness of the signals associated to the identification algorithm. Experiments on a laboratory prototype allows evaluating the performance of the approach. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

An iteratively reweighted least-squares approach to adaptive robust adjustment of parameters in linear regression models with autoregressive and t-distributed deviations

NASA Astrophysics Data System (ADS)

Kargoll, Boris; Omidalizarandi, Mohammad; Loth, Ina; Paffenholz, Jens-André; Alkhatib, Hamza

2018-03-01

In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student's) t-distribution. This error model allows for the stochastic modeling of multiple outliers and for an adaptive robust maximum likelihood (ML) estimation of the unknown regression and AR coefficients, the scale parameter, and the degree of freedom of the t-distribution. This approach is meant to be an extension of known estimators, which tend to focus only on the regression model, or on the AR error model, or on normally distributed errors. For the purpose of ML estimation, we derive an expectation conditional maximization either algorithm, which leads to an easy-to-implement version of iteratively reweighted least squares. The estimation performance of the algorithm is evaluated via Monte Carlo simulations for a Fourier as well as a spline model in connection with AR colored noise models of different orders and with three different sampling distributions generating the white noise components. We apply the algorithm to a vibration dataset recorded by a high-accuracy, single-axis accelerometer, focusing on the evaluation of the estimated AR colored noise model.

Use of Multi-class Empirical Orthogonal Function for Identification of Hydrogeological Parameters and Spatiotemporal Pattern of Multiple Recharges in Groundwater Modeling

NASA Astrophysics Data System (ADS)

Huang, C. L.; Hsu, N. S.; Yeh, W. W. G.; Hsieh, I. H.

2017-12-01

This study develops an innovative calibration method for regional groundwater modeling by using multi-class empirical orthogonal functions (EOFs). The developed method is an iterative approach. Prior to carrying out the iterative procedures, the groundwater storage hydrographs associated with the observation wells are calculated. The combined multi-class EOF amplitudes and EOF expansion coefficients of the storage hydrographs are then used to compute the initial gauss of the temporal and spatial pattern of multiple recharges. The initial guess of the hydrogeological parameters are also assigned according to in-situ pumping experiment. The recharges include net rainfall recharge and boundary recharge, and the hydrogeological parameters are riverbed leakage conductivity, horizontal hydraulic conductivity, vertical hydraulic conductivity, storage coefficient, and specific yield. The first step of the iterative algorithm is to conduct the numerical model (i.e. MODFLOW) by the initial guess / adjusted values of the recharges and parameters. Second, in order to determine the best EOF combination of the error storage hydrographs for determining the correction vectors, the objective function is devised as minimizing the root mean square error (RMSE) of the simulated storage hydrographs. The error storage hydrograph are the differences between the storage hydrographs computed from observed and simulated groundwater level fluctuations. Third, adjust the values of recharges and parameters and repeat the iterative procedures until the stopping criterion is reached. The established methodology was applied to the groundwater system of Ming-Chu Basin, Taiwan. The study period is from January 1st to December 2ed in 2012. Results showed that the optimal EOF combination for the multiple recharges and hydrogeological parameters can decrease the RMSE of the simulated storage hydrographs dramatically within three calibration iterations. It represents that the iterative approach that using EOF techniques can capture the groundwater flow tendency and detects the correction vector of the simulated error sources. Hence, the established EOF-based methodology can effectively and accurately identify the multiple recharges and hydrogeological parameters.

Use of machine learning methods to reduce predictive error of groundwater models.

PubMed

Xu, Tianfang; Valocchi, Albert J; Choi, Jaesik; Amir, Eyal

2014-01-01

Quantitative analyses of groundwater flow and transport typically rely on a physically-based model, which is inherently subject to error. Errors in model structure, parameter and data lead to both random and systematic error even in the output of a calibrated model. We develop complementary data-driven models (DDMs) to reduce the predictive error of physically-based groundwater models. Two machine learning techniques, the instance-based weighting and support vector regression, are used to build the DDMs. This approach is illustrated using two real-world case studies of the Republican River Compact Administration model and the Spokane Valley-Rathdrum Prairie model. The two groundwater models have different hydrogeologic settings, parameterization, and calibration methods. In the first case study, cluster analysis is introduced for data preprocessing to make the DDMs more robust and computationally efficient. The DDMs reduce the root-mean-square error (RMSE) of the temporal, spatial, and spatiotemporal prediction of piezometric head of the groundwater model by 82%, 60%, and 48%, respectively. In the second case study, the DDMs reduce the RMSE of the temporal prediction of piezometric head of the groundwater model by 77%. It is further demonstrated that the effectiveness of the DDMs depends on the existence and extent of the structure in the error of the physically-based model. © 2013, National GroundWater Association.

Searching the Force Field Electrostatic Multipole Parameter Space.

PubMed

Jakobsen, Sofie; Jensen, Frank

2016-04-12

We show by tensor decomposition analyses that the molecular electrostatic potential for amino acid peptide models has an effective rank less than twice the number of atoms. This rank indicates the number of parameters that can be derived from the electrostatic potential in a statistically significant way. Using this as a guideline, we investigate different strategies for deriving a reduced set of atomic charges, dipoles, and quadrupoles capable of reproducing the reference electrostatic potential with a low error. A full combinatorial search of selected parameter subspaces for N-methylacetamide and a cysteine peptide model indicates that there are many different parameter sets capable of providing errors close to that of the global minimum. Among the different reduced multipole parameter sets that have low errors, there is consensus that atoms involved in π-bonding require higher order multipole moments. The possible correlation between multipole parameters is investigated by exhaustive searches of combinations of up to four parameters distributed in all possible ways on all possible atomic sites. These analyses show that there is no advantage in considering combinations of multipoles compared to a simple approach where the importance of each multipole moment is evaluated sequentially. When combined with possible weighting factors related to the computational efficiency of each type of multipole moment, this may provide a systematic strategy for determining a computational efficient representation of the electrostatic component in force field calculations.

A Numerical Method for Calculating Stellar Occultation Light Curves from an Arbitrary Atmospheric Model

NASA Technical Reports Server (NTRS)

Chamberlain, D. M.; Elliot, J. L.

1997-01-01

We present a method for speeding up numerical calculations of a light curve for a stellar occultation by a planetary atmosphere with an arbitrary atmospheric model that has spherical symmetry. This improved speed makes least-squares fitting for model parameters practical. Our method takes as input several sets of values for the first two radial derivatives of the refractivity at different values of model parameters, and interpolates to obtain the light curve at intermediate values of one or more model parameters. It was developed for small occulting bodies such as Pluto and Triton, but is applicable to planets of all sizes. We also present the results of a series of tests showing that our method calculates light curves that are correct to an accuracy of 10(exp -4) of the unocculted stellar flux. The test benchmarks are (i) an atmosphere with a l/r dependence of temperature, which yields an analytic solution for the light curve, (ii) an atmosphere that produces an exponential refraction angle, and (iii) a small-planet isothermal model. With our method, least-squares fits to noiseless data also converge to values of parameters with fractional errors of no more than 10(exp -4), with the largest errors occurring in small planets. These errors are well below the precision of the best stellar occultation data available. Fits to noisy data had formal errors consistent with the level of synthetic noise added to the light curve. We conclude: (i) one should interpolate refractivity derivatives and then form light curves from the interpolated values, rather than interpolating the light curves themselves; (ii) for the most accuracy, one must specify the atmospheric model for radii many scale heights above half light; and (iii) for atmospheres with smoothly varying refractivity with altitude, light curves can be sampled as coarsely as two points per scale height.

A Comparison of the Forecast Skills among Three Numerical Models

NASA Astrophysics Data System (ADS)

Lu, D.; Reddy, S. R.; White, L. J.

2003-12-01

Three numerical weather forecast models, MM5, COAMPS and WRF, operating with a joint effort of NOAA HU-NCAS and Jackson State University (JSU) during summer 2003 have been chosen to study their forecast skills against observations. The models forecast over the same region with the same initialization, boundary condition, forecast length and spatial resolution. AVN global dataset have been ingested as initial conditions. Grib resolution of 27 km is chosen to represent the current mesoscale model. The forecasts with the length of 36h are performed to output the result with 12h interval. The key parameters used to evaluate the forecast skill include 12h accumulated precipitation, sea level pressure, wind, surface temperature and dew point. Precipitation is evaluated statistically using conventional skill scores, Threat Score (TS) and Bias Score (BS), for different threshold values based on 12h rainfall observations whereas other statistical methods such as Mean Error (ME), Mean Absolute Error(MAE) and Root Mean Square Error (RMSE) are applied to other forecast parameters.

Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations.

PubMed

Tornøe, Christoffer W; Overgaard, Rune V; Agersø, Henrik; Nielsen, Henrik A; Madsen, Henrik; Jonsson, E Niclas

2005-08-01

The objective of the present analysis was to explore the use of stochastic differential equations (SDEs) in population pharmacokinetic/pharmacodynamic (PK/PD) modeling. The intra-individual variability in nonlinear mixed-effects models based on SDEs is decomposed into two types of noise: a measurement and a system noise term. The measurement noise represents uncorrelated error due to, for example, assay error while the system noise accounts for structural misspecifications, approximations of the dynamical model, and true random physiological fluctuations. Since the system noise accounts for model misspecifications, the SDEs provide a diagnostic tool for model appropriateness. The focus of the article is on the implementation of the Extended Kalman Filter (EKF) in NONMEM for parameter estimation in SDE models. Various applications of SDEs in population PK/PD modeling are illustrated through a systematic model development example using clinical PK data of the gonadotropin releasing hormone (GnRH) antagonist degarelix. The dynamic noise estimates were used to track variations in model parameters and systematically build an absorption model for subcutaneously administered degarelix. The EKF-based algorithm was successfully implemented in NONMEM for parameter estimation in population PK/PD models described by systems of SDEs. The example indicated that it was possible to pinpoint structural model deficiencies, and that valuable information may be obtained by tracking unexplained variations in parameters.

Machine Learning Based Multi-Physical-Model Blending for Enhancing Renewable Energy Forecast -- Improvement via Situation Dependent Error Correction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Siyuan; Hwang, Youngdeok; Khabibrakhmanov, Ildar

With increasing penetration of solar and wind energy to the total energy supply mix, the pressing need for accurate energy forecasting has become well-recognized. Here we report the development of a machine-learning based model blending approach for statistically combining multiple meteorological models for improving the accuracy of solar/wind power forecast. Importantly, we demonstrate that in addition to parameters to be predicted (such as solar irradiance and power), including additional atmospheric state parameters which collectively define weather situations as machine learning input provides further enhanced accuracy for the blended result. Functional analysis of variance shows that the error of individual modelmore » has substantial dependence on the weather situation. The machine-learning approach effectively reduces such situation dependent error thus produces more accurate results compared to conventional multi-model ensemble approaches based on simplistic equally or unequally weighted model averaging. Validation over an extended period of time results show over 30% improvement in solar irradiance/power forecast accuracy compared to forecasts based on the best individual model.« less

Benchmarking NLDAS-2 Soil Moisture and Evapotranspiration to Separate Uncertainty Contributions

NASA Technical Reports Server (NTRS)

Nearing, Grey S.; Mocko, David M.; Peters-Lidard, Christa D.; Kumar, Sujay V.; Xia, Youlong

2016-01-01

Model benchmarking allows us to separate uncertainty in model predictions caused 1 by model inputs from uncertainty due to model structural error. We extend this method with a large-sample approach (using data from multiple field sites) to measure prediction uncertainty caused by errors in (i) forcing data, (ii) model parameters, and (iii) model structure, and use it to compare the efficiency of soil moisture state and evapotranspiration flux predictions made by the four land surface models in the North American Land Data Assimilation System Phase 2 (NLDAS-2). Parameters dominated uncertainty in soil moisture estimates and forcing data dominated uncertainty in evapotranspiration estimates; however, the models themselves used only a fraction of the information available to them. This means that there is significant potential to improve all three components of the NLDAS-2 system. In particular, continued work toward refining the parameter maps and look-up tables, the forcing data measurement and processing, and also the land surface models themselves, has potential to result in improved estimates of surface mass and energy balances.

Benchmarking NLDAS-2 Soil Moisture and Evapotranspiration to Separate Uncertainty Contributions

PubMed Central

Nearing, Grey S.; Mocko, David M.; Peters-Lidard, Christa D.; Kumar, Sujay V.; Xia, Youlong

2018-01-01

Model benchmarking allows us to separate uncertainty in model predictions caused by model inputs from uncertainty due to model structural error. We extend this method with a “large-sample” approach (using data from multiple field sites) to measure prediction uncertainty caused by errors in (i) forcing data, (ii) model parameters, and (iii) model structure, and use it to compare the efficiency of soil moisture state and evapotranspiration flux predictions made by the four land surface models in the North American Land Data Assimilation System Phase 2 (NLDAS-2). Parameters dominated uncertainty in soil moisture estimates and forcing data dominated uncertainty in evapotranspiration estimates; however, the models themselves used only a fraction of the information available to them. This means that there is significant potential to improve all three components of the NLDAS-2 system. In particular, continued work toward refining the parameter maps and look-up tables, the forcing data measurement and processing, and also the land surface models themselves, has potential to result in improved estimates of surface mass and energy balances. PMID:29697706

Benchmarking NLDAS-2 Soil Moisture and Evapotranspiration to Separate Uncertainty Contributions.

PubMed

Nearing, Grey S; Mocko, David M; Peters-Lidard, Christa D; Kumar, Sujay V; Xia, Youlong

2016-03-01

Model benchmarking allows us to separate uncertainty in model predictions caused by model inputs from uncertainty due to model structural error. We extend this method with a "large-sample" approach (using data from multiple field sites) to measure prediction uncertainty caused by errors in (i) forcing data, (ii) model parameters, and (iii) model structure, and use it to compare the efficiency of soil moisture state and evapotranspiration flux predictions made by the four land surface models in the North American Land Data Assimilation System Phase 2 (NLDAS-2). Parameters dominated uncertainty in soil moisture estimates and forcing data dominated uncertainty in evapotranspiration estimates; however, the models themselves used only a fraction of the information available to them. This means that there is significant potential to improve all three components of the NLDAS-2 system. In particular, continued work toward refining the parameter maps and look-up tables, the forcing data measurement and processing, and also the land surface models themselves, has potential to result in improved estimates of surface mass and energy balances.

Rotorcraft system identification techniques for handling qualities and stability and control evaluation

NASA Technical Reports Server (NTRS)

Hall, W. E., Jr.; Gupta, N. K.; Hansen, R. S.

1978-01-01

An integrated approach to rotorcraft system identification is described. This approach consists of sequential application of (1) data filtering to estimate states of the system and sensor errors, (2) model structure estimation to isolate significant model effects, and (3) parameter identification to quantify the coefficient of the model. An input design algorithm is described which can be used to design control inputs which maximize parameter estimation accuracy. Details of each aspect of the rotorcraft identification approach are given. Examples of both simulated and actual flight data processing are given to illustrate each phase of processing. The procedure is shown to provide means of calibrating sensor errors in flight data, quantifying high order state variable models from the flight data, and consequently computing related stability and control design models.

Theoretical study of the accuracy of the pulse method, frontal analysis, and frontal analysis by characteristic points for the determination of single component adsorption isotherms.

PubMed

Andrzejewska, Anna; Kaczmarski, Krzysztof; Guiochon, Georges

2009-02-13

The adsorption isotherms of selected compounds are our main source of information on the mechanisms of adsorption processes. Thus, the selection of the methods used to determine adsorption isotherm data and to evaluate the errors made is critical. Three chromatographic methods were evaluated, frontal analysis (FA), frontal analysis by characteristic point (FACP), and the pulse or perturbation method (PM), and their accuracies were compared. Using the equilibrium-dispersive (ED) model of chromatography, breakthrough curves of single components were generated corresponding to three different adsorption isotherm models: the Langmuir, the bi-Langmuir, and the Moreau isotherms. For each breakthrough curve, the best conventional procedures of each method (FA, FACP, PM) were used to calculate the corresponding data point, using typical values of the parameters of each isotherm model, for four different values of the column efficiency (N=500, 1000, 2000, and 10,000). Then, the data points were fitted to each isotherm model and the corresponding isotherm parameters were compared to those of the initial isotherm model. When isotherm data are derived with a chromatographic method, they may suffer from two types of errors: (1) the errors made in deriving the experimental data points from the chromatographic records; (2) the errors made in selecting an incorrect isotherm model and fitting to it the experimental data. Both errors decrease significantly with increasing column efficiency with FA and FACP, but not with PM.

Automated palpation for breast tissue discrimination based on viscoelastic biomechanical properties.

PubMed

Tsukune, Mariko; Kobayashi, Yo; Miyashita, Tomoyuki; Fujie, G Masakatsu

2015-05-01

Accurate, noninvasive methods are sought for breast tumor detection and diagnosis. In particular, a need for noninvasive techniques that measure both the nonlinear elastic and viscoelastic properties of breast tissue has been identified. For diagnostic purposes, it is important to select a nonlinear viscoelastic model with a small number of parameters that highly correlate with histological structure. However, the combination of conventional viscoelastic models with nonlinear elastic models requires a large number of parameters. A nonlinear viscoelastic model of breast tissue based on a simple equation with few parameters was developed and tested. The nonlinear viscoelastic properties of soft tissues in porcine breast were measured experimentally using fresh ex vivo samples. Robotic palpation was used for measurements employed in a finite element model. These measurements were used to calculate nonlinear viscoelastic parameters for fat, fibroglandular breast parenchyma and muscle. The ability of these parameters to distinguish the tissue types was evaluated in a two-step statistical analysis that included Holm's pairwise [Formula: see text] test. The discrimination error rate of a set of parameters was evaluated by the Mahalanobis distance. Ex vivo testing in porcine breast revealed significant differences in the nonlinear viscoelastic parameters among combinations of three tissue types. The discrimination error rate was low among all tested combinations of three tissue types. Although tissue discrimination was not achieved using only a single nonlinear viscoelastic parameter, a set of four nonlinear viscoelastic parameters were able to reliably and accurately discriminate fat, breast fibroglandular tissue and muscle.

Generalized Background Error covariance matrix model (GEN_BE v2.0)

NASA Astrophysics Data System (ADS)

Descombes, G.; Auligné, T.; Vandenberghe, F.; Barker, D. M.

2014-07-01

The specification of state background error statistics is a key component of data assimilation since it affects the impact observations will have on the analysis. In the variational data assimilation approach, applied in geophysical sciences, the dimensions of the background error covariance matrix (B) are usually too large to be explicitly determined and B needs to be modeled. Recent efforts to include new variables in the analysis such as cloud parameters and chemical species have required the development of the code to GENerate the Background Errors (GEN_BE) version 2.0 for the Weather Research and Forecasting (WRF) community model to allow for a simpler, flexible, robust, and community-oriented framework that gathers methods used by meteorological operational centers and researchers. We present the advantages of this new design for the data assimilation community by performing benchmarks and showing some of the new features on data assimilation test cases. As data assimilation for clouds remains a challenge, we present a multivariate approach that includes hydrometeors in the control variables and new correlated errors. In addition, the GEN_BE v2.0 code is employed to diagnose error parameter statistics for chemical species, which shows that it is a tool flexible enough to involve new control variables. While the generation of the background errors statistics code has been first developed for atmospheric research, the new version (GEN_BE v2.0) can be easily extended to other domains of science and be chosen as a testbed for diagnostic and new modeling of B. Initially developed for variational data assimilation, the model of the B matrix may be useful for variational ensemble hybrid methods as well.

Nonconservative force model parameter estimation strategy for TOPEX/Poseidon precision orbit determination

NASA Technical Reports Server (NTRS)

Luthcke, S. B.; Marshall, J. A.

1992-01-01

The TOPEX/Poseidon spacecraft was launched on August 10, 1992 to study the Earth's oceans. To achieve maximum benefit from the altimetric data it is to collect, mission requirements dictate that TOPEX/Poseidon's orbit must be computed at an unprecedented level of accuracy. To reach our pre-launch radial orbit accuracy goals, the mismodeling of the radiative nonconservative forces of solar radiation, Earth albedo an infrared re-radiation, and spacecraft thermal imbalances cannot produce in combination more than a 6 cm rms error over a 10 day period. Similarly, the 10-day drag modeling error cannot exceed 3 cm rms. In order to satisfy these requirements, a 'box-wing' representation of the satellite has been developed in which, the satellite is modelled as the combination of flat plates arranged in the shape of a box and a connected solar array. The radiative/thermal nonconservative forces acting on each of the eight surfaces are computed independently, yielding vector accelerations which are summed to compute the total aggregate effect on the satellite center-of-mass. Select parameters associated with the flat plates are adjusted to obtain a better representation of the satellite acceleration history. This study analyzes the estimation of these parameters from simulated TOPEX/Poseidon laser data in the presence of both nonconservative and gravity model errors. A 'best choice' of estimated parameters is derived and the ability to meet mission requirements with the 'box-wing' model evaluated.

Online automatic tuning and control for fed-batch cultivation

PubMed Central

van Straten, Gerrit; van der Pol, Leo A.; van Boxtel, Anton J. B.

2007-01-01

Performance of controllers applied in biotechnological production is often below expectation. Online automatic tuning has the capability to improve control performance by adjusting control parameters. This work presents automatic tuning approaches for model reference specific growth rate control during fed-batch cultivation. The approaches are direct methods that use the error between observed specific growth rate and its set point; systematic perturbations of the cultivation are not necessary. Two automatic tuning methods proved to be efficient, in which the adaptation rate is based on a combination of the error, squared error and integral error. These methods are relatively simple and robust against disturbances, parameter uncertainties, and initialization errors. Application of the specific growth rate controller yields a stable system. The controller and automatic tuning methods are qualified by simulations and laboratory experiments with Bordetella pertussis. PMID:18157554

Noise-induced errors in geophysical parameter estimation from retarding potential analyzers in low Earth orbit

NASA Astrophysics Data System (ADS)

Debchoudhury, Shantanab; Earle, Gregory

2017-04-01

Retarding Potential Analyzers (RPA) have a rich flight heritage. Standard curve-fitting analysis techniques exist that can infer state variables in the ionospheric plasma environment from RPA data, but the estimation process is prone to errors arising from a number of sources. Previous work has focused on the effects of grid geometry on uncertainties in estimation; however, no prior study has quantified the estimation errors due to additive noise. In this study, we characterize the errors in estimation of thermal plasma parameters by adding noise to the simulated data derived from the existing ionospheric models. We concentrate on low-altitude, mid-inclination orbits since a number of nano-satellite missions are focused on this region of the ionosphere. The errors are quantified and cross-correlated for varying geomagnetic conditions.

Robust estimation of thermodynamic parameters (ΔH, ΔS and ΔCp) for prediction of retention time in gas chromatography - Part II (Application).

PubMed

Claumann, Carlos Alberto; Wüst Zibetti, André; Bolzan, Ariovaldo; Machado, Ricardo A F; Pinto, Leonel Teixeira

2015-12-18

For this work, an analysis of parameter estimation for the retention factor in GC model was performed, considering two different criteria: sum of square error, and maximum error in absolute value; relevant statistics are described for each case. The main contribution of this work is the implementation of an initialization scheme (specialized) for the estimated parameters, which features fast convergence (low computational time) and is based on knowledge of the surface of the error criterion. In an application to a series of alkanes, specialized initialization resulted in significant reduction to the number of evaluations of the objective function (reducing computational time) in the parameter estimation. The obtained reduction happened between one and two orders of magnitude, compared with the simple random initialization. Copyright © 2015 Elsevier B.V. All rights reserved.

Integration of Error Compensation of Coordinate Measuring Machines into Feature Measurement: Part I—Model Development

PubMed Central

Calvo, Roque; D’Amato, Roberto; Gómez, Emilio; Domingo, Rosario

2016-01-01

The development of an error compensation model for coordinate measuring machines (CMMs) and its integration into feature measurement is presented. CMMs are widespread and dependable instruments in industry and laboratories for dimensional measurement. From the tip probe sensor to the machine display, there is a complex transformation of probed point coordinates through the geometrical feature model that makes the assessment of accuracy and uncertainty measurement results difficult. Therefore, error compensation is not standardized, conversely to other simpler instruments. Detailed coordinate error compensation models are generally based on CMM as a rigid-body and it requires a detailed mapping of the CMM’s behavior. In this paper a new model type of error compensation is proposed. It evaluates the error from the vectorial composition of length error by axis and its integration into the geometrical measurement model. The non-explained variability by the model is incorporated into the uncertainty budget. Model parameters are analyzed and linked to the geometrical errors and uncertainty of CMM response. Next, the outstanding measurement models of flatness, angle, and roundness are developed. The proposed models are useful for measurement improvement with easy integration into CMM signal processing, in particular in industrial environments where built-in solutions are sought. A battery of implementation tests are presented in Part II, where the experimental endorsement of the model is included. PMID:27690052

The effect of the dynamic wet troposphere on VLBI measurements

NASA Technical Reports Server (NTRS)

Treuhaft, R. N.; Lanyi, G. E.

1986-01-01

Calculations using a statistical model of water vapor fluctuations yield the effect of the dynamic wet troposphere on Very Long Baseline Interferometry (VLBI) measurements. The statistical model arises from two primary assumptions: (1) the spatial structure of refractivity fluctuations can be closely approximated by elementary (Kolmogorov) turbulence theory, and (2) temporal fluctuations are caused by spatial patterns which are moved over a site by the wind. The consequences of these assumptions are outlined for the VLBI delay and delay rate observables. For example, wet troposphere induced rms delays for Deep Space Network (DSN) VLBI at 20-deg elevation are about 3 cm of delay per observation, which is smaller, on the average, than other known error sources in the current DSN VLBI data set. At 20-deg elevation for 200-s time intervals, water vapor induces approximately 1.5 x 10 to the minus 13th power s/s in the Allan standard deviation of interferometric delay, which is a measure of the delay rate observable error. In contrast to the delay error, the delay rate measurement error is dominated by water vapor fluctuations. Water vapor induced VLBI parameter errors and correlations are calculated. For the DSN, baseline length parameter errors due to water vapor fluctuations are in the range of 3 to 5 cm. The above physical assumptions also lead to a method for including the water vapor fluctuations in the parameter estimation procedure, which is used to extract baseline and source information from the VLBI observables.

Comparison of optimal design methods in inverse problems

NASA Astrophysics Data System (ADS)

Banks, H. T.; Holm, K.; Kappel, F.

2011-07-01

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).

Aerodynamic Parameter Estimation for the X-43A (Hyper-X) from Flight Data

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.; Derry, Stephen D.; Smith, Mark S.

2005-01-01

Aerodynamic parameters were estimated based on flight data from the third flight of the X-43A hypersonic research vehicle, also called Hyper-X. Maneuvers were flown using multiple orthogonal phase-optimized sweep inputs applied as simultaneous control surface perturbations at Mach 8, 7, 6, 5, 4, and 3 during the vehicle descent. Aerodynamic parameters, consisting of non-dimensional longitudinal and lateral stability and control derivatives, were estimated from flight data at each Mach number. Multi-step inputs at nearly the same flight conditions were also flown to assess the prediction capability of the identified models. Prediction errors were found to be comparable in magnitude to the modeling errors, which indicates accurate modeling. Aerodynamic parameter estimates were plotted as a function of Mach number, and compared with estimates from the pre-flight aerodynamic database, which was based on wind-tunnel tests and computational fluid dynamics. Agreement between flight estimates and values computed from the aerodynamic database was excellent overall.

Multiscale measurement error models for aggregated small area health data.

PubMed

Aregay, Mehreteab; Lawson, Andrew B; Faes, Christel; Kirby, Russell S; Carroll, Rachel; Watjou, Kevin

2016-08-01

Spatial data are often aggregated from a finer (smaller) to a coarser (larger) geographical level. The process of data aggregation induces a scaling effect which smoothes the variation in the data. To address the scaling problem, multiscale models that link the convolution models at different scale levels via the shared random effect have been proposed. One of the main goals in aggregated health data is to investigate the relationship between predictors and an outcome at different geographical levels. In this paper, we extend multiscale models to examine whether a predictor effect at a finer level hold true at a coarser level. To adjust for predictor uncertainty due to aggregation, we applied measurement error models in the framework of multiscale approach. To assess the benefit of using multiscale measurement error models, we compare the performance of multiscale models with and without measurement error in both real and simulated data. We found that ignoring the measurement error in multiscale models underestimates the regression coefficient, while it overestimates the variance of the spatially structured random effect. On the other hand, accounting for the measurement error in multiscale models provides a better model fit and unbiased parameter estimates. © The Author(s) 2016.

Estimating riparian understory vegetation cover with beta regression and copula models

USGS Publications Warehouse

Eskelson, Bianca N.I.; Madsen, Lisa; Hagar, Joan C.; Temesgen, Hailemariam

2011-01-01

Understory vegetation communities are critical components of forest ecosystems. As a result, the importance of modeling understory vegetation characteristics in forested landscapes has become more apparent. Abundance measures such as shrub cover are bounded between 0 and 1, exhibit heteroscedastic error variance, and are often subject to spatial dependence. These distributional features tend to be ignored when shrub cover data are analyzed. The beta distribution has been used successfully to describe the frequency distribution of vegetation cover. Beta regression models ignoring spatial dependence (BR) and accounting for spatial dependence (BRdep) were used to estimate percent shrub cover as a function of topographic conditions and overstory vegetation structure in riparian zones in western Oregon. The BR models showed poor explanatory power (pseudo-R2 ≤ 0.34) but outperformed ordinary least-squares (OLS) and generalized least-squares (GLS) regression models with logit-transformed response in terms of mean square prediction error and absolute bias. We introduce a copula (COP) model that is based on the beta distribution and accounts for spatial dependence. A simulation study was designed to illustrate the effects of incorrectly assuming normality, equal variance, and spatial independence. It showed that BR, BRdep, and COP models provide unbiased parameter estimates, whereas OLS and GLS models result in slightly biased estimates for two of the three parameters. On the basis of the simulation study, 93–97% of the GLS, BRdep, and COP confidence intervals covered the true parameters, whereas OLS and BR only resulted in 84–88% coverage, which demonstrated the superiority of GLS, BRdep, and COP over OLS and BR models in providing standard errors for the parameter estimates in the presence of spatial dependence.

Statistical design and analysis for plant cover studies with multiple sources of observation errors

USGS Publications Warehouse

Wright, Wilson; Irvine, Kathryn M.; Warren, Jeffrey M .; Barnett, Jenny K.

2017-01-01

Effective wildlife habitat management and conservation requires understanding the factors influencing distribution and abundance of plant species. Field studies, however, have documented observation errors in visually estimated plant cover including measurements which differ from the true value (measurement error) and not observing a species that is present within a plot (detection error). Unlike the rapid expansion of occupancy and N-mixture models for analysing wildlife surveys, development of statistical models accounting for observation error in plants has not progressed quickly. Our work informs development of a monitoring protocol for managed wetlands within the National Wildlife Refuge System.Zero-augmented beta (ZAB) regression is the most suitable method for analysing areal plant cover recorded as a continuous proportion but assumes no observation errors. We present a model extension that explicitly includes the observation process thereby accounting for both measurement and detection errors. Using simulations, we compare our approach to a ZAB regression that ignores observation errors (naïve model) and an “ad hoc” approach using a composite of multiple observations per plot within the naïve model. We explore how sample size and within-season revisit design affect the ability to detect a change in mean plant cover between 2 years using our model.Explicitly modelling the observation process within our framework produced unbiased estimates and nominal coverage of model parameters. The naïve and “ad hoc” approaches resulted in underestimation of occurrence and overestimation of mean cover. The degree of bias was primarily driven by imperfect detection and its relationship with cover within a plot. Conversely, measurement error had minimal impacts on inferences. We found >30 plots with at least three within-season revisits achieved reasonable posterior probabilities for assessing change in mean plant cover.For rapid adoption and application, code for Bayesian estimation of our single-species ZAB with errors model is included. Practitioners utilizing our R-based simulation code can explore trade-offs among different survey efforts and parameter values, as we did, but tuned to their own investigation. Less abundant plant species of high ecological interest may warrant the additional cost of gathering multiple independent observations in order to guard against erroneous conclusions.

Embedded Model Error Representation and Propagation in Climate Models

NASA Astrophysics Data System (ADS)

Sargsyan, K.; Ricciuto, D. M.; Safta, C.; Thornton, P. E.

2017-12-01

Over the last decade, parametric uncertainty quantification (UQ) methods have reached a level of maturity, while the same can not be said about representation and quantification of structural or model errors. Lack of characterization of model errors, induced by physical assumptions, phenomenological parameterizations or constitutive laws, is a major handicap in predictive science. In particular, e.g. in climate models, significant computational resources are dedicated to model calibration without gaining improvement in predictive skill. Neglecting model errors during calibration/tuning will lead to overconfident and biased model parameters. At the same time, the most advanced methods accounting for model error merely correct output biases, augmenting model outputs with statistical error terms that can potentially violate physical laws, or make the calibrated model ineffective for extrapolative scenarios. This work will overview a principled path for representing and quantifying model errors, as well as propagating them together with the rest of the predictive uncertainty budget, including data noise, parametric uncertainties and surrogate-related errors. Namely, the model error terms will be embedded in select model components rather than as external corrections. Such embedding ensures consistency with physical constraints on model predictions, and renders calibrated model predictions meaningful and robust with respect to model errors. Besides, in the presence of observational data, the approach can effectively differentiate model structural deficiencies from those of data acquisition. The methodology is implemented in UQ Toolkit (www.sandia.gov/uqtoolkit), relying on a host of available forward and inverse UQ tools. We will demonstrate the application of the technique on few application of interest, including ACME Land Model calibration via a wide range of measurements obtained at select sites.

Evaluation of Approaches to Deal with Low-Frequency Nuisance Covariates in Population Pharmacokinetic Analyses.

PubMed

Lagishetty, Chakradhar V; Duffull, Stephen B

2015-11-01

Clinical studies include occurrences of rare variables, like genotypes, which due to their frequency and strength render their effects difficult to estimate from a dataset. Variables that influence the estimated value of a model-based parameter are termed covariates. It is often difficult to determine if such an effect is significant, since type I error can be inflated when the covariate is rare. Their presence may have either an insubstantial effect on the parameters of interest, hence are ignorable, or conversely they may be influential and therefore non-ignorable. In the case that these covariate effects cannot be estimated due to power and are non-ignorable, then these are considered nuisance, in that they have to be considered but due to type 1 error are of limited interest. This study assesses methods of handling nuisance covariate effects. The specific objectives include (1) calibrating the frequency of a covariate that is associated with type 1 error inflation, (2) calibrating its strength that renders it non-ignorable and (3) evaluating methods for handling these non-ignorable covariates in a nonlinear mixed effects model setting. Type 1 error was determined for the Wald test. Methods considered for handling the nuisance covariate effects were case deletion, Box-Cox transformation and inclusion of a specific fixed effects parameter. Non-ignorable nuisance covariates were found to be effectively handled through addition of a fixed effect parameter.

Application of an Optimal Tuner Selection Approach for On-Board Self-Tuning Engine Models

NASA Technical Reports Server (NTRS)

Simon, Donald L.; Armstrong, Jeffrey B.; Garg, Sanjay

2012-01-01

An enhanced design methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented in this paper. It specific-ally addresses the under-determined estimation problem, in which there are more unknown parameters than available sensor measurements. This work builds upon an existing technique for systematically selecting a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. While the existing technique was optimized for open-loop engine operation at a fixed design point, in this paper an alternative formulation is presented that enables the technique to be optimized for an engine operating under closed-loop control throughout the flight envelope. The theoretical Kalman filter mean squared estimation error at a steady-state closed-loop operating point is derived, and the tuner selection approach applied to minimize this error is discussed. A technique for constructing a globally optimal tuning parameter vector, which enables full-envelope application of the technology, is also presented, along with design steps for adjusting the dynamic response of the Kalman filter state estimates. Results from the application of the technique to linear and nonlinear aircraft engine simulations are presented and compared to the conventional approach of tuner selection. The new methodology is shown to yield a significant improvement in on-line Kalman filter estimation accuracy.

Application of identified sensitive physical parameters in reducing the uncertainty of numerical simulation

NASA Astrophysics Data System (ADS)

Sun, Guodong; Mu, Mu

2016-04-01

An important source of uncertainty, which then causes further uncertainty in numerical simulations, is that residing in the parameters describing physical processes in numerical models. There are many physical parameters in numerical models in the atmospheric and oceanic sciences, and it would cost a great deal to reduce uncertainties in all physical parameters. Therefore, finding a subset of these parameters, which are relatively more sensitive and important parameters, and reducing the errors in the physical parameters in this subset would be a far more efficient way to reduce the uncertainties involved in simulations. In this context, we present a new approach based on the conditional nonlinear optimal perturbation related to parameter (CNOP-P) method. The approach provides a framework to ascertain the subset of those relatively more sensitive and important parameters among the physical parameters. The Lund-Potsdam-Jena (LPJ) dynamical global vegetation model was utilized to test the validity of the new approach. The results imply that nonlinear interactions among parameters play a key role in the uncertainty of numerical simulations in arid and semi-arid regions of China compared to those in northern, northeastern and southern China. The uncertainties in the numerical simulations were reduced considerably by reducing the errors of the subset of relatively more sensitive and important parameters. The results demonstrate that our approach not only offers a new route to identify relatively more sensitive and important physical parameters but also that it is viable to then apply "target observations" to reduce the uncertainties in model parameters.

Evaluation of the geomorphometric results and residual values of a robust plane fitting method applied to different DTMs of various scales and accuracy

NASA Astrophysics Data System (ADS)

Koma, Zsófia; Székely, Balázs; Dorninger, Peter; Kovács, Gábor

2013-04-01

Due to the need for quantitative analysis of various geomorphological landforms, the importance of fast and effective automatic processing of the different kind of digital terrain models (DTMs) is increasing. The robust plane fitting (segmentation) method, developed at the Institute of Photogrammetry and Remote Sensing at Vienna University of Technology, allows the processing of large 3D point clouds (containing millions of points), performs automatic detection of the planar elements of the surface via parameter estimation, and provides a considerable data reduction for the modeled area. Its geoscientific application allows the modeling of different landforms with the fitted planes as planar facets. In our study we aim to analyze the accuracy of the resulting set of fitted planes in terms of accuracy, model reliability and dependence on the input parameters. To this end we used DTMs of different scales and accuracy: (1) artificially generated 3D point cloud model with different magnitudes of error; (2) LiDAR data with 0.1 m error; (3) SRTM (Shuttle Radar Topography Mission) DTM database with 5 m accuracy; (4) DTM data from HRSC (High Resolution Stereo Camera) of the planet Mars with 10 m error. The analysis of the simulated 3D point cloud with normally distributed errors comprised different kinds of statistical tests (for example Chi-square and Kolmogorov-Smirnov tests) applied on the residual values and evaluation of dependence of the residual values on the input parameters. These tests have been repeated on the real data supplemented with the categorization of the segmentation result depending on the input parameters, model reliability and the geomorphological meaning of the fitted planes. The simulation results show that for the artificially generated data with normally distributed errors the null hypothesis can be accepted based on the residual value distribution being also normal, but in case of the test on the real data the residual value distribution is often mixed or unknown. The residual values are found to be dependent on two input parameters (standard deviation and maximum point-plane distance both defining distance thresholds for assigning points to a segment) mainly and the curvature of the surface affected mostly the distributions. The results of the analysis helped to decide which parameter set is the best for further modelling and provides the highest accuracy. With these results in mind the success of quasi-automatic modelling of the planar (for example plateau-like) features became more successful and often provided more accuracy. These studies were carried out partly in the framework of TMIS.ascrea project (Nr. 2001978) financed by the Austrian Research Promotion Agency (FFG); the contribution of ZsK was partly funded by Campus Hungary Internship TÁMOP-424B1.

Seabed roughness parameters from joint backscatter and reflection inversion at the Malta Plateau.

PubMed

Steininger, Gavin; Holland, Charles W; Dosso, Stan E; Dettmer, Jan

2013-09-01

This paper presents estimates of seabed roughness and geoacoustic parameters and uncertainties on the Malta Plateau, Mediterranean Sea, by joint Bayesian inversion of mono-static backscatter and spherical wave reflection-coefficient data. The data are modeled using homogeneous fluid sediment layers overlying an elastic basement. The scattering model assumes a randomly rough water-sediment interface with a von Karman roughness power spectrum. Scattering and reflection data are inverted simultaneously using a population of interacting Markov chains to sample roughness and geoacoustic parameters as well as residual error parameters. Trans-dimensional sampling is applied to treat the number of sediment layers and the order (zeroth or first) of an autoregressive error model (to represent potential residual correlation) as unknowns. Results are considered in terms of marginal posterior probability profiles and distributions, which quantify the effective data information content to resolve scattering/geoacoustic structure. Results indicate well-defined scattering (roughness) parameters in good agreement with existing measurements, and a multi-layer sediment profile over a high-speed (elastic) basement, consistent with independent knowledge of sand layers over limestone.

Progressive sampling-based Bayesian optimization for efficient and automatic machine learning model selection.

PubMed

Zeng, Xueqiang; Luo, Gang

2017-12-01

Machine learning is broadly used for clinical data analysis. Before training a model, a machine learning algorithm must be selected. Also, the values of one or more model parameters termed hyper-parameters must be set. Selecting algorithms and hyper-parameter values requires advanced machine learning knowledge and many labor-intensive manual iterations. To lower the bar to machine learning, miscellaneous automatic selection methods for algorithms and/or hyper-parameter values have been proposed. Existing automatic selection methods are inefficient on large data sets. This poses a challenge for using machine learning in the clinical big data era. To address the challenge, this paper presents progressive sampling-based Bayesian optimization, an efficient and automatic selection method for both algorithms and hyper-parameter values. We report an implementation of the method. We show that compared to a state of the art automatic selection method, our method can significantly reduce search time, classification error rate, and standard deviation of error rate due to randomization. This is major progress towards enabling fast turnaround in identifying high-quality solutions required by many machine learning-based clinical data analysis tasks.

Ultraspectral sounding retrieval error budget and estimation

NASA Astrophysics Data System (ADS)

Zhou, Daniel K.; Larar, Allen M.; Liu, Xu; Smith, William L.; Strow, Larrabee L.; Yang, Ping

2011-11-01

The ultraspectral infrared radiances obtained from satellite observations provide atmospheric, surface, and/or cloud information. The intent of the measurement of the thermodynamic state is the initialization of weather and climate models. Great effort has been given to retrieving and validating these atmospheric, surface, and/or cloud properties. Error Consistency Analysis Scheme (ECAS), through fast radiative transfer model (RTM) forward and inverse calculations, has been developed to estimate the error budget in terms of absolute and standard deviation of differences in both spectral radiance and retrieved geophysical parameter domains. The retrieval error is assessed through ECAS without assistance of other independent measurements such as radiosonde data. ECAS re-evaluates instrument random noise, and establishes the link between radiometric accuracy and retrieved geophysical parameter accuracy. ECAS can be applied to measurements of any ultraspectral instrument and any retrieval scheme with associated RTM. In this paper, ECAS is described and demonstration is made with the measurements of the METOP-A satellite Infrared Atmospheric Sounding Interferometer (IASI).

Ultraspectral Sounding Retrieval Error Budget and Estimation

NASA Technical Reports Server (NTRS)

Zhou, Daniel K.; Larar, Allen M.; Liu, Xu; Smith, William L.; Strow, L. Larrabee; Yang, Ping

2011-01-01

The ultraspectral infrared radiances obtained from satellite observations provide atmospheric, surface, and/or cloud information. The intent of the measurement of the thermodynamic state is the initialization of weather and climate models. Great effort has been given to retrieving and validating these atmospheric, surface, and/or cloud properties. Error Consistency Analysis Scheme (ECAS), through fast radiative transfer model (RTM) forward and inverse calculations, has been developed to estimate the error budget in terms of absolute and standard deviation of differences in both spectral radiance and retrieved geophysical parameter domains. The retrieval error is assessed through ECAS without assistance of other independent measurements such as radiosonde data. ECAS re-evaluates instrument random noise, and establishes the link between radiometric accuracy and retrieved geophysical parameter accuracy. ECAS can be applied to measurements of any ultraspectral instrument and any retrieval scheme with associated RTM. In this paper, ECAS is described and demonstration is made with the measurements of the METOP-A satellite Infrared Atmospheric Sounding Interferometer (IASI)..

Dynamic modelling and parameter estimation of a hydraulic robot manipulator using a multi-objective genetic algorithm

NASA Astrophysics Data System (ADS)

Montazeri, A.; West, C.; Monk, S. D.; Taylor, C. J.

2017-04-01

This paper concerns the problem of dynamic modelling and parameter estimation for a seven degree of freedom hydraulic manipulator. The laboratory example is a dual-manipulator mobile robotic platform used for research into nuclear decommissioning. In contrast to earlier control model-orientated research using the same machine, the paper develops a nonlinear, mechanistic simulation model that can subsequently be used to investigate physically meaningful disturbances. The second contribution is to optimise the parameters of the new model, i.e. to determine reliable estimates of the physical parameters of a complex robotic arm which are not known in advance. To address the nonlinear and non-convex nature of the problem, the research relies on the multi-objectivisation of an output error single-performance index. The developed algorithm utilises a multi-objective genetic algorithm (GA) in order to find a proper solution. The performance of the model and the GA is evaluated using both simulated (i.e. with a known set of 'true' parameters) and experimental data. Both simulation and experimental results show that multi-objectivisation has improved convergence of the estimated parameters compared to the single-objective output error problem formulation. This is achieved by integrating the validation phase inside the algorithm implicitly and exploiting the inherent structure of the multi-objective GA for this specific system identification problem.

Optimal Tuner Selection for Kalman Filter-Based Aircraft Engine Performance Estimation

NASA Technical Reports Server (NTRS)

Simon, Donald L.; Garg, Sanjay

2010-01-01

A linear point design methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented. This technique specifically addresses the underdetermined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine which seeks to minimize the theoretical mean-squared estimation error. This paper derives theoretical Kalman filter estimation error bias and variance values at steady-state operating conditions, and presents the tuner selection routine applied to minimize these values. Results from the application of the technique to an aircraft engine simulation are presented and compared to the conventional approach of tuner selection. Experimental simulation results are found to be in agreement with theoretical predictions. The new methodology is shown to yield a significant improvement in on-line engine performance estimation accuracy

Improved methods for the measurement and analysis of stellar magnetic fields

NASA Technical Reports Server (NTRS)

Saar, Steven H.

1988-01-01

The paper presents several improved methods for the measurement of magnetic fields on cool stars which take into account simple radiative transfer effects and the exact Zeeman patterns. Using these methods, high-resolution, low-noise data can be fitted with theoretical line profiles to determine the mean magnetic field strength in stellar active regions and a model-dependent fraction of the stellar surface (filling factor) covered by these regions. Random errors in the derived field strength and filling factor are parameterized in terms of signal-to-noise ratio, wavelength, spectral resolution, stellar rotation rate, and the magnetic parameters themselves. Weak line blends, if left uncorrected, can have significant systematic effects on the derived magnetic parameters, and thus several methods are developed to compensate partially for them. The magnetic parameters determined by previous methods likely have systematic errors because of such line blends and because of line saturation effects. Other sources of systematic error are explored in detail. These sources of error currently make it difficult to determine the magnetic parameters of individual stars to better than about + or - 20 percent.

Efficient Reduction and Analysis of Model Predictive Error

NASA Astrophysics Data System (ADS)

Doherty, J.

2006-12-01

Most groundwater models are calibrated against historical measurements of head and other system states before being used to make predictions in a real-world context. Through the calibration process, parameter values are estimated or refined such that the model is able to reproduce historical behaviour of the system at pertinent observation points reasonably well. Predictions made by the model are deemed to have greater integrity because of this. Unfortunately, predictive integrity is not as easy to achieve as many groundwater practitioners would like to think. The level of parameterisation detail estimable through the calibration process (especially where estimation takes place on the basis of heads alone) is strictly limited, even where full use is made of modern mathematical regularisation techniques such as those encapsulated in the PEST calibration package. (Use of these mechanisms allows more information to be extracted from a calibration dataset than is possible using simpler regularisation devices such as zones of piecewise constancy.) Where a prediction depends on aspects of parameterisation detail that are simply not inferable through the calibration process (which is often the case for predictions related to contaminant movement, and/or many aspects of groundwater/surface water interaction), then that prediction may be just as much in error as it would have been if the model had not been calibrated at all. Model predictive error arises from two sources. These are (a) the presence of measurement noise within the calibration dataset through which linear combinations of parameters spanning the "calibration solution space" are inferred, and (b) the sensitivity of the prediction to members of the "calibration null space" spanned by linear combinations of parameters which are not inferable through the calibration process. The magnitude of the former contribution depends on the level of measurement noise. The magnitude of the latter contribution (which often dominates the former) depends on the "innate variability" of hydraulic properties within the model domain. Knowledge of both of these is a prerequisite for characterisation of the magnitude of possible model predictive error. Unfortunately, in most cases, such knowledge is incomplete and subjective. Nevertheless, useful analysis of model predictive error can still take place. The present paper briefly discusses the means by which mathematical regularisation can be employed in the model calibration process in order to extract as much information as possible on hydraulic property heterogeneity prevailing within the model domain, thereby reducing predictive error to the lowest that can be achieved on the basis of that dataset. It then demonstrates the means by which predictive error variance can be quantified based on information supplied by the regularised inversion process. Both linear and nonlinear predictive error variance analysis is demonstrated using a number of real-world and synthetic examples.

Determining Hypocentral Parameters for Local Earthquakes in 1-D Using a Genetic Algorithm and Two-point ray tracing

NASA Astrophysics Data System (ADS)

Kim, W.; Hahm, I.; Ahn, S. J.; Lim, D. H.

2005-12-01

This paper introduces a powerful method for determining hypocentral parameters for local earthquakes in 1-D using a genetic algorithm (GA) and two-point ray tracing. Using existing algorithms to determine hypocentral parameters is difficult, because these parameters can vary based on initial velocity models. We developed a new method to solve this problem by applying a GA to an existing algorithm, HYPO-71 (Lee and Larh, 1975). The original HYPO-71 algorithm was modified by applying two-point ray tracing and a weighting factor with respect to the takeoff angle at the source to reduce errors from the ray path and hypocenter depth. Artificial data, without error, were generated by computer using two-point ray tracing in a true model, in which velocity structure and hypocentral parameters were known. The accuracy of the calculated results was easily determined by comparing calculated and actual values. We examined the accuracy of this method for several cases by changing the true and modeled layer numbers and thicknesses. The computational results show that this method determines nearly exact hypocentral parameters without depending on initial velocity models. Furthermore, accurate and nearly unique hypocentral parameters were obtained, although the number of modeled layers and thicknesses differed from those in the true model. Therefore, this method can be a useful tool for determining hypocentral parameters in regions where reliable local velocity values are unknown. This method also provides the basic a priori information for 3-D studies. KEY -WORDS: hypocentral parameters, genetic algorithm (GA), two-point ray tracing

Comparison of three-dimensional parameters of Halo CMEs using three cone models

NASA Astrophysics Data System (ADS)

Na, H.; Moon, Y.; Jang, S.; Lee, K.

2012-12-01

Halo coronal mass ejections (HCMEs) are a major cause of geomagnetic storms and their three dimensional structures are important for space weather. In this study, we compare three cone models: an elliptical cone model, an ice-cream cone model, and an asymmetric cone model. These models allow us to determine the three dimensional parameters of HCMEs such as radial speed, angular width, and the angle (γ) between sky plane and cone axis. We compare these parameters obtained from three models using 62 well-observed HCMEs observed by SOHO/LASCO from 2001 to 2002. Then we obtain the root mean square error (RMS error) between maximum measured projection speeds and their calculated projection speeds from the cone models. As a result, we find that the radial speeds obtained from the models are well correlated with one another (R > 0.84). The correlation coefficients between angular widths are ranges from 0.04 to 0.53 and those between γ values are from -0.15 to 0.47, which are much smaller than expected. The reason may be due to different assumptions and methods. The RMS errors between the maximum measured projection speeds and the maximum estimated projection speeds of the elliptical cone model, the ice-cream cone model, and the asymmetric cone model are 213 km/s, 254 km/s, and 267 km/s, respectively. And we obtain the correlation coefficients between the location from the models and the flare location (R > 0.75). Finally, we discuss strengths and weaknesses of these models in terms of space weather application.

Using soft computing techniques to predict corrected air permeability using Thomeer parameters, air porosity and grain density

NASA Astrophysics Data System (ADS)

Nooruddin, Hasan A.; Anifowose, Fatai; Abdulraheem, Abdulazeez

2014-03-01

Soft computing techniques are recently becoming very popular in the oil industry. A number of computational intelligence-based predictive methods have been widely applied in the industry with high prediction capabilities. Some of the popular methods include feed-forward neural networks, radial basis function network, generalized regression neural network, functional networks, support vector regression and adaptive network fuzzy inference system. A comparative study among most popular soft computing techniques is presented using a large dataset published in literature describing multimodal pore systems in the Arab D formation. The inputs to the models are air porosity, grain density, and Thomeer parameters obtained using mercury injection capillary pressure profiles. Corrected air permeability is the target variable. Applying developed permeability models in recent reservoir characterization workflow ensures consistency between micro and macro scale information represented mainly by Thomeer parameters and absolute permeability. The dataset was divided into two parts with 80% of data used for training and 20% for testing. The target permeability variable was transformed to the logarithmic scale as a pre-processing step and to show better correlations with the input variables. Statistical and graphical analysis of the results including permeability cross-plots and detailed error measures were created. In general, the comparative study showed very close results among the developed models. The feed-forward neural network permeability model showed the lowest average relative error, average absolute relative error, standard deviations of error and root means squares making it the best model for such problems. Adaptive network fuzzy inference system also showed very good results.

How large are the consequences of covariate imbalance in cluster randomized trials: a simulation study with a continuous outcome and a binary covariate at the cluster level.

PubMed

Moerbeek, Mirjam; van Schie, Sander

2016-07-11

The number of clusters in a cluster randomized trial is often low. It is therefore likely random assignment of clusters to treatment conditions results in covariate imbalance. There are no studies that quantify the consequences of covariate imbalance in cluster randomized trials on parameter and standard error bias and on power to detect treatment effects. The consequences of covariance imbalance in unadjusted and adjusted linear mixed models are investigated by means of a simulation study. The factors in this study are the degree of imbalance, the covariate effect size, the cluster size and the intraclass correlation coefficient. The covariate is binary and measured at the cluster level; the outcome is continuous and measured at the individual level. The results show covariate imbalance results in negligible parameter bias and small standard error bias in adjusted linear mixed models. Ignoring the possibility of covariate imbalance while calculating the sample size at the cluster level may result in a loss in power of at most 25 % in the adjusted linear mixed model. The results are more severe for the unadjusted linear mixed model: parameter biases up to 100 % and standard error biases up to 200 % may be observed. Power levels based on the unadjusted linear mixed model are often too low. The consequences are most severe for large clusters and/or small intraclass correlation coefficients since then the required number of clusters to achieve a desired power level is smallest. The possibility of covariate imbalance should be taken into account while calculating the sample size of a cluster randomized trial. Otherwise more sophisticated methods to randomize clusters to treatments should be used, such as stratification or balance algorithms. All relevant covariates should be carefully identified, be actually measured and included in the statistical model to avoid severe levels of parameter and standard error bias and insufficient power levels.

On land-use modeling: A treatise of satellite imagery data and misclassification error

NASA Astrophysics Data System (ADS)

Sandler, Austin M.

Recent availability of satellite-based land-use data sets, including data sets with contiguous spatial coverage over large areas, relatively long temporal coverage, and fine-scale land cover classifications, is providing new opportunities for land-use research. However, care must be used when working with these datasets due to misclassification error, which causes inconsistent parameter estimates in the discrete choice models typically used to model land-use. I therefore adapt the empirical correction methods developed for other contexts (e.g., epidemiology) so that they can be applied to land-use modeling. I then use a Monte Carlo simulation, and an empirical application using actual satellite imagery data from the Northern Great Plains, to compare the results of a traditional model ignoring misclassification to those from models accounting for misclassification. Results from both the simulation and application indicate that ignoring misclassification will lead to biased results. Even seemingly insignificant levels of misclassification error (e.g., 1%) result in biased parameter estimates, which alter marginal effects enough to affect policy inference. At the levels of misclassification typical in current satellite imagery datasets (e.g., as high as 35%), ignoring misclassification can lead to systematically erroneous land-use probabilities and substantially biased marginal effects. The correction methods I propose, however, generate consistent parameter estimates and therefore consistent estimates of marginal effects and predicted land-use probabilities.

Software Would Largely Automate Design of Kalman Filter

NASA Technical Reports Server (NTRS)

Chuang, Jason C. H.; Negast, William J.

2005-01-01

Embedded Navigation Filter Automatic Designer (ENFAD) is a computer program being developed to automate the most difficult tasks in designing embedded software to implement a Kalman filter in a navigation system. The most difficult tasks are selection of error states of the filter and tuning of filter parameters, which are timeconsuming trial-and-error tasks that require expertise and rarely yield optimum results. An optimum selection of error states and filter parameters depends on navigation-sensor and vehicle characteristics, and on filter processing time. ENFAD would include a simulation module that would incorporate all possible error states with respect to a given set of vehicle and sensor characteristics. The first of two iterative optimization loops would vary the selection of error states until the best filter performance was achieved in Monte Carlo simulations. For a fixed selection of error states, the second loop would vary the filter parameter values until an optimal performance value was obtained. Design constraints would be satisfied in the optimization loops. Users would supply vehicle and sensor test data that would be used to refine digital models in ENFAD. Filter processing time and filter accuracy would be computed by ENFAD.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Petiteau, Antoine; Babak, Stanislav; Sesana, Alberto

Gravitational wave (GW) signals from coalescing massive black hole (MBH) binaries could be used as standard sirens to measure cosmological parameters. The future space-based GW observatory Laser Interferometer Space Antenna (LISA) will detect up to a hundred of those events, providing very accurate measurements of their luminosity distances. To constrain the cosmological parameters, we also need to measure the redshift of the galaxy (or cluster of galaxies) hosting the merger. This requires the identification of a distinctive electromagnetic event associated with the binary coalescence. However, putative electromagnetic signatures may be too weak to be observed. Instead, we study here themore » possibility of constraining the cosmological parameters by enforcing statistical consistency between all the possible hosts detected within the measurement error box of a few dozen of low-redshift (z < 3) events. We construct MBH populations using merger tree realizations of the dark matter hierarchy in a {Lambda}CDM universe, and we use data from the Millennium simulation to model the galaxy distribution in the LISA error box. We show that, assuming that all the other cosmological parameters are known, the parameter w describing the dark energy equation of state can be constrained to a 4%-8% level (2{sigma} error), competitive with current uncertainties obtained by type Ia supernovae measurements, providing an independent test of our cosmological model.« less

Artificial neural networks as alternative tool for minimizing error predictions in manufacturing ultradeformable nanoliposome formulations.

PubMed

León Blanco, José M; González-R, Pedro L; Arroyo García, Carmen Martina; Cózar-Bernal, María José; Calle Suárez, Marcos; Canca Ortiz, David; Rabasco Álvarez, Antonio María; González Rodríguez, María Luisa

2018-01-01

This work was aimed at determining the feasibility of artificial neural networks (ANN) by implementing backpropagation algorithms with default settings to generate better predictive models than multiple linear regression (MLR) analysis. The study was hypothesized on timolol-loaded liposomes. As tutorial data for ANN, causal factors were used, which were fed into the computer program. The number of training cycles has been identified in order to optimize the performance of the ANN. The optimization was performed by minimizing the error between the predicted and real response values in the training step. The results showed that training was stopped at 10 000 training cycles with 80% of the pattern values, because at this point the ANN generalizes better. Minimum validation error was achieved at 12 hidden neurons in a single layer. MLR has great prediction ability, with errors between predicted and real values lower than 1% in some of the parameters evaluated. Thus, the performance of this model was compared to that of the MLR using a factorial design. Optimal formulations were identified by minimizing the distance among measured and theoretical parameters, by estimating the prediction errors. Results indicate that the ANN shows much better predictive ability than the MLR model. These findings demonstrate the increased efficiency of the combination of ANN and design of experiments, compared to the conventional MLR modeling techniques.

Measurement uncertainty and feasibility study of a flush airdata system for a hypersonic flight experiment

NASA Technical Reports Server (NTRS)

Whitmore, Stephen A.; Moes, Timothy R.

1994-01-01

Presented is a feasibility and error analysis for a hypersonic flush airdata system on a hypersonic flight experiment (HYFLITE). HYFLITE heating loads make intrusive airdata measurement impractical. Although this analysis is specifically for the HYFLITE vehicle and trajectory, the problems analyzed are generally applicable to hypersonic vehicles. A layout of the flush-port matrix is shown. Surface pressures are related airdata parameters using a simple aerodynamic model. The model is linearized using small perturbations and inverted using nonlinear least-squares. Effects of various error sources on the overall uncertainty are evaluated using an error simulation. Error sources modeled include boundarylayer/viscous interactions, pneumatic lag, thermal transpiration in the sensor pressure tubing, misalignment in the matrix layout, thermal warping of the vehicle nose, sampling resolution, and transducer error. Using simulated pressure data for input to the estimation algorithm, effects caused by various error sources are analyzed by comparing estimator outputs with the original trajectory. To obtain ensemble averages the simulation is run repeatedly and output statistics are compiled. Output errors resulting from the various error sources are presented as a function of Mach number. Final uncertainties with all modeled error sources included are presented as a function of Mach number.

Angular motion estimation using dynamic models in a gyro-free inertial measurement unit.

PubMed

Edwan, Ezzaldeen; Knedlik, Stefan; Loffeld, Otmar

2012-01-01

In this paper, we summarize the results of using dynamic models borrowed from tracking theory in describing the time evolution of the state vector to have an estimate of the angular motion in a gyro-free inertial measurement unit (GF-IMU). The GF-IMU is a special type inertial measurement unit (IMU) that uses only a set of accelerometers in inferring the angular motion. Using distributed accelerometers, we get an angular information vector (AIV) composed of angular acceleration and quadratic angular velocity terms. We use a Kalman filter approach to estimate the angular velocity vector since it is not expressed explicitly within the AIV. The bias parameters inherent in the accelerometers measurements' produce a biased AIV and hence the AIV bias parameters are estimated within an augmented state vector. Using dynamic models, the appended bias parameters of the AIV become observable and hence we can have unbiased angular motion estimate. Moreover, a good model is required to extract the maximum amount of information from the observation. Observability analysis is done to determine the conditions for having an observable state space model. For higher grades of accelerometers and under relatively higher sampling frequency, the error of accelerometer measurements is dominated by the noise error. Consequently, simulations are conducted on two models, one has bias parameters appended in the state space model and the other is a reduced model without bias parameters.

Angular Motion Estimation Using Dynamic Models in a Gyro-Free Inertial Measurement Unit

PubMed Central

Edwan, Ezzaldeen; Knedlik, Stefan; Loffeld, Otmar

2012-01-01

In this paper, we summarize the results of using dynamic models borrowed from tracking theory in describing the time evolution of the state vector to have an estimate of the angular motion in a gyro-free inertial measurement unit (GF-IMU). The GF-IMU is a special type inertial measurement unit (IMU) that uses only a set of accelerometers in inferring the angular motion. Using distributed accelerometers, we get an angular information vector (AIV) composed of angular acceleration and quadratic angular velocity terms. We use a Kalman filter approach to estimate the angular velocity vector since it is not expressed explicitly within the AIV. The bias parameters inherent in the accelerometers measurements' produce a biased AIV and hence the AIV bias parameters are estimated within an augmented state vector. Using dynamic models, the appended bias parameters of the AIV become observable and hence we can have unbiased angular motion estimate. Moreover, a good model is required to extract the maximum amount of information from the observation. Observability analysis is done to determine the conditions for having an observable state space model. For higher grades of accelerometers and under relatively higher sampling frequency, the error of accelerometer measurements is dominated by the noise error. Consequently, simulations are conducted on two models, one has bias parameters appended in the state space model and the other is a reduced model without bias parameters. PMID:22778586

Evaluation Of Statistical Models For Forecast Errors From The HBV-Model

NASA Astrophysics Data System (ADS)

Engeland, K.; Kolberg, S.; Renard, B.; Stensland, I.

2009-04-01

Three statistical models for the forecast errors for inflow to the Langvatn reservoir in Northern Norway have been constructed and tested according to how well the distribution and median values of the forecasts errors fit to the observations. For the first model observed and forecasted inflows were transformed by the Box-Cox transformation before a first order autoregressive model was constructed for the forecast errors. The parameters were conditioned on climatic conditions. In the second model the Normal Quantile Transformation (NQT) was applied on observed and forecasted inflows before a similar first order autoregressive model was constructed for the forecast errors. For the last model positive and negative errors were modeled separately. The errors were first NQT-transformed before a model where the mean values were conditioned on climate, forecasted inflow and yesterday's error. To test the three models we applied three criterions: We wanted a) the median values to be close to the observed values; b) the forecast intervals to be narrow; c) the distribution to be correct. The results showed that it is difficult to obtain a correct model for the forecast errors, and that the main challenge is to account for the auto-correlation in the errors. Model 1 and 2 gave similar results, and the main drawback is that the distributions are not correct. The 95% forecast intervals were well identified, but smaller forecast intervals were over-estimated, and larger intervals were under-estimated. Model 3 gave a distribution that fits better, but the median values do not fit well since the auto-correlation is not properly accounted for. If the 95% forecast interval is of interest, Model 2 is recommended. If the whole distribution is of interest, Model 3 is recommended.

Angular ellipticity correlations in a composite alignment model for elliptical and spiral galaxies and inference from weak lensing

NASA Astrophysics Data System (ADS)

Tugendhat, Tim M.; Schäfer, Björn Malte

2018-05-01

We investigate a physical, composite alignment model for both spiral and elliptical galaxies and its impact on cosmological parameter estimation from weak lensing for a tomographic survey. Ellipticity correlation functions and angular ellipticity spectra for spiral and elliptical galaxies are derived on the basis of tidal interactions with the cosmic large-scale structure and compared to the tomographic weak-lensing signal. We find that elliptical galaxies cause a contribution to the weak-lensing dominated ellipticity correlation on intermediate angular scales between ℓ ≃ 40 and ℓ ≃ 400 before that of spiral galaxies dominates on higher multipoles. The predominant term on intermediate scales is the negative cross-correlation between intrinsic alignments and weak gravitational lensing (GI-alignment). We simulate parameter inference from weak gravitational lensing with intrinsic alignments unaccounted; the bias induced by ignoring intrinsic alignments in a survey like Euclid is shown to be several times larger than the statistical error and can lead to faulty conclusions when comparing to other observations. The biases generally point into different directions in parameter space, such that in some cases one can observe a partial cancellation effect. Furthermore, it is shown that the biases increase with the number of tomographic bins used for the parameter estimation process. We quantify this parameter estimation bias in units of the statistical error and compute the loss of Bayesian evidence for a model due to the presence of systematic errors as well as the Kullback-Leibler divergence to quantify the distance between the true model and the wrongly inferred one.

A comparison of two approaches to modelling snow cover dynamics at the Polish Polar Station at Hornsund

NASA Astrophysics Data System (ADS)

Luks, B.; Osuch, M.; Romanowicz, R. J.

2012-04-01

We compare two approaches to modelling snow cover dynamics at the Polish Polar Station at Hornsund. In the first approach we apply physically-based Utah Energy Balance Snow Accumulation and Melt Model (UEB) (Tarboton et al., 1995; Tarboton and Luce, 1996). The model uses a lumped representation of the snowpack with two primary state variables: snow water equivalence and energy. Its main driving inputs are: air temperature, precipitation, wind speed, humidity and radiation (estimated from the diurnal temperature range). Those variables are used for physically-based calculations of radiative, sensible, latent and advective heat exchanges with a 3 hours time step. The second method is an application of a statistically efficient lumped parameter time series approach to modelling the dynamics of snow cover , based on daily meteorological measurements from the same area. A dynamic Stochastic Transfer Function model is developed that follows the Data Based Mechanistic approach, where a stochastic data-based identification of model structure and an estimation of its parameters are followed by a physical interpretation. We focus on the analysis of uncertainty of both model outputs. In the time series approach, the applied techniques also provide estimates of the modeling errors and the uncertainty of the model parameters. In the first, physically-based approach the applied UEB model is deterministic. It assumes that the observations are without errors and that the model structure perfectly describes the processes within the snowpack. To take into account the model and observation errors, we applied a version of the Generalized Likelihood Uncertainty Estimation technique (GLUE). This technique also provide estimates of the modelling errors and the uncertainty of the model parameters. The observed snowpack water equivalent values are compared with those simulated with 95% confidence bounds. This work was supported by National Science Centre of Poland (grant no. 7879/B/P01/2011/40). Tarboton, D. G., T. G. Chowdhury and T. H. Jackson, 1995. A Spatially Distributed Energy Balance Snowmelt Model. In K. A. Tonnessen, M. W. Williams and M. Tranter (Ed.), Proceedings of a Boulder Symposium, July 3-14, IAHS Publ. no. 228, pp. 141-155. Tarboton, D. G. and C. H. Luce, 1996. Utah Energy Balance Snow Accumulation and Melt Model (UEB). Computer model technical description and users guide, Utah Water Research Laboratory and USDA Forest Service Intermountain Research Station (http://www.engineering.usu.edu/dtarb/). 64 pp.

Accelerated Brain DCE-MRI Using Iterative Reconstruction With Total Generalized Variation Penalty for Quantitative Pharmacokinetic Analysis: A Feasibility Study.

PubMed

Wang, Chunhao; Yin, Fang-Fang; Kirkpatrick, John P; Chang, Zheng

2017-08-01

To investigate the feasibility of using undersampled k-space data and an iterative image reconstruction method with total generalized variation penalty in the quantitative pharmacokinetic analysis for clinical brain dynamic contrast-enhanced magnetic resonance imaging. Eight brain dynamic contrast-enhanced magnetic resonance imaging scans were retrospectively studied. Two k-space sparse sampling strategies were designed to achieve a simulated image acquisition acceleration factor of 4. They are (1) a golden ratio-optimized 32-ray radial sampling profile and (2) a Cartesian-based random sampling profile with spatiotemporal-regularized sampling density constraints. The undersampled data were reconstructed to yield images using the investigated reconstruction technique. In quantitative pharmacokinetic analysis on a voxel-by-voxel basis, the rate constant K trans in the extended Tofts model and blood flow F B and blood volume V B from the 2-compartment exchange model were analyzed. Finally, the quantitative pharmacokinetic parameters calculated from the undersampled data were compared with the corresponding calculated values from the fully sampled data. To quantify each parameter's accuracy calculated using the undersampled data, error in volume mean, total relative error, and cross-correlation were calculated. The pharmacokinetic parameter maps generated from the undersampled data appeared comparable to the ones generated from the original full sampling data. Within the region of interest, most derived error in volume mean values in the region of interest was about 5% or lower, and the average error in volume mean of all parameter maps generated through either sampling strategy was about 3.54%. The average total relative error value of all parameter maps in region of interest was about 0.115, and the average cross-correlation of all parameter maps in region of interest was about 0.962. All investigated pharmacokinetic parameters had no significant differences between the result from original data and the reduced sampling data. With sparsely sampled k-space data in simulation of accelerated acquisition by a factor of 4, the investigated dynamic contrast-enhanced magnetic resonance imaging pharmacokinetic parameters can accurately estimate the total generalized variation-based iterative image reconstruction method for reliable clinical application.

Constraints on a scale-dependent bias from galaxy clustering

NASA Astrophysics Data System (ADS)

Amendola, L.; Menegoni, E.; Di Porto, C.; Corsi, M.; Branchini, E.

2017-01-01

We forecast the future constraints on scale-dependent parametrizations of galaxy bias and their impact on the estimate of cosmological parameters from the power spectrum of galaxies measured in a spectroscopic redshift survey. For the latter we assume a wide survey at relatively large redshifts, similar to the planned Euclid survey, as the baseline for future experiments. To assess the impact of the bias we perform a Fisher matrix analysis, and we adopt two different parametrizations of scale-dependent bias. The fiducial models for galaxy bias are calibrated using mock catalogs of H α emitting galaxies mimicking the expected properties of the objects that will be targeted by the Euclid survey. In our analysis we have obtained two main results. First of all, allowing for a scale-dependent bias does not significantly increase the errors on the other cosmological parameters apart from the rms amplitude of density fluctuations, σ8 , and the growth index γ , whose uncertainties increase by a factor up to 2, depending on the bias model adopted. Second, we find that the accuracy in the linear bias parameter b0 can be estimated to within 1%-2% at various redshifts regardless of the fiducial model. The nonlinear bias parameters have significantly large errors that depend on the model adopted. Despite this, in the more realistic scenarios departures from the simple linear bias prescription can be detected with a ˜2 σ significance at each redshift explored. Finally, we use the Fisher matrix formalism to assess the impact od assuming an incorrect bias model and find that the systematic errors induced on the cosmological parameters are similar or even larger than the statistical ones.

A back-fitting algorithm to improve real-time flood forecasting

NASA Astrophysics Data System (ADS)

Zhang, Xiaojing; Liu, Pan; Cheng, Lei; Liu, Zhangjun; Zhao, Yan

2018-07-01

Real-time flood forecasting is important for decision-making with regards to flood control and disaster reduction. The conventional approach involves a postprocessor calibration strategy that first calibrates the hydrological model and then estimates errors. This procedure can simulate streamflow consistent with observations, but obtained parameters are not optimal. Joint calibration strategies address this issue by refining hydrological model parameters jointly with the autoregressive (AR) model. In this study, five alternative schemes are used to forecast floods. Scheme I uses only the hydrological model, while scheme II includes an AR model for error correction. In scheme III, differencing is used to remove non-stationarity in the error series. A joint inference strategy employed in scheme IV calibrates the hydrological and AR models simultaneously. The back-fitting algorithm, a basic approach for training an additive model, is adopted in scheme V to alternately recalibrate hydrological and AR model parameters. The performance of the five schemes is compared with a case study of 15 recorded flood events from China's Baiyunshan reservoir basin. Our results show that (1) schemes IV and V outperform scheme III during the calibration and validation periods and (2) scheme V is inferior to scheme IV in the calibration period, but provides better results in the validation period. Joint calibration strategies can therefore improve the accuracy of flood forecasting. Additionally, the back-fitting recalibration strategy produces weaker overcorrection and a more robust performance compared with the joint inference strategy.

Iterative integral parameter identification of a respiratory mechanics model.

PubMed

Schranz, Christoph; Docherty, Paul D; Chiew, Yeong Shiong; Möller, Knut; Chase, J Geoffrey

2012-07-18

Patient-specific respiratory mechanics models can support the evaluation of optimal lung protective ventilator settings during ventilation therapy. Clinical application requires that the individual's model parameter values must be identified with information available at the bedside. Multiple linear regression or gradient-based parameter identification methods are highly sensitive to noise and initial parameter estimates. Thus, they are difficult to apply at the bedside to support therapeutic decisions. An iterative integral parameter identification method is applied to a second order respiratory mechanics model. The method is compared to the commonly used regression methods and error-mapping approaches using simulated and clinical data. The clinical potential of the method was evaluated on data from 13 Acute Respiratory Distress Syndrome (ARDS) patients. The iterative integral method converged to error minima 350 times faster than the Simplex Search Method using simulation data sets and 50 times faster using clinical data sets. Established regression methods reported erroneous results due to sensitivity to noise. In contrast, the iterative integral method was effective independent of initial parameter estimations, and converged successfully in each case tested. These investigations reveal that the iterative integral method is beneficial with respect to computing time, operator independence and robustness, and thus applicable at the bedside for this clinical application.

Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors

USGS Publications Warehouse

Langbein, John O.

2017-01-01

Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1/fα">1/fα1/fα with frequency, f. With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013. doi:10.1007/s00190-012-0605-0) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.

Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors

NASA Astrophysics Data System (ADS)

Langbein, John

2017-08-01

Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1/f^{α } with frequency, f. With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013. doi: 10.1007/s00190-012-0605-0) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.

The modelling of lead removal from water by deep eutectic solvents functionalized CNTs: artificial neural network (ANN) approach.

PubMed

Fiyadh, Seef Saadi; AlSaadi, Mohammed Abdulhakim; AlOmar, Mohamed Khalid; Fayaed, Sabah Saadi; Hama, Ako R; Bee, Sharifah; El-Shafie, Ahmed

2017-11-01

The main challenge in the lead removal simulation is the behaviour of non-linearity relationships between the process parameters. The conventional modelling technique usually deals with this problem by a linear method. The substitute modelling technique is an artificial neural network (ANN) system, and it is selected to reflect the non-linearity in the interaction among the variables in the function. Herein, synthesized deep eutectic solvents were used as a functionalized agent with carbon nanotubes as adsorbents of Pb 2+ . Different parameters were used in the adsorption study including pH (2.7 to 7), adsorbent dosage (5 to 20 mg), contact time (3 to 900 min) and Pb 2+ initial concentration (3 to 60 mg/l). The number of experimental trials to feed and train the system was 158 runs conveyed in laboratory scale. Two ANN types were designed in this work, the feed-forward back-propagation and layer recurrent; both methods are compared based on their predictive proficiency in terms of the mean square error (MSE), root mean square error, relative root mean square error, mean absolute percentage error and determination coefficient (R 2 ) based on the testing dataset. The ANN model of lead removal was subjected to accuracy determination and the results showed R 2 of 0.9956 with MSE of 1.66 × 10 -4 . The maximum relative error is 14.93% for the feed-forward back-propagation neural network model.

Impact of fitting algorithms on errors of parameter estimates in dynamic contrast-enhanced MRI

NASA Astrophysics Data System (ADS)

Debus, C.; Floca, R.; Nörenberg, D.; Abdollahi, A.; Ingrisch, M.

2017-12-01

Parameter estimation in dynamic contrast-enhanced MRI (DCE MRI) is usually performed by non-linear least square (NLLS) fitting of a pharmacokinetic model to a measured concentration-time curve. The two-compartment exchange model (2CXM) describes the compartments ‘plasma’ and ‘interstitial volume’ and their exchange in terms of plasma flow and capillary permeability. The model function can be defined by either a system of two coupled differential equations or a closed-form analytical solution. The aim of this study was to compare these two representations in terms of accuracy, robustness and computation speed, depending on parameter combination and temporal sampling. The impact on parameter estimation errors was investigated by fitting the 2CXM to simulated concentration-time curves. Parameter combinations representing five tissue types were used, together with two arterial input functions, a measured and a theoretical population based one, to generate 4D concentration images at three different temporal resolutions. Images were fitted by NLLS techniques, where the sum of squared residuals was calculated by either numeric integration with the Runge-Kutta method or convolution. Furthermore two example cases, a prostate carcinoma and a glioblastoma multiforme patient, were analyzed in order to investigate the validity of our findings in real patient data. The convolution approach yields improved results in precision and robustness of determined parameters. Precision and stability are limited in curves with low blood flow. The model parameter ve shows great instability and little reliability in all cases. Decreased temporal resolution results in significant errors for the differential equation approach in several curve types. The convolution excelled in computational speed by three orders of magnitude. Uncertainties in parameter estimation at low temporal resolution cannot be compensated by usage of the differential equations. Fitting with the convolution approach is superior in computational time, with better stability and accuracy at the same time.

Influence of tire dynamics on slip ratio estimation of independent driving wheel system

NASA Astrophysics Data System (ADS)

Li, Jianqiu; Song, Ziyou; Wei, Yintao; Ouyang, Minggao

2014-11-01

The independent driving wheel system, which is composed of in-wheel permanent magnet synchronous motor(I-PMSM) and tire, is more convenient to estimate the slip ratio because the rotary speed of the rotor can be accurately measured. However, the ring speed of the tire ring doesn't equal to the rotor speed considering the tire deformation. For this reason, a deformable tire and a detailed I-PMSM are modeled by using Matlab/Simulink. Moreover, the tire/road contact interface(a slippery road) is accurately described by the non-linear relaxation length-based model and the Magic Formula pragmatic model. Based on the relatively accurate model, the error of slip ratio estimated by the rotor rotary speed is analyzed in both time and frequency domains when a quarter car is started by the I-PMSM with a definite target torque input curve. In addition, the natural frequencies(NFs) of the driving wheel system with variable parameters are illustrated to present the relationship between the slip ratio estimation error and the NF. According to this relationship, a low-pass filter, whose cut-off frequency corresponds to the NF, is proposed to eliminate the error in the estimated slip ratio. The analysis, concerning the effect of the driving wheel parameters and road conditions on slip ratio estimation, shows that the peak estimation error can be reduced up to 75% when the LPF is adopted. The robustness and effectiveness of the LPF are therefore validated. This paper builds up the deformable tire model and the detailed I-PMSM models, and analyzes the effect of the driving wheel parameters and road conditions on slip ratio estimation.

Aeroelastic Modeling of X-56A Stiff-Wing Configuration Flight Test Data

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Boucher, Matthew J.

2017-01-01

Aeroelastic stability and control derivatives for the X-56A Multi-Utility Technology Testbed (MUTT), in the stiff-wing configuration, were estimated from flight test data using the output-error method. Practical aspects of the analysis are discussed. The orthogonal phase-optimized multisine inputs provided excellent data information for aeroelastic modeling. Consistent parameter estimates were determined using output error in both the frequency and time domains. The frequency domain analysis converged faster and was less sensitive to starting values for the model parameters, which was useful for determining the aeroelastic model structure and obtaining starting values for the time domain analysis. Including a modal description of the structure from a finite element model reduced the complexity of the estimation problem and improved the modeling results. Effects of reducing the model order on the short period stability and control derivatives were investigated.

A mechanistic modeling and data assimilation framework for Mojave Desert ecohydrology

USGS Publications Warehouse

Ng, Gene-Hua Crystal.; Bedford, David; Miller, David

2014-01-01

This study demonstrates and addresses challenges in coupled ecohydrological modeling in deserts, which arise due to unique plant adaptations, marginal growing conditions, slow net primary production rates, and highly variable rainfall. We consider model uncertainty from both structural and parameter errors and present a mechanistic model for the shrub Larrea tridentata (creosote bush) under conditions found in the Mojave National Preserve in southeastern California (USA). Desert-specific plant and soil features are incorporated into the CLM-CN model by Oleson et al. (2010). We then develop a data assimilation framework using the ensemble Kalman filter (EnKF) to estimate model parameters based on soil moisture and leaf-area index observations. A new implementation procedure, the “multisite loop EnKF,” tackles parameter estimation difficulties found to affect desert ecohydrological applications. Specifically, the procedure iterates through data from various observation sites to alleviate adverse filter impacts from non-Gaussianity in small desert vegetation state values. It also readjusts inconsistent parameters and states through a model spin-up step that accounts for longer dynamical time scales due to infrequent rainfall in deserts. Observation error variance inflation may also be needed to help prevent divergence of estimates from true values. Synthetic test results highlight the importance of adequate observations for reducing model uncertainty, which can be achieved through data quality or quantity.

Analysis of a Shock-Associated Noise Prediction Model Using Measured Jet Far-Field Noise Data

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Sharpe, Jacob A.

2014-01-01

A code for predicting supersonic jet broadband shock-associated noise was assessed using a database containing noise measurements of a jet issuing from a convergent nozzle. The jet was operated at 24 conditions covering six fully expanded Mach numbers with four total temperature ratios. To enable comparisons of the predicted shock-associated noise component spectra with data, the measured total jet noise spectra were separated into mixing noise and shock-associated noise component spectra. Comparisons between predicted and measured shock-associated noise component spectra were used to identify deficiencies in the prediction model. Proposed revisions to the model, based on a study of the overall sound pressure levels for the shock-associated noise component of the measured data, a sensitivity analysis of the model parameters with emphasis on the definition of the convection velocity parameter, and a least-squares fit of the predicted to the measured shock-associated noise component spectra, resulted in a new definition for the source strength spectrum in the model. An error analysis showed that the average error in the predicted spectra was reduced by as much as 3.5 dB for the revised model relative to the average error for the original model.

The Dipole Segment Model for Axisymmetrical Elongated Asteroids

NASA Astrophysics Data System (ADS)

Zeng, Xiangyuan; Zhang, Yonglong; Yu, Yang; Liu, Xiangdong

2018-02-01

Various simplified models have been investigated as a way to understand the complex dynamical environment near irregular asteroids. A dipole segment model is explored in this paper, one that is composed of a massive straight segment and two point masses at the extremities of the segment. Given an explicitly simple form of the potential function that is associated with the dipole segment model, five topological cases are identified with different sets of system parameters. Locations, stabilities, and variation trends of the system equilibrium points are investigated in a parametric way. The exterior potential distribution of nearly axisymmetrical elongated asteroids is approximated by minimizing the acceleration error in a test zone. The acceleration error minimization process determines the parameters of the dipole segment. The near-Earth asteroid (8567) 1996 HW1 is chosen as an example to evaluate the effectiveness of the approximation method for the exterior potential distribution. The advantages of the dipole segment model over the classical dipole and the traditional segment are also discussed. Percent error of acceleration and the degree of approximation are illustrated by using the dipole segment model to approximate four more asteroids. The high efficiency of the simplified model over the polyhedron is clearly demonstrated by comparing the CPU time.

Evaluating the effects of modeling errors for isolated finite three-dimensional targets

NASA Astrophysics Data System (ADS)

Henn, Mark-Alexander; Barnes, Bryan M.; Zhou, Hui

2017-10-01

Optical three-dimensional (3-D) nanostructure metrology utilizes a model-based metrology approach to determine critical dimensions (CDs) that are well below the inspection wavelength. Our project at the National Institute of Standards and Technology is evaluating how to attain key CD and shape parameters from engineered in-die capable metrology targets. More specifically, the quantities of interest are determined by varying the input parameters for a physical model until the simulations agree with the actual measurements within acceptable error bounds. As in most applications, establishing a reasonable balance between model accuracy and time efficiency is a complicated task. A well-established simplification is to model the intrinsically finite 3-D nanostructures as either periodic or infinite in one direction, reducing the computationally expensive 3-D simulations to usually less complex two-dimensional (2-D) problems. Systematic errors caused by this simplified model can directly influence the fitting of the model to the measurement data and are expected to become more apparent with decreasing lengths of the structures. We identify these effects using selected simulation results and present experimental setups, e.g., illumination numerical apertures and focal ranges, that can increase the validity of the 2-D approach.

Rapid determination of thermodynamic parameters from one-dimensional programmed-temperature gas chromatography for use in retention time prediction in comprehensive multidimensional chromatography.

PubMed

McGinitie, Teague M; Ebrahimi-Najafabadi, Heshmatollah; Harynuk, James J

2014-01-17

A new method for estimating the thermodynamic parameters of ΔH(T0), ΔS(T0), and ΔCP for use in thermodynamic modeling of GC×GC separations has been developed. The method is an alternative to the traditional isothermal separations required to fit a three-parameter thermodynamic model to retention data. Herein, a non-linear optimization technique is used to estimate the parameters from a series of temperature-programmed separations using the Nelder-Mead simplex algorithm. With this method, the time required to obtain estimates of thermodynamic parameters a series of analytes is significantly reduced. This new method allows for precise predictions of retention time with the average error being only 0.2s for 1D separations. Predictions for GC×GC separations were also in agreement with experimental measurements; having an average relative error of 0.37% for (1)tr and 2.1% for (2)tr. Copyright © 2013 Elsevier B.V. All rights reserved.

A new parametric method to smooth time-series data of metabolites in metabolic networks.

PubMed

Miyawaki, Atsuko; Sriyudthsak, Kansuporn; Hirai, Masami Yokota; Shiraishi, Fumihide

2016-12-01

Mathematical modeling of large-scale metabolic networks usually requires smoothing of metabolite time-series data to account for measurement or biological errors. Accordingly, the accuracy of smoothing curves strongly affects the subsequent estimation of model parameters. Here, an efficient parametric method is proposed for smoothing metabolite time-series data, and its performance is evaluated. To simplify parameter estimation, the method uses S-system-type equations with simple power law-type efflux terms. Iterative calculation using this method was found to readily converge, because parameters are estimated stepwise. Importantly, smoothing curves are determined so that metabolite concentrations satisfy mass balances. Furthermore, the slopes of smoothing curves are useful in estimating parameters, because they are probably close to their true behaviors regardless of errors that may be present in the actual data. Finally, calculations for each differential equation were found to converge in much less than one second if initial parameters are set at appropriate (guessed) values. Copyright © 2016 Elsevier Inc. All rights reserved.

A model of the human supervisor

NASA Technical Reports Server (NTRS)

Kok, J. J.; Vanwijk, R. A.

1977-01-01

A general model of the human supervisor's behavior is given. Submechanisms of the model include: the observer/reconstructor; decision-making; and controller. A set of hypothesis is postulated for the relations between the task variables and the parameters of the different submechanisms of the model. Verification of the model hypotheses is considered using variations in the task variables. An approach is suggested for the identification of the model parameters which makes use of a multidimensional error criterion. Each of the elements of this multidimensional criterion corresponds to a certain aspect of the supervisor's behavior, and is directly related to a particular part of the model and its parameters. This approach offers good possibilities for an efficient parameter adjustment procedure.

Design implementation in model-reference adaptive systems. [application and implementation on space shuttle

NASA Technical Reports Server (NTRS)

Boland, J. S., III

1973-01-01

The derivation of an approximate error characteristic equation describing the transient system error response is given, along with a procedure for selecting adaptive gain parameters so as to relate to the transient error response. A detailed example of the application and implementation of these methods for a space shuttle type vehicle is included. An extension of the characteristic equation technique is used to provide an estimate of the magnitude of the maximum system error and an estimate of the time of occurrence of this maximum after a plant parameter disturbance. Techniques for relaxing certain stability requirements and the conditions under which this can be done and still guarantee asymptotic stability of the system error are discussed. Such conditions are possible because the Lyapunov methods used in the stability derivation allow for overconstraining a problem in the process of insuring stability.

A water-vapor radiometer error model. [for ionosphere in geodetic microwave techniques

NASA Technical Reports Server (NTRS)

Beckman, B.

1985-01-01

The water-vapor radiometer (WVR) is used to calibrate unpredictable delays in the wet component of the troposphere in geodetic microwave techniques such as very-long-baseline interferometry (VLBI) and Global Positioning System (GPS) tracking. Based on experience with Jet Propulsion Laboratory (JPL) instruments, the current level of accuracy in wet-troposphere calibration limits the accuracy of local vertical measurements to 5-10 cm. The goal for the near future is 1-3 cm. Although the WVR is currently the best calibration method, many instruments are prone to systematic error. In this paper, a treatment of WVR data is proposed and evaluated. This treatment reduces the effect of WVR systematic errors by estimating parameters that specify an assumed functional form for the error. The assumed form of the treatment is evaluated by comparing the results of two similar WVR's operating near each other. Finally, the observability of the error parameters is estimated by covariance analysis.

A comparative study of kinetic and connectionist modeling for shelf-life prediction of Basundi mix.

PubMed

Ruhil, A P; Singh, R R B; Jain, D K; Patel, A A; Patil, G R

2011-04-01

A ready-to-reconstitute formulation of Basundi, a popular Indian dairy dessert was subjected to storage at various temperatures (10, 25 and 40 °C) and deteriorative changes in the Basundi mix were monitored using quality indices like pH, hydroxyl methyl furfural (HMF), bulk density (BD) and insolubility index (II). The multiple regression equations and the Arrhenius functions that describe the parameters' dependence on temperature for the four physico-chemical parameters were integrated to develop mathematical models for predicting sensory quality of Basundi mix. Connectionist model using multilayer feed forward neural network with back propagation algorithm was also developed for predicting the storage life of the product employing artificial neural network (ANN) tool box of MATLAB software. The quality indices served as the input parameters whereas the output parameters were the sensorily evaluated flavour and total sensory score. A total of 140 observations were used and the prediction performance was judged on the basis of per cent root mean square error. The results obtained from the two approaches were compared. Relatively lower magnitudes of percent root mean square error for both the sensory parameters indicated that the connectionist models were better fitted than kinetic models for predicting storage life.

Estimation and identification study for flexible vehicles

NASA Technical Reports Server (NTRS)

Jazwinski, A. H.; Englar, T. S., Jr.

1973-01-01

Techniques are studied for the estimation of rigid body and bending states and the identification of model parameters associated with the single-axis attitude dynamics of a flexible vehicle. This problem is highly nonlinear but completely observable provided sufficient attitude and attitude rate data is available and provided all system bending modes are excited in the observation interval. A sequential estimator tracks the system states in the presence of model parameter errors. A batch estimator identifies all model parameters with high accuracy.

Mathematical models of human paralyzed muscle after long-term training.

PubMed

Law, L A Frey; Shields, R K

2007-01-01

Spinal cord injury (SCI) results in major musculoskeletal adaptations, including muscle atrophy, faster contractile properties, increased fatigability, and bone loss. The use of functional electrical stimulation (FES) provides a method to prevent paralyzed muscle adaptations in order to sustain force-generating capacity. Mathematical muscle models may be able to predict optimal activation strategies during FES, however muscle properties further adapt with long-term training. The purpose of this study was to compare the accuracy of three muscle models, one linear and two nonlinear, for predicting paralyzed soleus muscle force after exposure to long-term FES training. Further, we contrasted the findings between the trained and untrained limbs. The three models' parameters were best fit to a single force train in the trained soleus muscle (N=4). Nine additional force trains (test trains) were predicted for each subject using the developed models. Model errors between predicted and experimental force trains were determined, including specific muscle force properties. The mean overall error was greatest for the linear model (15.8%) and least for the nonlinear Hill Huxley type model (7.8%). No significant error differences were observed between the trained versus untrained limbs, although model parameter values were significantly altered with training. This study confirmed that nonlinear models most accurately predict both trained and untrained paralyzed muscle force properties. Moreover, the optimized model parameter values were responsive to the relative physiological state of the paralyzed muscle (trained versus untrained). These findings are relevant for the design and control of neuro-prosthetic devices for those with SCI.

Systematic Biases in Parameter Estimation of Binary Black-Hole Mergers

NASA Technical Reports Server (NTRS)

Littenberg, Tyson B.; Baker, John G.; Buonanno, Alessandra; Kelly, Bernard J.

2012-01-01

Parameter estimation of binary-black-hole merger events in gravitational-wave data relies on matched filtering techniques, which, in turn, depend on accurate model waveforms. Here we characterize the systematic biases introduced in measuring astrophysical parameters of binary black holes by applying the currently most accurate effective-one-body templates to simulated data containing non-spinning numerical-relativity waveforms. For advanced ground-based detectors, we find that the systematic biases are well within the statistical error for realistic signal-to-noise ratios (SNR). These biases grow to be comparable to the statistical errors at high signal-to-noise ratios for ground-based instruments (SNR approximately 50) but never dominate the error budget. At the much larger signal-to-noise ratios expected for space-based detectors, these biases will become large compared to the statistical errors but are small enough (at most a few percent in the black-hole masses) that we expect they should not affect broad astrophysical conclusions that may be drawn from the data.

Dynamic Modeling Accuracy Dependence on Errors in Sensor Measurements, Mass Properties, and Aircraft Geometry

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2013-01-01

A nonlinear simulation of the NASA Generic Transport Model was used to investigate the effects of errors in sensor measurements, mass properties, and aircraft geometry on the accuracy of dynamic models identified from flight data. Measurements from a typical system identification maneuver were systematically and progressively deteriorated and then used to estimate stability and control derivatives within a Monte Carlo analysis. Based on the results, recommendations were provided for maximum allowable errors in sensor measurements, mass properties, and aircraft geometry to achieve desired levels of dynamic modeling accuracy. Results using other flight conditions, parameter estimation methods, and a full-scale F-16 nonlinear aircraft simulation were compared with these recommendations.

Corrigendum to “Thermophysical properties of U 3Si 2 to 1773 K”

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, Joshua Taylor; Nelson, Andrew Thomas; Dunwoody, John Tyler

2016-12-01

An error was discovered by the authors in the calculation of thermal diffusivity in “Thermophysical properties of U 3Si 2 to 1773 K”. The error was caused by operator error in entry of parameters used to fit the temperature rise versus time model necessary to calculate the thermal diffusivity. Lastly, this error propagated to the calculation of thermal conductivity, leading to values that were 18%–28% larger along with the corresponding calculated Lorenz values.

A support vector regression-firefly algorithm-based model for limiting velocity prediction in sewer pipes.

PubMed

Ebtehaj, Isa; Bonakdari, Hossein

2016-01-01

Sediment transport without deposition is an essential consideration in the optimum design of sewer pipes. In this study, a novel method based on a combination of support vector regression (SVR) and the firefly algorithm (FFA) is proposed to predict the minimum velocity required to avoid sediment settling in pipe channels, which is expressed as the densimetric Froude number (Fr). The efficiency of support vector machine (SVM) models depends on the suitable selection of SVM parameters. In this particular study, FFA is used by determining these SVM parameters. The actual effective parameters on Fr calculation are generally identified by employing dimensional analysis. The different dimensionless variables along with the models are introduced. The best performance is attributed to the model that employs the sediment volumetric concentration (C(V)), ratio of relative median diameter of particles to hydraulic radius (d/R), dimensionless particle number (D(gr)) and overall sediment friction factor (λ(s)) parameters to estimate Fr. The performance of the SVR-FFA model is compared with genetic programming, artificial neural network and existing regression-based equations. The results indicate the superior performance of SVR-FFA (mean absolute percentage error = 2.123%; root mean square error =0.116) compared with other methods.

Assessing the quality of life history information in publicly available databases.

PubMed

Thorson, James T; Cope, Jason M; Patrick, Wesley S

2014-01-01

Single-species life history parameters are central to ecological research and management, including the fields of macro-ecology, fisheries science, and ecosystem modeling. However, there has been little independent evaluation of the precision and accuracy of the life history values in global and publicly available databases. We therefore develop a novel method based on a Bayesian errors-in-variables model that compares database entries with estimates from local experts, and we illustrate this process by assessing the accuracy and precision of entries in FishBase, one of the largest and oldest life history databases. This model distinguishes biases among seven life history parameters, two types of information available in FishBase (i.e., published values and those estimated from other parameters), and two taxa (i.e., bony and cartilaginous fishes) relative to values from regional experts in the United States, while accounting for additional variance caused by sex- and region-specific life history traits. For published values in FishBase, the model identifies a small positive bias in natural mortality and negative bias in maximum age, perhaps caused by unacknowledged mortality caused by fishing. For life history values calculated by FishBase, the model identified large and inconsistent biases. The model also demonstrates greatest precision for body size parameters, decreased precision for values derived from geographically distant populations, and greatest between-sex differences in age at maturity. We recommend that our bias and precision estimates be used in future errors-in-variables models as a prior on measurement errors. This approach is broadly applicable to global databases of life history traits and, if used, will encourage further development and improvements in these databases.

Investigating the role of background and observation error correlations in improving a model forecast of forest carbon balance using four dimensional variational data assimilation.

NASA Astrophysics Data System (ADS)

Pinnington, Ewan; Casella, Eric; Dance, Sarah; Lawless, Amos; Morison, James; Nichols, Nancy; Wilkinson, Matthew; Quaife, Tristan

2016-04-01

Forest ecosystems play an important role in sequestering human emitted carbon-dioxide from the atmosphere and therefore greatly reduce the effect of anthropogenic induced climate change. For that reason understanding their response to climate change is of great importance. Efforts to implement variational data assimilation routines with functional ecology models and land surface models have been limited, with sequential and Markov chain Monte Carlo data assimilation methods being prevalent. When data assimilation has been used with models of carbon balance, background "prior" errors and observation errors have largely been treated as independent and uncorrelated. Correlations between background errors have long been known to be a key aspect of data assimilation in numerical weather prediction. More recently, it has been shown that accounting for correlated observation errors in the assimilation algorithm can considerably improve data assimilation results and forecasts. In this paper we implement a 4D-Var scheme with a simple model of forest carbon balance, for joint parameter and state estimation and assimilate daily observations of Net Ecosystem CO2 Exchange (NEE) taken at the Alice Holt forest CO2 flux site in Hampshire, UK. We then investigate the effect of specifying correlations between parameter and state variables in background error statistics and the effect of specifying correlations in time between observation error statistics. The idea of including these correlations in time is new and has not been previously explored in carbon balance model data assimilation. In data assimilation, background and observation error statistics are often described by the background error covariance matrix and the observation error covariance matrix. We outline novel methods for creating correlated versions of these matrices, using a set of previously postulated dynamical constraints to include correlations in the background error statistics and a Gaussian correlation function to include time correlations in the observation error statistics. The methods used in this paper will allow the inclusion of time correlations between many different observation types in the assimilation algorithm, meaning that previously neglected information can be accounted for. In our experiments we compared the results using our new correlated background and observation error covariance matrices and those using diagonal covariance matrices. We found that using the new correlated matrices reduced the root mean square error in the 14 year forecast of daily NEE by 44 % decreasing from 4.22 g C m-2 day-1 to 2.38 g C m-2 day-1.

Comparison of two laryngeal tissue fiber constitutive models

NASA Astrophysics Data System (ADS)

Hunter, Eric J.; Palaparthi, Anil Kumar Reddy; Siegmund, Thomas; Chan, Roger W.

2014-02-01

Biological tissues are complex time-dependent materials, and the best choice of the appropriate time-dependent constitutive description is not evident. This report reviews two constitutive models (a modified Kelvin model and a two-network Ogden-Boyce model) in the characterization of the passive stress-strain properties of laryngeal tissue under tensile deformation. The two models are compared, as are the automated methods for parameterization of tissue stress-strain data (a brute force vs. a common optimization method). Sensitivity (error curves) of parameters from both models and the optimized parameter set are calculated and contrast by optimizing to the same tissue stress-strain data. Both models adequately characterized empirical stress-strain datasets and could be used to recreate a good likeness of the data. Nevertheless, parameters in both models were sensitive to measurement errors or uncertainties in stress-strain, which would greatly hinder the confidence in those parameters. The modified Kelvin model emerges as a potential better choice for phonation models which use a tissue model as one component, or for general comparisons of the mechanical properties of one type of tissue to another (e.g., axial stress nonlinearity). In contrast, the Ogden-Boyce model would be more appropriate to provide a basic understanding of the tissue's mechanical response with better insights into the tissue's physical characteristics in terms of standard engineering metrics such as shear modulus and viscosity.

Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

2013-01-01

A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.

Bayesian network models for error detection in radiotherapy plans

NASA Astrophysics Data System (ADS)

Kalet, Alan M.; Gennari, John H.; Ford, Eric C.; Phillips, Mark H.

2015-04-01

The purpose of this study is to design and develop a probabilistic network for detecting errors in radiotherapy plans for use at the time of initial plan verification. Our group has initiated a multi-pronged approach to reduce these errors. We report on our development of Bayesian models of radiotherapy plans. Bayesian networks consist of joint probability distributions that define the probability of one event, given some set of other known information. Using the networks, we find the probability of obtaining certain radiotherapy parameters, given a set of initial clinical information. A low probability in a propagated network then corresponds to potential errors to be flagged for investigation. To build our networks we first interviewed medical physicists and other domain experts to identify the relevant radiotherapy concepts and their associated interdependencies and to construct a network topology. Next, to populate the network’s conditional probability tables, we used the Hugin Expert software to learn parameter distributions from a subset of de-identified data derived from a radiation oncology based clinical information database system. These data represent 4990 unique prescription cases over a 5 year period. Under test case scenarios with approximately 1.5% introduced error rates, network performance produced areas under the ROC curve of 0.88, 0.98, and 0.89 for the lung, brain and female breast cancer error detection networks, respectively. Comparison of the brain network to human experts performance (AUC of 0.90 ± 0.01) shows the Bayes network model performs better than domain experts under the same test conditions. Our results demonstrate the feasibility and effectiveness of comprehensive probabilistic models as part of decision support systems for improved detection of errors in initial radiotherapy plan verification procedures.

Estimation of Covariance Matrix on Bi-Response Longitudinal Data Analysis with Penalized Spline Regression

NASA Astrophysics Data System (ADS)

Islamiyati, A.; Fatmawati; Chamidah, N.

2018-03-01

The correlation assumption of the longitudinal data with bi-response occurs on the measurement between the subjects of observation and the response. It causes the auto-correlation of error, and this can be overcome by using a covariance matrix. In this article, we estimate the covariance matrix based on the penalized spline regression model. Penalized spline involves knot points and smoothing parameters simultaneously in controlling the smoothness of the curve. Based on our simulation study, the estimated regression model of the weighted penalized spline with covariance matrix gives a smaller error value compared to the error of the model without covariance matrix.

Influence of different dose calculation algorithms on the estimate of NTCP for lung complications.

PubMed

Hedin, Emma; Bäck, Anna

2013-09-06

Due to limitations and uncertainties in dose calculation algorithms, different algorithms can predict different dose distributions and dose-volume histograms for the same treatment. This can be a problem when estimating the normal tissue complication probability (NTCP) for patient-specific dose distributions. Published NTCP model parameters are often derived for a different dose calculation algorithm than the one used to calculate the actual dose distribution. The use of algorithm-specific NTCP model parameters can prevent errors caused by differences in dose calculation algorithms. The objective of this work was to determine how to change the NTCP model parameters for lung complications derived for a simple correction-based pencil beam dose calculation algorithm, in order to make them valid for three other common dose calculation algorithms. NTCP was calculated with the relative seriality (RS) and Lyman-Kutcher-Burman (LKB) models. The four dose calculation algorithms used were the pencil beam (PB) and collapsed cone (CC) algorithms employed by Oncentra, and the pencil beam convolution (PBC) and anisotropic analytical algorithm (AAA) employed by Eclipse. Original model parameters for lung complications were taken from four published studies on different grades of pneumonitis, and new algorithm-specific NTCP model parameters were determined. The difference between original and new model parameters was presented in relation to the reported model parameter uncertainties. Three different types of treatments were considered in the study: tangential and locoregional breast cancer treatment and lung cancer treatment. Changing the algorithm without the derivation of new model parameters caused changes in the NTCP value of up to 10 percentage points for the cases studied. Furthermore, the error introduced could be of the same magnitude as the confidence intervals of the calculated NTCP values. The new NTCP model parameters were tabulated as the algorithm was varied from PB to PBC, AAA, or CC. Moving from the PB to the PBC algorithm did not require new model parameters; however, moving from PB to AAA or CC did require a change in the NTCP model parameters, with CC requiring the largest change. It was shown that the new model parameters for a given algorithm are different for the different treatment types.

Custom map projections for regional groundwater models

USGS Publications Warehouse

Kuniansky, Eve L.

2017-01-01

For regional groundwater flow models (areas greater than 100,000 km2), improper choice of map projection parameters can result in model error for boundary conditions dependent on area (recharge or evapotranspiration simulated by application of a rate using cell area from model discretization) and length (rivers simulated with head-dependent flux boundary). Smaller model areas can use local map coordinates, such as State Plane (United States) or Universal Transverse Mercator (correct zone) without introducing large errors. Map projections vary in order to preserve one or more of the following properties: area, shape, distance (length), or direction. Numerous map projections are developed for different purposes as all four properties cannot be preserved simultaneously. Preservation of area and length are most critical for groundwater models. The Albers equal-area conic projection with custom standard parallels, selected by dividing the length north to south by 6 and selecting standard parallels 1/6th above or below the southern and northern extent, preserves both area and length for continental areas in mid latitudes oriented east-west. Custom map projection parameters can also minimize area and length error in non-ideal projections. Additionally, one must also use consistent vertical and horizontal datums for all geographic data. The generalized polygon for the Floridan aquifer system study area (306,247.59 km2) is used to provide quantitative examples of the effect of map projections on length and area with different projections and parameter choices. Use of improper map projection is one model construction problem easily avoided.

A new method to estimate average hourly global solar radiation on the horizontal surface

NASA Astrophysics Data System (ADS)

Pandey, Pramod K.; Soupir, Michelle L.

2012-10-01

A new model, Global Solar Radiation on Horizontal Surface (GSRHS), was developed to estimate the average hourly global solar radiation on the horizontal surfaces (Gh). The GSRHS model uses the transmission function (Tf,ij), which was developed to control hourly global solar radiation, for predicting solar radiation. The inputs of the model were: hour of day, day (Julian) of year, optimized parameter values, solar constant (H0), latitude, and longitude of the location of interest. The parameter values used in the model were optimized at a location (Albuquerque, NM), and these values were applied into the model for predicting average hourly global solar radiations at four different locations (Austin, TX; El Paso, TX; Desert Rock, NV; Seattle, WA) of the United States. The model performance was assessed using correlation coefficient (r), Mean Absolute Bias Error (MABE), Root Mean Square Error (RMSE), and coefficient of determinations (R2). The sensitivities of parameter to prediction were estimated. Results show that the model performed very well. The correlation coefficients (r) range from 0.96 to 0.99, while coefficients of determination (R2) range from 0.92 to 0.98. For daily and monthly prediction, error percentages (i.e. MABE and RMSE) were less than 20%. The approach we proposed here can be potentially useful for predicting average hourly global solar radiation on the horizontal surface for different locations, with the use of readily available data (i.e. latitude and longitude of the location) as inputs.

Evaluation of algorithms for geological thermal-inertia mapping

NASA Technical Reports Server (NTRS)

Miller, S. H.; Watson, K.

1977-01-01

The errors incurred in producing a thermal inertia map are of three general types: measurement, analysis, and model simplification. To emphasize the geophysical relevance of these errors, they were expressed in terms of uncertainty in thermal inertia and compared with the thermal inertia values of geologic materials. Thus the applications and practical limitations of the technique were illustrated. All errors were calculated using the parameter values appropriate to a site at the Raft River, Id. Although these error values serve to illustrate the magnitudes that can be expected from the three general types of errors, extrapolation to other sites should be done using parameter values particular to the area. Three surface temperature algorithms were evaluated: linear Fourier series, finite difference, and Laplace transform. In terms of resulting errors in thermal inertia, the Laplace transform method is the most accurate (260 TIU), the forward finite difference method is intermediate (300 TIU), and the linear Fourier series method the least accurate (460 TIU).

Examination of Different Item Response Theory Models on Tests Composed of Testlets

ERIC Educational Resources Information Center

Kogar, Esin Yilmaz; Kelecioglu, Hülya

2017-01-01

The purpose of this research is to first estimate the item and ability parameters and the standard error values related to those parameters obtained from Unidimensional Item Response Theory (UIRT), bifactor (BIF) and Testlet Response Theory models (TRT) in the tests including testlets, when the number of testlets, number of independent items, and…

Contribution Of The SWOT Mission To Large-Scale Hydrological Modeling Using Data Assimilation

NASA Astrophysics Data System (ADS)

Emery, C. M.; Biancamaria, S.; Boone, A. A.; Ricci, S. M.; Rochoux, M. C.; Garambois, P. A.; Paris, A.; Calmant, S.

2016-12-01

The purpose of this work is to improve water fluxes estimation on the continental surfaces, at interanual and interseasonal scale (from few years to decennial time period). More specifically, it studies contribution of the incoming SWOT satellite mission to improve hydrology model at global scale, and using the land surface model ISBA-TRIP. This model corresponds to the continental component of the CNRM (French meteorological research center)'s climatic model. This study explores the potential of satellite data to correct either input parameters of the river routing scheme TRIP or its state variables. To do so, a data assimilation platform (using an Ensemble Kalman Filter, EnKF) has been implemented to assimilate SWOT virtual observations as well as discharges estimated from real nadir altimetry data. A series of twin experiments is used to test and validate the parameter estimation module of the platform. SWOT virtual-observations of water heights along SWOT tracks (with a 10 cm white noise model error) are assimilated to correct the river routing model parameters. To begin with, we chose to focus exclusively on the river manning coefficient, with the possibility to easily extend to other parameters such as the river widths. First results show that the platform is able to recover the "true" Manning distribution assimilating SWOT-like water heights. The error on the coefficients goes from 35 % before assimilation to 9 % after four SWOT orbit repeat period of 21 days. In the state estimation mode, daily assimilation cycles are realized to correct TRIP river water storage initial state by assimilating ENVISAT-based discharge. Those observations are derived from ENVISAT water elevation measures, using rating curves from the MGB-IPH hydrological model (calibrated over the Amazon using in situ gages discharge). Using such kind of observation allows going beyond idealized twin experiments and also to test contribution of a remotely-sensed discharge product, which could prefigure the SWOT discharge product. The results show that discharge after assimilation are globally improved : the root-mean-square error between the analysis discharge ensemble mean and in situ discharges is reduced by 30 %, compared to the root-mean-square error between the free run and in situ discharges.

A Rigorous Temperature-Dependent Stochastic Modelling and Testing for MEMS-Based Inertial Sensor Errors.

PubMed

El-Diasty, Mohammed; Pagiatakis, Spiros

2009-01-01

In this paper, we examine the effect of changing the temperature points on MEMS-based inertial sensor random error. We collect static data under different temperature points using a MEMS-based inertial sensor mounted inside a thermal chamber. Rigorous stochastic models, namely Autoregressive-based Gauss-Markov (AR-based GM) models are developed to describe the random error behaviour. The proposed AR-based GM model is initially applied to short stationary inertial data to develop the stochastic model parameters (correlation times). It is shown that the stochastic model parameters of a MEMS-based inertial unit, namely the ADIS16364, are temperature dependent. In addition, field kinematic test data collected at about 17 °C are used to test the performance of the stochastic models at different temperature points in the filtering stage using Unscented Kalman Filter (UKF). It is shown that the stochastic model developed at 20 °C provides a more accurate inertial navigation solution than the ones obtained from the stochastic models developed at -40 °C, -20 °C, 0 °C, +40 °C, and +60 °C. The temperature dependence of the stochastic model is significant and should be considered at all times to obtain optimal navigation solution for MEMS-based INS/GPS integration.

Model Performance Evaluation and Scenario Analysis ...

EPA Pesticide Factsheets

This tool consists of two parts: model performance evaluation and scenario analysis (MPESA). The model performance evaluation consists of two components: model performance evaluation metrics and model diagnostics. These metrics provides modelers with statistical goodness-of-fit measures that capture magnitude only, sequence only, and combined magnitude and sequence errors. The performance measures include error analysis, coefficient of determination, Nash-Sutcliffe efficiency, and a new weighted rank method. These performance metrics only provide useful information about the overall model performance. Note that MPESA is based on the separation of observed and simulated time series into magnitude and sequence components. The separation of time series into magnitude and sequence components and the reconstruction back to time series provides diagnostic insights to modelers. For example, traditional approaches lack the capability to identify if the source of uncertainty in the simulated data is due to the quality of the input data or the way the analyst adjusted the model parameters. This report presents a suite of model diagnostics that identify if mismatches between observed and simulated data result from magnitude or sequence related errors. MPESA offers graphical and statistical options that allow HSPF users to compare observed and simulated time series and identify the parameter values to adjust or the input data to modify. The scenario analysis part of the too

How allele frequency and study design affect association test statistics with misrepresentation errors.

PubMed

Escott-Price, Valentina; Ghodsi, Mansoureh; Schmidt, Karl Michael

2014-04-01

We evaluate the effect of genotyping errors on the type-I error of a general association test based on genotypes, showing that, in the presence of errors in the case and control samples, the test statistic asymptotically follows a scaled non-central $\\chi ^2$ distribution. We give explicit formulae for the scaling factor and non-centrality parameter for the symmetric allele-based genotyping error model and for additive and recessive disease models. They show how genotyping errors can lead to a significantly higher false-positive rate, growing with sample size, compared with the nominal significance levels. The strength of this effect depends very strongly on the population distribution of the genotype, with a pronounced effect in the case of rare alleles, and a great robustness against error in the case of large minor allele frequency. We also show how these results can be used to correct $p$-values.

Real-Time Dynamic Modeling - Data Information Requirements and Flight Test Results

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.; Smith, Mark S.

2008-01-01

Practical aspects of identifying dynamic models for aircraft in real time were studied. Topics include formulation of an equation-error method in the frequency domain to estimate non-dimensional stability and control derivatives in real time, data information content for accurate modeling results, and data information management techniques such as data forgetting, incorporating prior information, and optimized excitation. Real-time dynamic modeling was applied to simulation data and flight test data from a modified F-15B fighter aircraft, and to operational flight data from a subscale jet transport aircraft. Estimated parameter standard errors and comparisons with results from a batch output-error method in the time domain were used to demonstrate the accuracy of the identified real-time models.

Real-Time Dynamic Modeling - Data Information Requirements and Flight Test Results

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.; Smith, Mark S.

2010-01-01

Practical aspects of identifying dynamic models for aircraft in real time were studied. Topics include formulation of an equation-error method in the frequency domain to estimate non-dimensional stability and control derivatives in real time, data information content for accurate modeling results, and data information management techniques such as data forgetting, incorporating prior information, and optimized excitation. Real-time dynamic modeling was applied to simulation data and flight test data from a modified F-15B fighter aircraft, and to operational flight data from a subscale jet transport aircraft. Estimated parameter standard errors, prediction cases, and comparisons with results from a batch output-error method in the time domain were used to demonstrate the accuracy of the identified real-time models.

Data assimilation for groundwater flow modelling using Unbiased Ensemble Square Root Filter: Case study in Guantao, North China Plain

NASA Astrophysics Data System (ADS)

Li, N.; Kinzelbach, W.; Li, H.; Li, W.; Chen, F.; Wang, L.

2017-12-01

Data assimilation techniques are widely used in hydrology to improve the reliability of hydrological models and to reduce model predictive uncertainties. This provides critical information for decision makers in water resources management. This study aims to evaluate a data assimilation system for the Guantao groundwater flow model coupled with a one-dimensional soil column simulation (Hydrus 1D) using an Unbiased Ensemble Square Root Filter (UnEnSRF) originating from the Ensemble Kalman Filter (EnKF) to update parameters and states, separately or simultaneously. To simplify the coupling between unsaturated and saturated zone, a linear relationship obtained from analyzing inputs to and outputs from Hydrus 1D is applied in the data assimilation process. Unlike EnKF, the UnEnSRF updates parameter ensemble mean and ensemble perturbations separately. In order to keep the ensemble filter working well during the data assimilation, two factors are introduced in the study. One is called damping factor to dampen the update amplitude of the posterior ensemble mean to avoid nonrealistic values. The other is called inflation factor to relax the posterior ensemble perturbations close to prior to avoid filter inbreeding problems. The sensitivities of the two factors are studied and their favorable values for the Guantao model are determined. The appropriate observation error and ensemble size were also determined to facilitate the further analysis. This study demonstrated that the data assimilation of both model parameters and states gives a smaller model prediction error but with larger uncertainty while the data assimilation of only model states provides a smaller predictive uncertainty but with a larger model prediction error. Data assimilation in a groundwater flow model will improve model prediction and at the same time make the model converge to the true parameters, which provides a successful base for applications in real time modelling or real time controlling strategies in groundwater resources management.

Updating finite element dynamic models using an element-by-element sensitivity methodology

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Hemez, Francois M.

1993-01-01

A sensitivity-based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented. The proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the finite element model while correcting these errors. The updating algorithm is derived from the unconstrained minimization of the squared L sub 2 norms of the modal dynamic residuals via an iterative two-step staggered procedure. At each iteration, the measured mode shapes are first expanded assuming that the model is error free, then the model parameters are corrected assuming that the expanded mode shapes are exact. The numerical algorithm is implemented in an element-by-element fashion and is capable of 'zooming' on the detected error locations. Several simulation examples which demonstate the potential of the proposed methodology are discussed.

Random Weighting, Strong Tracking, and Unscented Kalman Filter for Soft Tissue Characterization.

PubMed

Shin, Jaehyun; Zhong, Yongmin; Oetomo, Denny; Gu, Chengfan

2018-05-21

This paper presents a new nonlinear filtering method based on the Hunt-Crossley model for online nonlinear soft tissue characterization. This method overcomes the problem of performance degradation in the unscented Kalman filter due to contact model error. It adopts the concept of Mahalanobis distance to identify contact model error, and further incorporates a scaling factor in predicted state covariance to compensate identified model error. This scaling factor is determined according to the principle of innovation orthogonality to avoid the cumbersome computation of Jacobian matrix, where the random weighting concept is adopted to improve the estimation accuracy of innovation covariance. A master-slave robotic indentation system is developed to validate the performance of the proposed method. Simulation and experimental results as well as comparison analyses demonstrate that the efficacy of the proposed method for online characterization of soft tissue parameters in the presence of contact model error.

Input Uncertainty and its Implications on Parameter Assessment in Hydrologic and Hydroclimatic Modelling Studies

NASA Astrophysics Data System (ADS)

Chowdhury, S.; Sharma, A.

2005-12-01

Hydrological model inputs are often derived from measurements at point locations taken at discrete time steps. The nature of uncertainty associated with such inputs is thus a function of the quality and number of measurements available in time. A change in these characteristics (such as a change in the number of rain-gauge inputs used to derive spatially averaged rainfall) results in inhomogeneity in the associated distributional profile. Ignoring such uncertainty can lead to models that aim to simulate based on the observed input variable instead of the true measurement, resulting in a biased representation of the underlying system dynamics as well as an increase in both bias and the predictive uncertainty in simulations. This is especially true of cases where the nature of uncertainty likely in the future is significantly different to that in the past. Possible examples include situations where the accuracy of the catchment averaged rainfall has increased substantially due to an increase in the rain-gauge density, or accuracy of climatic observations (such as sea surface temperatures) increased due to the use of more accurate remote sensing technologies. We introduce here a method to ascertain the true value of parameters in the presence of additive uncertainty in model inputs. This method, known as SIMulation EXtrapolation (SIMEX, [Cook, 1994]) operates on the basis of an empirical relationship between parameters and the level of additive input noise (or uncertainty). The method starts with generating a series of alternate realisations of model inputs by artificially adding white noise in increasing multiples of the known error variance. The alternate realisations lead to alternate sets of parameters that are increasingly biased with respect to the truth due to the increased variability in the inputs. Once several such realisations have been drawn, one is able to formulate an empirical relationship between the parameter values and the level of additive noise present. SIMEX is based on theory that the trend in alternate parameters can be extrapolated back to the notional error free zone. We illustrate the utility of SIMEX in a synthetic rainfall-runoff modelling scenario and an application to study the dependence of uncertain distributed sea surface temperature anomalies with an indicator of the El Nino Southern Oscillation, the Southern Oscillation Index (SOI). The errors in rainfall data and its affect is explored using Sacramento rainfall runoff model. The rainfall uncertainty is assumed to be multiplicative and temporally invariant. The model used to relate the sea surface temperature anomalies (SSTA) to the SOI is assumed to be of a linear form. The nature of uncertainty in the SSTA is additive and varies with time. The SIMEX framework allows assessment of the relationship between the error free inputs and response. Cook, J.R., Stefanski, L. A., Simulation-Extrapolation Estimation in Parametric Measurement Error Models, Journal of the American Statistical Association, 89 (428), 1314-1328, 1994.

Adaptive control: Myths and realities

NASA Technical Reports Server (NTRS)

Athans, M.; Valavani, L.

1984-01-01

It was found that all currently existing globally stable adaptive algorithms have three basic properties in common: positive realness of the error equation, square-integrability of the parameter adjustment law and, need for sufficient excitation for asymptotic parameter convergence. Of the three, the first property is of primary importance since it satisfies a sufficient condition for stabillity of the overall system, which is a baseline design objective. The second property has been instrumental in the proof of asymptotic error convergence to zero, while the third addresses the issue of parameter convergence. Positive-real error dynamics can be generated only if the relative degree (excess of poles over zeroes) of the process to be controlled is known exactly; this, in turn, implies perfect modeling. This and other assumptions, such as absence of nonminimum phase plant zeros on which the mathematical arguments are based, do not necessarily reflect properties of real systems. As a result, it is natural to inquire what happens to the designs under less than ideal assumptions. The issues arising from violation of the exact modeling assumption which is extremely restrictive in practice and impacts the most important system property, stability, are discussed.

Neutrino masses and cosmological parameters from a Euclid-like survey: Markov Chain Monte Carlo forecasts including theoretical errors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Audren, Benjamin; Lesgourgues, Julien; Bird, Simeon

2013-01-01

We present forecasts for the accuracy of determining the parameters of a minimal cosmological model and the total neutrino mass based on combined mock data for a future Euclid-like galaxy survey and Planck. We consider two different galaxy surveys: a spectroscopic redshift survey and a cosmic shear survey. We make use of the Monte Carlo Markov Chains (MCMC) technique and assume two sets of theoretical errors. The first error is meant to account for uncertainties in the modelling of the effect of neutrinos on the non-linear galaxy power spectrum and we assume this error to be fully correlated in Fouriermore » space. The second error is meant to parametrize the overall residual uncertainties in modelling the non-linear galaxy power spectrum at small scales, and is conservatively assumed to be uncorrelated and to increase with the ratio of a given scale to the scale of non-linearity. It hence increases with wavenumber and decreases with redshift. With these two assumptions for the errors and assuming further conservatively that the uncorrelated error rises above 2% at k = 0.4 h/Mpc and z = 0.5, we find that a future Euclid-like cosmic shear/galaxy survey achieves a 1-σ error on M{sub ν} close to 32 meV/25 meV, sufficient for detecting the total neutrino mass with good significance. If the residual uncorrelated errors indeed rises rapidly towards smaller scales in the non-linear regime as we have assumed here then the data on non-linear scales does not increase the sensitivity to the total neutrino mass. Assuming instead a ten times smaller theoretical error with the same scale dependence, the error on the total neutrino mass decreases moderately from σ(M{sub ν}) = 18 meV to 14 meV when mildly non-linear scales with 0.1 h/Mpc < k < 0.6 h/Mpc are included in the analysis of the galaxy survey data.« less

Determination of nutritional parameters of yoghurts by FT Raman spectroscopy

NASA Astrophysics Data System (ADS)

Czaja, Tomasz; Baranowska, Maria; Mazurek, Sylwester; Szostak, Roman

2018-05-01

FT-Raman quantitative analysis of nutritional parameters of yoghurts was performed with the help of partial least squares models. The relative standard errors of prediction for fat, lactose and protein determination in the quantified commercial samples equalled to 3.9, 3.2 and 3.6%, respectively. Models based on attenuated total reflectance spectra of the liquid yoghurt samples and of dried yoghurt films collected with the single reflection diamond accessory showed relative standard errors of prediction values of 1.6-5.0% and 2.7-5.2%, respectively, for the analysed components. Despite a relatively low signal-to-noise ratio in the obtained spectra, Raman spectroscopy, combined with chemometrics, constitutes a fast and powerful tool for macronutrients quantification in yoghurts. Errors received for attenuated total reflectance method were found to be relatively higher than those for Raman spectroscopy due to inhomogeneity of the analysed samples.

Computational solution verification and validation applied to a thermal model of a ruggedized instrumentation package

DOE PAGES

Scott, Sarah Nicole; Templeton, Jeremy Alan; Hough, Patricia Diane; ...

2014-01-01

This study details a methodology for quantification of errors and uncertainties of a finite element heat transfer model applied to a Ruggedized Instrumentation Package (RIP). The proposed verification and validation (V&V) process includes solution verification to examine errors associated with the code's solution techniques, and model validation to assess the model's predictive capability for quantities of interest. The model was subjected to mesh resolution and numerical parameters sensitivity studies to determine reasonable parameter values and to understand how they change the overall model response and performance criteria. To facilitate quantification of the uncertainty associated with the mesh, automatic meshing andmore » mesh refining/coarsening algorithms were created and implemented on the complex geometry of the RIP. Automated software to vary model inputs was also developed to determine the solution’s sensitivity to numerical and physical parameters. The model was compared with an experiment to demonstrate its accuracy and determine the importance of both modelled and unmodelled physics in quantifying the results' uncertainty. An emphasis is placed on automating the V&V process to enable uncertainty quantification within tight development schedules.« less

A new multistage groundwater transport inverse method: presentation, evaluation, and implications

USGS Publications Warehouse

Anderman, Evan R.; Hill, Mary C.

1999-01-01

More computationally efficient methods of using concentration data are needed to estimate groundwater flow and transport parameters. This work introduces and evaluates a three‐stage nonlinear‐regression‐based iterative procedure in which trial advective‐front locations link decoupled flow and transport models. Method accuracy and efficiency are evaluated by comparing results to those obtained when flow‐ and transport‐model parameters are estimated simultaneously. The new method is evaluated as conclusively as possible by using a simple test case that includes distinct flow and transport parameters, but does not include any approximations that are problem dependent. The test case is analytical; the only flow parameter is a constant velocity, and the transport parameters are longitudinal and transverse dispersivity. Any difficulties detected using the new method in this ideal situation are likely to be exacerbated in practical problems. Monte‐Carlo analysis of observation error ensures that no specific error realization obscures the results. Results indicate that, while this, and probably other, multistage methods do not always produce optimal parameter estimates, the computational advantage may make them useful in some circumstances, perhaps as a precursor to using a simultaneous method.

Modeling clear-sky solar radiation across a range of elevations in Hawai‘i: Comparing the use of input parameters at different temporal resolutions

NASA Astrophysics Data System (ADS)

Longman, Ryan J.; Giambelluca, Thomas W.; Frazier, Abby G.

2012-01-01

Estimates of clear sky global solar irradiance using the parametric model SPCTRAL2 were tested against clear sky radiation observations at four sites in Hawai`i using daily, mean monthly, and 1 year mean model parameter settings. Atmospheric parameters in SPCTRAL2 and similar models are usually set at site-specific values and are not varied to represent the effects of fluctuating humidity, aerosol amount and type, or ozone concentration, because time-dependent atmospheric parameter estimates are not available at most sites of interest. In this study, we sought to determine the added value of using time dependent as opposed to fixed model input parameter settings. At the AERONET site, Mauna Loa Observatory (MLO) on the island of Hawai`i, where daily measurements of atmospheric optical properties and hourly solar radiation observations are available, use of daily rather than 1 year mean aerosol parameter values reduced mean bias error (MBE) from 18 to 10 W m-2 and root mean square error from 25 to 17 W m-2. At three stations in the HaleNet climate network, located at elevations of 960, 1640, and 2590 m on the island of Maui, where aerosol-related parameter settings were interpolated from observed values for AERONET sites at MLO (3397 m) and Lāna`i (20 m), and precipitable water was estimated using radiosonde-derived humidity profiles from nearby Hilo, the model performed best when using constant 1 year mean parameter values. At HaleNet Station 152, for example, MBE was 18, 10, and 8 W m-2 for daily, monthly, and 1 year mean parameters, respectively.

Classical simulation of quantum error correction in a Fibonacci anyon code

NASA Astrophysics Data System (ADS)

Burton, Simon; Brell, Courtney G.; Flammia, Steven T.

2017-02-01

Classically simulating the dynamics of anyonic excitations in two-dimensional quantum systems is likely intractable in general because such dynamics are sufficient to implement universal quantum computation. However, processes of interest for the study of quantum error correction in anyon systems are typically drawn from a restricted class that displays significant structure over a wide range of system parameters. We exploit this structure to classically simulate, and thereby demonstrate the success of, an error-correction protocol for a quantum memory based on the universal Fibonacci anyon model. We numerically simulate a phenomenological model of the system and noise processes on lattice sizes of up to 128 ×128 sites, and find a lower bound on the error-correction threshold of approximately 0.125 errors per edge, which is comparable to those previously known for Abelian and (nonuniversal) non-Abelian anyon models.

Quantitative evaluation of statistical errors in small-angle X-ray scattering measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sedlak, Steffen M.; Bruetzel, Linda K.; Lipfert, Jan

A new model is proposed for the measurement errors incurred in typical small-angle X-ray scattering (SAXS) experiments, which takes into account the setup geometry and physics of the measurement process. The model accurately captures the experimentally determined errors from a large range of synchrotron and in-house anode-based measurements. Its most general formulation gives for the variance of the buffer-subtracted SAXS intensity σ 2(q) = [I(q) + const.]/(kq), whereI(q) is the scattering intensity as a function of the momentum transferq;kand const. are fitting parameters that are characteristic of the experimental setup. The model gives a concrete procedure for calculating realistic measurementmore » errors for simulated SAXS profiles. In addition, the results provide guidelines for optimizing SAXS measurements, which are in line with established procedures for SAXS experiments, and enable a quantitative evaluation of measurement errors.« less

A robust interpolation procedure for producing tidal current ellipse inputs for regional and coastal ocean numerical models

NASA Astrophysics Data System (ADS)

Byun, Do-Seong; Hart, Deirdre E.

2017-04-01

Regional and/or coastal ocean models can use tidal current harmonic forcing, together with tidal harmonic forcing along open boundaries in order to successfully simulate tides and tidal currents. These inputs can be freely generated using online open-access data, but the data produced are not always at the resolution required for regional or coastal models. Subsequent interpolation procedures can produce tidal current forcing data errors for parts of the world's coastal ocean where tidal ellipse inclinations and phases move across the invisible mathematical "boundaries" between 359° and 0° degrees (or 179° and 0°). In nature, such "boundaries" are in fact smooth transitions, but if these mathematical "boundaries" are not treated correctly during interpolation, they can produce inaccurate input data and hamper the accurate simulation of tidal currents in regional and coastal ocean models. These avoidable errors arise due to procedural shortcomings involving vector embodiment problems (i.e., how a vector is represented mathematically, for example as velocities or as coordinates). Automated solutions for producing correct tidal ellipse parameter input data are possible if a series of steps are followed correctly, including the use of Cartesian coordinates during interpolation. This note comprises the first published description of scenarios where tidal ellipse parameter interpolation errors can arise, and of a procedure to successfully avoid these errors when generating tidal inputs for regional and/or coastal ocean numerical models. We explain how a straightforward sequence of data production, format conversion, interpolation, and format reconversion steps may be used to check for the potential occurrence and avoidance of tidal ellipse interpolation and phase errors. This sequence is demonstrated via a case study of the M2 tidal constituent in the seas around Korea but is designed to be universally applicable. We also recommend employing tidal ellipse parameter calculation methods that avoid the use of Foreman's (1978) "northern semi-major axis convention" since, as revealed in our analysis, this commonly used conversion can result in inclination interpolation errors even when Cartesian coordinate-based "vector embodiment" solutions are employed.

Considerations for analysis of time-to-event outcomes measured with error: Bias and correction with SIMEX.

PubMed

Oh, Eric J; Shepherd, Bryan E; Lumley, Thomas; Shaw, Pamela A

2018-04-15

For time-to-event outcomes, a rich literature exists on the bias introduced by covariate measurement error in regression models, such as the Cox model, and methods of analysis to address this bias. By comparison, less attention has been given to understanding the impact or addressing errors in the failure time outcome. For many diseases, the timing of an event of interest (such as progression-free survival or time to AIDS progression) can be difficult to assess or reliant on self-report and therefore prone to measurement error. For linear models, it is well known that random errors in the outcome variable do not bias regression estimates. With nonlinear models, however, even random error or misclassification can introduce bias into estimated parameters. We compare the performance of 2 common regression models, the Cox and Weibull models, in the setting of measurement error in the failure time outcome. We introduce an extension of the SIMEX method to correct for bias in hazard ratio estimates from the Cox model and discuss other analysis options to address measurement error in the response. A formula to estimate the bias induced into the hazard ratio by classical measurement error in the event time for a log-linear survival model is presented. Detailed numerical studies are presented to examine the performance of the proposed SIMEX method under varying levels and parametric forms of the error in the outcome. We further illustrate the method with observational data on HIV outcomes from the Vanderbilt Comprehensive Care Clinic. Copyright © 2017 John Wiley & Sons, Ltd.

A fuzzy logic-based model for noise control at industrial workplaces.

PubMed

Aluclu, I; Dalgic, A; Toprak, Z F

2008-05-01

Ergonomics is a broad science encompassing the wide variety of working conditions that can affect worker comfort and health, including factors such as lighting, noise, temperature, vibration, workstation design, tool design, machine design, etc. This paper describes noise-human response and a fuzzy logic model developed by comprehensive field studies on noise measurements (including atmospheric parameters) and control measures. The model has two subsystems constructed on noise reduction quantity in dB. The first subsystem of the fuzzy model depending on 549 linguistic rules comprises acoustical features of all materials used in any workplace. Totally 984 patterns were used, 503 patterns for model development and the rest 481 patterns for testing the model. The second subsystem deals with atmospheric parameter interactions with noise and has 52 linguistic rules. Similarly, 94 field patterns were obtained; 68 patterns were used for training stage of the model and the rest 26 patterns for testing the model. These rules were determined by taking into consideration formal standards, experiences of specialists and the measurements patterns. The results of the model were compared with various statistics (correlation coefficients, max-min, standard deviation, average and coefficient of skewness) and error modes (root mean square error and relative error). The correlation coefficients were significantly high, error modes were quite low and the other statistics were very close to the data. This statement indicates the validity of the model. Therefore, the model can be used for noise control in any workplace and helpful to the designer in planning stage of a workplace.

Assessing FPAR Source and Parameter Optimization Scheme in Application of a Diagnostic Carbon Flux Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turner, D P; Ritts, W D; Wharton, S

2009-02-26

The combination of satellite remote sensing and carbon cycle models provides an opportunity for regional to global scale monitoring of terrestrial gross primary production, ecosystem respiration, and net ecosystem production. FPAR (the fraction of photosynthetically active radiation absorbed by the plant canopy) is a critical input to diagnostic models, however little is known about the relative effectiveness of FPAR products from different satellite sensors nor about the sensitivity of flux estimates to different parameterization approaches. In this study, we used multiyear observations of carbon flux at four eddy covariance flux tower sites within the conifer biome to evaluate these factors.more » FPAR products from the MODIS and SeaWiFS sensors, and the effects of single site vs. cross-site parameter optimization were tested with the CFLUX model. The SeaWiFs FPAR product showed greater dynamic range across sites and resulted in slightly reduced flux estimation errors relative to the MODIS product when using cross-site optimization. With site-specific parameter optimization, the flux model was effective in capturing seasonal and interannual variation in the carbon fluxes at these sites. The cross-site prediction errors were lower when using parameters from a cross-site optimization compared to parameter sets from optimization at single sites. These results support the practice of multisite optimization within a biome for parameterization of diagnostic carbon flux models.« less

On the Reliability of Photovoltaic Short-Circuit Current Temperature Coefficient Measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osterwald, Carl R.; Campanelli, Mark; Kelly, George J.

2015-06-14

The changes in short-circuit current of photovoltaic (PV) cells and modules with temperature are routinely modeled through a single parameter, the temperature coefficient (TC). This parameter is vital for the translation equations used in system sizing, yet in practice is very difficult to measure. In this paper, we discuss these inherent problems and demonstrate how they can introduce unacceptably large errors in PV ratings. A method for quantifying the spectral dependence of TCs is derived, and then used to demonstrate that databases of module parameters commonly contain values that are physically unreasonable. Possible ways to reduce measurement errors are alsomore » discussed.« less

Analysis of Relationships between the Level of Errors in Leg and Monofin Movement and Stroke Parameters in Monofin Swimming

PubMed Central

Rejman, Marek

2013-01-01

The aim of this study was to analyze the error structure in propulsive movements with regard to its influence on monofin swimming speed. The random cycles performed by six swimmers were filmed during a progressive test (900m). An objective method to estimate errors committed in the area of angular displacement of the feet and monofin segments was employed. The parameters were compared with a previously described model. Mutual dependences between the level of errors, stroke frequency, stroke length and amplitude in relation to swimming velocity were analyzed. The results showed that proper foot movements and the avoidance of errors, arising at the distal part of the fin, ensure the progression of swimming speed. The individual stroke parameters distribution which consists of optimally increasing stroke frequency to the maximal possible level that enables the stabilization of stroke length leads to the minimization of errors. Identification of key elements in the stroke structure based on the analysis of errors committed should aid in improving monofin swimming technique. Key points The monofin swimming technique was evaluated through the prism of objectively defined errors committed by the swimmers. The dependences between the level of errors, stroke rate, stroke length and amplitude in relation to swimming velocity were analyzed. Optimally increasing stroke rate to the maximal possible level that enables the stabilization of stroke length leads to the minimization of errors. Propriety foot movement and the avoidance of errors arising at the distal part of fin, provide for the progression of swimming speed. The key elements improving monofin swimming technique, based on the analysis of errors committed, were designated. PMID:24149742

Quantifying the predictive consequences of model error with linear subspace analysis

USGS Publications Warehouse

White, Jeremy T.; Doherty, John E.; Hughes, Joseph D.

2014-01-01

All computer models are simplified and imperfect simulators of complex natural systems. The discrepancy arising from simplification induces bias in model predictions, which may be amplified by the process of model calibration. This paper presents a new method to identify and quantify the predictive consequences of calibrating a simplified computer model. The method is based on linear theory, and it scales efficiently to the large numbers of parameters and observations characteristic of groundwater and petroleum reservoir models. The method is applied to a range of predictions made with a synthetic integrated surface-water/groundwater model with thousands of parameters. Several different observation processing strategies and parameterization/regularization approaches are examined in detail, including use of the Karhunen-Loève parameter transformation. Predictive bias arising from model error is shown to be prediction specific and often invisible to the modeler. The amount of calibration-induced bias is influenced by several factors, including how expert knowledge is applied in the design of parameterization schemes, the number of parameters adjusted during calibration, how observations and model-generated counterparts are processed, and the level of fit with observations achieved through calibration. Failure to properly implement any of these factors in a prediction-specific manner may increase the potential for predictive bias in ways that are not visible to the calibration and uncertainty analysis process.

A Sensor Dynamic Measurement Error Prediction Model Based on NAPSO-SVM

PubMed Central

Jiang, Minlan; Jiang, Lan; Jiang, Dingde; Li, Fei

2018-01-01

Dynamic measurement error correction is an effective way to improve sensor precision. Dynamic measurement error prediction is an important part of error correction, and support vector machine (SVM) is often used for predicting the dynamic measurement errors of sensors. Traditionally, the SVM parameters were always set manually, which cannot ensure the model’s performance. In this paper, a SVM method based on an improved particle swarm optimization (NAPSO) is proposed to predict the dynamic measurement errors of sensors. Natural selection and simulated annealing are added in the PSO to raise the ability to avoid local optima. To verify the performance of NAPSO-SVM, three types of algorithms are selected to optimize the SVM’s parameters: the particle swarm optimization algorithm (PSO), the improved PSO optimization algorithm (NAPSO), and the glowworm swarm optimization (GSO). The dynamic measurement error data of two sensors are applied as the test data. The root mean squared error and mean absolute percentage error are employed to evaluate the prediction models’ performances. The experimental results show that among the three tested algorithms the NAPSO-SVM method has a better prediction precision and a less prediction errors, and it is an effective method for predicting the dynamic measurement errors of sensors. PMID:29342942

Dynamic modelling and estimation of the error due to asynchronism in a redundant asynchronous multiprocessor system

NASA Technical Reports Server (NTRS)

Huynh, Loc C.; Duval, R. W.

1986-01-01

The use of Redundant Asynchronous Multiprocessor System to achieve ultrareliable Fault Tolerant Control Systems shows great promise. The development has been hampered by the inability to determine whether differences in the outputs of redundant CPU's are due to failures or to accrued error built up by slight differences in CPU clock intervals. This study derives an analytical dynamic model of the difference between redundant CPU's due to differences in their clock intervals and uses this model with on-line parameter identification to idenitify the differences in the clock intervals. The ability of this methodology to accurately track errors due to asynchronisity generate an error signal with the effect of asynchronisity removed and this signal may be used to detect and isolate actual system failures.

Transfer-function-parameter estimation from frequency response data: A FORTRAN program

NASA Technical Reports Server (NTRS)

Seidel, R. C.

1975-01-01

A FORTRAN computer program designed to fit a linear transfer function model to given frequency response magnitude and phase data is presented. A conjugate gradient search is used that minimizes the integral of the absolute value of the error squared between the model and the data. The search is constrained to insure model stability. A scaling of the model parameters by their own magnitude aids search convergence. Efficient computer algorithms result in a small and fast program suitable for a minicomputer. A sample problem with different model structures and parameter estimates is reported.

ECHO: A reference-free short-read error correction algorithm

PubMed Central

Kao, Wei-Chun; Chan, Andrew H.; Song, Yun S.

2011-01-01

Developing accurate, scalable algorithms to improve data quality is an important computational challenge associated with recent advances in high-throughput sequencing technology. In this study, a novel error-correction algorithm, called ECHO, is introduced for correcting base-call errors in short-reads, without the need of a reference genome. Unlike most previous methods, ECHO does not require the user to specify parameters of which optimal values are typically unknown a priori. ECHO automatically sets the parameters in the assumed model and estimates error characteristics specific to each sequencing run, while maintaining a running time that is within the range of practical use. ECHO is based on a probabilistic model and is able to assign a quality score to each corrected base. Furthermore, it explicitly models heterozygosity in diploid genomes and provides a reference-free method for detecting bases that originated from heterozygous sites. On both real and simulated data, ECHO is able to improve the accuracy of previous error-correction methods by several folds to an order of magnitude, depending on the sequence coverage depth and the position in the read. The improvement is most pronounced toward the end of the read, where previous methods become noticeably less effective. Using a whole-genome yeast data set, it is demonstrated here that ECHO is capable of coping with nonuniform coverage. Also, it is shown that using ECHO to perform error correction as a preprocessing step considerably facilitates de novo assembly, particularly in the case of low-to-moderate sequence coverage depth. PMID:21482625

High-order dynamic modeling and parameter identification of structural discontinuities in Timoshenko beams by using reflection coefficients

NASA Astrophysics Data System (ADS)

Fan, Qiang; Huang, Zhenyu; Zhang, Bing; Chen, Dayue

2013-02-01

Properties of discontinuities, such as bolt joints and cracks in the waveguide structures, are difficult to evaluate by either analytical or numerical methods due to the complexity and uncertainty of the discontinuities. In this paper, the discontinuity in a Timoshenko beam is modeled with high-order parameters and then these parameters are identified by using reflection coefficients at the discontinuity. The high-order model is composed of several one-order sub-models in series and each sub-model consists of inertia, stiffness and damping components in parallel. The order of the discontinuity model is determined based on the characteristics of the reflection coefficient curve and the accuracy requirement of the dynamic modeling. The model parameters are identified through the least-square fitting iteration method, of which the undetermined model parameters are updated in iteration to fit the dynamic reflection coefficient curve with the wave-based one. By using the spectral super-element method (SSEM), simulation cases, including one-order discontinuities on infinite- and finite-beams and a two-order discontinuity on an infinite beam, were employed to evaluate both the accuracy of the discontinuity model and the effectiveness of the identification method. For practical considerations, effects of measurement noise on the discontinuity parameter identification are investigated by adding different levels of noise to the simulated data. The simulation results were then validated by the corresponding experiments. Both the simulation and experimental results show that (1) the one-order discontinuities can be identified accurately with the maximum errors of 6.8% and 8.7%, respectively; (2) and the high-order discontinuities can be identified with the maximum errors of 15.8% and 16.2%, respectively; and (3) the high-order model can predict the complex discontinuity much more accurately than the one-order discontinuity model.

Hydromagnetic couple-stress nanofluid flow over a moving convective wall: OHAM analysis

NASA Astrophysics Data System (ADS)

Awais, M.; Saleem, S.; Hayat, T.; Irum, S.

2016-12-01

This communication presents the magnetohydrodynamics (MHD) flow of a couple-stress nanofluid over a convective moving wall. The flow dynamics are analyzed in the boundary layer region. Convective cooling phenomenon combined with thermophoresis and Brownian motion effects has been discussed. Similarity transforms are utilized to convert the system of partial differential equations into coupled non-linear ordinary differential equation. Optimal homotopy analysis method (OHAM) is utilized and the concept of minimization is employed by defining the average squared residual errors. Effects of couple-stress parameter, convective cooling process parameter and energy enhancement parameters are displayed via graphs and discussed in detail. Various tables are also constructed to present the error analysis and a comparison of obtained results with the already published data. Stream lines are plotted showing a difference of Newtonian fluid model and couplestress fluid model.

Multiple-generator errors are unavoidable under model misspecification.

PubMed

Jewett, D L; Zhang, Z

1995-08-01

Model misspecification poses a major problem for dipole source localization (DSL) because it causes insidious multiple-generator errors (MulGenErrs) to occur in the fitted dipole parameters. This paper describes how and why this occurs, based upon simple algebraic considerations. MulGenErrs must occur, to some degree, in any DSL analysis of real data because there is model misspecification and mathematically the equations used for the simultaneously active generators must be of a different form than the equations for each generator active alone.

Inference of reactive transport model parameters using a Bayesian multivariate approach

NASA Astrophysics Data System (ADS)

Carniato, Luca; Schoups, Gerrit; van de Giesen, Nick

2014-08-01

Parameter estimation of subsurface transport models from multispecies data requires the definition of an objective function that includes different types of measurements. Common approaches are weighted least squares (WLS), where weights are specified a priori for each measurement, and weighted least squares with weight estimation (WLS(we)) where weights are estimated from the data together with the parameters. In this study, we formulate the parameter estimation task as a multivariate Bayesian inference problem. The WLS and WLS(we) methods are special cases in this framework, corresponding to specific prior assumptions about the residual covariance matrix. The Bayesian perspective allows for generalizations to cases where residual correlation is important and for efficient inference by analytically integrating out the variances (weights) and selected covariances from the joint posterior. Specifically, the WLS and WLS(we) methods are compared to a multivariate (MV) approach that accounts for specific residual correlations without the need for explicit estimation of the error parameters. When applied to inference of reactive transport model parameters from column-scale data on dissolved species concentrations, the following results were obtained: (1) accounting for residual correlation between species provides more accurate parameter estimation for high residual correlation levels whereas its influence for predictive uncertainty is negligible, (2) integrating out the (co)variances leads to an efficient estimation of the full joint posterior with a reduced computational effort compared to the WLS(we) method, and (3) in the presence of model structural errors, none of the methods is able to identify the correct parameter values.

Incorporating approximation error in surrogate based Bayesian inversion

NASA Astrophysics Data System (ADS)

Zhang, J.; Zeng, L.; Li, W.; Wu, L.

2015-12-01

There are increasing interests in applying surrogates for inverse Bayesian modeling to reduce repetitive evaluations of original model. In this way, the computational cost is expected to be saved. However, the approximation error of surrogate model is usually overlooked. This is partly because that it is difficult to evaluate the approximation error for many surrogates. Previous studies have shown that, the direct combination of surrogates and Bayesian methods (e.g., Markov Chain Monte Carlo, MCMC) may lead to biased estimations when the surrogate cannot emulate the highly nonlinear original system. This problem can be alleviated by implementing MCMC in a two-stage manner. However, the computational cost is still high since a relatively large number of original model simulations are required. In this study, we illustrate the importance of incorporating approximation error in inverse Bayesian modeling. Gaussian process (GP) is chosen to construct the surrogate for its convenience in approximation error evaluation. Numerical cases of Bayesian experimental design and parameter estimation for contaminant source identification are used to illustrate this idea. It is shown that, once the surrogate approximation error is well incorporated into Bayesian framework, promising results can be obtained even when the surrogate is directly used, and no further original model simulations are required.

Inversion of surface parameters using fast learning neural networks

NASA Technical Reports Server (NTRS)

Dawson, M. S.; Olvera, J.; Fung, A. K.; Manry, M. T.

1992-01-01

A neural network approach to the inversion of surface scattering parameters is presented. Simulated data sets based on a surface scattering model are used so that the data may be viewed as taken from a completely known randomly rough surface. The fast learning (FL) neural network and a multilayer perceptron (MLP) trained with backpropagation learning (BP network) are tested on the simulated backscattering data. The RMS error of training the FL network is found to be less than one half the error of the BP network while requiring one to two orders of magnitude less CPU time. When applied to inversion of parameters from a statistically rough surface, the FL method is successful at recovering the surface permittivity, the surface correlation length, and the RMS surface height in less time and with less error than the BP network. Further applications of the FL neural network to the inversion of parameters from backscatter measurements of an inhomogeneous layer above a half space are shown.

A stochastic differential equation model of diurnal cortisol patterns

NASA Technical Reports Server (NTRS)

Brown, E. N.; Meehan, P. M.; Dempster, A. P.

2001-01-01

Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.

Design of analytical failure detection using secondary observers

NASA Technical Reports Server (NTRS)

Sisar, M.

1982-01-01

The problem of designing analytical failure-detection systems (FDS) for sensors and actuators, using observers, is addressed. The use of observers in FDS is related to the examination of the n-dimensional observer error vector which carries the necessary information on possible failures. The problem is that in practical systems, in which only some of the components of the state vector are measured, one has access only to the m-dimensional observer-output error vector, with m or = to n. In order to cope with these cases, a secondary observer is synthesized to reconstruct the entire observer-error vector from the observer output error vector. This approach leads toward the design of highly sensitive and reliable FDS, with the possibility of obtaining a unique fingerprint for every possible failure. In order to keep the observer's (or Kalman filter) false-alarm rate under a certain specified value, it is necessary to have an acceptable matching between the observer (or Kalman filter) models and the system parameters. A previously developed adaptive observer algorithm is used to maintain the desired system-observer model matching, despite initial mismatching or system parameter variations. Conditions for convergence for the adaptive process are obtained, leading to a simple adaptive law (algorithm) with the possibility of an a priori choice of fixed adaptive gains. Simulation results show good tracking performance with small observer output errors, while accurate and fast parameter identification, in both deterministic and stochastic cases, is obtained.

Quantifying Variations In Multi-parameter Models With The Photon Clean Method (PCM) And Bootstrap Methods

NASA Astrophysics Data System (ADS)

Carpenter, Matthew H.; Jernigan, J. G.

2007-05-01

We present examples of an analysis progression consisting of a synthesis of the Photon Clean Method (Carpenter, Jernigan, Brown, Beiersdorfer 2007) and bootstrap methods to quantify errors and variations in many-parameter models. The Photon Clean Method (PCM) works well for model spaces with large numbers of parameters proportional to the number of photons, therefore a Monte Carlo paradigm is a natural numerical approach. Consequently, PCM, an "inverse Monte-Carlo" method, requires a new approach for quantifying errors as compared to common analysis methods for fitting models of low dimensionality. This presentation will explore the methodology and presentation of analysis results derived from a variety of public data sets, including observations with XMM-Newton, Chandra, and other NASA missions. Special attention is given to the visualization of both data and models including dynamic interactive presentations. This work was performed under the auspices of the Department of Energy under contract No. W-7405-Eng-48. We thank Peter Beiersdorfer and Greg Brown for their support of this technical portion of a larger program related to science with the LLNL EBIT program.

Estimation et validation des derivees de stabilite et controle du modele dynamique non-lineaire d'un drone a voilure fixe

NASA Astrophysics Data System (ADS)

Courchesne, Samuel

Knowledge of the dynamic characteristics of a fixed-wing UAV is necessary to design flight control laws and to conceive a high quality flight simulator. The basic features of a flight mechanic model include the properties of mass, inertia and major aerodynamic terms. They respond to a complex process involving various numerical analysis techniques and experimental procedures. This thesis focuses on the analysis of estimation techniques applied to estimate problems of stability and control derivatives from flight test data provided by an experimental UAV. To achieve this objective, a modern identification methodology (Quad-M) is used to coordinate the processing tasks from multidisciplinary fields, such as parameter estimation modeling, instrumentation, the definition of flight maneuvers and validation. The system under study is a non-linear model with six degrees of freedom with a linear aerodynamic model. The time domain techniques are used for identification of the drone. The first technique, the equation error method is used to determine the structure of the aerodynamic model. Thereafter, the output error method and filter error method are used to estimate the aerodynamic coefficients values. The Matlab scripts for estimating the parameters obtained from the American Institute of Aeronautics and Astronautics (AIAA) are used and modified as necessary to achieve the desired results. A commendable effort in this part of research is devoted to the design of experiments. This includes an awareness of the system data acquisition onboard and the definition of flight maneuvers. The flight tests were conducted under stable flight conditions and with low atmospheric disturbance. Nevertheless, the identification results showed that the filter error method is most effective for estimating the parameters of the drone due to the presence of process noise and measurement. The aerodynamic coefficients are validated using a numerical analysis of the vortex method. In addition, a simulation model incorporating the estimated parameters is used to compare the behavior of states measured. Finally, a good correspondence between the results is demonstrated despite a limited number of flight data. Keywords: drone, identification, estimation, nonlinear, flight test, system, aerodynamic coefficient.

Linear modeling of human hand-arm dynamics relevant to right-angle torque tool interaction.

PubMed

Ay, Haluk; Sommerich, Carolyn M; Luscher, Anthony F

2013-10-01

A new protocol was evaluated for identification of stiffness, mass, and damping parameters employing a linear model for human hand-arm dynamics relevant to right-angle torque tool use. Powered torque tools are widely used to tighten fasteners in manufacturing industries. While these tools increase accuracy and efficiency of tightening processes, operators are repetitively exposed to impulsive forces, posing risk of upper extremity musculoskeletal injury. A novel testing apparatus was developed that closely mimics biomechanical exposure in torque tool operation. Forty experienced torque tool operators were tested with the apparatus to determine model parameters and validate the protocol for physical capacity assessment. A second-order hand-arm model with parameters extracted in the time domain met model accuracy criterion of 5% for time-to-peak displacement error in 93% of trials (vs. 75% for frequency domain). Average time-to-peak handle displacement and relative peak handle force errors were 0.69 ms and 0.21%, respectively. Model parameters were significantly affected by gender and working posture. Protocol and numerical calculation procedures provide an alternative method for assessing mechanical parameters relevant to right-angle torque tool use. The protocol more closely resembles tool use, and calculation procedures demonstrate better performance of parameter extraction using time domain system identification methods versus frequency domain. Potential future applications include parameter identification for in situ torque tool operation and equipment development for human hand-arm dynamics simulation under impulsive forces that could be used for assessing torque tools based on factors relevant to operator health (handle dynamics and hand-arm reaction force).

The impact of 14-nm photomask uncertainties on computational lithography solutions

NASA Astrophysics Data System (ADS)

Sturtevant, John; Tejnil, Edita; Lin, Tim; Schultze, Steffen; Buck, Peter; Kalk, Franklin; Nakagawa, Kent; Ning, Guoxiang; Ackmann, Paul; Gans, Fritz; Buergel, Christian

2013-04-01

Computational lithography solutions rely upon accurate process models to faithfully represent the imaging system output for a defined set of process and design inputs. These models, which must balance accuracy demands with simulation runtime boundary conditions, rely upon the accurate representation of multiple parameters associated with the scanner and the photomask. While certain system input variables, such as scanner numerical aperture, can be empirically tuned to wafer CD data over a small range around the presumed set point, it can be dangerous to do so since CD errors can alias across multiple input variables. Therefore, many input variables for simulation are based upon designed or recipe-requested values or independent measurements. It is known, however, that certain measurement methodologies, while precise, can have significant inaccuracies. Additionally, there are known errors associated with the representation of certain system parameters. With shrinking total CD control budgets, appropriate accounting for all sources of error becomes more important, and the cumulative consequence of input errors to the computational lithography model can become significant. In this work, we examine with a simulation sensitivity study, the impact of errors in the representation of photomask properties including CD bias, corner rounding, refractive index, thickness, and sidewall angle. The factors that are most critical to be accurately represented in the model are cataloged. CD Bias values are based on state of the art mask manufacturing data and other variables changes are speculated, highlighting the need for improved metrology and awareness.

Predicting Air Permeability of Handloom Fabrics: A Comparative Analysis of Regression and Artificial Neural Network Models

NASA Astrophysics Data System (ADS)

Mitra, Ashis; Majumdar, Prabal Kumar; Bannerjee, Debamalya

2013-03-01

This paper presents a comparative analysis of two modeling methodologies for the prediction of air permeability of plain woven handloom cotton fabrics. Four basic fabric constructional parameters namely ends per inch, picks per inch, warp count and weft count have been used as inputs for artificial neural network (ANN) and regression models. Out of the four regression models tried, interaction model showed very good prediction performance with a meager mean absolute error of 2.017 %. However, ANN models demonstrated superiority over the regression models both in terms of correlation coefficient and mean absolute error. The ANN model with 10 nodes in the single hidden layer showed very good correlation coefficient of 0.982 and 0.929 and mean absolute error of only 0.923 and 2.043 % for training and testing data respectively.

Uncertainty analysis of hydrological modeling in a tropical area using different algorithms

NASA Astrophysics Data System (ADS)

Rafiei Emam, Ammar; Kappas, Martin; Fassnacht, Steven; Linh, Nguyen Hoang Khanh

2018-01-01

Hydrological modeling outputs are subject to uncertainty resulting from different sources of errors (e.g., error in input data, model structure, and model parameters), making quantification of uncertainty in hydrological modeling imperative and meant to improve reliability of modeling results. The uncertainty analysis must solve difficulties in calibration of hydrological models, which further increase in areas with data scarcity. The purpose of this study is to apply four uncertainty analysis algorithms to a semi-distributed hydrological model, quantifying different source of uncertainties (especially parameter uncertainty) and evaluate their performance. In this study, the Soil and Water Assessment Tools (SWAT) eco-hydrological model was implemented for the watershed in the center of Vietnam. The sensitivity of parameters was analyzed, and the model was calibrated. The uncertainty analysis for the hydrological model was conducted based on four algorithms: Generalized Likelihood Uncertainty Estimation (GLUE), Sequential Uncertainty Fitting (SUFI), Parameter Solution method (ParaSol) and Particle Swarm Optimization (PSO). The performance of the algorithms was compared using P-factor and Rfactor, coefficient of determination (R 2), the Nash Sutcliffe coefficient of efficiency (NSE) and Percent Bias (PBIAS). The results showed the high performance of SUFI and PSO with P-factor>0.83, R-factor <0.56 and R 2>0.91, NSE>0.89, and 0.18

Statistical model for speckle pattern optimization.

PubMed

Su, Yong; Zhang, Qingchuan; Gao, Zeren

2017-11-27

Image registration is the key technique of optical metrologies such as digital image correlation (DIC), particle image velocimetry (PIV), and speckle metrology. Its performance depends critically on the quality of image pattern, and thus pattern optimization attracts extensive attention. In this article, a statistical model is built to optimize speckle patterns that are composed of randomly positioned speckles. It is found that the process of speckle pattern generation is essentially a filtered Poisson process. The dependence of measurement errors (including systematic errors, random errors, and overall errors) upon speckle pattern generation parameters is characterized analytically. By minimizing the errors, formulas of the optimal speckle radius are presented. Although the primary motivation is from the field of DIC, we believed that scholars in other optical measurement communities, such as PIV and speckle metrology, will benefit from these discussions.

Weighted-density functionals for cavity formation and dispersion energies in continuum solvation models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sundararaman, Ravishankar; Gunceler, Deniz; Arias, T. A.

2014-10-07

Continuum solvation models enable efficient first principles calculations of chemical reactions in solution, but require extensive parametrization and fitting for each solvent and class of solute systems. Here, we examine the assumptions of continuum solvation models in detail and replace empirical terms with physical models in order to construct a minimally-empirical solvation model. Specifically, we derive solvent radii from the nonlocal dielectric response of the solvent from ab initio calculations, construct a closed-form and parameter-free weighted-density approximation for the free energy of the cavity formation, and employ a pair-potential approximation for the dispersion energy. We show that the resulting modelmore » with a single solvent-independent parameter: the electron density threshold (n c), and a single solvent-dependent parameter: the dispersion scale factor (s 6), reproduces solvation energies of organic molecules in water, chloroform, and carbon tetrachloride with RMS errors of 1.1, 0.6 and 0.5 kcal/mol, respectively. We additionally show that fitting the solvent-dependent s 6 parameter to the solvation energy of a single non-polar molecule does not substantially increase these errors. Parametrization of this model for other solvents, therefore, requires minimal effort and is possible without extensive databases of experimental solvation free energies.« less

Weighted-density functionals for cavity formation and dispersion energies in continuum solvation models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sundararaman, Ravishankar; Gunceler, Deniz; Arias, T. A.

2014-10-07

Continuum solvation models enable efficient first principles calculations of chemical reactions in solution, but require extensive parametrization and fitting for each solvent and class of solute systems. Here, we examine the assumptions of continuum solvation models in detail and replace empirical terms with physical models in order to construct a minimally-empirical solvation model. Specifically, we derive solvent radii from the nonlocal dielectric response of the solvent from ab initio calculations, construct a closed-form and parameter-free weighted-density approximation for the free energy of the cavity formation, and employ a pair-potential approximation for the dispersion energy. We show that the resulting modelmore » with a single solvent-independent parameter: the electron density threshold (n{sub c}), and a single solvent-dependent parameter: the dispersion scale factor (s{sub 6}), reproduces solvation energies of organic molecules in water, chloroform, and carbon tetrachloride with RMS errors of 1.1, 0.6 and 0.5 kcal/mol, respectively. We additionally show that fitting the solvent-dependent s{sub 6} parameter to the solvation energy of a single non-polar molecule does not substantially increase these errors. Parametrization of this model for other solvents, therefore, requires minimal effort and is possible without extensive databases of experimental solvation free energies.« less

Computer simulation of storm runoff for three watersheds in Albuquerque, New Mexico

USGS Publications Warehouse

Knutilla, R.L.; Veenhuis, J.E.

1994-01-01

Rainfall-runoff data from three watersheds were selected for calibration and verification of the U.S. Geological Survey's Distributed Routing Rainfall-Runoff Model. The watersheds chosen are residentially developed. The conceptually based model uses an optimization process that adjusts selected parameters to achieve the best fit between measured and simulated runoff volumes and peak discharges. Three of these optimization parameters represent soil-moisture conditions, three represent infiltration, and one accounts for effective impervious area. Each watershed modeled was divided into overland-flow segments and channel segments. The overland-flow segments were further subdivided to reflect pervious and impervious areas. Each overland-flow and channel segment was assigned representative values of area, slope, percentage of imperviousness, and roughness coefficients. Rainfall-runoff data for each watershed were separated into two sets for use in calibration and verification. For model calibration, seven input parameters were optimized to attain a best fit of the data. For model verification, parameter values were set using values from model calibration. The standard error of estimate for calibration of runoff volumes ranged from 19 to 34 percent, and for peak discharge calibration ranged from 27 to 44 percent. The standard error of estimate for verification of runoff volumes ranged from 26 to 31 percent, and for peak discharge verification ranged from 31 to 43 percent.

Estimating pole/zero errors in GSN-IRIS/USGS network calibration metadata

USGS Publications Warehouse

Ringler, A.T.; Hutt, C.R.; Aster, R.; Bolton, H.; Gee, L.S.; Storm, T.

2012-01-01

Mapping the digital record of a seismograph into true ground motion requires the correction of the data by some description of the instrument's response. For the Global Seismographic Network (Butler et al., 2004), as well as many other networks, this instrument response is represented as a Laplace domain pole–zero model and published in the Standard for the Exchange of Earthquake Data (SEED) format. This Laplace representation assumes that the seismometer behaves as a linear system, with any abrupt changes described adequately via multiple time-invariant epochs. The SEED format allows for published instrument response errors as well, but these typically have not been estimated or provided to users. We present an iterative three-step method to estimate the instrument response parameters (poles and zeros) and their associated errors using random calibration signals. First, we solve a coarse nonlinear inverse problem using a least-squares grid search to yield a first approximation to the solution. This approach reduces the likelihood of poorly estimated parameters (a local-minimum solution) caused by noise in the calibration records and enhances algorithm convergence. Second, we iteratively solve a nonlinear parameter estimation problem to obtain the least-squares best-fit Laplace pole–zero–gain model. Third, by applying the central limit theorem, we estimate the errors in this pole–zero model by solving the inverse problem at each frequency in a two-thirds octave band centered at each best-fit pole–zero frequency. This procedure yields error estimates of the 99% confidence interval. We demonstrate the method by applying it to a number of recent Incorporated Research Institutions in Seismology/United States Geological Survey (IRIS/USGS) network calibrations (network code IU).

Simultaneous Estimation of Microphysical Parameters and Atmospheric State Variables With Radar Data and Ensemble Square-root Kalman Filter

NASA Astrophysics Data System (ADS)

Tong, M.; Xue, M.

2006-12-01

An important source of model error for convective-scale data assimilation and prediction is microphysical parameterization. This study investigates the possibility of estimating up to five fundamental microphysical parameters, which are closely involved in the definition of drop size distribution of microphysical species in a commonly used single-moment ice microphysics scheme, using radar observations and the ensemble Kalman filter method. The five parameters include the intercept parameters for rain, snow and hail/graupel, and the bulk densities of hail/graupel and snow. Parameter sensitivity and identifiability are first examined. The ensemble square-root Kalman filter (EnSRF) is employed for simultaneous state and parameter estimation. OSS experiments are performed for a model-simulated supercell storm, in which the five microphysical parameters are estimated individually or in different combinations starting from different initial guesses. When error exists in only one of the microphysical parameters, the parameter can be successfully estimated without exception. The estimation of multiple parameters is found to be less robust, with end results of estimation being sensitive to the realization of the initial parameter perturbation. This is believed to be because of the reduced parameter identifiability and the existence of non-unique solutions. The results of state estimation are, however, always improved when simultaneous parameter estimation is performed, even when the estimated parameters values are not accurate.

Computation of physiological human vocal fold parameters by mathematical optimization of a biomechanical model

PubMed Central

Yang, Anxiong; Stingl, Michael; Berry, David A.; Lohscheller, Jörg; Voigt, Daniel; Eysholdt, Ulrich; Döllinger, Michael

2011-01-01

With the use of an endoscopic, high-speed camera, vocal fold dynamics may be observed clinically during phonation. However, observation and subjective judgment alone may be insufficient for clinical diagnosis and documentation of improved vocal function, especially when the laryngeal disease lacks any clear morphological presentation. In this study, biomechanical parameters of the vocal folds are computed by adjusting the corresponding parameters of a three-dimensional model until the dynamics of both systems are similar. First, a mathematical optimization method is presented. Next, model parameters (such as pressure, tension and masses) are adjusted to reproduce vocal fold dynamics, and the deduced parameters are physiologically interpreted. Various combinations of global and local optimization techniques are attempted. Evaluation of the optimization procedure is performed using 50 synthetically generated data sets. The results show sufficient reliability, including 0.07 normalized error, 96% correlation, and 91% accuracy. The technique is also demonstrated on data from human hemilarynx experiments, in which a low normalized error (0.16) and high correlation (84%) values were achieved. In the future, this technique may be applied to clinical high-speed images, yielding objective measures with which to document improved vocal function of patients with voice disorders. PMID:21877808

Greedy Sampling and Incremental Surrogate Model-Based Tailoring of Aeroservoelastic Model Database for Flexible Aircraft

NASA Technical Reports Server (NTRS)

Wang, Yi; Pant, Kapil; Brenner, Martin J.; Ouellette, Jeffrey A.

2018-01-01

This paper presents a data analysis and modeling framework to tailor and develop linear parameter-varying (LPV) aeroservoelastic (ASE) model database for flexible aircrafts in broad 2D flight parameter space. The Kriging surrogate model is constructed using ASE models at a fraction of grid points within the original model database, and then the ASE model at any flight condition can be obtained simply through surrogate model interpolation. The greedy sampling algorithm is developed to select the next sample point that carries the worst relative error between the surrogate model prediction and the benchmark model in the frequency domain among all input-output channels. The process is iterated to incrementally improve surrogate model accuracy till a pre-determined tolerance or iteration budget is met. The methodology is applied to the ASE model database of a flexible aircraft currently being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies indicate that the proposed method can reduce the number of models in the original database by 67%. Even so the ASE models obtained through Kriging interpolation match the model in the original database constructed directly from the physics-based tool with the worst relative error far below 1%. The interpolated ASE model exhibits continuously-varying gains along a set of prescribed flight conditions. More importantly, the selected grid points are distributed non-uniformly in the parameter space, a) capturing the distinctly different dynamic behavior and its dependence on flight parameters, and b) reiterating the need and utility for adaptive space sampling techniques for ASE model database compaction. The present framework is directly extendible to high-dimensional flight parameter space, and can be used to guide the ASE model development, model order reduction, robust control synthesis and novel vehicle design of flexible aircraft.

SU-E-T-144: Effective Analysis of VMAT QA Generated Trajectory Log Files for Medical Accelerator Predictive Maintenance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Able, CM; Baydush, AH; Nguyen, C

Purpose: To determine the effectiveness of SPC analysis for a model predictive maintenance process that uses accelerator generated parameter and performance data contained in trajectory log files. Methods: Each trajectory file is decoded and a total of 131 axes positions are recorded (collimator jaw position, gantry angle, each MLC, etc.). This raw data is processed and either axis positions are extracted at critical points during the delivery or positional change over time is used to determine axis velocity. The focus of our analysis is the accuracy, reproducibility and fidelity of each axis. A reference positional trace of the gantry andmore » each MLC is used as a motion baseline for cross correlation (CC) analysis. A total of 494 parameters (482 MLC related) were analyzed using Individual and Moving Range (I/MR) charts. The chart limits were calculated using a hybrid technique that included the use of the standard 3σ limits and parameter/system specifications. Synthetic errors/changes were introduced to determine the initial effectiveness of I/MR charts in detecting relevant changes in operating parameters. The magnitude of the synthetic errors/changes was based on: TG-142 and published analysis of VMAT delivery accuracy. Results: All errors introduced were detected. Synthetic positional errors of 2mm for collimator jaw and MLC carriage exceeded the chart limits. Gantry speed and each MLC speed are analyzed at two different points in the delivery. Simulated Gantry speed error (0.2 deg/sec) and MLC speed error (0.1 cm/sec) exceeded the speed chart limits. Gantry position error of 0.2 deg was detected by the CC maximum value charts. The MLC position error of 0.1 cm was detected by the CC maximum value location charts for every MLC. Conclusion: SPC I/MR evaluation of trajectory log file parameters may be effective in providing an early warning of performance degradation or component failure for medical accelerator systems.« less

Estimation of ice activation parameters within a particle tracking Lagrangian cloud model using the ensemble Kalman filter to match ISCDAC golden case observations

NASA Astrophysics Data System (ADS)

Reisner, J. M.; Dubey, M. K.

2010-12-01

To both quantify and reduce uncertainty in ice activation parameterizations for stratus clouds occurring in the temperature range between -5 to -10 C ensemble simulations of an ISDAC golden case have been conducted. To formulate the ensemble, three parameters found within an ice activation model have been sampled using a Latin hypercube technique over a parameter range that induces large variability in both number and mass of ice. The ice activation model is contained within a Lagrangian cloud model that simulates particle number as a function of radius for cloud ice, snow, graupel, cloud, and rain particles. A unique aspect of this model is that it produces very low levels of numerical diffusion that enable the model to accurately resolve the sharp cloud edges associated with the ISDAC stratus deck. Another important aspect of the model is that near the cloud edges the number of particles can be significantly increased to reduce sampling errors and accurately resolve physical processes such as collision-coalescence that occur in this region. Thus, given these relatively low numerical errors, as compared to traditional bin models, the sensitivity of a stratus deck to changes in parameters found within the activation model can be examined without fear of numerical contamination. Likewise, once the ensemble has been completed, ISDAC observations can be incorporated into a Kalman filter to optimally estimate the ice activation parameters and reduce overall model uncertainty. Hence, this work will highlight the ability of an ensemble Kalman filter system coupled to a highly accurate numerical model to estimate important parameters found within microphysical parameterizations containing high uncertainty.

Characterization of performance-emission indices of a diesel engine using ANFIS operating in dual-fuel mode with LPG

NASA Astrophysics Data System (ADS)

Chakraborty, Amitav; Roy, Sumit; Banerjee, Rahul

2018-03-01

This experimental work highlights the inherent capability of an adaptive-neuro fuzzy inference system (ANFIS) based model to act as a robust system identification tool (SIT) in prognosticating the performance and emission parameters of an existing diesel engine running of diesel-LPG dual fuel mode. The developed model proved its adeptness by successfully harnessing the effects of the input parameters of load, injection duration and LPG energy share on output parameters of BSFCEQ, BTE, NOX, SOOT, CO and HC. Successive evaluation of the ANFIS model, revealed high levels of resemblance with the already forecasted ANN results for the same input parameters and it was evident that similar to ANN, ANFIS also has the innate ability to act as a robust SIT. The ANFIS predicted data harmonized the experimental data with high overall accuracy. The correlation coefficient (R) values are stretched in between 0.99207 to 0.999988. The mean absolute percentage error (MAPE) tallies were recorded in the range of 0.02-0.173% with the root mean square errors (RMSE) in acceptable margins. Hence the developed model is capable of emulating the actual engine parameters with commendable ranges of accuracy, which in turn would act as a robust prediction platform in the future domains of optimization.

Parameter screening: the use of a dummy parameter to identify non-influential parameters in a global sensitivity analysis

NASA Astrophysics Data System (ADS)

Khorashadi Zadeh, Farkhondeh; Nossent, Jiri; van Griensven, Ann; Bauwens, Willy

2017-04-01

Parameter estimation is a major concern in hydrological modeling, which may limit the use of complex simulators with a large number of parameters. To support the selection of parameters to include in or exclude from the calibration process, Global Sensitivity Analysis (GSA) is widely applied in modeling practices. Based on the results of GSA, the influential and the non-influential parameters are identified (i.e. parameters screening). Nevertheless, the choice of the screening threshold below which parameters are considered non-influential is a critical issue, which has recently received more attention in GSA literature. In theory, the sensitivity index of a non-influential parameter has a value of zero. However, since numerical approximations, rather than analytical solutions, are utilized in GSA methods to calculate the sensitivity indices, small but non-zero indices may be obtained for the indices of non-influential parameters. In order to assess the threshold that identifies non-influential parameters in GSA methods, we propose to calculate the sensitivity index of a "dummy parameter". This dummy parameter has no influence on the model output, but will have a non-zero sensitivity index, representing the error due to the numerical approximation. Hence, the parameters whose indices are above the sensitivity index of the dummy parameter can be classified as influential, whereas the parameters whose indices are below this index are within the range of the numerical error and should be considered as non-influential. To demonstrated the effectiveness of the proposed "dummy parameter approach", 26 parameters of a Soil and Water Assessment Tool (SWAT) model are selected to be analyzed and screened, using the variance-based Sobol' and moment-independent PAWN methods. The sensitivity index of the dummy parameter is calculated from sampled data, without changing the model equations. Moreover, the calculation does not even require additional model evaluations for the Sobol' method. A formal statistical test validates these parameter screening results. Based on the dummy parameter screening, 11 model parameters are identified as influential. Therefore, it can be denoted that the "dummy parameter approach" can facilitate the parameter screening process and provide guidance for GSA users to define a screening-threshold, with only limited additional resources. Key words: Parameter screening, Global sensitivity analysis, Dummy parameter, Variance-based method, Moment-independent method

Verifiable Adaptive Control with Analytical Stability Margins by Optimal Control Modification

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2010-01-01

This paper presents a verifiable model-reference adaptive control method based on an optimal control formulation for linear uncertain systems. A predictor model is formulated to enable a parameter estimation of the system parametric uncertainty. The adaptation is based on both the tracking error and predictor error. Using a singular perturbation argument, it can be shown that the closed-loop system tends to a linear time invariant model asymptotically under an assumption of fast adaptation. A stability margin analysis is given to estimate a lower bound of the time delay margin using a matrix measure method. Using this analytical method, the free design parameter n of the optimal control modification adaptive law can be determined to meet a specification of stability margin for verification purposes.

Top-of-Climb Matching Method for Reducing Aircraft Trajectory Prediction Errors.

PubMed

Thipphavong, David P

2016-09-01

The inaccuracies of the aircraft performance models utilized by trajectory predictors with regard to takeoff weight, thrust, climb profile, and other parameters result in altitude errors during the climb phase that often exceed the vertical separation standard of 1000 feet. This study investigates the potential reduction in altitude trajectory prediction errors that could be achieved for climbing flights if just one additional parameter is made available: top-of-climb (TOC) time. The TOC-matching method developed and evaluated in this paper is straightforward: a set of candidate trajectory predictions is generated using different aircraft weight parameters, and the one that most closely matches TOC in terms of time is selected. This algorithm was tested using more than 1000 climbing flights in Fort Worth Center. Compared to the baseline trajectory predictions of a real-time research prototype (Center/TRACON Automation System), the TOC-matching method reduced the altitude root mean square error (RMSE) for a 5-minute prediction time by 38%. It also decreased the percentage of flights with absolute altitude error greater than the vertical separation standard of 1000 ft for the same look-ahead time from 55% to 30%.

Top-of-Climb Matching Method for Reducing Aircraft Trajectory Prediction Errors

PubMed Central

Thipphavong, David P.

2017-01-01

The inaccuracies of the aircraft performance models utilized by trajectory predictors with regard to takeoff weight, thrust, climb profile, and other parameters result in altitude errors during the climb phase that often exceed the vertical separation standard of 1000 feet. This study investigates the potential reduction in altitude trajectory prediction errors that could be achieved for climbing flights if just one additional parameter is made available: top-of-climb (TOC) time. The TOC-matching method developed and evaluated in this paper is straightforward: a set of candidate trajectory predictions is generated using different aircraft weight parameters, and the one that most closely matches TOC in terms of time is selected. This algorithm was tested using more than 1000 climbing flights in Fort Worth Center. Compared to the baseline trajectory predictions of a real-time research prototype (Center/TRACON Automation System), the TOC-matching method reduced the altitude root mean square error (RMSE) for a 5-minute prediction time by 38%. It also decreased the percentage of flights with absolute altitude error greater than the vertical separation standard of 1000 ft for the same look-ahead time from 55% to 30%. PMID:28684883

Top-of-Climb Matching Method for Reducing Aircraft Trajectory Prediction Errors

NASA Technical Reports Server (NTRS)

Thipphavong, David P.

2016-01-01

The inaccuracies of the aircraft performance models utilized by trajectory predictors with regard to takeoff weight, thrust, climb profile, and other parameters result in altitude errors during the climb phase that often exceed the vertical separation standard of 1000 feet. This study investigates the potential reduction in altitude trajectory prediction errors that could be achieved for climbing flights if just one additional parameter is made available: top-of-climb (TOC) time. The TOC-matching method developed and evaluated in this paper is straightforward: a set of candidate trajectory predictions is generated using different aircraft weight parameters, and the one that most closely matches TOC in terms of time is selected. This algorithm was tested using more than 1000 climbing flights in Fort Worth Center. Compared to the baseline trajectory predictions of a real-time research prototype (Center/TRACON Automation System), the TOC-matching method reduced the altitude root mean square error (RMSE) for a 5-minute prediction time by 38%. It also decreased the percentage of flights with absolute altitude error greater than the vertical separation standard of 1000 ft for the same look-ahead time from 55% to 30%.

Estimation of Ecosystem Parameters of the Community Land Model with DREAM: Evaluation of the Potential for Upscaling Net Ecosystem Exchange

NASA Astrophysics Data System (ADS)

Hendricks Franssen, H. J.; Post, H.; Vrugt, J. A.; Fox, A. M.; Baatz, R.; Kumbhar, P.; Vereecken, H.

2015-12-01

Estimation of net ecosystem exchange (NEE) by land surface models is strongly affected by uncertain ecosystem parameters and initial conditions. A possible approach is the estimation of plant functional type (PFT) specific parameters for sites with measurement data like NEE and application of the parameters at other sites with the same PFT and no measurements. This upscaling strategy was evaluated in this work for sites in Germany and France. Ecosystem parameters and initial conditions were estimated with NEE-time series of one year length, or a time series of only one season. The DREAM(zs) algorithm was used for the estimation of parameters and initial conditions. DREAM(zs) is not limited to Gaussian distributions and can condition to large time series of measurement data simultaneously. DREAM(zs) was used in combination with the Community Land Model (CLM) v4.5. Parameter estimates were evaluated by model predictions at the same site for an independent verification period. In addition, the parameter estimates were evaluated at other, independent sites situated >500km away with the same PFT. The main conclusions are: i) simulations with estimated parameters reproduced better the NEE measurement data in the verification periods, including the annual NEE-sum (23% improvement), annual NEE-cycle and average diurnal NEE course (error reduction by factor 1,6); ii) estimated parameters based on seasonal NEE-data outperformed estimated parameters based on yearly data; iii) in addition, those seasonal parameters were often also significantly different from their yearly equivalents; iv) estimated parameters were significantly different if initial conditions were estimated together with the parameters. We conclude that estimated PFT-specific parameters improve land surface model predictions significantly at independent verification sites and for independent verification periods so that their potential for upscaling is demonstrated. However, simulation results also indicate that possibly the estimated parameters mask other model errors. This would imply that their application at climatic time scales would not improve model predictions. A central question is whether the integration of many different data streams (e.g., biomass, remotely sensed LAI) could solve the problems indicated here.

A Two-Stage Algorithm for Origin-Destination Matrices Estimation Considering Dynamic Dispersion Parameter for Route Choice

PubMed Central

Wang, Yong; Ma, Xiaolei; Liu, Yong; Gong, Ke; Henricakson, Kristian C.; Xu, Maozeng; Wang, Yinhai

2016-01-01

This paper proposes a two-stage algorithm to simultaneously estimate origin-destination (OD) matrix, link choice proportion, and dispersion parameter using partial traffic counts in a congested network. A non-linear optimization model is developed which incorporates a dynamic dispersion parameter, followed by a two-stage algorithm in which Generalized Least Squares (GLS) estimation and a Stochastic User Equilibrium (SUE) assignment model are iteratively applied until the convergence is reached. To evaluate the performance of the algorithm, the proposed approach is implemented in a hypothetical network using input data with high error, and tested under a range of variation coefficients. The root mean squared error (RMSE) of the estimated OD demand and link flows are used to evaluate the model estimation results. The results indicate that the estimated dispersion parameter theta is insensitive to the choice of variation coefficients. The proposed approach is shown to outperform two established OD estimation methods and produce parameter estimates that are close to the ground truth. In addition, the proposed approach is applied to an empirical network in Seattle, WA to validate the robustness and practicality of this methodology. In summary, this study proposes and evaluates an innovative computational approach to accurately estimate OD matrices using link-level traffic flow data, and provides useful insight for optimal parameter selection in modeling travelers’ route choice behavior. PMID:26761209

Predicting root zone soil moisture with soil properties and satellite near-surface moisture data across the conterminous United States

NASA Astrophysics Data System (ADS)

Baldwin, D.; Manfreda, S.; Keller, K.; Smithwick, E. A. H.

2017-03-01

Satellite-based near-surface (0-2 cm) soil moisture estimates have global coverage, but do not capture variations of soil moisture in the root zone (up to 100 cm depth) and may be biased with respect to ground-based soil moisture measurements. Here, we present an ensemble Kalman filter (EnKF) hydrologic data assimilation system that predicts bias in satellite soil moisture data to support the physically based Soil Moisture Analytical Relationship (SMAR) infiltration model, which estimates root zone soil moisture with satellite soil moisture data. The SMAR-EnKF model estimates a regional-scale bias parameter using available in situ data. The regional bias parameter is added to satellite soil moisture retrievals before their use in the SMAR model, and the bias parameter is updated continuously over time with the EnKF algorithm. In this study, the SMAR-EnKF assimilates in situ soil moisture at 43 Soil Climate Analysis Network (SCAN) monitoring locations across the conterminous U.S. Multivariate regression models are developed to estimate SMAR parameters using soil physical properties and the moderate resolution imaging spectroradiometer (MODIS) evapotranspiration data product as covariates. SMAR-EnKF root zone soil moisture predictions are in relatively close agreement with in situ observations when using optimal model parameters, with root mean square errors averaging 0.051 [cm3 cm-3] (standard error, s.e. = 0.005). The average root mean square error associated with a 20-fold cross-validation analysis with permuted SMAR parameter regression models increases moderately (0.082 [cm3 cm-3], s.e. = 0.004). The expected regional-scale satellite correction bias is negative in four out of six ecoregions studied (mean = -0.12 [-], s.e. = 0.002), excluding the Great Plains and Eastern Temperate Forests (0.053 [-], s.e. = 0.001). With its capability of estimating regional-scale satellite bias, the SMAR-EnKF system can predict root zone soil moisture over broad extents and has applications in drought predictions and other operational hydrologic modeling purposes.

Models for patients' recruitment in clinical trials and sensitivity analysis.

PubMed

Mijoule, Guillaume; Savy, Stéphanie; Savy, Nicolas

2012-07-20

Taking a decision on the feasibility and estimating the duration of patients' recruitment in a clinical trial are very important but very hard questions to answer, mainly because of the huge variability of the system. The more elaborated works on this topic are those of Anisimov and co-authors, where they investigate modelling of the enrolment period by using Gamma-Poisson processes, which allows to develop statistical tools that can help the manager of the clinical trial to answer these questions and thus help him to plan the trial. The main idea is to consider an ongoing study at an intermediate time, denoted t(1). Data collected on [0,t(1)] allow to calibrate the parameters of the model, which are then used to make predictions on what will happen after t(1). This method allows us to estimate the probability of ending the trial on time and give possible corrective actions to the trial manager especially regarding how many centres have to be open to finish on time. In this paper, we investigate a Pareto-Poisson model, which we compare with the Gamma-Poisson one. We will discuss the accuracy of the estimation of the parameters and compare the models on a set of real case data. We make the comparison on various criteria : the expected recruitment duration, the quality of fitting to the data and its sensitivity to parameter errors. We discuss the influence of the centres opening dates on the estimation of the duration. This is a very important question to deal with in the setting of our data set. In fact, these dates are not known. For this discussion, we consider a uniformly distributed approach. Finally, we study the sensitivity of the expected duration of the trial with respect to the parameters of the model : we calculate to what extent an error on the estimation of the parameters generates an error in the prediction of the duration.

Extracting harmonic signal from a chaotic background with local linear model

NASA Astrophysics Data System (ADS)

Li, Chenlong; Su, Liyun

2017-02-01

In this paper, the problems of blind detection and estimation of harmonic signal in strong chaotic background are analyzed, and new methods by using local linear (LL) model are put forward. The LL model has been exhaustively researched and successfully applied for fitting and forecasting chaotic signal in many chaotic fields. We enlarge the modeling capacity substantially. Firstly, we can predict the short-term chaotic signal and obtain the fitting error based on the LL model. Then we detect the frequencies from the fitting error by periodogram, a property on the fitting error is proposed which has not been addressed before, and this property ensures that the detected frequencies are similar to that of harmonic signal. Secondly, we establish a two-layer LL model to estimate the determinate harmonic signal in strong chaotic background. To estimate this simply and effectively, we develop an efficient backfitting algorithm to select and optimize the parameters that are hard to be exhaustively searched for. In the method, based on sensitivity to initial value of chaos motion, the minimum fitting error criterion is used as the objective function to get the estimation of the parameters of the two-layer LL model. Simulation shows that the two-layer LL model and its estimation technique have appreciable flexibility to model the determinate harmonic signal in different chaotic backgrounds (Lorenz, Henon and Mackey-Glass (M-G) equations). Specifically, the harmonic signal can be extracted well with low SNR and the developed background algorithm satisfies the condition of convergence in repeated 3-5 times.

Measuring Parameters of Massive Black Hole Binaries with Partially-Aligned Spins

NASA Technical Reports Server (NTRS)

Lang, Ryan N.; Hughes, Scott A.; Cornish, Neil J.

2010-01-01

It is important to understand how well the gravitational-wave observatory LISA can measure parameters of massive black hole binaries. It has been shown that including spin precession in the waveform breaks degeneracies and produces smaller expected parameter errors than a simpler, precession-free analysis. However, recent work has shown that gas in binaries can partially align the spins with the orbital angular momentum, thus reducing the precession effect. We show how this degrades the earlier results, producing more pessimistic errors in gaseous mergers. However, we then add higher harmonics to the signal model; these also break degeneracies, but they are not affected by the presence of gas. The harmonics often restore the errors in partially-aligned binaries to the same as, or better than/ those that are obtained for fully precessing binaries with no harmonics. Finally, we investigate what LISA measurements of spin alignment can tell us about the nature of gas around a binary,

Kinetic modelling for zinc (II) ions biosorption onto Luffa cylindrica

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oboh, I., E-mail: innocentoboh@uniuyo.edu.ng; Aluyor, E.; Audu, T.

The biosorption of Zinc (II) ions onto a biomaterial - Luffa cylindrica has been studied. This biomaterial was characterized by elemental analysis, surface area, pore size distribution, scanning electron microscopy, and the biomaterial before and after sorption, was characterized by Fourier Transform Infra Red (FTIR) spectrometer. The kinetic nonlinear models fitted were Pseudo-first order, Pseudo-second order and Intra-particle diffusion. A comparison of non-linear regression method in selecting the kinetic model was made. Four error functions, namely coefficient of determination (R{sup 2}), hybrid fractional error function (HYBRID), average relative error (ARE), and sum of the errors squared (ERRSQ), were used tomore » predict the parameters of the kinetic models. The strength of this study is that a biomaterial with wide distribution particularly in the tropical world and which occurs as waste material could be put into effective utilization as a biosorbent to address a crucial environmental problem.« less

Joint Seasonal ARMA Approach for Modeling of Load Forecast Errors in Planning Studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hafen, Ryan P.; Samaan, Nader A.; Makarov, Yuri V.

2014-04-14

To make informed and robust decisions in the probabilistic power system operation and planning process, it is critical to conduct multiple simulations of the generated combinations of wind and load parameters and their forecast errors to handle the variability and uncertainty of these time series. In order for the simulation results to be trustworthy, the simulated series must preserve the salient statistical characteristics of the real series. In this paper, we analyze day-ahead load forecast error data from multiple balancing authority locations and characterize statistical properties such as mean, standard deviation, autocorrelation, correlation between series, time-of-day bias, and time-of-day autocorrelation.more » We then construct and validate a seasonal autoregressive moving average (ARMA) model to model these characteristics, and use the model to jointly simulate day-ahead load forecast error series for all BAs.« less

Kinetic modelling for zinc (II) ions biosorption onto Luffa cylindrica

NASA Astrophysics Data System (ADS)

Oboh, I.; Aluyor, E.; Audu, T.

2015-03-01

The biosorption of Zinc (II) ions onto a biomaterial - Luffa cylindrica has been studied. This biomaterial was characterized by elemental analysis, surface area, pore size distribution, scanning electron microscopy, and the biomaterial before and after sorption, was characterized by Fourier Transform Infra Red (FTIR) spectrometer. The kinetic nonlinear models fitted were Pseudo-first order, Pseudo-second order and Intra-particle diffusion. A comparison of non-linear regression method in selecting the kinetic model was made. Four error functions, namely coefficient of determination (R2), hybrid fractional error function (HYBRID), average relative error (ARE), and sum of the errors squared (ERRSQ), were used to predict the parameters of the kinetic models. The strength of this study is that a biomaterial with wide distribution particularly in the tropical world and which occurs as waste material could be put into effective utilization as a biosorbent to address a crucial environmental problem.

Maximum entropy approach to statistical inference for an ocean acoustic waveguide.

PubMed

Knobles, D P; Sagers, J D; Koch, R A

2012-02-01

A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations. © 2012 Acoustical Society of America

Sensitivity of tumor motion simulation accuracy to lung biomechanical modeling approaches and parameters.

PubMed

Tehrani, Joubin Nasehi; Yang, Yin; Werner, Rene; Lu, Wei; Low, Daniel; Guo, Xiaohu; Wang, Jing

2015-11-21

Finite element analysis (FEA)-based biomechanical modeling can be used to predict lung respiratory motion. In this technique, elastic models and biomechanical parameters are two important factors that determine modeling accuracy. We systematically evaluated the effects of lung and lung tumor biomechanical modeling approaches and related parameters to improve the accuracy of motion simulation of lung tumor center of mass (TCM) displacements. Experiments were conducted with four-dimensional computed tomography (4D-CT). A Quasi-Newton FEA was performed to simulate lung and related tumor displacements between end-expiration (phase 50%) and other respiration phases (0%, 10%, 20%, 30%, and 40%). Both linear isotropic and non-linear hyperelastic materials, including the neo-Hookean compressible and uncoupled Mooney-Rivlin models, were used to create a finite element model (FEM) of lung and tumors. Lung surface displacement vector fields (SDVFs) were obtained by registering the 50% phase CT to other respiration phases, using the non-rigid demons registration algorithm. The obtained SDVFs were used as lung surface displacement boundary conditions in FEM. The sensitivity of TCM displacement to lung and tumor biomechanical parameters was assessed in eight patients for all three models. Patient-specific optimal parameters were estimated by minimizing the TCM motion simulation errors between phase 50% and phase 0%. The uncoupled Mooney-Rivlin material model showed the highest TCM motion simulation accuracy. The average TCM motion simulation absolute errors for the Mooney-Rivlin material model along left-right, anterior-posterior, and superior-inferior directions were 0.80 mm, 0.86 mm, and 1.51 mm, respectively. The proposed strategy provides a reliable method to estimate patient-specific biomechanical parameters in FEM for lung tumor motion simulation.

Sensitivity of Tumor Motion Simulation Accuracy to Lung Biomechanical Modeling Approaches and Parameters

PubMed Central

Tehrani, Joubin Nasehi; Yang, Yin; Werner, Rene; Lu, Wei; Low, Daniel; Guo, Xiaohu

2015-01-01

Finite element analysis (FEA)-based biomechanical modeling can be used to predict lung respiratory motion. In this technique, elastic models and biomechanical parameters are two important factors that determine modeling accuracy. We systematically evaluated the effects of lung and lung tumor biomechanical modeling approaches and related parameters to improve the accuracy of motion simulation of lung tumor center of mass (TCM) displacements. Experiments were conducted with four-dimensional computed tomography (4D-CT). A Quasi-Newton FEA was performed to simulate lung and related tumor displacements between end-expiration (phase 50%) and other respiration phases (0%, 10%, 20%, 30%, and 40%). Both linear isotropic and non-linear hyperelastic materials, including the Neo-Hookean compressible and uncoupled Mooney-Rivlin models, were used to create a finite element model (FEM) of lung and tumors. Lung surface displacement vector fields (SDVFs) were obtained by registering the 50% phase CT to other respiration phases, using the non-rigid demons registration algorithm. The obtained SDVFs were used as lung surface displacement boundary conditions in FEM. The sensitivity of TCM displacement to lung and tumor biomechanical parameters was assessed in eight patients for all three models. Patient-specific optimal parameters were estimated by minimizing the TCM motion simulation errors between phase 50% and phase 0%. The uncoupled Mooney-Rivlin material model showed the highest TCM motion simulation accuracy. The average TCM motion simulation absolute errors for the Mooney-Rivlin material model along left-right (LR), anterior-posterior (AP), and superior-inferior (SI) directions were 0.80 mm, 0.86 mm, and 1.51 mm, respectively. The proposed strategy provides a reliable method to estimate patient-specific biomechanical parameters in FEM for lung tumor motion simulation. PMID:26531324

To image analysis in computed tomography

NASA Astrophysics Data System (ADS)

Chukalina, Marina; Nikolaev, Dmitry; Ingacheva, Anastasia; Buzmakov, Alexey; Yakimchuk, Ivan; Asadchikov, Victor

2017-03-01

The presence of errors in tomographic image may lead to misdiagnosis when computed tomography (CT) is used in medicine, or the wrong decision about parameters of technological processes when CT is used in the industrial applications. Two main reasons produce these errors. First, the errors occur on the step corresponding to the measurement, e.g. incorrect calibration and estimation of geometric parameters of the set-up. The second reason is the nature of the tomography reconstruction step. At the stage a mathematical model to calculate the projection data is created. Applied optimization and regularization methods along with their numerical implementations of the method chosen have their own specific errors. Nowadays, a lot of research teams try to analyze these errors and construct the relations between error sources. In this paper, we do not analyze the nature of the final error, but present a new approach for the calculation of its distribution in the reconstructed volume. We hope that the visualization of the error distribution will allow experts to clarify the medical report impression or expert summary given by them after analyzing of CT results. To illustrate the efficiency of the proposed approach we present both the simulation and real data processing results.

Can a simple lumped parameter model simulate complex transit time distributions? Benchmarking experiments in a virtual watershed.

NASA Astrophysics Data System (ADS)

Wilusz, D. C.; Maxwell, R. M.; Buda, A. R.; Ball, W. P.; Harman, C. J.

2016-12-01

The catchment transit-time distribution (TTD) is the time-varying, probabilistic distribution of water travel times through a watershed. The TTD is increasingly recognized as a useful descriptor of a catchment's flow and transport processes. However, TTDs are temporally complex and cannot be observed directly at watershed scale. Estimates of TTDs depend on available environmental tracers (such as stable water isotopes) and an assumed model whose parameters can be inverted from tracer data. All tracers have limitations though, such as (typically) short periods of observation or non-conservative behavior. As a result, models that faithfully simulate tracer observations may nonetheless yield TTD estimates with significant errors at certain times and water ages, conditioned on the tracer data available and the model structure. Recent advances have shown that time-varying catchment TTDs can be parsimoniously modeled by the lumped parameter rank StorAge Selection (rSAS) model, in which an rSAS function relates the distribution of water ages in outflows to the composition of age-ranked water in storage. Like other TTD models, rSAS is calibrated and evaluated against environmental tracer data, and the relative influence of tracer-dependent and model-dependent error on its TTD estimates is poorly understood. The purpose of this study is to benchmark the ability of different rSAS formulations to simulate TTDs in a complex, synthetic watershed where the lumped model can be calibrated and directly compared to a virtually "true" TTD. This experimental design allows for isolation of model-dependent error from tracer-dependent error. The integrated hydrologic model ParFlow with SLIM-FAST particle tracking code is used to simulate the watershed and its true TTD. To add field intelligence, the ParFlow model is populated with over forty years of hydrometric and physiographic data from the WE-38 subwatershed of the USDA's Mahantango Creek experimental catchment in PA, USA. The results are intended to give practical insight into tradeoffs between rSAS model structure and skill, and define a new performance benchmark to which other transit time models can be compared.

Comparison of Asymmetric and Ice-cream Cone Models for Halo Coronal Mass Ejections

NASA Astrophysics Data System (ADS)

Na, H.; Moon, Y.

2011-12-01

Halo coronal mass ejections (HCMEs) are major cause of the geomagnetic storms. To minimize the projection effect by coronagraph observation, several cone models have been suggested: an ice-cream cone model, an asymmetric cone model etc. These models allow us to determine the three dimensional parameters of HCMEs such as radial speed, angular width, and the angle between sky plane and central axis of the cone. In this study, we compare these parameters obtained from different models using 48 well-observed HCMEs from 2001 to 2002. And we obtain the root mean square error (RMS error) between measured projection speeds and calculated projection speeds for both cone models. As a result, we find that the radial speeds obtained from the models are well correlated with each other (R = 0.86), and the correlation coefficient of angular width is 0.6. The correlation coefficient of the angle between sky plane and central axis of the cone is 0.31, which is much smaller than expected. The reason may be due to the fact that the source locations of the asymmetric cone model are distributed near the center, while those of the ice-cream cone model are located in a wide range. The average RMS error of the asymmetric cone model (85.6km/s) is slightly smaller than that of the ice-cream cone model (87.8km/s).

Error Modeling of Multi-baseline Optical Truss. Part II; Application to SIM Metrology Truss Field Dependent Error

NASA Technical Reports Server (NTRS)

Zhang, Liwei Dennis; Milman, Mark; Korechoff, Robert

2004-01-01

The current design of the Space Interferometry Mission (SIM) employs a 19 laser-metrology-beam system (also called L19 external metrology truss) to monitor changes of distances between the fiducials of the flight system's multiple baselines. The function of the external metrology truss is to aid in the determination of the time-variations of the interferometer baseline. The largest contributor to truss error occurs in SIM wide-angle observations when the articulation of the siderostat mirrors (in order to gather starlight from different sky coordinates) brings to light systematic errors due to offsets at levels of instrument components (which include comer cube retro-reflectors, etc.). This error is labeled external metrology wide-angle field-dependent error. Physics-based model of field-dependent error at single metrology gauge level is developed and linearly propagated to errors in interferometer delay. In this manner delay error sensitivity to various error parameters or their combination can be studied using eigenvalue/eigenvector analysis. Also validation of physics-based field-dependent model on SIM testbed lends support to the present approach. As a first example, dihedral error model is developed for the comer cubes (CC) attached to the siderostat mirrors. Then the delay errors due to this effect can be characterized using the eigenvectors of composite CC dihedral error. The essence of the linear error model is contained in an error-mapping matrix. A corresponding Zernike component matrix approach is developed in parallel, first for convenience of describing the RMS of errors across the field-of-regard (FOR), and second for convenience of combining with additional models. Average and worst case residual errors are computed when various orders of field-dependent terms are removed from the delay error. Results of the residual errors are important in arriving at external metrology system component requirements. Double CCs with ideally co-incident vertices reside with the siderostat. The non-common vertex error (NCVE) is treated as a second example. Finally combination of models, and various other errors are discussed.

Modeling methodology for MLS range navigation system errors using flight test data

NASA Technical Reports Server (NTRS)

Karmali, M. S.; Phatak, A. V.

1982-01-01

Flight test data was used to develop a methodology for modeling MLS range navigation system errors. The data used corresponded to the constant velocity and glideslope approach segment of a helicopter landing trajectory. The MLS range measurement was assumed to consist of low frequency and random high frequency components. The random high frequency component was extracted from the MLS range measurements. This was done by appropriate filtering of the range residual generated from a linearization of the range profile for the final approach segment. This range navigation system error was then modeled as an autoregressive moving average (ARMA) process. Maximum likelihood techniques were used to identify the parameters of the ARMA process.

Molecular radiotherapy: the NUKFIT software for calculating the time-integrated activity coefficient.

PubMed

Kletting, P; Schimmel, S; Kestler, H A; Hänscheid, H; Luster, M; Fernández, M; Bröer, J H; Nosske, D; Lassmann, M; Glatting, G

2013-10-01

Calculation of the time-integrated activity coefficient (residence time) is a crucial step in dosimetry for molecular radiotherapy. However, available software is deficient in that it is either not tailored for the use in molecular radiotherapy and/or does not include all required estimation methods. The aim of this work was therefore the development and programming of an algorithm which allows for an objective and reproducible determination of the time-integrated activity coefficient and its standard error. The algorithm includes the selection of a set of fitting functions from predefined sums of exponentials and the choice of an error model for the used data. To estimate the values of the adjustable parameters an objective function, depending on the data, the parameters of the error model, the fitting function and (if required and available) Bayesian information, is minimized. To increase reproducibility and user-friendliness the starting values are automatically determined using a combination of curve stripping and random search. Visual inspection, the coefficient of determination, the standard error of the fitted parameters, and the correlation matrix are provided to evaluate the quality of the fit. The functions which are most supported by the data are determined using the corrected Akaike information criterion. The time-integrated activity coefficient is estimated by analytically integrating the fitted functions. Its standard error is determined assuming Gaussian error propagation. The software was implemented using MATLAB. To validate the proper implementation of the objective function and the fit functions, the results of NUKFIT and SAAM numerical, a commercially available software tool, were compared. The automatic search for starting values was successfully tested for reproducibility. The quality criteria applied in conjunction with the Akaike information criterion allowed the selection of suitable functions. Function fit parameters and their standard error estimated by using SAAM numerical and NUKFIT showed differences of <1%. The differences for the time-integrated activity coefficients were also <1% (standard error between 0.4% and 3%). In general, the application of the software is user-friendly and the results are mathematically correct and reproducible. An application of NUKFIT is presented for three different clinical examples. The software tool with its underlying methodology can be employed to objectively and reproducibly estimate the time integrated activity coefficient and its standard error for most time activity data in molecular radiotherapy.

Technical note: Bayesian calibration of dynamic ruminant nutrition models.

PubMed

Reed, K F; Arhonditsis, G B; France, J; Kebreab, E

2016-08-01

Mechanistic models of ruminant digestion and metabolism have advanced our understanding of the processes underlying ruminant animal physiology. Deterministic modeling practices ignore the inherent variation within and among individual animals and thus have no way to assess how sources of error influence model outputs. We introduce Bayesian calibration of mathematical models to address the need for robust mechanistic modeling tools that can accommodate error analysis by remaining within the bounds of data-based parameter estimation. For the purpose of prediction, the Bayesian approach generates a posterior predictive distribution that represents the current estimate of the value of the response variable, taking into account both the uncertainty about the parameters and model residual variability. Predictions are expressed as probability distributions, thereby conveying significantly more information than point estimates in regard to uncertainty. Our study illustrates some of the technical advantages of Bayesian calibration and discusses the future perspectives in the context of animal nutrition modeling. Copyright © 2016 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

An algebraic aspect of Pareto mixture parameter estimation using censored sample: A Bayesian approach.

PubMed

Saleem, Muhammad; Sharif, Kashif; Fahmi, Aliya

2018-04-27

Applications of Pareto distribution are common in reliability, survival and financial studies. In this paper, A Pareto mixture distribution is considered to model a heterogeneous population comprising of two subgroups. Each of two subgroups is characterized by the same functional form with unknown distinct shape and scale parameters. Bayes estimators have been derived using flat and conjugate priors using squared error loss function. Standard errors have also been derived for the Bayes estimators. An interesting feature of this study is the preparation of components of Fisher Information matrix.

Optimal solutions for a bio mathematical model for the evolution of smoking habit

NASA Astrophysics Data System (ADS)

Sikander, Waseem; Khan, Umar; Ahmed, Naveed; Mohyud-Din, Syed Tauseef

In this study, we apply Variation of Parameter Method (VPM) coupled with an auxiliary parameter to obtain the approximate solutions for the epidemic model for the evolution of smoking habit in a constant population. Convergence of the developed algorithm, namely VPM with an auxiliary parameter is studied. Furthermore, a simple way is considered for obtaining an optimal value of auxiliary parameter via minimizing the total residual error over the domain of problem. Comparison of the obtained results with standard VPM shows that an auxiliary parameter is very feasible and reliable in controlling the convergence of approximate solutions.

Modeling polyvinyl chloride Plasma Modification by Neural Networks

NASA Astrophysics Data System (ADS)

Wang, Changquan

2018-03-01

Neural networks model were constructed to analyze the connection between dielectric barrier discharge parameters and surface properties of material. The experiment data were generated from polyvinyl chloride plasma modification by using uniform design. Discharge voltage, discharge gas gap and treatment time were as neural network input layer parameters. The measured values of contact angle were as the output layer parameters. A nonlinear mathematical model of the surface modification for polyvinyl chloride was developed based upon the neural networks. The optimum model parameters were obtained by the simulation evaluation and error analysis. The results of the optimal model show that the predicted value is very close to the actual test value. The prediction model obtained here are useful for discharge plasma surface modification analysis.

Joint estimation over multiple individuals improves behavioural state inference from animal movement data.

PubMed

Jonsen, Ian

2016-02-08

State-space models provide a powerful way to scale up inference of movement behaviours from individuals to populations when the inference is made across multiple individuals. Here, I show how a joint estimation approach that assumes individuals share identical movement parameters can lead to improved inference of behavioural states associated with different movement processes. I use simulated movement paths with known behavioural states to compare estimation error between nonhierarchical and joint estimation formulations of an otherwise identical state-space model. Behavioural state estimation error was strongly affected by the degree of similarity between movement patterns characterising the behavioural states, with less error when movements were strongly dissimilar between states. The joint estimation model improved behavioural state estimation relative to the nonhierarchical model for simulated data with heavy-tailed Argos location errors. When applied to Argos telemetry datasets from 10 Weddell seals, the nonhierarchical model estimated highly uncertain behavioural state switching probabilities for most individuals whereas the joint estimation model yielded substantially less uncertainty. The joint estimation model better resolved the behavioural state sequences across all seals. Hierarchical or joint estimation models should be the preferred choice for estimating behavioural states from animal movement data, especially when location data are error-prone.

Incorporating rainfall uncertainty in a SWAT model: the river Zenne basin (Belgium) case study

NASA Astrophysics Data System (ADS)

Tolessa Leta, Olkeba; Nossent, Jiri; van Griensven, Ann; Bauwens, Willy

2013-04-01

The European Union Water Framework Directive (EU-WFD) called its member countries to achieve a good ecological status for all inland and coastal water bodies by 2015. According to recent studies, the river Zenne (Belgium) is far from this objective. Therefore, an interuniversity and multidisciplinary project "Towards a Good Ecological Status in the river Zenne (GESZ)" was launched to evaluate the effects of wastewater management plans on the river. In this project, different models have been developed and integrated using the Open Modelling Interface (OpenMI). The hydrologic, semi-distributed Soil and Water Assessment Tool (SWAT) is hereby used as one of the model components in the integrated modelling chain in order to model the upland catchment processes. The assessment of the uncertainty of SWAT is an essential aspect of the decision making process, in order to design robust management strategies that take the predicted uncertainties into account. Model uncertainty stems from the uncertainties on the model parameters, the input data (e.g, rainfall), the calibration data (e.g., stream flows) and on the model structure itself. The objective of this paper is to assess the first three sources of uncertainty in a SWAT model of the river Zenne basin. For the assessment of rainfall measurement uncertainty, first, we identified independent rainfall periods, based on the daily precipitation and stream flow observations and using the Water Engineering Time Series PROcessing tool (WETSPRO). Secondly, we assigned a rainfall multiplier parameter for each of the independent rainfall periods, which serves as a multiplicative input error corruption. Finally, we treated these multipliers as latent parameters in the model optimization and uncertainty analysis (UA). For parameter uncertainty assessment, due to the high number of parameters of the SWAT model, first, we screened out its most sensitive parameters using the Latin Hypercube One-factor-At-a-Time (LH-OAT) technique. Subsequently, we only considered the most sensitive parameters for parameter optimization and UA. To explicitly account for the stream flow uncertainty, we assumed that the stream flow measurement error increases linearly with the stream flow value. To assess the uncertainty and infer posterior distributions of the parameters, we used a Markov Chain Monte Carlo (MCMC) sampler - differential evolution adaptive metropolis (DREAM) that uses sampling from an archive of past states to generate candidate points in each individual chain. It is shown that the marginal posterior distributions of the rainfall multipliers vary widely between individual events, as a consequence of rainfall measurement errors and the spatial variability of the rain. Only few of the rainfall events are well defined. The marginal posterior distributions of the SWAT model parameter values are well defined and identified by DREAM, within their prior ranges. The posterior distributions of output uncertainty parameter values also show that the stream flow data is highly uncertain. The approach of using rainfall multipliers to treat rainfall uncertainty for a complex model has an impact on the model parameter marginal posterior distributions and on the model results Corresponding author: Tel.: +32 (0)2629 3027; fax: +32(0)2629 3022. E-mail: otolessa@vub.ac.be

Analysis of a Shock-Associated Noise Prediction Model Using Measured Jet Far-Field Noise Data

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Sharpe, Jacob A.

2014-01-01

A code for predicting supersonic jet broadband shock-associated noise was assessed us- ing a database containing noise measurements of a jet issuing from a convergent nozzle. The jet was operated at 24 conditions covering six fully expanded Mach numbers with four total temperature ratios. To enable comparisons of the predicted shock-associated noise component spectra with data, the measured total jet noise spectra were separated into mixing noise and shock-associated noise component spectra. Comparisons between predicted and measured shock-associated noise component spectra were used to identify de ciencies in the prediction model. Proposed revisions to the model, based on a study of the overall sound pressure levels for the shock-associated noise component of the mea- sured data, a sensitivity analysis of the model parameters with emphasis on the de nition of the convection velocity parameter, and a least-squares t of the predicted to the mea- sured shock-associated noise component spectra, resulted in a new de nition for the source strength spectrum in the model. An error analysis showed that the average error in the predicted spectra was reduced by as much as 3.5 dB for the revised model relative to the average error for the original model.

Effects of modeling errors on trajectory predictions in air traffic control automation

NASA Technical Reports Server (NTRS)

Jackson, Michael R. C.; Zhao, Yiyuan; Slattery, Rhonda

1996-01-01

Air traffic control automation synthesizes aircraft trajectories for the generation of advisories. Trajectory computation employs models of aircraft performances and weather conditions. In contrast, actual trajectories are flown in real aircraft under actual conditions. Since synthetic trajectories are used in landing scheduling and conflict probing, it is very important to understand the differences between computed trajectories and actual trajectories. This paper examines the effects of aircraft modeling errors on the accuracy of trajectory predictions in air traffic control automation. Three-dimensional point-mass aircraft equations of motion are assumed to be able to generate actual aircraft flight paths. Modeling errors are described as uncertain parameters or uncertain input functions. Pilot or autopilot feedback actions are expressed as equality constraints to satisfy control objectives. A typical trajectory is defined by a series of flight segments with different control objectives for each flight segment and conditions that define segment transitions. A constrained linearization approach is used to analyze trajectory differences caused by various modeling errors by developing a linear time varying system that describes the trajectory errors, with expressions to transfer the trajectory errors across moving segment transitions. A numerical example is presented for a complete commercial aircraft descent trajectory consisting of several flight segments.

Spatiotemporal integration for tactile localization during arm movements: a probabilistic approach.

PubMed

Maij, Femke; Wing, Alan M; Medendorp, W Pieter

2013-12-01

It has been shown that people make systematic errors in the localization of a brief tactile stimulus that is delivered to the index finger while they are making an arm movement. Here we modeled these spatial errors with a probabilistic approach, assuming that they follow from temporal uncertainty about the occurrence of the stimulus. In the model, this temporal uncertainty converts into a spatial likelihood about the external stimulus location, depending on arm velocity. We tested the prediction of the model that the localization errors depend on arm velocity. Participants (n = 8) were instructed to localize a tactile stimulus that was presented to their index finger while they were making either slow- or fast-targeted arm movements. Our results confirm the model's prediction that participants make larger localization errors when making faster arm movements. The model, which was used to fit the errors for both slow and fast arm movements simultaneously, accounted very well for all the characteristics of these data with temporal uncertainty in stimulus processing as the only free parameter. We conclude that spatial errors in dynamic tactile perception stem from the temporal precision with which tactile inputs are processed.

Comparison of interplanetary CME arrival times and solar wind parameters based on the WSA-ENLIL model with three cone types and observations

NASA Astrophysics Data System (ADS)

Jang, Soojeong; Moon, Y.-J.; Lee, Jae-Ok; Na, Hyeonock

2014-09-01

We have made a comparison between coronal mass ejection (CME)-associated shock propagations based on the Wang-Sheeley-Arge (WSA)-ENLIL model using three cone types and in situ observations. For this we use 28 full-halo CMEs, whose cone parameters are determined and their corresponding interplanetary shocks were observed at the Earth, from 2001 to 2002. We consider three different cone types (an asymmetric cone model, an ice cream cone model, and an elliptical cone model) to determine 3-D CME cone parameters (radial velocity, angular width, and source location), which are the input values of the WSA-ENLIL model. The mean absolute error of the CME-associated shock travel times for the WSA-ENLIL model using the ice-cream cone model is 9.9 h, which is about 1 h smaller than those of the other models. We compare the peak values and profiles of solar wind parameters (speed and density) with in situ observations. We find that the root-mean-square errors of solar wind peak speed and density for the ice cream and asymmetric cone model are about 190 km/s and 24/cm3, respectively. We estimate the cross correlations between the models and observations within the time lag of ± 2 days from the shock travel time. The correlation coefficients between the solar wind speeds from the WSA-ENLIL model using three cone types and in situ observations are approximately 0.7, which is larger than those of solar wind density (cc ˜0.6). Our preliminary investigations show that the ice cream cone model seems to be better than the other cone models in terms of the input parameters of the WSA-ENLIL model.

Uncertainty analysis of an inflow forecasting model: extension of the UNEEC machine learning-based method

NASA Astrophysics Data System (ADS)

Pianosi, Francesca; Lal Shrestha, Durga; Solomatine, Dimitri

2010-05-01

This research presents an extension of UNEEC (Uncertainty Estimation based on Local Errors and Clustering, Shrestha and Solomatine, 2006, 2008 & Solomatine and Shrestha, 2009) method in the direction of explicit inclusion of parameter uncertainty. UNEEC method assumes that there is an optimal model and the residuals of the model can be used to assess the uncertainty of the model prediction. It is assumed that all sources of uncertainty including input, parameter and model structure uncertainty are explicitly manifested in the model residuals. In this research, theses assumptions are relaxed, and the UNEEC method is extended to consider parameter uncertainty as well (abbreviated as UNEEC-P). In UNEEC-P, first we use Monte Carlo (MC) sampling in parameter space to generate N model realizations (each of which is a time series), estimate the prediction quantiles based on the empirical distribution functions of the model residuals considering all the residual realizations, and only then apply the standard UNEEC method that encapsulates the uncertainty of a hydrologic model (expressed by quantiles of the error distribution) in a machine learning model (e.g., ANN). UNEEC-P is applied first to a linear regression model of synthetic data, and then to a real case study of forecasting inflow to lake Lugano in northern Italy. The inflow forecasting model is a stochastic heteroscedastic model (Pianosi and Soncini-Sessa, 2009). The preliminary results show that the UNEEC-P method produces wider uncertainty bounds, which is consistent with the fact that the method considers also parameter uncertainty of the optimal model. In the future UNEEC method will be further extended to consider input and structure uncertainty which will provide more realistic estimation of model predictions.

CME Arrival-time Validation of Real-time WSA-ENLIL+Cone Simulations at the CCMC/SWRC

NASA Astrophysics Data System (ADS)

Wold, A. M.; Mays, M. L.; Taktakishvili, A.; Jian, L.; Odstrcil, D.; MacNeice, P. J.

2016-12-01

The Wang-Sheeley-Arge (WSA)-ENLIL+Cone model is used extensively in space weather operations worldwide to model CME propagation, as such it is important to assess its performance. We present validation results of the WSA-ENLIL+Cone model installed at the Community Coordinated Modeling Center (CCMC) and executed in real-time by the CCMC/Space Weather Research Center (SWRC). The SWRC is a CCMC sub-team that provides space weather services to NASA robotic mission operators and science campaigns, and also prototypes new forecasting models and techniques. CCMC/SWRC uses the WSA-ENLIL+Cone model to predict CME arrivals at NASA missions throughout the inner heliosphere. In this work we compare model predicted CME arrival-times to in-situ ICME shock observations near Earth (ACE, Wind), STEREO-A and B for simulations completed between March 2010 - July 2016 (over 1500 runs). We report hit, miss, false alarm, and correct rejection statistics for all three spacecraft. For hits we compute the bias, RMSE, and average absolute CME arrival time error, and the dependence of these errors on CME input parameters. We compare the predicted geomagnetic storm strength (Kp index) to the CME arrival time error for Earth-directed CMEs. The predicted Kp index is computed using the WSA-ENLIL+Cone plasma parameters at Earth with a modified Newell et al. (2007) coupling function. We also explore the impact of the multi-spacecraft observations on the CME parameters used initialize the model by comparing model validation results before and after the STEREO-B communication loss (since September 2014) and STEREO-A side-lobe operations (August 2014-December 2015). This model validation exercise has significance for future space weather mission planning such as L5 missions.

Parameter estimation for an immortal model of colonic stem cell division using approximate Bayesian computation.

PubMed

Walters, Kevin

2012-08-07

In this paper we use approximate Bayesian computation to estimate the parameters in an immortal model of colonic stem cell division. We base the inferences on the observed DNA methylation patterns of cells sampled from the human colon. Utilising DNA methylation patterns as a form of molecular clock is an emerging area of research and has been used in several studies investigating colonic stem cell turnover. There is much debate concerning the two competing models of stem cell turnover: the symmetric (immortal) and asymmetric models. Early simulation studies concluded that the observed methylation data were not consistent with the immortal model. A later modified version of the immortal model that included preferential strand segregation was subsequently shown to be consistent with the same methylation data. Most of this earlier work assumes site independent methylation models that do not take account of the known processivity of methyltransferases whilst other work does not take into account the methylation errors that occur in differentiated cells. This paper addresses both of these issues for the immortal model and demonstrates that approximate Bayesian computation provides accurate estimates of the parameters in this neighbour-dependent model of methylation error rates. The results indicate that if colonic stem cells divide asymmetrically then colon stem cell niches are maintained by more than 8 stem cells. Results also indicate the possibility of preferential strand segregation and provide clear evidence against a site-independent model for methylation errors. In addition, algebraic expressions for some of the summary statistics used in the approximate Bayesian computation (that allow for the additional variation arising from cell division in differentiated cells) are derived and their utility discussed. Copyright © 2012 Elsevier Ltd. All rights reserved.

Generalized sensitivity analysis of the minimal model of the intravenous glucose tolerance test.

PubMed

Munir, Mohammad

2018-06-01

Generalized sensitivity functions characterize the sensitivity of the parameter estimates with respect to the nominal parameters. We observe from the generalized sensitivity analysis of the minimal model of the intravenous glucose tolerance test that the measurements of insulin, 62 min after the administration of the glucose bolus into the experimental subject's body, possess no information about the parameter estimates. The glucose measurements possess the information about the parameter estimates up to three hours. These observations have been verified by the parameter estimation of the minimal model. The standard errors of the estimates and crude Monte Carlo process also confirm this observation. Copyright © 2018 Elsevier Inc. All rights reserved.

Low Frequency Error Analysis and Calibration for High-Resolution Optical Satellite's Uncontrolled Geometric Positioning

NASA Astrophysics Data System (ADS)

Wang, Mi; Fang, Chengcheng; Yang, Bo; Cheng, Yufeng

2016-06-01

The low frequency error is a key factor which has affected uncontrolled geometry processing accuracy of the high-resolution optical image. To guarantee the geometric quality of imagery, this paper presents an on-orbit calibration method for the low frequency error based on geometric calibration field. Firstly, we introduce the overall flow of low frequency error on-orbit analysis and calibration, which includes optical axis angle variation detection of star sensor, relative calibration among star sensors, multi-star sensor information fusion, low frequency error model construction and verification. Secondly, we use optical axis angle change detection method to analyze the law of low frequency error variation. Thirdly, we respectively use the method of relative calibration and information fusion among star sensors to realize the datum unity and high precision attitude output. Finally, we realize the low frequency error model construction and optimal estimation of model parameters based on DEM/DOM of geometric calibration field. To evaluate the performance of the proposed calibration method, a certain type satellite's real data is used. Test results demonstrate that the calibration model in this paper can well describe the law of the low frequency error variation. The uncontrolled geometric positioning accuracy of the high-resolution optical image in the WGS-84 Coordinate Systems is obviously improved after the step-wise calibration.

Effect of formal and informal likelihood functions on uncertainty assessment in a single event rainfall-runoff model

NASA Astrophysics Data System (ADS)

Nourali, Mahrouz; Ghahraman, Bijan; Pourreza-Bilondi, Mohsen; Davary, Kamran

2016-09-01

In the present study, DREAM(ZS), Differential Evolution Adaptive Metropolis combined with both formal and informal likelihood functions, is used to investigate uncertainty of parameters of the HEC-HMS model in Tamar watershed, Golestan province, Iran. In order to assess the uncertainty of 24 parameters used in HMS, three flood events were used to calibrate and one flood event was used to validate the posterior distributions. Moreover, performance of seven different likelihood functions (L1-L7) was assessed by means of DREAM(ZS)approach. Four likelihood functions, L1-L4, Nash-Sutcliffe (NS) efficiency, Normalized absolute error (NAE), Index of agreement (IOA), and Chiew-McMahon efficiency (CM), is considered as informal, whereas remaining (L5-L7) is represented in formal category. L5 focuses on the relationship between the traditional least squares fitting and the Bayesian inference, and L6, is a hetereoscedastic maximum likelihood error (HMLE) estimator. Finally, in likelihood function L7, serial dependence of residual errors is accounted using a first-order autoregressive (AR) model of the residuals. According to the results, sensitivities of the parameters strongly depend on the likelihood function, and vary for different likelihood functions. Most of the parameters were better defined by formal likelihood functions L5 and L7 and showed a high sensitivity to model performance. Posterior cumulative distributions corresponding to the informal likelihood functions L1, L2, L3, L4 and the formal likelihood function L6 are approximately the same for most of the sub-basins, and these likelihood functions depict almost a similar effect on sensitivity of parameters. 95% total prediction uncertainty bounds bracketed most of the observed data. Considering all the statistical indicators and criteria of uncertainty assessment, including RMSE, KGE, NS, P-factor and R-factor, results showed that DREAM(ZS) algorithm performed better under formal likelihood functions L5 and L7, but likelihood function L5 may result in biased and unreliable estimation of parameters due to violation of the residualerror assumptions. Thus, likelihood function L7 provides posterior distribution of model parameters credibly and therefore can be employed for further applications.

Unified Computational Methods for Regression Analysis of Zero-Inflated and Bound-Inflated Data

PubMed Central

Yang, Yan; Simpson, Douglas

2010-01-01

Bounded data with excess observations at the boundary are common in many areas of application. Various individual cases of inflated mixture models have been studied in the literature for bound-inflated data, yet the computational methods have been developed separately for each type of model. In this article we use a common framework for computing these models, and expand the range of models for both discrete and semi-continuous data with point inflation at the lower boundary. The quasi-Newton and EM algorithms are adapted and compared for estimation of model parameters. The numerical Hessian and generalized Louis method are investigated as means for computing standard errors after optimization. Correlated data are included in this framework via generalized estimating equations. The estimation of parameters and effectiveness of standard errors are demonstrated through simulation and in the analysis of data from an ultrasound bioeffect study. The unified approach enables reliable computation for a wide class of inflated mixture models and comparison of competing models. PMID:20228950

Minimization of the hole overcut and cylindricity errors during rotary ultrasonic drilling of Ti-6Al-4V

NASA Astrophysics Data System (ADS)

Nasr, M.; Anwar, S.; El-Tamimi, A.; Pervaiz, S.

2018-04-01

Titanium and its alloys e.g. Ti6Al4V have widespread applications in aerospace, automotive and medical industry. At the same time titanium and its alloys are regarded as difficult to machine materials due to their high strength and low thermal conductivity. Significant efforts have been dispensed to improve the accuracy of the machining processes for Ti6Al4V. The current study present the use of the rotary ultrasonic drilling (RUD) process for machining high quality holes in Ti6Al4V. The study takes into account the effects of the main RUD input parameters including spindle speed, ultrasonic power, feed rate and tool diameter on the key output responses related to the accuracy of the drilled holes including cylindricity and overcut errors. Analysis of variance (ANOVA) was employed to study the influence of the input parameters on cylindricity and overcut error. Later, regression models were developed to find the optimal set of input parameters to minimize the cylindricity and overcut errors.

Dependency of Optimal Parameters of the IRIS Template on Image Quality and Border Detection Error

NASA Astrophysics Data System (ADS)

Matveev, I. A.; Novik, V. P.

2017-05-01

Generation of a template containing spatial-frequency features of iris is an important stage of identification. The template is obtained by a wavelet transform in an image region specified by iris borders. One of the main characteristics of the identification system is the value of recognition error, equal error rate (EER) is used as criterion here. The optimal values (in sense of minimizing the EER) of wavelet transform parameters depend on many factors: image quality, sharpness, size of characteristic objects, etc. It is hard to isolate these factors and their influences. The work presents an attempt to study an influence of following factors to EER: iris segmentation precision, defocus level, noise level. Several public domain iris image databases were involved in experiments. The images were subjected to modelled distortions of said types. The dependencies of wavelet parameter and EER values from the distortion levels were build. It is observed that the increase of the segmentation error and image noise leads to the increase of the optimal wavelength of the wavelets, whereas the increase of defocus level leads to decreasing of this value.

Multilevel Modeling with Correlated Effects

ERIC Educational Resources Information Center

Kim, Jee-Seon; Frees, Edward W.

2007-01-01

When there exist omitted effects, measurement error, and/or simultaneity in multilevel models, explanatory variables may be correlated with random components, and standard estimation methods do not provide consistent estimates of model parameters. This paper introduces estimators that are consistent under such conditions. By employing generalized…

Regression dilution in the proportional hazards model.

PubMed

Hughes, M D

1993-12-01

The problem of regression dilution arising from covariate measurement error is investigated for survival data using the proportional hazards model. The naive approach to parameter estimation is considered whereby observed covariate values are used, inappropriately, in the usual analysis instead of the underlying covariate values. A relationship between the estimated parameter in large samples and the true parameter is obtained showing that the bias does not depend on the form of the baseline hazard function when the errors are normally distributed. With high censorship, adjustment of the naive estimate by the factor 1 + lambda, where lambda is the ratio of within-person variability about an underlying mean level to the variability of these levels in the population sampled, removes the bias. As censorship increases, the adjustment required increases and when there is no censorship is markedly higher than 1 + lambda and depends also on the true risk relationship.

Application of empirical and dynamical closure methods to simple climate models

NASA Astrophysics Data System (ADS)

Padilla, Lauren Elizabeth

This dissertation applies empirically- and physically-based methods for closure of uncertain parameters and processes to three model systems that lie on the simple end of climate model complexity. Each model isolates one of three sources of closure uncertainty: uncertain observational data, large dimension, and wide ranging length scales. They serve as efficient test systems toward extension of the methods to more realistic climate models. The empirical approach uses the Unscented Kalman Filter (UKF) to estimate the transient climate sensitivity (TCS) parameter in a globally-averaged energy balance model. Uncertainty in climate forcing and historical temperature make TCS difficult to determine. A range of probabilistic estimates of TCS computed for various assumptions about past forcing and natural variability corroborate ranges reported in the IPCC AR4 found by different means. Also computed are estimates of how quickly uncertainty in TCS may be expected to diminish in the future as additional observations become available. For higher system dimensions the UKF approach may become prohibitively expensive. A modified UKF algorithm is developed in which the error covariance is represented by a reduced-rank approximation, substantially reducing the number of model evaluations required to provide probability densities for unknown parameters. The method estimates the state and parameters of an abstract atmospheric model, known as Lorenz 96, with accuracy close to that of a full-order UKF for 30-60% rank reduction. The physical approach to closure uses the Multiscale Modeling Framework (MMF) to demonstrate closure of small-scale, nonlinear processes that would not be resolved directly in climate models. A one-dimensional, abstract test model with a broad spatial spectrum is developed. The test model couples the Kuramoto-Sivashinsky equation to a transport equation that includes cloud formation and precipitation-like processes. In the test model, three main sources of MMF error are evaluated independently. Loss of nonlinear multi-scale interactions and periodic boundary conditions in closure models were dominant sources of error. Using a reduced order modeling approach to maximize energy content allowed reduction of the closure model dimension up to 75% without loss in accuracy. MMF and a comparable alternative model peformed equally well compared to direct numerical simulation.

A Systematic Approach for Model-Based Aircraft Engine Performance Estimation

NASA Technical Reports Server (NTRS)

Simon, Donald L.; Garg, Sanjay

2010-01-01

A requirement for effective aircraft engine performance estimation is the ability to account for engine degradation, generally described in terms of unmeasurable health parameters such as efficiencies and flow capacities related to each major engine module. This paper presents a linear point design methodology for minimizing the degradation-induced error in model-based aircraft engine performance estimation applications. The technique specifically focuses on the underdetermined estimation problem, where there are more unknown health parameters than available sensor measurements. A condition for Kalman filter-based estimation is that the number of health parameters estimated cannot exceed the number of sensed measurements. In this paper, the estimated health parameter vector will be replaced by a reduced order tuner vector whose dimension is equivalent to the sensed measurement vector. The reduced order tuner vector is systematically selected to minimize the theoretical mean squared estimation error of a maximum a posteriori estimator formulation. This paper derives theoretical estimation errors at steady-state operating conditions, and presents the tuner selection routine applied to minimize these values. Results from the application of the technique to an aircraft engine simulation are presented and compared to the estimation accuracy achieved through conventional maximum a posteriori and Kalman filter estimation approaches. Maximum a posteriori estimation results demonstrate that reduced order tuning parameter vectors can be found that approximate the accuracy of estimating all health parameters directly. Kalman filter estimation results based on the same reduced order tuning parameter vectors demonstrate that significantly improved estimation accuracy can be achieved over the conventional approach of selecting a subset of health parameters to serve as the tuner vector. However, additional development is necessary to fully extend the methodology to Kalman filter-based estimation applications.

An automated construction of error models for uncertainty quantification and model calibration

NASA Astrophysics Data System (ADS)

Josset, L.; Lunati, I.

2015-12-01

To reduce the computational cost of stochastic predictions, it is common practice to rely on approximate flow solvers (or «proxy»), which provide an inexact, but computationally inexpensive response [1,2]. Error models can be constructed to correct the proxy response: based on a learning set of realizations for which both exact and proxy simulations are performed, a transformation is sought to map proxy into exact responses. Once the error model is constructed a prediction of the exact response is obtained at the cost of a proxy simulation for any new realization. Despite its effectiveness [2,3], the methodology relies on several user-defined parameters, which impact the accuracy of the predictions. To achieve a fully automated construction, we propose a novel methodology based on an iterative scheme: we first initialize the error model with a small training set of realizations; then, at each iteration, we add a new realization both to improve the model and to evaluate its performance. More specifically, at each iteration we use the responses predicted by the updated model to identify the realizations that need to be considered to compute the quantity of interest. Another user-defined parameter is the number of dimensions of the response spaces between which the mapping is sought. To identify the space dimensions that optimally balance mapping accuracy and risk of overfitting, we follow a Leave-One-Out Cross Validation. Also, the definition of a stopping criterion is central to an automated construction. We use a stability measure based on bootstrap techniques to stop the iterative procedure when the iterative model has converged. The methodology is illustrated with two test cases in which an inverse problem has to be solved and assess the performance of the method. We show that an iterative scheme is crucial to increase the applicability of the approach. [1] Josset, L., and I. Lunati, Local and global error models for improving uncertainty quantification, Math.ematical Geosciences, 2013 [2] Josset, L., D. Ginsbourger, and I. Lunati, Functional Error Modeling for uncertainty quantification in hydrogeology, Water Resources Research, 2015 [3] Josset, L., V. Demyanov, A.H. Elsheikhb, and I. Lunati, Accelerating Monte Carlo Markov chains with proxy and error models, Computer & Geosciences, 2015 (In press)

Incorporating Measurement Error from Modeled Air Pollution Exposures into Epidemiological Analyses.

PubMed

Samoli, Evangelia; Butland, Barbara K

2017-12-01

Outdoor air pollution exposures used in epidemiological studies are commonly predicted from spatiotemporal models incorporating limited measurements, temporal factors, geographic information system variables, and/or satellite data. Measurement error in these exposure estimates leads to imprecise estimation of health effects and their standard errors. We reviewed methods for measurement error correction that have been applied in epidemiological studies that use model-derived air pollution data. We identified seven cohort studies and one panel study that have employed measurement error correction methods. These methods included regression calibration, risk set regression calibration, regression calibration with instrumental variables, the simulation extrapolation approach (SIMEX), and methods under the non-parametric or parameter bootstrap. Corrections resulted in small increases in the absolute magnitude of the health effect estimate and its standard error under most scenarios. Limited application of measurement error correction methods in air pollution studies may be attributed to the absence of exposure validation data and the methodological complexity of the proposed methods. Future epidemiological studies should consider in their design phase the requirements for the measurement error correction method to be later applied, while methodological advances are needed under the multi-pollutants setting.

An aerosol activation metamodel of v1.2.0 of the pyrcel cloud parcel model: development and offline assessment for use in an aerosol–climate model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rothenberg, Daniel; Wang, Chien

We describe an emulator of a detailed cloud parcel model which has been trained to assess droplet nucleation from a complex, multimodal aerosol size distribution simulated by a global aerosol–climate model. The emulator is constructed using a sensitivity analysis approach (polynomial chaos expansion) which reproduces the behavior of the targeted parcel model across the full range of aerosol properties and meteorology simulated by the parent climate model. An iterative technique using aerosol fields sampled from a global model is used to identify the critical aerosol size distribution parameters necessary for accurately predicting activation. Across the large parameter space used tomore » train them, the emulators estimate cloud droplet number concentration (CDNC) with a mean relative error of 9.2% for aerosol populations without giant cloud condensation nuclei (CCN) and 6.9% when including them. Versus a parcel model driven by those same aerosol fields, the best-performing emulator has a mean relative error of 4.6%, which is comparable with two commonly used activation schemes also evaluated here (which have mean relative errors of 2.9 and 6.7%, respectively). We identify the potential for regional biases in modeled CDNC, particularly in oceanic regimes, where our best-performing emulator tends to overpredict by 7%, whereas the reference activation schemes range in mean relative error from -3 to 7%. The emulators which include the effects of giant CCN are more accurate in continental regimes (mean relative error of 0.3%) but strongly overestimate CDNC in oceanic regimes by up to 22%, particularly in the Southern Ocean. Finally, the biases in CDNC resulting from the subjective choice of activation scheme could potentially influence the magnitude of the indirect effect diagnosed from the model incorporating it.« less

An aerosol activation metamodel of v1.2.0 of the pyrcel cloud parcel model: development and offline assessment for use in an aerosol–climate model

DOE PAGES

Rothenberg, Daniel; Wang, Chien

2017-04-27

We describe an emulator of a detailed cloud parcel model which has been trained to assess droplet nucleation from a complex, multimodal aerosol size distribution simulated by a global aerosol–climate model. The emulator is constructed using a sensitivity analysis approach (polynomial chaos expansion) which reproduces the behavior of the targeted parcel model across the full range of aerosol properties and meteorology simulated by the parent climate model. An iterative technique using aerosol fields sampled from a global model is used to identify the critical aerosol size distribution parameters necessary for accurately predicting activation. Across the large parameter space used tomore » train them, the emulators estimate cloud droplet number concentration (CDNC) with a mean relative error of 9.2% for aerosol populations without giant cloud condensation nuclei (CCN) and 6.9% when including them. Versus a parcel model driven by those same aerosol fields, the best-performing emulator has a mean relative error of 4.6%, which is comparable with two commonly used activation schemes also evaluated here (which have mean relative errors of 2.9 and 6.7%, respectively). We identify the potential for regional biases in modeled CDNC, particularly in oceanic regimes, where our best-performing emulator tends to overpredict by 7%, whereas the reference activation schemes range in mean relative error from -3 to 7%. The emulators which include the effects of giant CCN are more accurate in continental regimes (mean relative error of 0.3%) but strongly overestimate CDNC in oceanic regimes by up to 22%, particularly in the Southern Ocean. Finally, the biases in CDNC resulting from the subjective choice of activation scheme could potentially influence the magnitude of the indirect effect diagnosed from the model incorporating it.« less

Kalman filter estimation of human pilot-model parameters

NASA Technical Reports Server (NTRS)

Schiess, J. R.; Roland, V. R.

1975-01-01

The parameters of a human pilot-model transfer function are estimated by applying the extended Kalman filter to the corresponding retarded differential-difference equations in the time domain. Use of computer-generated data indicates that most of the parameters, including the implicit time delay, may be reasonably estimated in this way. When applied to two sets of experimental data obtained from a closed-loop tracking task performed by a human, the Kalman filter generated diverging residuals for one of the measurement types, apparently because of model assumption errors. Application of a modified adaptive technique was found to overcome the divergence and to produce reasonable estimates of most of the parameters.

Extending the Solvation-Layer Interface Condition Continum Electrostatic Model to a Linearized Poisson-Boltzmann Solvent.

PubMed

Molavi Tabrizi, Amirhossein; Goossens, Spencer; Mehdizadeh Rahimi, Ali; Cooper, Christopher D; Knepley, Matthew G; Bardhan, Jaydeep P

2017-06-13

We extend the linearized Poisson-Boltzmann (LPB) continuum electrostatic model for molecular solvation to address charge-hydration asymmetry. Our new solvation-layer interface condition (SLIC)/LPB corrects for first-shell response by perturbing the traditional continuum-theory interface conditions at the protein-solvent and the Stern-layer interfaces. We also present a GPU-accelerated treecode implementation capable of simulating large proteins, and our results demonstrate that the new model exhibits significant accuracy improvements over traditional LPB models, while reducing the number of fitting parameters from dozens (atomic radii) to just five parameters, which have physical meanings related to first-shell water behavior at an uncharged interface. In particular, atom radii in the SLIC model are not optimized but uniformly scaled from their Lennard-Jones radii. Compared to explicit-solvent free-energy calculations of individual atoms in small molecules, SLIC/LPB is significantly more accurate than standard parametrizations (RMS error 0.55 kcal/mol for SLIC, compared to RMS error of 3.05 kcal/mol for standard LPB). On parametrizing the electrostatic model with a simple nonpolar component for total molecular solvation free energies, our model predicts octanol/water transfer free energies with an RMS error 1.07 kcal/mol. A more detailed assessment illustrates that standard continuum electrostatic models reproduce total charging free energies via a compensation of significant errors in atomic self-energies; this finding offers a window into improving the accuracy of Generalized-Born theories and other coarse-grained models. Most remarkably, the SLIC model also reproduces positive charging free energies for atoms in hydrophobic groups, whereas standard PB models are unable to generate positive charging free energies regardless of the parametrized radii. The GPU-accelerated solver is freely available online, as is a MATLAB implementation.

SPS pilot signal design and power transponder analysis, volume 2, phase 3

NASA Technical Reports Server (NTRS)

Lindsey, W. C.; Scholtz, R. A.; Chie, C. M.

1980-01-01

The problem of pilot signal parameter optimization and the related problem of power transponder performance analysis for the Solar Power Satellite reference phase control system are addressed. Signal and interference models were established to enable specifications of the front end filters including both the notch filter and the antenna frequency response. A simulation program package was developed to be included in SOLARSIM to perform tradeoffs of system parameters based on minimizing the phase error for the pilot phase extraction. An analytical model that characterizes the overall power transponder operation was developed. From this model, the effects of different phase noise disturbance sources that contribute to phase variations at the output of the power transponders were studied and quantified. Results indicate that it is feasible to hold the antenna array phase error to less than one degree per power module for the type of disturbances modeled.

Tolerance assignment in optical design

NASA Astrophysics Data System (ADS)

Youngworth, Richard Neil

2002-09-01

Tolerance assignment is necessary in any engineering endeavor because fabricated systems---due to the stochastic nature of manufacturing and assembly processes---necessarily deviate from the nominal design. This thesis addresses the problem of optical tolerancing. The work can logically be split into three different components that all play an essential role. The first part addresses the modeling of manufacturing errors in contemporary fabrication and assembly methods. The second component is derived from the design aspect---the development of a cost-based tolerancing procedure. The third part addresses the modeling of image quality in an efficient manner that is conducive to the tolerance assignment process. The purpose of the first component, modeling manufacturing errors, is twofold---to determine the most critical tolerancing parameters and to understand better the effects of fabrication errors. Specifically, mid-spatial-frequency errors, typically introduced in sub-aperture grinding and polishing fabrication processes, are modeled. The implication is that improving process control and understanding better the effects of the errors makes the task of tolerance assignment more manageable. Conventional tolerancing methods do not directly incorporate cost. Consequently, tolerancing approaches tend to focus more on image quality. The goal of the second part of the thesis is to develop cost-based tolerancing procedures that facilitate optimum system fabrication by generating the loosest acceptable tolerances. This work has the potential to impact a wide range of optical designs. The third element, efficient modeling of image quality, is directly related to the cost-based optical tolerancing method. Cost-based tolerancing requires efficient and accurate modeling of the effects of errors on the performance of optical systems. Thus it is important to be able to compute the gradient and the Hessian, with respect to the parameters that need to be toleranced, of the figure of merit that measures the image quality of a system. An algebraic method for computing the gradient and the Hessian is developed using perturbation theory.

Error analysis in stereo vision for location measurement of 3D point

NASA Astrophysics Data System (ADS)

Li, Yunting; Zhang, Jun; Tian, Jinwen

2015-12-01

Location measurement of 3D point in stereo vision is subjected to different sources of uncertainty that propagate to the final result. For current methods of error analysis, most of them are based on ideal intersection model to calculate the uncertainty region of point location via intersecting two fields of view of pixel that may produce loose bounds. Besides, only a few of sources of error such as pixel error or camera position are taken into account in the process of analysis. In this paper we present a straightforward and available method to estimate the location error that is taken most of source of error into account. We summed up and simplified all the input errors to five parameters by rotation transformation. Then we use the fast algorithm of midpoint method to deduce the mathematical relationships between target point and the parameters. Thus, the expectations and covariance matrix of 3D point location would be obtained, which can constitute the uncertainty region of point location. Afterwards, we turned back to the error propagation of the primitive input errors in the stereo system and throughout the whole analysis process from primitive input errors to localization error. Our method has the same level of computational complexity as the state-of-the-art method. Finally, extensive experiments are performed to verify the performance of our methods.