Solutions to Some Nonlinear Equations from Nonmetric Data.

ERIC Educational Resources Information Center

Rule, Stanley J.

1979-01-01

A method to provide estimates of parameters of specified nonlinear equations from ordinal data generated from a crossed design is presented. The statistical basis for the method, called NOPE (nonmetric parameter estimation), as well as examples using artifical data, are presented. (Author/JKS)

Regional evaporation estimates in the eastern monsoon region of China: Assessment of a nonlinear formulation of the complementary principle

NASA Astrophysics Data System (ADS)

Liu, Xiaomang; Liu, Changming; Brutsaert, Wilfried

2016-12-01

The performance of a nonlinear formulation of the complementary principle for evaporation estimation was investigated in 241 catchments with different climate conditions in the eastern monsoon region of China. Evaporation (Ea) calculated by the water balance equation was used as the reference. Ea estimated by the calibrated nonlinear formulation was generally in good agreement with the water balance results, especially in relatively dry catchments. The single parameter in the nonlinear formulation, namely αe as a weak analog of the alpha parameter of Priestley and Taylor (), tended to exhibit larger values in warmer and humid near-coastal areas, but smaller values in colder, drier environments inland, with a significant dependency on the aridity index (AI). The nonlinear formulation combined with the equation relating the one parameter and AI provides a promising method to estimate regional Ea with standard and routinely measured meteorological data.

Linear theory for filtering nonlinear multiscale systems with model error

PubMed Central

Berry, Tyrus; Harlim, John

2014-01-01

In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure, simultaneously produce accurate filtering and equilibrium statistical prediction. In contrast, an offline estimation technique based on a linear regression, which fits the parameters to a training dataset without using the filter, yields filter estimates which are worse than the observations or even divergent when the slow variables are not fully observed. This finding does not imply that all offline methods are inherently inferior to the online method for nonlinear estimation problems, it only suggests that an ideal estimation technique should estimate all parameters simultaneously whether it is online or offline. PMID:25002829

Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models

NASA Astrophysics Data System (ADS)

Boudineau, Mégane; Carfantan, Hervé; Bourguignon, Sébastien; Bazot, Michael

2016-06-01

We address the sparse approximation problem in the case where the data are approximated by the linear combination of a small number of elementary signals, each of these signals depending non-linearly on additional parameters. Sparsity is explicitly expressed through a Bernoulli-Gaussian hierarchical model in a Bayesian framework. Posterior mean estimates are computed using Markov Chain Monte-Carlo algorithms. We generalize the partially marginalized Gibbs sampler proposed in the linear case in [1], and build an hybrid Hastings-within-Gibbs algorithm in order to account for the nonlinear parameters. All model parameters are then estimated in an unsupervised procedure. The resulting method is evaluated on a sparse spectral analysis problem. It is shown to converge more efficiently than the classical joint estimation procedure, with only a slight increase of the computational cost per iteration, consequently reducing the global cost of the estimation procedure.

Parameter estimating state reconstruction

NASA Technical Reports Server (NTRS)

George, E. B.

1976-01-01

Parameter estimation is considered for systems whose entire state cannot be measured. Linear observers are designed to recover the unmeasured states to a sufficient accuracy to permit the estimation process. There are three distinct dynamics that must be accommodated in the system design: the dynamics of the plant, the dynamics of the observer, and the system updating of the parameter estimation. The latter two are designed to minimize interaction of the involved systems. These techniques are extended to weakly nonlinear systems. The application to a simulation of a space shuttle POGO system test is of particular interest. A nonlinear simulation of the system is developed, observers designed, and the parameters estimated.

Comparative analysis of linear and non-linear method of estimating the sorption isotherm parameters for malachite green onto activated carbon.

PubMed

Kumar, K Vasanth

2006-08-21

The experimental equilibrium data of malachite green onto activated carbon were fitted to the Freundlich, Langmuir and Redlich-Peterson isotherms by linear and non-linear method. A comparison between linear and non-linear of estimating the isotherm parameters was discussed. The four different linearized form of Langmuir isotherm were also discussed. The results confirmed that the non-linear method as a better way to obtain isotherm parameters. The best fitting isotherm was Langmuir and Redlich-Peterson isotherm. Redlich-Peterson is a special case of Langmuir when the Redlich-Peterson isotherm constant g was unity.

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

NASA Technical Reports Server (NTRS)

Murphy, Patrick Charles

1985-01-01

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

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.

On a variational approach to some parameter estimation problems

NASA Technical Reports Server (NTRS)

Banks, H. T.

1985-01-01

Examples (1-D seismic, large flexible structures, bioturbation, nonlinear population dispersal) in which a variation setting can provide a convenient framework for convergence and stability arguments in parameter estimation problems are considered. Some of these examples are 1-D seismic, large flexible structures, bioturbation, and nonlinear population dispersal. Arguments for convergence and stability via a variational approach of least squares formulations of parameter estimation problems for partial differential equations is one aspect of the problem considered.

On-line implementation of nonlinear parameter estimation for the Space Shuttle main engine

NASA Technical Reports Server (NTRS)

Buckland, Julia H.; Musgrave, Jeffrey L.; Walker, Bruce K.

1992-01-01

We investigate the performance of a nonlinear estimation scheme applied to the estimation of several parameters in a performance model of the Space Shuttle Main Engine. The nonlinear estimator is based upon the extended Kalman filter which has been augmented to provide estimates of several key performance variables. The estimated parameters are directly related to the efficiency of both the low pressure and high pressure fuel turbopumps. Decreases in the parameter estimates may be interpreted as degradations in turbine and/or pump efficiencies which can be useful measures for an online health monitoring algorithm. This paper extends previous work which has focused on off-line parameter estimation by investigating the filter's on-line potential from a computational standpoint. ln addition, we examine the robustness of the algorithm to unmodeled dynamics. The filter uses a reduced-order model of the engine that includes only fuel-side dynamics. The on-line results produced during this study are comparable to off-line results generated previously. The results show that the parameter estimates are sensitive to dynamics not included in the filter model. Off-line results using an extended Kalman filter with a full order engine model to address the robustness problems of the reduced-order model are also presented.

On Least Squares Fitting Nonlinear Submodels.

ERIC Educational Resources Information Center

Bechtel, Gordon G.

Three simplifying conditions are given for obtaining least squares (LS) estimates for a nonlinear submodel of a linear model. If these are satisfied, and if the subset of nonlinear parameters may be LS fit to the corresponding LS estimates of the linear model, then one attains the desired LS estimates for the entire submodel. Two illustrative…

A Bayesian approach to identifying structural nonlinearity using free-decay response: Application to damage detection in composites

USGS Publications Warehouse

Nichols, J.M.; Link, W.A.; Murphy, K.D.; Olson, C.C.

2010-01-01

This work discusses a Bayesian approach to approximating the distribution of parameters governing nonlinear structural systems. Specifically, we use a Markov Chain Monte Carlo method for sampling the posterior parameter distributions thus producing both point and interval estimates for parameters. The method is first used to identify both linear and nonlinear parameters in a multiple degree-of-freedom structural systems using free-decay vibrations. The approach is then applied to the problem of identifying the location, size, and depth of delamination in a model composite beam. The influence of additive Gaussian noise on the response data is explored with respect to the quality of the resulting parameter estimates.

Weighted linear least squares estimation of diffusion MRI parameters: strengths, limitations, and pitfalls.

PubMed

Veraart, Jelle; Sijbers, Jan; Sunaert, Stefan; Leemans, Alexander; Jeurissen, Ben

2013-11-01

Linear least squares estimators are widely used in diffusion MRI for the estimation of diffusion parameters. Although adding proper weights is necessary to increase the precision of these linear estimators, there is no consensus on how to practically define them. In this study, the impact of the commonly used weighting strategies on the accuracy and precision of linear diffusion parameter estimators is evaluated and compared with the nonlinear least squares estimation approach. Simulation and real data experiments were done to study the performance of the weighted linear least squares estimators with weights defined by (a) the squares of the respective noisy diffusion-weighted signals; and (b) the squares of the predicted signals, which are reconstructed from a previous estimate of the diffusion model parameters. The negative effect of weighting strategy (a) on the accuracy of the estimator was surprisingly high. Multi-step weighting strategies yield better performance and, in some cases, even outperformed the nonlinear least squares estimator. If proper weighting strategies are applied, the weighted linear least squares approach shows high performance characteristics in terms of accuracy/precision and may even be preferred over nonlinear estimation methods. Copyright © 2013 Elsevier Inc. All rights reserved.

A different approach to estimate nonlinear regression model using numerical methods

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

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

Resimulation of noise: a precision estimator for least square error curve-fitting tested for axial strain time constant imaging

NASA Astrophysics Data System (ADS)

Nair, S. P.; Righetti, R.

2015-05-01

Recent elastography techniques focus on imaging information on properties of materials which can be modeled as viscoelastic or poroelastic. These techniques often require the fitting of temporal strain data, acquired from either a creep or stress-relaxation experiment to a mathematical model using least square error (LSE) parameter estimation. It is known that the strain versus time relationships for tissues undergoing creep compression have a non-linear relationship. In non-linear cases, devising a measure of estimate reliability can be challenging. In this article, we have developed and tested a method to provide non linear LSE parameter estimate reliability: which we called Resimulation of Noise (RoN). RoN provides a measure of reliability by estimating the spread of parameter estimates from a single experiment realization. We have tested RoN specifically for the case of axial strain time constant parameter estimation in poroelastic media. Our tests show that the RoN estimated precision has a linear relationship to the actual precision of the LSE estimator. We have also compared results from the RoN derived measure of reliability against a commonly used reliability measure: the correlation coefficient (CorrCoeff). Our results show that CorrCoeff is a poor measure of estimate reliability for non-linear LSE parameter estimation. While the RoN is specifically tested only for axial strain time constant imaging, a general algorithm is provided for use in all LSE parameter estimation.

Error vector magnitude based parameter estimation for digital filter back-propagation mitigating SOA distortions in 16-QAM.

PubMed

Amiralizadeh, Siamak; Nguyen, An T; Rusch, Leslie A

2013-08-26

We investigate the performance of digital filter back-propagation (DFBP) using coarse parameter estimation for mitigating SOA nonlinearity in coherent communication systems. We introduce a simple, low overhead method for parameter estimation for DFBP based on error vector magnitude (EVM) as a figure of merit. The bit error rate (BER) penalty achieved with this method has negligible penalty as compared to DFBP with fine parameter estimation. We examine different bias currents for two commercial SOAs used as booster amplifiers in our experiments to find optimum operating points and experimentally validate our method. The coarse parameter DFBP efficiently compensates SOA-induced nonlinearity for both SOA types in 80 km propagation of 16-QAM signal at 22 Gbaud.

Identifiability of large-scale non-linear dynamic network models applied to the ADM1-case study.

PubMed

Nimmegeers, Philippe; Lauwers, Joost; Telen, Dries; Logist, Filip; Impe, Jan Van

2017-06-01

In this work, both the structural and practical identifiability of the Anaerobic Digestion Model no. 1 (ADM1) is investigated, which serves as a relevant case study of large non-linear dynamic network models. The structural identifiability is investigated using the probabilistic algorithm, adapted to deal with the specifics of the case study (i.e., a large-scale non-linear dynamic system of differential and algebraic equations). The practical identifiability is analyzed using a Monte Carlo parameter estimation procedure for a 'non-informative' and 'informative' experiment, which are heuristically designed. The model structure of ADM1 has been modified by replacing parameters by parameter combinations, to provide a generally locally structurally identifiable version of ADM1. This means that in an idealized theoretical situation, the parameters can be estimated accurately. Furthermore, the generally positive structural identifiability results can be explained from the large number of interconnections between the states in the network structure. This interconnectivity, however, is also observed in the parameter estimates, making uncorrelated parameter estimations in practice difficult. Copyright © 2017. Published by Elsevier Inc.

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

NASA Astrophysics Data System (ADS)

Sandhu, Rimple; Poirel, Dominique; Pettit, Chris; Khalil, Mohammad; Sarkar, Abhijit

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid-structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib-Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

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

Sandhu, Rimple; Poirel, Dominique; Pettit, Chris

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic systemmore » leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.« less

Comparison of linear and non-linear method in estimating the sorption isotherm parameters for safranin onto activated carbon.

PubMed

Kumar, K Vasanth; Sivanesan, S

2005-08-31

Comparison analysis of linear least square method and non-linear method for estimating the isotherm parameters was made using the experimental equilibrium data of safranin onto activated carbon at two different solution temperatures 305 and 313 K. Equilibrium data were fitted to Freundlich, Langmuir and Redlich-Peterson isotherm equations. All the three isotherm equations showed a better fit to the experimental equilibrium data. The results showed that non-linear method could be a better way to obtain the isotherm parameters. Redlich-Peterson isotherm is a special case of Langmuir isotherm when the Redlich-Peterson isotherm constant g was unity.

Estimation of nonlinear pilot model parameters including time delay.

NASA Technical Reports Server (NTRS)

Schiess, J. R.; Roland, V. R.; Wells, W. R.

1972-01-01

Investigation of the feasibility of using a Kalman filter estimator for the identification of unknown parameters in nonlinear dynamic systems with a time delay. The problem considered is the application of estimation theory to determine the parameters of a family of pilot models containing delayed states. In particular, the pilot-plant dynamics are described by differential-difference equations of the retarded type. The pilot delay, included as one of the unknown parameters to be determined, is kept in pure form as opposed to the Pade approximations generally used for these systems. Problem areas associated with processing real pilot response data are included in the discussion.

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.

Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable

ERIC Educational Resources Information Center

du Toit, Stephen H. C.; Cudeck, Robert

2009-01-01

A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution…

Non-linear Parameter Estimates from Non-stationary MEG Data

PubMed Central

Martínez-Vargas, Juan D.; López, Jose D.; Baker, Adam; Castellanos-Dominguez, German; Woolrich, Mark W.; Barnes, Gareth

2016-01-01

We demonstrate a method to estimate key electrophysiological parameters from resting state data. In this paper, we focus on the estimation of head-position parameters. The recovery of these parameters is especially challenging as they are non-linearly related to the measured field. In order to do this we use an empirical Bayesian scheme to estimate the cortical current distribution due to a range of laterally shifted head-models. We compare different methods of approaching this problem from the division of M/EEG data into stationary sections and performing separate source inversions, to explaining all of the M/EEG data with a single inversion. We demonstrate this through estimation of head position in both simulated and empirical resting state MEG data collected using a head-cast. PMID:27597815

Robust ridge regression estimators for nonlinear models with applications to high throughput screening assay data.

PubMed

Lim, Changwon

2015-03-30

Nonlinear regression is often used to evaluate the toxicity of a chemical or a drug by fitting data from a dose-response study. Toxicologists and pharmacologists may draw a conclusion about whether a chemical is toxic by testing the significance of the estimated parameters. However, sometimes the null hypothesis cannot be rejected even though the fit is quite good. One possible reason for such cases is that the estimated standard errors of the parameter estimates are extremely large. In this paper, we propose robust ridge regression estimation procedures for nonlinear models to solve this problem. The asymptotic properties of the proposed estimators are investigated; in particular, their mean squared errors are derived. The performances of the proposed estimators are compared with several standard estimators using simulation studies. The proposed methodology is also illustrated using high throughput screening assay data obtained from the National Toxicology Program. Copyright © 2014 John Wiley & Sons, Ltd.

Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter.

PubMed

Song, Xuegang; Zhang, Yuexin; Liang, Dakai

2017-10-10

This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF) was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.

A method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

PubMed

Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

2016-05-01

The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

Quantitative body DW-MRI biomarkers uncertainty estimation using unscented wild-bootstrap.

PubMed

Freiman, M; Voss, S D; Mulkern, R V; Perez-Rossello, J M; Warfield, S K

2011-01-01

We present a new method for the uncertainty estimation of diffusion parameters for quantitative body DW-MRI assessment. Diffusion parameters uncertainty estimation from DW-MRI is necessary for clinical applications that use these parameters to assess pathology. However, uncertainty estimation using traditional techniques requires repeated acquisitions, which is undesirable in routine clinical use. Model-based bootstrap techniques, for example, assume an underlying linear model for residuals rescaling and cannot be utilized directly for body diffusion parameters uncertainty estimation due to the non-linearity of the body diffusion model. To offset this limitation, our method uses the Unscented transform to compute the residuals rescaling parameters from the non-linear body diffusion model, and then applies the wild-bootstrap method to infer the body diffusion parameters uncertainty. Validation through phantom and human subject experiments shows that our method identify the regions with higher uncertainty in body DWI-MRI model parameters correctly with realtive error of -36% in the uncertainty values.

Estimating contrast transfer function and associated parameters by constrained non-linear optimization.

PubMed

Yang, C; Jiang, W; Chen, D-H; Adiga, U; Ng, E G; Chiu, W

2009-03-01

The three-dimensional reconstruction of macromolecules from two-dimensional single-particle electron images requires determination and correction of the contrast transfer function (CTF) and envelope function. A computational algorithm based on constrained non-linear optimization is developed to estimate the essential parameters in the CTF and envelope function model simultaneously and automatically. The application of this estimation method is demonstrated with focal series images of amorphous carbon film as well as images of ice-embedded icosahedral virus particles suspended across holes.

Parameter estimation in nonlinear distributed systems - Approximation theory and convergence results

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.

Detecting influential observations in nonlinear regression modeling of groundwater flow

USGS Publications Warehouse

Yager, Richard M.

1998-01-01

Nonlinear regression is used to estimate optimal parameter values in models of groundwater flow to ensure that differences between predicted and observed heads and flows do not result from nonoptimal parameter values. Parameter estimates can be affected, however, by observations that disproportionately influence the regression, such as outliers that exert undue leverage on the objective function. Certain statistics developed for linear regression can be used to detect influential observations in nonlinear regression if the models are approximately linear. This paper discusses the application of Cook's D, which measures the effect of omitting a single observation on a set of estimated parameter values, and the statistical parameter DFBETAS, which quantifies the influence of an observation on each parameter. The influence statistics were used to (1) identify the influential observations in the calibration of a three-dimensional, groundwater flow model of a fractured-rock aquifer through nonlinear regression, and (2) quantify the effect of omitting influential observations on the set of estimated parameter values. Comparison of the spatial distribution of Cook's D with plots of model sensitivity shows that influential observations correspond to areas where the model heads are most sensitive to certain parameters, and where predicted groundwater flow rates are largest. Five of the six discharge observations were identified as influential, indicating that reliable measurements of groundwater flow rates are valuable data in model calibration. DFBETAS are computed and examined for an alternative model of the aquifer system to identify a parameterization error in the model design that resulted in overestimation of the effect of anisotropy on horizontal hydraulic conductivity.

A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems. Ph.D. Thesis - George Washington Univ., Apr. 1985

NASA Technical Reports Server (NTRS)

Murphy, P. C.

1986-01-01

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.

Stochastic filtering for damage identification through nonlinear structural finite element model updating

NASA Astrophysics Data System (ADS)

Astroza, Rodrigo; Ebrahimian, Hamed; Conte, Joel P.

2015-03-01

This paper describes a novel framework that combines advanced mechanics-based nonlinear (hysteretic) finite element (FE) models and stochastic filtering techniques to estimate unknown time-invariant parameters of nonlinear inelastic material models used in the FE model. Using input-output data recorded during earthquake events, the proposed framework updates the nonlinear FE model of the structure. The updated FE model can be directly used for damage identification and further used for damage prognosis. To update the unknown time-invariant parameters of the FE model, two alternative stochastic filtering methods are used: the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). A three-dimensional, 5-story, 2-by-1 bay reinforced concrete (RC) frame is used to verify the proposed framework. The RC frame is modeled using fiber-section displacement-based beam-column elements with distributed plasticity and is subjected to the ground motion recorded at the Sylmar station during the 1994 Northridge earthquake. The results indicate that the proposed framework accurately estimate the unknown material parameters of the nonlinear FE model. The UKF outperforms the EKF when the relative root-mean-square error of the recorded responses are compared. In addition, the results suggest that the convergence of the estimate of modeling parameters is smoother and faster when the UKF is utilized.

Nonlinear Curve-Fitting Program

NASA Technical Reports Server (NTRS)

Everhart, Joel L.; Badavi, Forooz F.

1989-01-01

Nonlinear optimization algorithm helps in finding best-fit curve. Nonlinear Curve Fitting Program, NLINEAR, interactive curve-fitting routine based on description of quadratic expansion of X(sup 2) statistic. Utilizes nonlinear optimization algorithm calculating best statistically weighted values of parameters of fitting function and X(sup 2) minimized. Provides user with such statistical information as goodness of fit and estimated values of parameters producing highest degree of correlation between experimental data and mathematical model. Written in FORTRAN 77.

Development of the One-Sided Nonlinear Adaptive Doppler Shift Estimation

NASA Technical Reports Server (NTRS)

Beyon, Jeffrey Y.; Koch, Grady J.; Singh, Upendra N.; Kavaya, Michael J.; Serror, Judith A.

2009-01-01

The new development of a one-sided nonlinear adaptive shift estimation technique (NADSET) is introduced. The background of the algorithm and a brief overview of NADSET are presented. The new technique is applied to the wind parameter estimates from a 2-micron wavelength coherent Doppler lidar system called VALIDAR located in NASA Langley Research Center in Virginia. The new technique enhances wind parameters such as Doppler shift and power estimates in low Signal-To-Noise-Ratio (SNR) regimes using the estimates in high SNR regimes as the algorithm scans the range bins from low to high altitude. The original NADSET utilizes the statistics in both the lower and the higher range bins to refine the wind parameter estimates in between. The results of the two different approaches of NADSET are compared.

Design of asymptotic estimators: an approach based on neural networks and nonlinear programming.

PubMed

Alessandri, Angelo; Cervellera, Cristiano; Sanguineti, Marcello

2007-01-01

A methodology to design state estimators for a class of nonlinear continuous-time dynamic systems that is based on neural networks and nonlinear programming is proposed. The estimator has the structure of a Luenberger observer with a linear gain and a parameterized (in general, nonlinear) function, whose argument is an innovation term representing the difference between the current measurement and its prediction. The problem of the estimator design consists in finding the values of the gain and of the parameters that guarantee the asymptotic stability of the estimation error. Toward this end, if a neural network is used to take on this function, the parameters (i.e., the neural weights) are chosen, together with the gain, by constraining the derivative of a quadratic Lyapunov function for the estimation error to be negative definite on a given compact set. It is proved that it is sufficient to impose the negative definiteness of such a derivative only on a suitably dense grid of sampling points. The gain is determined by solving a Lyapunov equation. The neural weights are searched for via nonlinear programming by minimizing a cost penalizing grid-point constraints that are not satisfied. Techniques based on low-discrepancy sequences are applied to deal with a small number of sampling points, and, hence, to reduce the computational burden required to optimize the parameters. Numerical results are reported and comparisons with those obtained by the extended Kalman filter are made.

Bayesian nonlinear structural FE model and seismic input identification for damage assessment of civil structures

NASA Astrophysics Data System (ADS)

Astroza, Rodrigo; Ebrahimian, Hamed; Li, Yong; Conte, Joel P.

2017-09-01

A methodology is proposed to update mechanics-based nonlinear finite element (FE) models of civil structures subjected to unknown input excitation. The approach allows to jointly estimate unknown time-invariant model parameters of a nonlinear FE model of the structure and the unknown time histories of input excitations using spatially-sparse output response measurements recorded during an earthquake event. The unscented Kalman filter, which circumvents the computation of FE response sensitivities with respect to the unknown model parameters and unknown input excitations by using a deterministic sampling approach, is employed as the estimation tool. The use of measurement data obtained from arrays of heterogeneous sensors, including accelerometers, displacement sensors, and strain gauges is investigated. Based on the estimated FE model parameters and input excitations, the updated nonlinear FE model can be interrogated to detect, localize, classify, and assess damage in the structure. Numerically simulated response data of a three-dimensional 4-story 2-by-1 bay steel frame structure with six unknown model parameters subjected to unknown bi-directional horizontal seismic excitation, and a three-dimensional 5-story 2-by-1 bay reinforced concrete frame structure with nine unknown model parameters subjected to unknown bi-directional horizontal seismic excitation are used to illustrate and validate the proposed methodology. The results of the validation studies show the excellent performance and robustness of the proposed algorithm to jointly estimate unknown FE model parameters and unknown input excitations.

Exploratory Study for Continuous-time Parameter Estimation of Ankle Dynamics

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Boyle, Richard D.

2014-01-01

Recently, a parallel pathway model to describe ankle dynamics was proposed. This model provides a relationship between ankle angle and net ankle torque as the sum of a linear and nonlinear contribution. A technique to identify parameters of this model in discrete-time has been developed. However, these parameters are a nonlinear combination of the continuous-time physiology, making insight into the underlying physiology impossible. The stable and accurate estimation of continuous-time parameters is critical for accurate disease modeling, clinical diagnosis, robotic control strategies, development of optimal exercise protocols for longterm space exploration, sports medicine, etc. This paper explores the development of a system identification technique to estimate the continuous-time parameters of ankle dynamics. The effectiveness of this approach is assessed via simulation of a continuous-time model of ankle dynamics with typical parameters found in clinical studies. The results show that although this technique improves estimates, it does not provide robust estimates of continuous-time parameters of ankle dynamics. Due to this we conclude that alternative modeling strategies and more advanced estimation techniques be considered for future work.

Chaos synchronization and Nelder-Mead search for parameter estimation in nonlinear pharmacological systems: Estimating tumor antigenicity in a model of immunotherapy.

PubMed

Pillai, Nikhil; Craig, Morgan; Dokoumetzidis, Aristeidis; Schwartz, Sorell L; Bies, Robert; Freedman, Immanuel

2018-06-19

In mathematical pharmacology, models are constructed to confer a robust method for optimizing treatment. The predictive capability of pharmacological models depends heavily on the ability to track the system and to accurately determine parameters with reference to the sensitivity in projected outcomes. To closely track chaotic systems, one may choose to apply chaos synchronization. An advantageous byproduct of this methodology is the ability to quantify model parameters. In this paper, we illustrate the use of chaos synchronization combined with Nelder-Mead search to estimate parameters of the well-known Kirschner-Panetta model of IL-2 immunotherapy from noisy data. Chaos synchronization with Nelder-Mead search is shown to provide more accurate and reliable estimates than Nelder-Mead search based on an extended least squares (ELS) objective function. Our results underline the strength of this approach to parameter estimation and provide a broader framework of parameter identification for nonlinear models in pharmacology. Copyright © 2018 Elsevier Ltd. All rights reserved.

State, Parameter, and Unknown Input Estimation Problems in Active Automotive Safety Applications

NASA Astrophysics Data System (ADS)

Phanomchoeng, Gridsada

A variety of driver assistance systems such as traction control, electronic stability control (ESC), rollover prevention and lane departure avoidance systems are being developed by automotive manufacturers to reduce driver burden, partially automate normal driving operations, and reduce accidents. The effectiveness of these driver assistance systems can be significant enhanced if the real-time values of several vehicle parameters and state variables, namely tire-road friction coefficient, slip angle, roll angle, and rollover index, can be known. Since there are no inexpensive sensors available to measure these variables, it is necessary to estimate them. However, due to the significant nonlinear dynamics in a vehicle, due to unknown and changing plant parameters, and due to the presence of unknown input disturbances, the design of estimation algorithms for this application is challenging. This dissertation develops a new approach to observer design for nonlinear systems in which the nonlinearity has a globally (or locally) bounded Jacobian. The developed approach utilizes a modified version of the mean value theorem to express the nonlinearity in the estimation error dynamics as a convex combination of known matrices with time varying coefficients. The observer gains are then obtained by solving linear matrix inequalities (LMIs). A number of illustrative examples are presented to show that the developed approach is less conservative and more useful than the standard Lipschitz assumption based nonlinear observer. The developed nonlinear observer is utilized for estimation of slip angle, longitudinal vehicle velocity, and vehicle roll angle. In order to predict and prevent vehicle rollovers in tripped situations, it is necessary to estimate the vertical tire forces in the presence of unknown road disturbance inputs. An approach to estimate unknown disturbance inputs in nonlinear systems using dynamic model inversion and a modified version of the mean value theorem is presented. The developed theory is used to estimate vertical tire forces and predict tripped rollovers in situations involving road bumps, potholes, and lateral unknown force inputs. To estimate the tire-road friction coefficients at each individual tire of the vehicle, algorithms to estimate longitudinal forces and slip ratios at each tire are proposed. Subsequently, tire-road friction coefficients are obtained using recursive least squares parameter estimators that exploit the relationship between longitudinal force and slip ratio at each tire. The developed approaches are evaluated through simulations with industry standard software, CARSIM, with experimental tests on a Volvo XC90 sport utility vehicle and with experimental tests on a 1/8th scaled vehicle. The simulation and experimental results show that the developed approaches can reliably estimate the vehicle parameters and state variables needed for effective ESC and rollover prevention applications.

Stochastic parameter estimation in nonlinear time-delayed vibratory systems with distributed delay

NASA Astrophysics Data System (ADS)

Torkamani, Shahab; Butcher, Eric A.

2013-07-01

The stochastic estimation of parameters and states in linear and nonlinear time-delayed vibratory systems with distributed delay is explored. The approach consists of first employing a continuous time approximation to approximate the delayed integro-differential system with a large set of ordinary differential equations having stochastic excitations. Then the problem of state and parameter estimation in the resulting stochastic ordinary differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman-Bucy filter to the augmented filtering problem, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states. Similarly, the upper bound of the distributed delay can also be estimated by the proposed technique. As an illustrative example to a practical problem in vibrations, the parameter, delay upper bound, and state estimation from noise-corrupted measurements in a distributed force model widely used for modeling machine tool vibrations in the turning operation is investigated.

Poster — Thur Eve — 44: Linearization of Compartmental Models for More Robust Estimates of Regional Hemodynamic, Metabolic and Functional Parameters using DCE-CT/PET Imaging

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

Blais, AR; Dekaban, M; Lee, T-Y

2014-08-15

Quantitative analysis of dynamic positron emission tomography (PET) data usually involves minimizing a cost function with nonlinear regression, wherein the choice of starting parameter values and the presence of local minima affect the bias and variability of the estimated kinetic parameters. These nonlinear methods can also require lengthy computation time, making them unsuitable for use in clinical settings. Kinetic modeling of PET aims to estimate the rate parameter k{sub 3}, which is the binding affinity of the tracer to a biological process of interest and is highly susceptible to noise inherent in PET image acquisition. We have developed linearized kineticmore » models for kinetic analysis of dynamic contrast enhanced computed tomography (DCE-CT)/PET imaging, including a 2-compartment model for DCE-CT and a 3-compartment model for PET. Use of kinetic parameters estimated from DCE-CT can stabilize the kinetic analysis of dynamic PET data, allowing for more robust estimation of k{sub 3}. Furthermore, these linearized models are solved with a non-negative least squares algorithm and together they provide other advantages including: 1) only one possible solution and they do not require a choice of starting parameter values, 2) parameter estimates are comparable in accuracy to those from nonlinear models, 3) significantly reduced computational time. Our simulated data show that when blood volume and permeability are estimated with DCE-CT, the bias of k{sub 3} estimation with our linearized model is 1.97 ± 38.5% for 1,000 runs with a signal-to-noise ratio of 10. In summary, we have developed a computationally efficient technique for accurate estimation of k{sub 3} from noisy dynamic PET data.« less

Combined state and parameter identification of nonlinear structural dynamical systems based on Rao-Blackwellization and Markov chain Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Abhinav, S.; Manohar, C. S.

2018-03-01

The problem of combined state and parameter estimation in nonlinear state space models, based on Bayesian filtering methods, is considered. A novel approach, which combines Rao-Blackwellized particle filters for state estimation with Markov chain Monte Carlo (MCMC) simulations for parameter identification, is proposed. In order to ensure successful performance of the MCMC samplers, in situations involving large amount of dynamic measurement data and (or) low measurement noise, the study employs a modified measurement model combined with an importance sampling based correction. The parameters of the process noise covariance matrix are also included as quantities to be identified. The study employs the Rao-Blackwellization step at two stages: one, associated with the state estimation problem in the particle filtering step, and, secondly, in the evaluation of the ratio of likelihoods in the MCMC run. The satisfactory performance of the proposed method is illustrated on three dynamical systems: (a) a computational model of a nonlinear beam-moving oscillator system, (b) a laboratory scale beam traversed by a loaded trolley, and (c) an earthquake shake table study on a bending-torsion coupled nonlinear frame subjected to uniaxial support motion.

Maximum profile likelihood estimation of differential equation parameters through model based smoothing state estimates.

PubMed

Campbell, D A; Chkrebtii, O

2013-12-01

Statistical inference for biochemical models often faces a variety of characteristic challenges. In this paper we examine state and parameter estimation for the JAK-STAT intracellular signalling mechanism, which exemplifies the implementation intricacies common in many biochemical inference problems. We introduce an extension to the Generalized Smoothing approach for estimating delay differential equation models, addressing selection of complexity parameters, choice of the basis system, and appropriate optimization strategies. Motivated by the JAK-STAT system, we further extend the generalized smoothing approach to consider a nonlinear observation process with additional unknown parameters, and highlight how the approach handles unobserved states and unevenly spaced observations. The methodology developed is generally applicable to problems of estimation for differential equation models with delays, unobserved states, nonlinear observation processes, and partially observed histories. Crown Copyright © 2013. Published by Elsevier Inc. All rights reserved.

Parameter estimation of variable-parameter nonlinear Muskingum model using excel solver

NASA Astrophysics Data System (ADS)

Kang, Ling; Zhou, Liwei

2018-02-01

Abstract . The Muskingum model is an effective flood routing technology in hydrology and water resources Engineering. With the development of optimization technology, more and more variable-parameter Muskingum models were presented to improve effectiveness of the Muskingum model in recent decades. A variable-parameter nonlinear Muskingum model (NVPNLMM) was proposed in this paper. According to the results of two real and frequently-used case studies by various models, the NVPNLMM could obtain better values of evaluation criteria, which are used to describe the superiority of the estimated outflows and compare the accuracies of flood routing using various models, and the optimal estimated outflows by the NVPNLMM were closer to the observed outflows than the ones by other models.

Adaptive estimation of nonlinear parameters of a nonholonomic spherical robot using a modified fuzzy-based speed gradient algorithm

NASA Astrophysics Data System (ADS)

Roozegar, Mehdi; Mahjoob, Mohammad J.; Ayati, Moosa

2017-05-01

This paper deals with adaptive estimation of the unknown parameters and states of a pendulum-driven spherical robot (PDSR), which is a nonlinear in parameters (NLP) chaotic system with parametric uncertainties. Firstly, the mathematical model of the robot is deduced by applying the Newton-Euler methodology for a system of rigid bodies. Then, based on the speed gradient (SG) algorithm, the states and unknown parameters of the robot are estimated online for different step length gains and initial conditions. The estimated parameters are updated adaptively according to the error between estimated and true state values. Since the errors of the estimated states and parameters as well as the convergence rates depend significantly on the value of step length gain, this gain should be chosen optimally. Hence, a heuristic fuzzy logic controller is employed to adjust the gain adaptively. Simulation results indicate that the proposed approach is highly encouraging for identification of this NLP chaotic system even if the initial conditions change and the uncertainties increase; therefore, it is reliable to be implemented on a real robot.

A nondestructive method for estimation of the fracture toughness of CrMoV rotor steels based on ultrasonic nonlinearity.

PubMed

Jeong, Hyunjo; Nahm, Seung-Hoon; Jhang, Kyung-Young; Nam, Young-Hyun

2003-09-01

The objective of this paper is to develop a nondestructive method for estimating the fracture toughness (K(IC)) of CrMoV steels used as the rotor material of steam turbines in power plants. To achieve this objective, a number of CrMoV steel samples were heat-treated, and the fracture appearance transition temperature (FATT) was determined as a function of aging time. Nonlinear ultrasonics was employed as the theoretical basis to explain the harmonic generation in a damaged material, and the nonlinearity parameter of the second harmonic wave was the experimental measure used to be correlated to the fracture toughness of the rotor steel. The nondestructive procedure for estimating the K(IC) consists of two steps. First, the correlations between the nonlinearity parameter and the FATT are sought. The FATT values are then used to estimate K(IC) using the K(IC) versus excess temperature (i.e., T-FATT) correlation that is available in the literature for CrMoV rotor steel.

Linear and nonlinear ARMA model parameter estimation using an artificial neural network

NASA Technical Reports Server (NTRS)

Chon, K. H.; Cohen, R. J.

1997-01-01

This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

Robust gaze-steering of an active vision system against errors in the estimated parameters

NASA Astrophysics Data System (ADS)

Han, Youngmo

2015-01-01

Gaze-steering is often used to broaden the viewing range of an active vision system. Gaze-steering procedures are usually based on estimated parameters such as image position, image velocity, depth and camera calibration parameters. However, there may be uncertainties in these estimated parameters because of measurement noise and estimation errors. In this case, robust gaze-steering cannot be guaranteed. To compensate for such problems, this paper proposes a gaze-steering method based on a linear matrix inequality (LMI). In this method, we first propose a proportional derivative (PD) control scheme on the unit sphere that does not use depth parameters. This proposed PD control scheme can avoid uncertainties in the estimated depth and camera calibration parameters, as well as inconveniences in their estimation process, including the use of auxiliary feature points and highly non-linear computation. Furthermore, the control gain of the proposed PD control scheme on the unit sphere is designed using LMI such that the designed control is robust in the presence of uncertainties in the other estimated parameters, such as image position and velocity. Simulation results demonstrate that the proposed method provides a better compensation for uncertainties in the estimated parameters than the contemporary linear method and steers the gaze of the camera more steadily over time than the contemporary non-linear method.

Sensorless Estimation and Nonlinear Control of a Rotational Energy Harvester

NASA Astrophysics Data System (ADS)

Nunna, Kameswarie; Toh, Tzern T.; Mitcheson, Paul D.; Astolfi, Alessandro

2013-12-01

It is important to perform sensorless monitoring of parameters in energy harvesting devices in order to determine the operating states of the system. However, physical measurements of these parameters is often a challenging task due to the unavailability of access points. This paper presents, as an example application, the design of a nonlinear observer and a nonlinear feedback controller for a rotational energy harvester. A dynamic model of a rotational energy harvester with its power electronic interface is derived and validated. This model is then used to design a nonlinear observer and a nonlinear feedback controller which yield a sensorless closed-loop system. The observer estimates the mechancial quantities from the measured electrical quantities while the control law sustains power generation across a range of source rotation speeds. The proposed scheme is assessed through simulations and experiments.

Incorporation of prior information on parameters into nonlinear regression groundwater flow models: 1. Theory

USGS Publications Warehouse

Cooley, Richard L.

1982-01-01

Prior information on the parameters of a groundwater flow model can be used to improve parameter estimates obtained from nonlinear regression solution of a modeling problem. Two scales of prior information can be available: (1) prior information having known reliability (that is, bias and random error structure) and (2) prior information consisting of best available estimates of unknown reliability. A regression method that incorporates the second scale of prior information assumes the prior information to be fixed for any particular analysis to produce improved, although biased, parameter estimates. Approximate optimization of two auxiliary parameters of the formulation is used to help minimize the bias, which is almost always much smaller than that resulting from standard ridge regression. It is shown that if both scales of prior information are available, then a combined regression analysis may be made.

Overview and benchmark analysis of fuel cell parameters estimation for energy management purposes

NASA Astrophysics Data System (ADS)

Kandidayeni, M.; Macias, A.; Amamou, A. A.; Boulon, L.; Kelouwani, S.; Chaoui, H.

2018-03-01

Proton exchange membrane fuel cells (PEMFCs) have become the center of attention for energy conversion in many areas such as automotive industry, where they confront a high dynamic behavior resulting in their characteristics variation. In order to ensure appropriate modeling of PEMFCs, accurate parameters estimation is in demand. However, parameter estimation of PEMFC models is highly challenging due to their multivariate, nonlinear, and complex essence. This paper comprehensively reviews PEMFC models parameters estimation methods with a specific view to online identification algorithms, which are considered as the basis of global energy management strategy design, to estimate the linear and nonlinear parameters of a PEMFC model in real time. In this respect, different PEMFC models with different categories and purposes are discussed first. Subsequently, a thorough investigation of PEMFC parameter estimation methods in the literature is conducted in terms of applicability. Three potential algorithms for online applications, Recursive Least Square (RLS), Kalman filter, and extended Kalman filter (EKF), which has escaped the attention in previous works, have been then utilized to identify the parameters of two well-known semi-empirical models in the literature, Squadrito et al. and Amphlett et al. Ultimately, the achieved results and future challenges are discussed.

NONLINEAR AND FIBER OPTICS: Influence of nonlinearity of the parameters of guided modes in fiber waveguides

NASA Astrophysics Data System (ADS)

Goncharenko, I. A.

1990-04-01

The shift formula method is used to obtain analytic expressions which provide estimates of the influence of nonlinearity on the parameters of fiber waveguide modes. Depending on the sign of the nonlinear susceptibility of the waveguide core, the nonlinearity can improve or impair (right down to complete loss) the waveguiding properties of fibers. The optical power at which a fiber loses its guiding properties is constant far from the cutoff, but rises steeply near the critical cutoff frequency. The nonlinearity can be used to vary the zero dispersion wavelength and the range of single-mode operation of a fiber waveguide.

Economic policy optimization based on both one stochastic model and the parametric control theory

NASA Astrophysics Data System (ADS)

Ashimov, Abdykappar; Borovskiy, Yuriy; Onalbekov, Mukhit

2016-06-01

A nonlinear dynamic stochastic general equilibrium model with financial frictions is developed to describe two interacting national economies in the environment of the rest of the world. Parameters of nonlinear model are estimated based on its log-linearization by the Bayesian approach. The nonlinear model is verified by retroprognosis, estimation of stability indicators of mappings specified by the model, and estimation the degree of coincidence for results of internal and external shocks' effects on macroeconomic indicators on the basis of the estimated nonlinear model and its log-linearization. On the base of the nonlinear model, the parametric control problems of economic growth and volatility of macroeconomic indicators of Kazakhstan are formulated and solved for two exchange rate regimes (free floating and managed floating exchange rates)

Evaluation of unconfined-aquifer parameters from pumping test data by nonlinear least squares

NASA Astrophysics Data System (ADS)

Heidari, Manoutchehr; Wench, Allen

1997-05-01

Nonlinear least squares (NLS) with automatic differentiation was used to estimate aquifer parameters from drawdown data obtained from published pumping tests conducted in homogeneous, water-table aquifers. The method is based on a technique that seeks to minimize the squares of residuals between observed and calculated drawdown subject to bounds that are placed on the parameter of interest. The analytical model developed by Neuman for flow to a partially penetrating well of infinitesimal diameter situated in an infinite, homogeneous and anisotropic aquifer was used to obtain calculated drawdown. NLS was first applied to synthetic drawdown data from a hypothetical but realistic aquifer to demonstrate that the relevant hydraulic parameters (storativity, specific yield, and horizontal and vertical hydraulic conductivity) can be evaluated accurately. Next the method was used to estimate the parameters at three field sites with widely varying hydraulic properties. NLS produced unbiased estimates of the aquifer parameters that are close to the estimates obtained with the same data using a visual curve-matching approach. Small differences in the estimates are a consequence of subjective interpretation introduced in the visual approach.

Evaluation of unconfined-aquifer parameters from pumping test data by nonlinear least squares

USGS Publications Warehouse

Heidari, M.; Moench, A.

1997-01-01

Nonlinear least squares (NLS) with automatic differentiation was used to estimate aquifer parameters from drawdown data obtained from published pumping tests conducted in homogeneous, water-table aquifers. The method is based on a technique that seeks to minimize the squares of residuals between observed and calculated drawdown subject to bounds that are placed on the parameter of interest. The analytical model developed by Neuman for flow to a partially penetrating well of infinitesimal diameter situated in an infinite, homogeneous and anisotropic aquifer was used to obtain calculated drawdown. NLS was first applied to synthetic drawdown data from a hypothetical but realistic aquifer to demonstrate that the relevant hydraulic parameters (storativity, specific yield, and horizontal and vertical hydraulic conductivity) can be evaluated accurately. Next the method was used to estimate the parameters at three field sites with widely varying hydraulic properties. NLS produced unbiased estimates of the aquifer parameters that are close to the estimates obtained with the same data using a visual curve-matching approach. Small differences in the estimates are a consequence of subjective interpretation introduced in the visual approach.

Nonlinear Quantum Metrology of Many-Body Open Systems

NASA Astrophysics Data System (ADS)

Beau, M.; del Campo, A.

2017-07-01

We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a k -body Hamiltonian and p -body Lindblad operators, the estimation error of a Hamiltonian parameter using a Greenberger-Horne-Zeilinger state as a probe is shown to scale as N-[k -(p /2 )], surpassing the shot-noise limit for 2 k >p +1 . Metrology equivalence between initial product states and maximally entangled states is established for p ≥1 . We further show that one can estimate the system-environment coupling parameter with precision N-(p /2 ), while many-body decoherence enhances the precision to N-k in the noise-amplitude estimation of a fluctuating k -body Hamiltonian. For the long-range Ising model, we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.

Parameter estimation techniques based on optimizing goodness-of-fit statistics for structural reliability

NASA Technical Reports Server (NTRS)

Starlinger, Alois; Duffy, Stephen F.; Palko, Joseph L.

1993-01-01

New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell's numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper's nonlinear regression algorithm.

Recent results of nonlinear estimators applied to hereditary systems.

NASA Technical Reports Server (NTRS)

Schiess, J. R.; Roland, V. R.; Wells, W. R.

1972-01-01

An application of the extended Kalman filter to delayed systems to estimate the state and time delay is presented. Two nonlinear estimators are discussed and the results compared with those of the Kalman filter. For all the filters considered, the hereditary system was treated with the delay in the pure form and by using Pade approximations of the delay. A summary of the convergence properties of the filters studied is given. The results indicate that the linear filter applied to the delayed system performs inadequately while the nonlinear filters provide reasonable estimates of both the state and the parameters.

A LEAST ABSOLUTE SHRINKAGE AND SELECTION OPERATOR (LASSO) FOR NONLINEAR SYSTEM IDENTIFICATION

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Lofberg, Johan; Brenner, Martin J.

2006-01-01

Identification of parametric nonlinear models involves estimating unknown parameters and detecting its underlying structure. Structure computation is concerned with selecting a subset of parameters to give a parsimonious description of the system which may afford greater insight into the functionality of the system or a simpler controller design. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of nonlinear systems. The LASSO minimises the residual sum of squares by the addition of a 1 penalty term on the parameter vector of the traditional 2 minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. The performance of this LASSO structure detection method was evaluated by using it to estimate the structure of a nonlinear polynomial model. Applicability of the method to more complex systems such as those encountered in aerospace applications was shown by identifying a parsimonious system description of the F/A-18 Active Aeroelastic Wing using flight test data.

Reliability analysis of structural ceramic components using a three-parameter Weibull distribution

NASA Technical Reports Server (NTRS)

Duffy, Stephen F.; Powers, Lynn M.; Starlinger, Alois

1992-01-01

Described here are nonlinear regression estimators for the three-Weibull distribution. Issues relating to the bias and invariance associated with these estimators are examined numerically using Monte Carlo simulation methods. The estimators were used to extract parameters from sintered silicon nitride failure data. A reliability analysis was performed on a turbopump blade utilizing the three-parameter Weibull distribution and the estimates from the sintered silicon nitride data.

Parameter identification for nonlinear aerodynamic systems

NASA Technical Reports Server (NTRS)

Pearson, Allan E.

1990-01-01

Parameter identification for nonlinear aerodynamic systems is examined. It is presumed that the underlying model can be arranged into an input/output (I/O) differential operator equation of a generic form. The algorithm estimation is especially efficient since the equation error can be integrated exactly given any I/O pair to obtain an algebraic function of the parameters. The algorithm for parameter identification was extended to the order determination problem for linear differential system. The degeneracy in a least squares estimate caused by feedback was addressed. A method of frequency analysis for determining the transfer function G(j omega) from transient I/O data was formulated using complex valued Fourier based modulating functions in contrast with the trigonometric modulating functions for the parameter estimation problem. A simulation result of applying the algorithm is given under noise-free conditions for a system with a low pass transfer function.

Robust and efficient pharmacokinetic parameter non-linear least squares estimation for dynamic contrast enhanced MRI of the prostate.

PubMed

Kargar, Soudabeh; Borisch, Eric A; Froemming, Adam T; Kawashima, Akira; Mynderse, Lance A; Stinson, Eric G; Trzasko, Joshua D; Riederer, Stephen J

2018-05-01

To describe an efficient numerical optimization technique using non-linear least squares to estimate perfusion parameters for the Tofts and extended Tofts models from dynamic contrast enhanced (DCE) MRI data and apply the technique to prostate cancer. Parameters were estimated by fitting the two Tofts-based perfusion models to the acquired data via non-linear least squares. We apply Variable Projection (VP) to convert the fitting problem from a multi-dimensional to a one-dimensional line search to improve computational efficiency and robustness. Using simulation and DCE-MRI studies in twenty patients with suspected prostate cancer, the VP-based solver was compared against the traditional Levenberg-Marquardt (LM) strategy for accuracy, noise amplification, robustness to converge, and computation time. The simulation demonstrated that VP and LM were both accurate in that the medians closely matched assumed values across typical signal to noise ratio (SNR) levels for both Tofts models. VP and LM showed similar noise sensitivity. Studies using the patient data showed that the VP method reliably converged and matched results from LM with approximate 3× and 2× reductions in computation time for the standard (two-parameter) and extended (three-parameter) Tofts models. While LM failed to converge in 14% of the patient data, VP converged in the ideal 100%. The VP-based method for non-linear least squares estimation of perfusion parameters for prostate MRI is equivalent in accuracy and robustness to noise, while being more reliably (100%) convergent and computationally about 3× (TM) and 2× (ETM) faster than the LM-based method. Copyright © 2017 Elsevier Inc. All rights reserved.

Estimation of a Nonlinear Intervention Phase Trajectory for Multiple-Baseline Design Data

ERIC Educational Resources Information Center

Hembry, Ian; Bunuan, Rommel; Beretvas, S. Natasha; Ferron, John M.; Van den Noortgate, Wim

2015-01-01

A multilevel logistic model for estimating a nonlinear trajectory in a multiple-baseline design is introduced. The model is applied to data from a real multiple-baseline design study to demonstrate interpretation of relevant parameters. A simple change-in-levels (?"Levels") model and a model involving a quadratic function…

Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation

NASA Astrophysics Data System (ADS)

Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.; de Callafon, Raymond A.

2017-02-01

This paper presents a framework for structural health monitoring (SHM) and damage identification of civil structures. This framework integrates advanced mechanics-based nonlinear finite element (FE) modeling and analysis techniques with a batch Bayesian estimation approach to estimate time-invariant model parameters used in the FE model of the structure of interest. The framework uses input excitation and dynamic response of the structure and updates a nonlinear FE model of the structure to minimize the discrepancies between predicted and measured response time histories. The updated FE model can then be interrogated to detect, localize, classify, and quantify the state of damage and predict the remaining useful life of the structure. As opposed to recursive estimation methods, in the batch Bayesian estimation approach, the entire time history of the input excitation and output response of the structure are used as a batch of data to estimate the FE model parameters through a number of iterations. In the case of non-informative prior, the batch Bayesian method leads to an extended maximum likelihood (ML) estimation method to estimate jointly time-invariant model parameters and the measurement noise amplitude. The extended ML estimation problem is solved efficiently using a gradient-based interior-point optimization algorithm. Gradient-based optimization algorithms require the FE response sensitivities with respect to the model parameters to be identified. The FE response sensitivities are computed accurately and efficiently using the direct differentiation method (DDM). The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem by computing the exact Fisher Information matrix using the FE response sensitivities with respect to the model parameters. The accuracy of the proposed uncertainty quantification approach is verified using a sampling approach based on the unscented transformation. Two validation studies, based on realistic structural FE models of a bridge pier and a moment resisting steel frame, are performed to validate the performance and accuracy of the presented nonlinear FE model updating approach and demonstrate its application to SHM. These validation studies show the excellent performance of the proposed framework for SHM and damage identification even in the presence of high measurement noise and/or way-out initial estimates of the model parameters. Furthermore, the detrimental effects of the input measurement noise on the performance of the proposed framework are illustrated and quantified through one of the validation studies.

Simulating the effect of non-linear mode coupling in cosmological parameter estimation

NASA Astrophysics Data System (ADS)

Kiessling, A.; Taylor, A. N.; Heavens, A. F.

2011-09-01

Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment and to optimize the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimization it is usually assumed that the power-spectrum covariance matrix is diagonal in Fourier space. However, in the low-redshift Universe, non-linear mode coupling will tend to correlate small-scale power, moving information from lower to higher order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naïve Gaussian Fisher matrix forecasts with a maximum likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2D and tomographic shear analysis of a Euclid-like survey. In both cases, we find that the 68 per cent confidence area of the Ωm-σ8 plane increases by a factor of 5. However, the marginal errors increase by just 20-40 per cent. We propose a new method to model the effects of non-linear shear-power mode coupling in the Fisher matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. We find that this approximation can reproduce the 68 per cent confidence regions of the full maximum likelihood analysis in the Ωm-σ8 plane to high accuracy for both 2D and tomographic weak lensing surveys. Finally, we perform a multiparameter analysis of Ωm, σ8, h, ns, w0 and wa to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. The 6D volume of the 1σ error contours for the non-linear Fisher analysis is a factor of 3 larger than for the Gaussian case, and the shape of the 68 per cent confidence volume is modified. We propose that future Fisher matrix estimates of cosmological parameter accuracies should include mode-coupling effects.

Nonlinear observation of internal states of fuel cell cathode utilizing a high-order sliding-mode algorithm

NASA Astrophysics Data System (ADS)

Xu, Liangfei; Hu, Junming; Cheng, Siliang; Fang, Chuan; Li, Jianqiu; Ouyang, Minggao; Lehnert, Werner

2017-07-01

A scheme for designing a second-order sliding-mode (SOSM) observer that estimates critical internal states on the cathode side of a polymer electrolyte membrane (PEM) fuel cell system is presented. A nonlinear, isothermal dynamic model for the cathode side and a membrane electrolyte assembly are first described. A nonlinear observer topology based on an SOSM algorithm is then introduced, and equations for the SOSM observer deduced. Online calculation of the inverse matrix produces numerical errors, so a modified matrix is introduced to eliminate the negative effects of these on the observer. The simulation results indicate that the SOSM observer performs well for the gas partial pressures and air stoichiometry. The estimation results follow the simulated values in the model with relative errors within ± 2% at stable status. Large errors occur during the fast dynamic processes (<1 s). Moreover, the nonlinear observer shows good robustness against variations in the initial values of the internal states, but less robustness against variations in system parameters. The partial pressures are more sensitive than the air stoichiometry to system parameters. Finally, the order of effects of parameter uncertainties on the estimation results is outlined and analyzed.

On three dimensional object recognition and pose-determination: An abstraction based approach. Ph.D. Thesis - Michigan Univ. Final Report

NASA Technical Reports Server (NTRS)

Quek, Kok How Francis

1990-01-01

A method of computing reliable Gaussian and mean curvature sign-map descriptors from the polynomial approximation of surfaces was demonstrated. Such descriptors which are invariant under perspective variation are suitable for hypothesis generation. A means for determining the pose of constructed geometric forms whose algebraic surface descriptors are nonlinear in terms of their orienting parameters was developed. This was done by means of linear functions which are capable of approximating nonlinear forms and determining their parameters. It was shown that biquadratic surfaces are suitable companion linear forms for cylindrical approximation and parameter estimation. The estimates provided the initial parametric approximations necessary for a nonlinear regression stage to fine tune the estimates by fitting the actual nonlinear form to the data. A hypothesis-based split-merge algorithm for extraction and pose determination of cylinders and planes which merge smoothly into other surfaces was developed. It was shown that all split-merge algorithms are hypothesis-based. A finite-state algorithm for the extraction of the boundaries of run-length regions was developed. The computation takes advantage of the run list topology and boundary direction constraints implicit in the run-length encoding.

Procedure for estimating stability and control parameters from flight test data by using maximum likelihood methods employing a real-time digital system

NASA Technical Reports Server (NTRS)

Grove, R. D.; Bowles, R. L.; Mayhew, S. C.

1972-01-01

A maximum likelihood parameter estimation procedure and program were developed for the extraction of the stability and control derivatives of aircraft from flight test data. Nonlinear six-degree-of-freedom equations describing aircraft dynamics were used to derive sensitivity equations for quasilinearization. The maximum likelihood function with quasilinearization was used to derive the parameter change equations, the covariance matrices for the parameters and measurement noise, and the performance index function. The maximum likelihood estimator was mechanized into an iterative estimation procedure utilizing a real time digital computer and graphic display system. This program was developed for 8 measured state variables and 40 parameters. Test cases were conducted with simulated data for validation of the estimation procedure and program. The program was applied to a V/STOL tilt wing aircraft, a military fighter airplane, and a light single engine airplane. The particular nonlinear equations of motion, derivation of the sensitivity equations, addition of accelerations into the algorithm, operational features of the real time digital system, and test cases are described.

Two-dimensional advective transport in ground-water flow parameter estimation

USGS Publications Warehouse

Anderman, E.R.; Hill, M.C.; Poeter, E.P.

1996-01-01

Nonlinear regression is useful in ground-water flow parameter estimation, but problems of parameter insensitivity and correlation often exist given commonly available hydraulic-head and head-dependent flow (for example, stream and lake gain or loss) observations. To address this problem, advective-transport observations are added to the ground-water flow, parameter-estimation model MODFLOWP using particle-tracking methods. The resulting model is used to investigate the importance of advective-transport observations relative to head-dependent flow observations when either or both are used in conjunction with hydraulic-head observations in a simulation of the sewage-discharge plume at Otis Air Force Base, Cape Cod, Massachusetts, USA. The analysis procedure for evaluating the probable effect of new observations on the regression results consists of two steps: (1) parameter sensitivities and correlations calculated at initial parameter values are used to assess the model parameterization and expected relative contributions of different types of observations to the regression; and (2) optimal parameter values are estimated by nonlinear regression and evaluated. In the Cape Cod parameter-estimation model, advective-transport observations did not significantly increase the overall parameter sensitivity; however: (1) inclusion of advective-transport observations decreased parameter correlation enough for more unique parameter values to be estimated by the regression; (2) realistic uncertainties in advective-transport observations had a small effect on parameter estimates relative to the precision with which the parameters were estimated; and (3) the regression results and sensitivity analysis provided insight into the dynamics of the ground-water flow system, especially the importance of accurate boundary conditions. In this work, advective-transport observations improved the calibration of the model and the estimation of ground-water flow parameters, and use of regression and related techniques produced significant insight into the physical system.

A rigorous multiple independent binding site model for determining cell-based equilibrium dissociation constants.

PubMed

Drake, Andrew W; Klakamp, Scott L

2007-01-10

A new 4-parameter nonlinear equation based on the standard multiple independent binding site model (MIBS) is presented for fitting cell-based ligand titration data in order to calculate the ligand/cell receptor equilibrium dissociation constant and the number of receptors/cell. The most commonly used linear (Scatchard Plot) or nonlinear 2-parameter model (a single binding site model found in commercial programs like Prism(R)) used for analysis of ligand/receptor binding data assumes only the K(D) influences the shape of the titration curve. We demonstrate using simulated data sets that, depending upon the cell surface receptor expression level, the number of cells titrated, and the magnitude of the K(D) being measured, this assumption of always being under K(D)-controlled conditions can be erroneous and can lead to unreliable estimates for the binding parameters. We also compare and contrast the fitting of simulated data sets to the commonly used cell-based binding equation versus our more rigorous 4-parameter nonlinear MIBS model. It is shown through these simulations that the new 4-parameter MIBS model, when used for cell-based titrations under optimal conditions, yields highly accurate estimates of all binding parameters and hence should be the preferred model to fit cell-based experimental nonlinear titration data.

R programming for parameters estimation of geographically weighted ordinal logistic regression (GWOLR) model based on Newton Raphson

NASA Astrophysics Data System (ADS)

Zuhdi, Shaifudin; Saputro, Dewi Retno Sari

2017-03-01

GWOLR model used for represent relationship between dependent variable has categories and scale of category is ordinal with independent variable influenced the geographical location of the observation site. Parameters estimation of GWOLR model use maximum likelihood provide system of nonlinear equations and hard to be found the result in analytic resolution. By finishing it, it means determine the maximum completion, this thing associated with optimizing problem. The completion nonlinear system of equations optimize use numerical approximation, which one is Newton Raphson method. The purpose of this research is to make iteration algorithm Newton Raphson and program using R software to estimate GWOLR model. Based on the research obtained that program in R can be used to estimate the parameters of GWOLR model by forming a syntax program with command "while".

A Multi-Resolution Nonlinear Mapping Technique for Design and Analysis Applications

NASA Technical Reports Server (NTRS)

Phan, Minh Q.

1998-01-01

This report describes a nonlinear mapping technique where the unknown static or dynamic system is approximated by a sum of dimensionally increasing functions (one-dimensional curves, two-dimensional surfaces, etc.). These lower dimensional functions are synthesized from a set of multi-resolution basis functions, where the resolutions specify the level of details at which the nonlinear system is approximated. The basis functions also cause the parameter estimation step to become linear. This feature is taken advantage of to derive a systematic procedure to determine and eliminate basis functions that are less significant for the particular system under identification. The number of unknown parameters that must be estimated is thus reduced and compact models obtained. The lower dimensional functions (identified curves and surfaces) permit a kind of "visualization" into the complexity of the nonlinearity itself.

A Multi-Resolution Nonlinear Mapping Technique for Design and Analysis Application

NASA Technical Reports Server (NTRS)

Phan, Minh Q.

1997-01-01

This report describes a nonlinear mapping technique where the unknown static or dynamic system is approximated by a sum of dimensionally increasing functions (one-dimensional curves, two-dimensional surfaces, etc.). These lower dimensional functions are synthesized from a set of multi-resolution basis functions, where the resolutions specify the level of details at which the nonlinear system is approximated. The basis functions also cause the parameter estimation step to become linear. This feature is taken advantage of to derive a systematic procedure to determine and eliminate basis functions that are less significant for the particular system under identification. The number of unknown parameters that must be estimated is thus reduced and compact models obtained. The lower dimensional functions (identified curves and surfaces) permit a kind of "visualization" into the complexity of the nonlinearity itself.

A computer program (MODFLOWP) for estimating parameters of a transient, three-dimensional ground-water flow model using nonlinear regression

USGS Publications Warehouse

Hill, Mary Catherine

1992-01-01

This report documents a new version of the U.S. Geological Survey modular, three-dimensional, finite-difference, ground-water flow model (MODFLOW) which, with the new Parameter-Estimation Package that also is documented in this report, can be used to estimate parameters by nonlinear regression. The new version of MODFLOW is called MODFLOWP (pronounced MOD-FLOW*P), and functions nearly identically to MODFLOW when the ParameterEstimation Package is not used. Parameters are estimated by minimizing a weighted least-squares objective function by the modified Gauss-Newton method or by a conjugate-direction method. Parameters used to calculate the following MODFLOW model inputs can be estimated: Transmissivity and storage coefficient of confined layers; hydraulic conductivity and specific yield of unconfined layers; vertical leakance; vertical anisotropy (used to calculate vertical leakance); horizontal anisotropy; hydraulic conductance of the River, Streamflow-Routing, General-Head Boundary, and Drain Packages; areal recharge rates; maximum evapotranspiration; pumpage rates; and the hydraulic head at constant-head boundaries. Any spatial variation in parameters can be defined by the user. Data used to estimate parameters can include existing independent estimates of parameter values, observed hydraulic heads or temporal changes in hydraulic heads, and observed gains and losses along head-dependent boundaries (such as streams). Model output includes statistics for analyzing the parameter estimates and the model; these statistics can be used to quantify the reliability of the resulting model, to suggest changes in model construction, and to compare results of models constructed in different ways.

Multi-objective optimization in quantum parameter estimation

NASA Astrophysics Data System (ADS)

Gong, BeiLi; Cui, Wei

2018-04-01

We investigate quantum parameter estimation based on linear and Kerr-type nonlinear controls in an open quantum system, and consider the dissipation rate as an unknown parameter. We show that while the precision of parameter estimation is improved, it usually introduces a significant deformation to the system state. Moreover, we propose a multi-objective model to optimize the two conflicting objectives: (1) maximizing the Fisher information, improving the parameter estimation precision, and (2) minimizing the deformation of the system state, which maintains its fidelity. Finally, simulations of a simplified ɛ-constrained model demonstrate the feasibility of the Hamiltonian control in improving the precision of the quantum parameter estimation.

System health monitoring using multiple-model adaptive estimation techniques

NASA Astrophysics Data System (ADS)

Sifford, Stanley Ryan

Monitoring system health for fault detection and diagnosis by tracking system parameters concurrently with state estimates is approached using a new multiple-model adaptive estimation (MMAE) method. This novel method is called GRid-based Adaptive Parameter Estimation (GRAPE). GRAPE expands existing MMAE methods by using new techniques to sample the parameter space. GRAPE expands on MMAE with the hypothesis that sample models can be applied and resampled without relying on a predefined set of models. GRAPE is initially implemented in a linear framework using Kalman filter models. A more generalized GRAPE formulation is presented using extended Kalman filter (EKF) models to represent nonlinear systems. GRAPE can handle both time invariant and time varying systems as it is designed to track parameter changes. Two techniques are presented to generate parameter samples for the parallel filter models. The first approach is called selected grid-based stratification (SGBS). SGBS divides the parameter space into equally spaced strata. The second approach uses Latin Hypercube Sampling (LHS) to determine the parameter locations and minimize the total number of required models. LHS is particularly useful when the parameter dimensions grow. Adding more parameters does not require the model count to increase for LHS. Each resample is independent of the prior sample set other than the location of the parameter estimate. SGBS and LHS can be used for both the initial sample and subsequent resamples. Furthermore, resamples are not required to use the same technique. Both techniques are demonstrated for both linear and nonlinear frameworks. The GRAPE framework further formalizes the parameter tracking process through a general approach for nonlinear systems. These additional methods allow GRAPE to either narrow the focus to converged values within a parameter range or expand the range in the appropriate direction to track the parameters outside the current parameter range boundary. Customizable rules define the specific resample behavior when the GRAPE parameter estimates converge. Convergence itself is determined from the derivatives of the parameter estimates using a simple moving average window to filter out noise. The system can be tuned to match the desired performance goals by making adjustments to parameters such as the sample size, convergence criteria, resample criteria, initial sampling method, resampling method, confidence in prior sample covariances, sample delay, and others.

PARTICLE FILTERING WITH SEQUENTIAL PARAMETER LEARNING FOR NONLINEAR BOLD fMRI SIGNALS.

PubMed

Xia, Jing; Wang, Michelle Yongmei

Analyzing the blood oxygenation level dependent (BOLD) effect in the functional magnetic resonance imaging (fMRI) is typically based on recent ground-breaking time series analysis techniques. This work represents a significant improvement over existing approaches to system identification using nonlinear hemodynamic models. It is important for three reasons. First, instead of using linearized approximations of the dynamics, we present a nonlinear filtering based on the sequential Monte Carlo method to capture the inherent nonlinearities in the physiological system. Second, we simultaneously estimate the hidden physiological states and the system parameters through particle filtering with sequential parameter learning to fully take advantage of the dynamic information of the BOLD signals. Third, during the unknown static parameter learning, we employ the low-dimensional sufficient statistics for efficiency and avoiding potential degeneration of the parameters. The performance of the proposed method is validated using both the simulated data and real BOLD fMRI data.

A new method for parameter estimation in nonlinear dynamical equations

NASA Astrophysics Data System (ADS)

Wang, Liu; He, Wen-Ping; Liao, Le-Jian; Wan, Shi-Quan; He, Tao

2015-01-01

Parameter estimation is an important scientific problem in various fields such as chaos control, chaos synchronization and other mathematical models. In this paper, a new method for parameter estimation in nonlinear dynamical equations is proposed based on evolutionary modelling (EM). This will be achieved by utilizing the following characteristics of EM which includes self-organizing, adaptive and self-learning features which are inspired by biological natural selection, and mutation and genetic inheritance. The performance of the new method is demonstrated by using various numerical tests on the classic chaos model—Lorenz equation (Lorenz 1963). The results indicate that the new method can be used for fast and effective parameter estimation irrespective of whether partial parameters or all parameters are unknown in the Lorenz equation. Moreover, the new method has a good convergence rate. Noises are inevitable in observational data. The influence of observational noises on the performance of the presented method has been investigated. The results indicate that the strong noises, such as signal noise ratio (SNR) of 10 dB, have a larger influence on parameter estimation than the relatively weak noises. However, it is found that the precision of the parameter estimation remains acceptable for the relatively weak noises, e.g. SNR is 20 or 30 dB. It indicates that the presented method also has some anti-noise performance.

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems

PubMed Central

Rodriguez-Fernandez, Maria; Egea, Jose A; Banga, Julio R

2006-01-01

Background We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness. Results We have developed a new procedure based on the scatter search methodology for nonlinear optimization of dynamic models of arbitrary (or even unknown) structure (i.e. black-box models). In this contribution, we describe and apply this novel metaheuristic, inspired by recent developments in the field of operations research, to a set of complex identification problems and we make a critical comparison with respect to the previous (above mentioned) successful methods. Conclusion Robust and efficient methods for parameter estimation are of key importance in systems biology and related areas. The new metaheuristic presented in this paper aims to ensure the proper solution of these problems by adopting a global optimization approach, while keeping the computational effort under reasonable values. This new metaheuristic was applied to a set of three challenging parameter estimation problems of nonlinear dynamic biological systems, outperforming very significantly all the methods previously used for these benchmark problems. PMID:17081289

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems.

PubMed

Rodriguez-Fernandez, Maria; Egea, Jose A; Banga, Julio R

2006-11-02

We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness. We have developed a new procedure based on the scatter search methodology for nonlinear optimization of dynamic models of arbitrary (or even unknown) structure (i.e. black-box models). In this contribution, we describe and apply this novel metaheuristic, inspired by recent developments in the field of operations research, to a set of complex identification problems and we make a critical comparison with respect to the previous (above mentioned) successful methods. Robust and efficient methods for parameter estimation are of key importance in systems biology and related areas. The new metaheuristic presented in this paper aims to ensure the proper solution of these problems by adopting a global optimization approach, while keeping the computational effort under reasonable values. This new metaheuristic was applied to a set of three challenging parameter estimation problems of nonlinear dynamic biological systems, outperforming very significantly all the methods previously used for these benchmark problems.

A Note on Recurring Misconceptions When Fitting Nonlinear Mixed Models.

PubMed

Harring, Jeffrey R; Blozis, Shelley A

2016-01-01

Nonlinear mixed-effects (NLME) models are used when analyzing continuous repeated measures data taken on each of a number of individuals where the focus is on characteristics of complex, nonlinear individual change. Challenges with fitting NLME models and interpreting analytic results have been well documented in the statistical literature. However, parameter estimates as well as fitted functions from NLME analyses in recent articles have been misinterpreted, suggesting the need for clarification of these issues before these misconceptions become fact. These misconceptions arise from the choice of popular estimation algorithms, namely, the first-order linearization method (FO) and Gaussian-Hermite quadrature (GHQ) methods, and how these choices necessarily lead to population-average (PA) or subject-specific (SS) interpretations of model parameters, respectively. These estimation approaches also affect the fitted function for the typical individual, the lack-of-fit of individuals' predicted trajectories, and vice versa.

A new analytical method for characterizing nonlinear visual processes with stimuli of arbitrary distribution: Theory and applications.

PubMed

Hayashi, Ryusuke; Watanabe, Osamu; Yokoyama, Hiroki; Nishida, Shin'ya

2017-06-01

Characterization of the functional relationship between sensory inputs and neuronal or observers' perceptual responses is one of the fundamental goals of systems neuroscience and psychophysics. Conventional methods, such as reverse correlation and spike-triggered data analyses are limited in their ability to resolve complex and inherently nonlinear neuronal/perceptual processes because these methods require input stimuli to be Gaussian with a zero mean. Recent studies have shown that analyses based on a generalized linear model (GLM) do not require such specific input characteristics and have advantages over conventional methods. GLM, however, relies on iterative optimization algorithms and its calculation costs become very expensive when estimating the nonlinear parameters of a large-scale system using large volumes of data. In this paper, we introduce a new analytical method for identifying a nonlinear system without relying on iterative calculations and yet also not requiring any specific stimulus distribution. We demonstrate the results of numerical simulations, showing that our noniterative method is as accurate as GLM in estimating nonlinear parameters in many cases and outperforms conventional, spike-triggered data analyses. As an example of the application of our method to actual psychophysical data, we investigated how different spatiotemporal frequency channels interact in assessments of motion direction. The nonlinear interaction estimated by our method was consistent with findings from previous vision studies and supports the validity of our method for nonlinear system identification.

Comparison between Linear and Nonlinear Regression in a Laboratory Heat Transfer Experiment

ERIC Educational Resources Information Center

Gonçalves, Carine Messias; Schwaab, Marcio; Pinto, José Carlos

2013-01-01

In order to interpret laboratory experimental data, undergraduate students are used to perform linear regression through linearized versions of nonlinear models. However, the use of linearized models can lead to statistically biased parameter estimates. Even so, it is not an easy task to introduce nonlinear regression and show for the students…

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

NASA Technical Reports Server (NTRS)

Lisano, Michael E.

2007-01-01

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

An evolutionary firefly algorithm for the estimation of nonlinear biological model parameters.

PubMed

Abdullah, Afnizanfaizal; Deris, Safaai; Anwar, Sohail; Arjunan, Satya N V

2013-01-01

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.

An Evolutionary Firefly Algorithm for the Estimation of Nonlinear Biological Model Parameters

PubMed Central

Abdullah, Afnizanfaizal; Deris, Safaai; Anwar, Sohail; Arjunan, Satya N. V.

2013-01-01

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test. PMID:23469172

From Spiking Neuron Models to Linear-Nonlinear Models

PubMed Central

Ostojic, Srdjan; Brunel, Nicolas

2011-01-01

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates. PMID:21283777

From spiking neuron models to linear-nonlinear models.

PubMed

Ostojic, Srdjan; Brunel, Nicolas

2011-01-20

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.

Fatigue Life Prediction of Metallic Materials Based on the Combined Nonlinear Ultrasonic Parameter

NASA Astrophysics Data System (ADS)

Zhang, Yuhua; Li, Xinxin; Wu, Zhenyong; Huang, Zhenfeng; Mao, Hanling

2017-08-01

The fatigue life prediction of metallic materials is always a tough problem that needs to be solved in the mechanical engineering field because it is very important for the secure service of mechanical components. In this paper, a combined nonlinear ultrasonic parameter based on the collinear wave mixing technique is applied for fatigue life prediction of a metallic material. Sweep experiments are first conducted to explore the influence of driving frequency on the interaction of two driving signals and the fatigue damage of specimens, and the amplitudes of sidebands at the difference frequency and sum frequency are tracked when the driving frequency changes. Then, collinear wave mixing tests are carried out on a pair of cylindrically notched specimens with different fatigue damage to explore the relationship between the fatigue damage and the relative nonlinear parameters. The experimental results show when the fatigue degree is below 65% the relative nonlinear parameter increases quickly, and the growth rate is approximately 130%. If the fatigue degree is above 65%, the increase in the relative nonlinear parameter is slow, which has a close relationship with the microstructure evolution of specimens. A combined nonlinear ultrasonic parameter is proposed to highlight the relationship of the relative nonlinear parameter and fatigue degree of specimens; the fatigue life prediction model is built based on the relationship, and the prediction error is below 3%, which is below the prediction error based on the relative nonlinear parameters at the difference and sum frequencies. Therefore, the combined nonlinear ultrasonic parameter using the collinear wave mixing method can effectively estimate the fatigue degree of specimens, which provides a fast and convenient method for fatigue life prediction.

Adaptive control of nonlinear uncertain active suspension systems with prescribed performance.

PubMed

Huang, Yingbo; Na, Jing; Wu, Xing; Liu, Xiaoqin; Guo, Yu

2015-01-01

This paper proposes adaptive control designs for vehicle active suspension systems with unknown nonlinear dynamics (e.g., nonlinear spring and piece-wise linear damper dynamics). An adaptive control is first proposed to stabilize the vertical vehicle displacement and thus to improve the ride comfort and to guarantee other suspension requirements (e.g., road holding and suspension space limitation) concerning the vehicle safety and mechanical constraints. An augmented neural network is developed to online compensate for the unknown nonlinearities, and a novel adaptive law is developed to estimate both NN weights and uncertain model parameters (e.g., sprung mass), where the parameter estimation error is used as a leakage term superimposed on the classical adaptations. To further improve the control performance and simplify the parameter tuning, a prescribed performance function (PPF) characterizing the error convergence rate, maximum overshoot and steady-state error is used to propose another adaptive control. The stability for the closed-loop system is proved and particular performance requirements are analyzed. Simulations are included to illustrate the effectiveness of the proposed control schemes. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Can you trust the parametric standard errors in nonlinear least squares? Yes, with provisos.

PubMed

Tellinghuisen, Joel

2018-04-01

Questions about the reliability of parametric standard errors (SEs) from nonlinear least squares (LS) algorithms have led to a general mistrust of these precision estimators that is often unwarranted. The importance of non-Gaussian parameter distributions is illustrated by converting linear models to nonlinear by substituting e A , ln A, and 1/A for a linear parameter a. Monte Carlo (MC) simulations characterize parameter distributions in more complex cases, including when data have varying uncertainty and should be weighted, but weights are neglected. This situation leads to loss of precision and erroneous parametric SEs, as is illustrated for the Lineweaver-Burk analysis of enzyme kinetics data and the analysis of isothermal titration calorimetry data. Non-Gaussian parameter distributions are generally asymmetric and biased. However, when the parametric SE is <10% of the magnitude of the parameter, both the bias and the asymmetry can usually be ignored. Sometimes nonlinear estimators can be redefined to give more normal distributions and better convergence properties. Variable data uncertainty, or heteroscedasticity, can sometimes be handled by data transforms but more generally requires weighted LS, which in turn require knowledge of the data variance. Parametric SEs are rigorously correct in linear LS under the usual assumptions, and are a trustworthy approximation in nonlinear LS provided they are sufficiently small - a condition favored by the abundant, precise data routinely collected in many modern instrumental methods. Copyright © 2018 Elsevier B.V. All rights reserved.

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.

Single neuron modeling and data assimilation in BNST neurons

NASA Astrophysics Data System (ADS)

Farsian, Reza

Neurons, although tiny in size, are vastly complicated systems, which are responsible for the most basic yet essential functions of any nervous system. Even the most simple models of single neurons are usually high dimensional, nonlinear, and contain many parameters and states which are unobservable in a typical neurophysiological experiment. One of the most fundamental problems in experimental neurophysiology is the estimation of these parameters and states, since knowing their values is essential in identification, model construction, and forward prediction of biological neurons. Common methods of parameter and state estimation do not perform well for neural models due to their high dimensionality and nonlinearity. In this dissertation, two alternative approaches for parameters and state estimation of biological neurons have been demonstrated: dynamical parameter estimation (DPE) and a Markov Chain Monte Carlo (MCMC) method. The first method uses elements of chaos control and synchronization theory for parameter and state estimation. MCMC is a statistical approach which uses a path integral formulation to evaluate a mean and an error bound for these unobserved parameters and states. These methods have been applied to biological system of neurons in Bed Nucleus of Stria Termialis neurons (BNST) of rats. State and parameters of neurons in both systems were estimated, and their value were used for recreating a realistic model and predicting the behavior of the neurons successfully. The knowledge of biological parameters can ultimately provide a better understanding of the internal dynamics of a neuron in order to build robust models of neuron networks.

The Inverse Problem for Confined Aquifer Flow: Identification and Estimation With Extensions

NASA Astrophysics Data System (ADS)

Loaiciga, Hugo A.; MariñO, Miguel A.

1987-01-01

The contributions of this work are twofold. First, a methodology for estimating the elements of parameter matrices in the governing equation of flow in a confined aquifer is developed. The estimation techniques for the distributed-parameter inverse problem pertain to linear least squares and generalized least squares methods. The linear relationship among the known heads and unknown parameters of the flow equation provides the background for developing criteria for determining the identifiability status of unknown parameters. Under conditions of exact or overidentification it is possible to develop statistically consistent parameter estimators and their asymptotic distributions. The estimation techniques, namely, two-stage least squares and three stage least squares, are applied to a specific groundwater inverse problem and compared between themselves and with an ordinary least squares estimator. The three-stage estimator provides the closer approximation to the actual parameter values, but it also shows relatively large standard errors as compared to the ordinary and two-stage estimators. The estimation techniques provide the parameter matrices required to simulate the unsteady groundwater flow equation. Second, a nonlinear maximum likelihood estimation approach to the inverse problem is presented. The statistical properties of maximum likelihood estimators are derived, and a procedure to construct confidence intervals and do hypothesis testing is given. The relative merits of the linear and maximum likelihood estimators are analyzed. Other topics relevant to the identification and estimation methodologies, i.e., a continuous-time solution to the flow equation, coping with noise-corrupted head measurements, and extension of the developed theory to nonlinear cases are also discussed. A simulation study is used to evaluate the methods developed in this study.

Nonlinear soil parameter effects on dynamic embedment of offshore pipeline on soft clay

NASA Astrophysics Data System (ADS)

Yu, Su Young; Choi, Han Suk; Lee, Seung Keon; Park, Kyu-Sik; Kim, Do Kyun

2015-06-01

In this paper, the effects of nonlinear soft clay on dynamic embedment of offshore pipeline were investigated. Seabed embedment by pipe-soil interactions has impacts on the structural boundary conditions for various subsea structures such as pipeline, riser, pile, and many other systems. A number of studies have been performed to estimate real soil behavior, but their estimation of seabed embedment has not been fully identified and there are still many uncertainties. In this regards, comparison of embedment between field survey and existing empirical models has been performed to identify uncertainties and investigate the effect of nonlinear soil parameter on dynamic embedment. From the comparison, it is found that the dynamic embedment with installation effects based on nonlinear soil model have an influence on seabed embedment. Therefore, the pipe embedment under dynamic condition by nonlinear parameters of soil models was investigated by Dynamic Embedment Factor (DEF) concept, which is defined as the ratio of the dynamic and static embedment of pipeline, in order to overcome the gap between field embedment and currently used empirical and numerical formula. Although DEF through various researches is suggested, its range is too wide and it does not consider dynamic laying effect. It is difficult to find critical parameters that are affecting to the embedment result. Therefore, the study on dynamic embedment factor by soft clay parameters of nonlinear soil model was conducted and the sensitivity analyses about parameters of nonlinear soil model were performed as well. The tendency on dynamic embedment factor was found by conducting numerical analyses using OrcaFlex software. It is found that DEF was influenced by shear strength gradient than other factors. The obtained results will be useful to understand the pipe embedment on soft clay seabed for applying offshore pipeline designs such as on-bottom stability and free span analyses.

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

Nonlinear Inference in Partially Observed Physical Systems and Deep Neural Networks

NASA Astrophysics Data System (ADS)

Rozdeba, Paul J.

The problem of model state and parameter estimation is a significant challenge in nonlinear systems. Due to practical considerations of experimental design, it is often the case that physical systems are partially observed, meaning that data is only available for a subset of the degrees of freedom required to fully model the observed system's behaviors and, ultimately, predict future observations. Estimation in this context is highly complicated by the presence of chaos, stochasticity, and measurement noise in dynamical systems. One of the aims of this dissertation is to simultaneously analyze state and parameter estimation in as a regularized inverse problem, where the introduction of a model makes it possible to reverse the forward problem of partial, noisy observation; and as a statistical inference problem using data assimilation to transfer information from measurements to the model states and parameters. Ultimately these two formulations achieve the same goal. Similar aspects that appear in both are highlighted as a means for better understanding the structure of the nonlinear inference problem. An alternative approach to data assimilation that uses model reduction is then examined as a way to eliminate unresolved nonlinear gating variables from neuron models. In this formulation, only measured variables enter into the model, and the resulting errors are themselves modeled by nonlinear stochastic processes with memory. Finally, variational annealing, a data assimilation method previously applied to dynamical systems, is introduced as a potentially useful tool for understanding deep neural network training in machine learning by exploiting similarities between the two problems.

Parameter estimation in a structural acoustic system with fully nonlinear coupling conditions

NASA Technical Reports Server (NTRS)

Banks, H. T.; Smith, Ralph C.

1994-01-01

A methodology for estimating physical parameters in a class of structural acoustic systems is presented. The general model under consideration consists of an interior cavity which is separated from an exterior noise source by an enclosing elastic structure. Piezoceramic patches are bonded to or embedded in the structure; these can be used both as actuators and sensors in applications ranging from the control of interior noise levels to the determination of structural flaws through nondestructive evaluation techniques. The presence and excitation of patches, however, changes the geometry and material properties of the structure as well as involves unknown patch parameters, thus necessitating the development of parameter estimation techniques which are applicable in this coupled setting. In developing a framework for approximation, parameter estimation and implementation, strong consideration is given to the fact that the input operator is unbonded due to the discrete nature of the patches. Moreover, the model is weakly nonlinear. As a result of the coupling mechanism between the structural vibrations and the interior acoustic dynamics. Within this context, an illustrating model is given, well-posedness and approximations results are discussed and an applicable parameter estimation methodology is presented. The scheme is then illustrated through several numerical examples with simulations modeling a variety of commonly used structural acoustic techniques for systems excitations and data collection.

Multidimensional density shaping by sigmoids.

PubMed

Roth, Z; Baram, Y

1996-01-01

An estimate of the probability density function of a random vector is obtained by maximizing the output entropy of a feedforward network of sigmoidal units with respect to the input weights. Classification problems can be solved by selecting the class associated with the maximal estimated density. Newton's optimization method, applied to the estimated density, yields a recursive estimator for a random variable or a random sequence. A constrained connectivity structure yields a linear estimator, which is particularly suitable for "real time" prediction. A Gaussian nonlinearity yields a closed-form solution for the network's parameters, which may also be used for initializing the optimization algorithm when other nonlinearities are employed. A triangular connectivity between the neurons and the input, which is naturally suggested by the statistical setting, reduces the number of parameters. Applications to classification and forecasting problems are demonstrated.

Assessing first-order emulator inference for physical parameters in nonlinear mechanistic models

USGS Publications Warehouse

Hooten, Mevin B.; Leeds, William B.; Fiechter, Jerome; Wikle, Christopher K.

2011-01-01

We present an approach for estimating physical parameters in nonlinear models that relies on an approximation to the mechanistic model itself for computational efficiency. The proposed methodology is validated and applied in two different modeling scenarios: (a) Simulation and (b) lower trophic level ocean ecosystem model. The approach we develop relies on the ability to predict right singular vectors (resulting from a decomposition of computer model experimental output) based on the computer model input and an experimental set of parameters. Critically, we model the right singular vectors in terms of the model parameters via a nonlinear statistical model. Specifically, we focus our attention on first-order models of these right singular vectors rather than the second-order (covariance) structure.

Kalman filter control of a model of spatiotemporal cortical dynamics

PubMed Central

Schiff, Steven J; Sauer, Tim

2007-01-01

Recent advances in Kalman filtering to estimate system state and parameters in nonlinear systems have offered the potential to apply such approaches to spatiotemporal nonlinear systems. We here adapt the nonlinear method of unscented Kalman filtering to observe the state and estimate parameters in a computational spatiotemporal excitable system that serves as a model for cerebral cortex. We demonstrate the ability to track spiral wave dynamics, and to use an observer system to calculate control signals delivered through applied electrical fields. We demonstrate how this strategy can control the frequency of such a system, or quench the wave patterns, while minimizing the energy required for such results. These findings are readily testable in experimental applications, and have the potential to be applied to the treatment of human disease. PMID:18310806

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

The Novel Nonlinear Adaptive Doppler Shift Estimation Technique and the Coherent Doppler Lidar System Validation Lidar

NASA Technical Reports Server (NTRS)

Beyon, Jeffrey Y.; Koch, Grady J.

2006-01-01

The signal processing aspect of a 2-m wavelength coherent Doppler lidar system under development at NASA Langley Research Center in Virginia is investigated in this paper. The lidar system is named VALIDAR (validation lidar) and its signal processing program estimates and displays various wind parameters in real-time as data acquisition occurs. The goal is to improve the quality of the current estimates such as power, Doppler shift, wind speed, and wind direction, especially in low signal-to-noise-ratio (SNR) regime. A novel Nonlinear Adaptive Doppler Shift Estimation Technique (NADSET) is developed on such behalf and its performance is analyzed using the wind data acquired over a long period of time by VALIDAR. The quality of Doppler shift and power estimations by conventional Fourier-transform-based spectrum estimation methods deteriorates rapidly as SNR decreases. NADSET compensates such deterioration in the quality of wind parameter estimates by adaptively utilizing the statistics of Doppler shift estimate in a strong SNR range and identifying sporadic range bins where good Doppler shift estimates are found. The authenticity of NADSET is established by comparing the trend of wind parameters with and without NADSET applied to the long-period lidar return data.

Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model.

PubMed

Steven Ernest, C; Nyberg, Joakim; Karlsson, Mats O; Hooker, Andrew C

2014-12-01

D-optimal designs for discrete-type responses have been derived using generalized linear mixed models, simulation based methods and analytical approximations for computing the fisher information matrix (FIM) of non-linear mixed effect models with homogeneous probabilities over time. In this work, D-optimal designs using an analytical approximation of the FIM for a dichotomous, non-homogeneous, Markov-chain phase advanced sleep non-linear mixed effect model was investigated. The non-linear mixed effect model consisted of transition probabilities of dichotomous sleep data estimated as logistic functions using piecewise linear functions. Theoretical linear and nonlinear dose effects were added to the transition probabilities to modify the probability of being in either sleep stage. D-optimal designs were computed by determining an analytical approximation the FIM for each Markov component (one where the previous state was awake and another where the previous state was asleep). Each Markov component FIM was weighted either equally or by the average probability of response being awake or asleep over the night and summed to derive the total FIM (FIM(total)). The reference designs were placebo, 0.1, 1-, 6-, 10- and 20-mg dosing for a 2- to 6-way crossover study in six dosing groups. Optimized design variables were dose and number of subjects in each dose group. The designs were validated using stochastic simulation/re-estimation (SSE). Contrary to expectations, the predicted parameter uncertainty obtained via FIM(total) was larger than the uncertainty in parameter estimates computed by SSE. Nevertheless, the D-optimal designs decreased the uncertainty of parameter estimates relative to the reference designs. Additionally, the improvement for the D-optimal designs were more pronounced using SSE than predicted via FIM(total). Through the use of an approximate analytic solution and weighting schemes, the FIM(total) for a non-homogeneous, dichotomous Markov-chain phase advanced sleep model was computed and provided more efficient trial designs and increased nonlinear mixed-effects modeling parameter precision.

Stochastic Modeling and Analysis of Multiple Nonlinear Accelerated Degradation Processes through Information Fusion

PubMed Central

Sun, Fuqiang; Liu, Le; Li, Xiaoyang; Liao, Haitao

2016-01-01

Accelerated degradation testing (ADT) is an efficient technique for evaluating the lifetime of a highly reliable product whose underlying failure process may be traced by the degradation of the product’s performance parameters with time. However, most research on ADT mainly focuses on a single performance parameter. In reality, the performance of a modern product is usually characterized by multiple parameters, and the degradation paths are usually nonlinear. To address such problems, this paper develops a new s-dependent nonlinear ADT model for products with multiple performance parameters using a general Wiener process and copulas. The general Wiener process models the nonlinear ADT data, and the dependency among different degradation measures is analyzed using the copula method. An engineering case study on a tuner’s ADT data is conducted to demonstrate the effectiveness of the proposed method. The results illustrate that the proposed method is quite effective in estimating the lifetime of a product with s-dependent performance parameters. PMID:27509499

Stochastic Modeling and Analysis of Multiple Nonlinear Accelerated Degradation Processes through Information Fusion.

PubMed

Sun, Fuqiang; Liu, Le; Li, Xiaoyang; Liao, Haitao

2016-08-06

Accelerated degradation testing (ADT) is an efficient technique for evaluating the lifetime of a highly reliable product whose underlying failure process may be traced by the degradation of the product's performance parameters with time. However, most research on ADT mainly focuses on a single performance parameter. In reality, the performance of a modern product is usually characterized by multiple parameters, and the degradation paths are usually nonlinear. To address such problems, this paper develops a new s-dependent nonlinear ADT model for products with multiple performance parameters using a general Wiener process and copulas. The general Wiener process models the nonlinear ADT data, and the dependency among different degradation measures is analyzed using the copula method. An engineering case study on a tuner's ADT data is conducted to demonstrate the effectiveness of the proposed method. The results illustrate that the proposed method is quite effective in estimating the lifetime of a product with s-dependent performance parameters.

Determination of power system component parameters using nonlinear dead beat estimation method

NASA Astrophysics Data System (ADS)

Kolluru, Lakshmi

Power systems are considered the most complex man-made wonders in existence today. In order to effectively supply the ever increasing demands of the consumers, power systems are required to remain stable at all times. Stability and monitoring of these complex systems are achieved by strategically placed computerized control centers. State and parameter estimation is an integral part of these facilities, as they deal with identifying the unknown states and/or parameters of the systems. Advancements in measurement technologies and the introduction of phasor measurement units (PMU) provide detailed and dynamic information of all measurements. Accurate availability of dynamic measurements provides engineers the opportunity to expand and explore various possibilities in power system dynamic analysis/control. This thesis discusses the development of a parameter determination algorithm for nonlinear power systems, using dynamic data obtained from local measurements. The proposed algorithm was developed by observing the dead beat estimator used in state space estimation of linear systems. The dead beat estimator is considered to be very effective as it is capable of obtaining the required results in a fixed number of steps. The number of steps required is related to the order of the system and the number of parameters to be estimated. The proposed algorithm uses the idea of dead beat estimator and nonlinear finite difference methods to create an algorithm which is user friendly and can determine the parameters fairly accurately and effectively. The proposed algorithm is based on a deterministic approach, which uses dynamic data and mathematical models of power system components to determine the unknown parameters. The effectiveness of the algorithm is tested by implementing it to identify the unknown parameters of a synchronous machine. MATLAB environment is used to create three test cases for dynamic analysis of the system with assumed known parameters. Faults are introduced in the virtual test systems and the dynamic data obtained in each case is analyzed and recorded. Ideally, actual measurements are to be provided to the algorithm. As the measurements are not readily available the data obtained from simulations is fed into the determination algorithm as inputs. The obtained results are then compared to the original (or assumed) values of the parameters. The results obtained suggest that the algorithm is able to determine the parameters of a synchronous machine when crisp data is available.

A Nonlinear, Multiinput, Multioutput Process Control Laboratory Experiment

ERIC Educational Resources Information Center

Young, Brent R.; van der Lee, James H.; Svrcek, William Y.

2006-01-01

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

An approximation theory for nonlinear partial differential equations with applications to identification and control

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1982-01-01

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Computational system identification of continuous-time nonlinear systems using approximate Bayesian computation

NASA Astrophysics Data System (ADS)

Krishnanathan, Kirubhakaran; Anderson, Sean R.; Billings, Stephen A.; Kadirkamanathan, Visakan

2016-11-01

In this paper, we derive a system identification framework for continuous-time nonlinear systems, for the first time using a simulation-focused computational Bayesian approach. Simulation approaches to nonlinear system identification have been shown to outperform regression methods under certain conditions, such as non-persistently exciting inputs and fast-sampling. We use the approximate Bayesian computation (ABC) algorithm to perform simulation-based inference of model parameters. The framework has the following main advantages: (1) parameter distributions are intrinsically generated, giving the user a clear description of uncertainty, (2) the simulation approach avoids the difficult problem of estimating signal derivatives as is common with other continuous-time methods, and (3) as noted above, the simulation approach improves identification under conditions of non-persistently exciting inputs and fast-sampling. Term selection is performed by judging parameter significance using parameter distributions that are intrinsically generated as part of the ABC procedure. The results from a numerical example demonstrate that the method performs well in noisy scenarios, especially in comparison to competing techniques that rely on signal derivative estimation.

Model-on-Demand Predictive Control for Nonlinear Hybrid Systems With Application to Adaptive Behavioral Interventions

PubMed Central

Nandola, Naresh N.; Rivera, Daniel E.

2011-01-01

This paper presents a data-centric modeling and predictive control approach for nonlinear hybrid systems. System identification of hybrid systems represents a challenging problem because model parameters depend on the mode or operating point of the system. The proposed algorithm applies Model-on-Demand (MoD) estimation to generate a local linear approximation of the nonlinear hybrid system at each time step, using a small subset of data selected by an adaptive bandwidth selector. The appeal of the MoD approach lies in the fact that model parameters are estimated based on a current operating point; hence estimation of locations or modes governed by autonomous discrete events is achieved automatically. The local MoD model is then converted into a mixed logical dynamical (MLD) system representation which can be used directly in a model predictive control (MPC) law for hybrid systems using multiple-degree-of-freedom tuning. The effectiveness of the proposed MoD predictive control algorithm for nonlinear hybrid systems is demonstrated on a hypothetical adaptive behavioral intervention problem inspired by Fast Track, a real-life preventive intervention for improving parental function and reducing conduct disorder in at-risk children. Simulation results demonstrate that the proposed algorithm can be useful for adaptive intervention problems exhibiting both nonlinear and hybrid character. PMID:21874087

Theoretical Advances in Sequential Data Assimilation for the Atmosphere and Oceans

NASA Astrophysics Data System (ADS)

Ghil, M.

2007-05-01

We concentrate here on two aspects of advanced Kalman--filter-related methods: (i) the stability of the forecast- assimilation cycle, and (ii) parameter estimation for the coupled ocean-atmosphere system. The nonlinear stability of a prediction-assimilation system guarantees the uniqueness of the sequentially estimated solutions in the presence of partial and inaccurate observations, distributed in space and time; this stability is shown to be a necessary condition for the convergence of the state estimates to the true evolution of the turbulent flow. The stability properties of the governing nonlinear equations and of several data assimilation systems are studied by computing the spectrum of the associated Lyapunov exponents. These ideas are applied to a simple and an intermediate model of atmospheric variability and we show that the degree of stabilization depends on the type and distribution of the observations, as well as on the data assimilation method. These results represent joint work with A. Carrassi, A. Trevisan and F. Uboldi. Much is known by now about the main physical mechanisms that give rise to and modulate the El-Nino/Southern- Oscillation (ENSO), but the values of several parameters that enter these mechanisms are an important unknown. We apply Extended Kalman Filtering (EKF) for both model state and parameter estimation in an intermediate, nonlinear, coupled ocean-atmosphere model of ENSO. Model behavior is very sensitive to two key parameters: (a) "mu", the ocean-atmosphere coupling coefficient between the sea-surface temperature (SST) and wind stress anomalies; and (b) "delta-s", the surface-layer coefficient. Previous work has shown that "delta- s" determines the period of the model's self-sustained oscillation, while "mu' measures the degree of nonlinearity. Depending on the values of these parameters, the spatio-temporal pattern of model solutions is either that of a delayed oscillator or of a westward propagating mode. Assimilation of SST data from the NCEP- NCAR Reanalysis-2 shows that the parameters can vary on fairly short time scales and switch between values that approximate the two distinct modes of ENSO behavior. Rapid adjustments of these parameters occur, in particular, during strong ENSO events. Ways to apply EKF parameter estimation efficiently to state-of-the-art coupled ocean-atmosphere GCMs will be discussed. These results arise from joint work with D. Kondrashov and C.-j. Sun.

Variational algorithms for nonlinear smoothing applications

NASA Technical Reports Server (NTRS)

Bach, R. E., Jr.

1977-01-01

A variational approach is presented for solving a nonlinear, fixed-interval smoothing problem with application to offline processing of noisy data for trajectory reconstruction and parameter estimation. The nonlinear problem is solved as a sequence of linear two-point boundary value problems. Second-order convergence properties are demonstrated. Algorithms for both continuous and discrete versions of the problem are given, and example solutions are provided.

A modified NARMAX model-based self-tuner with fault tolerance for unknown nonlinear stochastic hybrid systems with an input-output direct feed-through term.

PubMed

Tsai, Jason S-H; Hsu, Wen-Teng; Lin, Long-Guei; Guo, Shu-Mei; Tann, Joseph W

2014-01-01

A modified nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuner with fault tolerance is proposed in this paper for the unknown nonlinear stochastic hybrid system with a direct transmission matrix from input to output. Through the off-line observer/Kalman filter identification method, one has a good initial guess of modified NARMAX model to reduce the on-line system identification process time. Then, based on the modified NARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown continuous-time nonlinear system, with an input-output direct transmission term, which also has measurement and system noises and inaccessible system states. Besides, an effective state space self-turner with fault tolerance scheme is presented for the unknown multivariable stochastic system. A quantitative criterion is suggested by comparing the innovation process error estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm is utilized to achieve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the fault detection. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS

USGS Publications Warehouse

Bolker, Benjamin M.; Gardner, Beth; Maunder, Mark; Berg, Casper W.; Brooks, Mollie; Comita, Liza; Crone, Elizabeth; Cubaynes, Sarah; Davies, Trevor; de Valpine, Perry; Ford, Jessica; Gimenez, Olivier; Kéry, Marc; Kim, Eun Jung; Lennert-Cody, Cleridy; Magunsson, Arni; Martell, Steve; Nash, John; Nielson, Anders; Regentz, Jim; Skaug, Hans; Zipkin, Elise

2013-01-01

1. Ecologists often use nonlinear fitting techniques to estimate the parameters of complex ecological models, with attendant frustration. This paper compares three open-source model fitting tools and discusses general strategies for defining and fitting models. 2. R is convenient and (relatively) easy to learn, AD Model Builder is fast and robust but comes with a steep learning curve, while BUGS provides the greatest flexibility at the price of speed. 3. Our model-fitting suggestions range from general cultural advice (where possible, use the tools and models that are most common in your subfield) to specific suggestions about how to change the mathematical description of models to make them more amenable to parameter estimation. 4. A companion web site (https://groups.nceas.ucsb.edu/nonlinear-modeling/projects) presents detailed examples of application of the three tools to a variety of typical ecological estimation problems; each example links both to a detailed project report and to full source code and data.

Discrete-time switching periodic adaptive control for time-varying parameters with unknown periodicity

NASA Astrophysics Data System (ADS)

Yu, Miao; Huang, Deqing; Yang, Wanqiu

2018-06-01

In this paper, we address the problem of unknown periodicity for a class of discrete-time nonlinear parametric systems without assuming any growth conditions on the nonlinearities. The unknown periodicity hides in the parametric uncertainties, which is difficult to estimate with existing techniques. By incorporating a logic-based switching mechanism, we identify the period and bound of unknown parameter simultaneously. Lyapunov-based analysis is given to demonstrate that a finite number of switchings can guarantee the asymptotic tracking for the nonlinear parametric systems. The simulation result also shows the efficacy of the proposed switching periodic adaptive control approach.

Smoothing-based compressed state Kalman filter for joint state-parameter estimation: Applications in reservoir characterization and CO2 storage monitoring

NASA Astrophysics Data System (ADS)

Li, Y. J.; Kokkinaki, Amalia; Darve, Eric F.; Kitanidis, Peter K.

2017-08-01

The operation of most engineered hydrogeological systems relies on simulating physical processes using numerical models with uncertain parameters and initial conditions. Predictions by such uncertain models can be greatly improved by Kalman-filter techniques that sequentially assimilate monitoring data. Each assimilation constitutes a nonlinear optimization, which is solved by linearizing an objective function about the model prediction and applying a linear correction to this prediction. However, if model parameters and initial conditions are uncertain, the optimization problem becomes strongly nonlinear and a linear correction may yield unphysical results. In this paper, we investigate the utility of one-step ahead smoothing, a variant of the traditional filtering process, to eliminate nonphysical results and reduce estimation artifacts caused by nonlinearities. We present the smoothing-based compressed state Kalman filter (sCSKF), an algorithm that combines one step ahead smoothing, in which current observations are used to correct the state and parameters one step back in time, with a nonensemble covariance compression scheme, that reduces the computational cost by efficiently exploring the high-dimensional state and parameter space. Numerical experiments show that when model parameters are uncertain and the states exhibit hyperbolic behavior with sharp fronts, as in CO2 storage applications, one-step ahead smoothing reduces overshooting errors and, by design, gives physically consistent state and parameter estimates. We compared sCSKF with commonly used data assimilation methods and showed that for the same computational cost, combining one step ahead smoothing and nonensemble compression is advantageous for real-time characterization and monitoring of large-scale hydrogeological systems with sharp moving fronts.

Electron acoustic nonlinear structures in planetary magnetospheres

NASA Astrophysics Data System (ADS)

Shah, K. H.; Qureshi, M. N. S.; Masood, W.; Shah, H. A.

2018-04-01

In this paper, we have studied linear and nonlinear propagation of electron acoustic waves (EAWs) comprising cold and hot populations in which the ions form the neutralizing background. The hot electrons have been assumed to follow the generalized ( r , q ) distribution which has the advantage that it mimics most of the distribution functions observed in space plasmas. Interestingly, it has been found that unlike Maxwellian and kappa distributions, the electron acoustic waves admit not only rarefactive structures but also allow the formation of compressive solitary structures for generalized ( r , q ) distribution. It has been found that the flatness parameter r , tail parameter q , and the nonlinear propagation velocity u affect the propagation characteristics of nonlinear EAWs. Using the plasmas parameters, typically found in Saturn's magnetosphere and the Earth's auroral region, where two populations of electrons and electron acoustic solitary waves (EASWs) have been observed, we have given an estimate of the scale lengths over which these nonlinear waves are expected to form and how the size of these structures would vary with the change in the shape of the distribution function and with the change of the plasma parameters.

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

NASA Astrophysics Data System (ADS)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking, they are able to extract smallest possible gravitational signals from modern and future satellite tracking measurements, leading to the production of global high-precision, high-resolution gravitational models. By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits are measured with random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton's governing differential equations as a condition adjustment model with unknown parameters, or equivalently, the weighted least squares estimation of unknown differential equation parameters with equality constraints, for the reconstruction of global high-precision, high-resolution gravitational models from modern (and future) satellite tracking measurements.

Characteristics and Impact Factors of Parameter Alpha in the Nonlinear Advection-Aridity Method for Estimating Evapotranspiration at Interannual Scale in the Loess Plateau

NASA Astrophysics Data System (ADS)

Zhou, H.; Liu, W.; Ning, T.

2017-12-01

Land surface actual evapotranspiration plays a key role in the global water and energy cycles. Accurate estimation of evapotranspiration is crucial for understanding the interactions between the land surface and the atmosphere, as well as for managing water resources. The nonlinear advection-aridity approach was formulated by Brutsaert to estimate actual evapotranspiration in 2015. Subsequently, this approach has been verified, applied and developed by many scholars. The estimation, impact factors and correlation analysis of the parameter alpha (αe) of this approach has become important aspects of the research. According to the principle of this approach, the potential evapotranspiration (ETpo) (taking αe as 1) and the apparent potential evapotranspiration (ETpm) were calculated using the meteorological data of 123 sites of the Loess Plateau and its surrounding areas. Then the mean spatial values of precipitation (P), ETpm and ETpo for 13 catchments were obtained by a CoKriging interpolation algorithm. Based on the runoff data of the 13 catchments, actual evapotranspiration was calculated using the catchment water balance equation at the hydrological year scale (May to April of the following year) by ignoring the change of catchment water storage. Thus, the parameter was estimated, and its relationships with P, ETpm and aridity index (ETpm/P) were further analyzed. The results showed that the general range of annual parameter value was 0.385-1.085, with an average value of 0.751 and a standard deviation of 0.113. The mean annual parameter αe value showed different spatial characteristics, with lower values in northern and higher values in southern. The annual scale parameter linearly related with annual P (R2=0.89) and ETpm (R2=0.49), while it exhibited a power function relationship with the aridity index (R2=0.83). Considering the ETpm is a variable in the nonlinear advection-aridity approach in which its effect has been incorporated, the relationship of precipitation and parameter (αe=1.0×10-3*P+0.301) was developed. The value of αe in this study is lower than those in the published literature. The reason is unclear at this point and yet need further investigation. The preliminary application of the nonlinear advection-aridity approach in the Loess Plateau has shown promising results.

Optimal estimation of parameters and states in stochastic time-varying systems with time delay

NASA Astrophysics Data System (ADS)

Torkamani, Shahab; Butcher, Eric A.

2013-08-01

In this study estimation of parameters and states in stochastic linear and nonlinear delay differential systems with time-varying coefficients and constant delay is explored. The approach consists of first employing a continuous time approximation to approximate the stochastic delay differential equation with a set of stochastic ordinary differential equations. Then the problem of parameter estimation in the resulting stochastic differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman-Bucy filter to the resulting system, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states.

Parameter estimation for chaotic systems using improved bird swarm algorithm

NASA Astrophysics Data System (ADS)

Xu, Chuangbiao; Yang, Renhuan

2017-12-01

Parameter estimation of chaotic systems is an important problem in nonlinear science and has aroused increasing interest of many research fields, which can be basically reduced to a multidimensional optimization problem. In this paper, an improved boundary bird swarm algorithm is used to estimate the parameters of chaotic systems. This algorithm can combine the good global convergence and robustness of the bird swarm algorithm and the exploitation capability of improved boundary learning strategy. Experiments are conducted on the Lorenz system and the coupling motor system. Numerical simulation results reveal the effectiveness and with desirable performance of IBBSA for parameter estimation of chaotic systems.

Robust adaptive uniform exact tracking control for uncertain Euler-Lagrange system

NASA Astrophysics Data System (ADS)

Yang, Yana; Hua, Changchun; Li, Junpeng; Guan, Xinping

2017-12-01

This paper offers a solution to the robust adaptive uniform exact tracking control for uncertain nonlinear Euler-Lagrange (EL) system. An adaptive finite-time tracking control algorithm is designed by proposing a novel nonsingular integral terminal sliding-mode surface. Moreover, a new adaptive parameter tuning law is also developed by making good use of the system tracking errors and the adaptive parameter estimation errors. Thus, both the trajectory tracking and the parameter estimation can be achieved in a guaranteed time adjusted arbitrarily based on practical demands, simultaneously. Additionally, the control result for the EL system proposed in this paper can be extended to high-order nonlinear systems easily. Finally, a test-bed 2-DOF robot arm is set-up to demonstrate the performance of the new control algorithm.

Comparison of least squares and exponential sine sweep methods for Parallel Hammerstein Models estimation

NASA Astrophysics Data System (ADS)

Rebillat, Marc; Schoukens, Maarten

2018-05-01

Linearity is a common assumption for many real-life systems, but in many cases the nonlinear behavior of systems cannot be ignored and must be modeled and estimated. Among the various existing classes of nonlinear models, Parallel Hammerstein Models (PHM) are interesting as they are at the same time easy to interpret as well as to estimate. One way to estimate PHM relies on the fact that the estimation problem is linear in the parameters and thus that classical least squares (LS) estimation algorithms can be used. In that area, this article introduces a regularized LS estimation algorithm inspired on some of the recently developed regularized impulse response estimation techniques. Another mean to estimate PHM consists in using parametric or non-parametric exponential sine sweeps (ESS) based methods. These methods (LS and ESS) are founded on radically different mathematical backgrounds but are expected to tackle the same issue. A methodology is proposed here to compare them with respect to (i) their accuracy, (ii) their computational cost, and (iii) their robustness to noise. Tests are performed on simulated systems for several values of methods respective parameters and of signal to noise ratio. Results show that, for a given set of data points, the ESS method is less demanding in computational resources than the LS method but that it is also less accurate. Furthermore, the LS method needs parameters to be set in advance whereas the ESS method is not subject to conditioning issues and can be fully non-parametric. In summary, for a given set of data points, ESS method can provide a first, automatic, and quick overview of a nonlinear system than can guide more computationally demanding and precise methods, such as the regularized LS one proposed here.

Noise normalization and windowing functions for VALIDAR in wind parameter estimation

NASA Astrophysics Data System (ADS)

Beyon, Jeffrey Y.; Koch, Grady J.; Li, Zhiwen

2006-05-01

The wind parameter estimates from a state-of-the-art 2-μm coherent lidar system located at NASA Langley, Virginia, named VALIDAR (validation lidar), were compared after normalizing the noise by its estimated power spectra via the periodogram and the linear predictive coding (LPC) scheme. The power spectra and the Doppler shift estimates were the main parameter estimates for comparison. Different types of windowing functions were implemented in VALIDAR data processing algorithm and their impact on the wind parameter estimates was observed. Time and frequency independent windowing functions such as Rectangular, Hanning, and Kaiser-Bessel and time and frequency dependent apodized windowing function were compared. The briefing of current nonlinear algorithm development for Doppler shift correction subsequently follows.

Automated Land Cover Change Detection and Mapping from Hidden Parameter Estimates of Normalized Difference Vegetation Index (NDVI) Time-Series

NASA Astrophysics Data System (ADS)

Chakraborty, S.; Banerjee, A.; Gupta, S. K. S.; Christensen, P. R.; Papandreou-Suppappola, A.

2017-12-01

Multitemporal observations acquired frequently by satellites with short revisit periods such as the Moderate Resolution Imaging Spectroradiometer (MODIS), is an important source for modeling land cover. Due to the inherent seasonality of the land cover, harmonic modeling reveals hidden state parameters characteristic to it, which is used in classifying different land cover types and in detecting changes due to natural or anthropogenic factors. In this work, we use an eight day MODIS composite to create a Normalized Difference Vegetation Index (NDVI) time-series of ten years. Improved hidden parameter estimates of the nonlinear harmonic NDVI model are obtained using the Particle Filter (PF), a sequential Monte Carlo estimator. The nonlinear estimation based on PF is shown to improve parameter estimation for different land cover types compared to existing techniques that use the Extended Kalman Filter (EKF), due to linearization of the harmonic model. As these parameters are representative of a given land cover, its applicability in near real-time detection of land cover change is also studied by formulating a metric that captures parameter deviation due to change. The detection methodology is evaluated by considering change as a rare class problem. This approach is shown to detect change with minimum delay. Additionally, the degree of change within the change perimeter is non-uniform. By clustering the deviation in parameters due to change, this spatial variation in change severity is effectively mapped and validated with high spatial resolution change maps of the given regions.

Adaptive control of Parkinson's state based on a nonlinear computational model with unknown parameters.

PubMed

Su, Fei; Wang, Jiang; Deng, Bin; Wei, Xi-Le; Chen, Ying-Yuan; Liu, Chen; Li, Hui-Yan

2015-02-01

The objective here is to explore the use of adaptive input-output feedback linearization method to achieve an improved deep brain stimulation (DBS) algorithm for closed-loop control of Parkinson's state. The control law is based on a highly nonlinear computational model of Parkinson's disease (PD) with unknown parameters. The restoration of thalamic relay reliability is formulated as the desired outcome of the adaptive control methodology, and the DBS waveform is the control input. The control input is adjusted in real time according to estimates of unknown parameters as well as the feedback signal. Simulation results show that the proposed adaptive control algorithm succeeds in restoring the relay reliability of the thalamus, and at the same time achieves accurate estimation of unknown parameters. Our findings point to the potential value of adaptive control approach that could be used to regulate DBS waveform in more effective treatment of PD.

A new linear least squares method for T1 estimation from SPGR signals with multiple TRs

NASA Astrophysics Data System (ADS)

Chang, Lin-Ching; Koay, Cheng Guan; Basser, Peter J.; Pierpaoli, Carlo

2009-02-01

The longitudinal relaxation time, T1, can be estimated from two or more spoiled gradient recalled echo x (SPGR) images with two or more flip angles and one or more repetition times (TRs). The function relating signal intensity and the parameters are nonlinear; T1 maps can be computed from SPGR signals using nonlinear least squares regression. A widely-used linear method transforms the nonlinear model by assuming a fixed TR in SPGR images. This constraint is not desirable since multiple TRs are a clinically practical way to reduce the total acquisition time, to satisfy the required resolution, and/or to combine SPGR data acquired at different times. A new linear least squares method is proposed using the first order Taylor expansion. Monte Carlo simulations of SPGR experiments are used to evaluate the accuracy and precision of the estimated T1 from the proposed linear and the nonlinear methods. We show that the new linear least squares method provides T1 estimates comparable in both precision and accuracy to those from the nonlinear method, allowing multiple TRs and reducing computation time significantly.

A nonlinear SIR with stability

NASA Astrophysics Data System (ADS)

Trisilowati, Darti, I.; Fitri, S.

2014-02-01

The aim of this work is to develop a mathematical model of a nonlinear susceptible-infectious-removed (SIR) epidemic model with vaccination. We analyze the stability of the model by linearizing the model around the equilibrium point. Then, diphtheria data from East Java province is fitted to the model. From these estimated parameters, we investigate which parameters that play important role in the epidemic model. Some numerical simulations are given to illustrate the analytical results and the behavior of the model.

Supervised nonlinear spectral unmixing using a postnonlinear mixing model for hyperspectral imagery.

PubMed

Altmann, Yoann; Halimi, Abderrahim; Dobigeon, Nicolas; Tourneret, Jean-Yves

2012-06-01

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data.

Least-squares sequential parameter and state estimation for large space structures

NASA Technical Reports Server (NTRS)

Thau, F. E.; Eliazov, T.; Montgomery, R. C.

1982-01-01

This paper presents the formulation of simultaneous state and parameter estimation problems for flexible structures in terms of least-squares minimization problems. The approach combines an on-line order determination algorithm, with least-squares algorithms for finding estimates of modal approximation functions, modal amplitudes, and modal parameters. The approach combines previous results on separable nonlinear least squares estimation with a regression analysis formulation of the state estimation problem. The technique makes use of sequential Householder transformations. This allows for sequential accumulation of matrices required during the identification process. The technique is used to identify the modal prameters of a flexible beam.

Volterra series truncation and kernel estimation of nonlinear systems in the frequency domain

NASA Astrophysics Data System (ADS)

Zhang, B.; Billings, S. A.

2017-02-01

The Volterra series model is a direct generalisation of the linear convolution integral and is capable of displaying the intrinsic features of a nonlinear system in a simple and easy to apply way. Nonlinear system analysis using Volterra series is normally based on the analysis of its frequency-domain kernels and a truncated description. But the estimation of Volterra kernels and the truncation of Volterra series are coupled with each other. In this paper, a novel complex-valued orthogonal least squares algorithm is developed. The new algorithm provides a powerful tool to determine which terms should be included in the Volterra series expansion and to estimate the kernels and thus solves the two problems all together. The estimated results are compared with those determined using the analytical expressions of the kernels to validate the method. To further evaluate the effectiveness of the method, the physical parameters of the system are also extracted from the measured kernels. Simulation studies demonstrates that the new approach not only can truncate the Volterra series expansion and estimate the kernels of a weakly nonlinear system, but also can indicate the applicability of the Volterra series analysis in a severely nonlinear system case.

Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

PubMed

Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji

2016-09-01

It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

Propagation regimes and populations of internal waves in the Mediterranean Sea basin

NASA Astrophysics Data System (ADS)

Kurkina, Oxana; Rouvinskaya, Ekaterina; Talipova, Tatiana; Soomere, Tarmo

2017-02-01

The geographical and seasonal distributions of kinematic and nonlinear parameters of long internal waves are derived from the Generalized Digital Environmental Model (GDEM) climatology for the Mediterranean Sea region, including the Black Sea. The considered parameters are phase speed of long internal waves and the coefficients at the dispersion, quadratic and cubic terms of the weakly-nonlinear Korteweg-de Vries-type models (in particular, the Gardner model). These parameters govern the possible polarities and shapes of solitary internal waves, their limiting amplitudes and propagation speeds. The key outcome is an express estimate of the expected parameters of internal waves for different regions of the Mediterranean basin.

Estimation of regions of attraction and ultimate boundedness for multiloop LQ regulators. [Linear Quadratic

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1984-01-01

Closed-loop stability is investigated for multivariable linear time-invariant systems controlled by optimal full state feedback linear quadratic (LQ) regulators, with nonlinear gains present in the feedback channels. Estimates are obtained for the region of attraction when the nonlinearities escape the (0.5, infinity) sector in regions away from the origin and for the region of ultimate boundedness when the nonlinearities escape the sector near the origin. The expressions for these regions also provide methods for selecting the performance function parameters in order to obtain LQ designs with better tolerance for nonlinearities. The analytical results are illustrated by applying them to the problem of controlling the rigid-body pitch angle and elastic motion of a large, flexible space antenna.

The pEst version 2.1 user's manual

NASA Technical Reports Server (NTRS)

Murray, James E.; Maine, Richard E.

1987-01-01

This report is a user's manual for version 2.1 of pEst, a FORTRAN 77 computer program for interactive parameter estimation in nonlinear dynamic systems. The pEst program allows the user complete generality in definig the nonlinear equations of motion used in the analysis. The equations of motion are specified by a set of FORTRAN subroutines; a set of routines for a general aircraft model is supplied with the program and is described in the report. The report also briefly discusses the scope of the parameter estimation problem the program addresses. The report gives detailed explanations of the purpose and usage of all available program commands and a description of the computational algorithms used in the program.

Convergent Cross Mapping: Basic concept, influence of estimation parameters and practical application.

PubMed

Schiecke, Karin; Pester, Britta; Feucht, Martha; Leistritz, Lutz; Witte, Herbert

2015-01-01

In neuroscience, data are typically generated from neural network activity. Complex interactions between measured time series are involved, and nothing or only little is known about the underlying dynamic system. Convergent Cross Mapping (CCM) provides the possibility to investigate nonlinear causal interactions between time series by using nonlinear state space reconstruction. Aim of this study is to investigate the general applicability, and to show potentials and limitation of CCM. Influence of estimation parameters could be demonstrated by means of simulated data, whereas interval-based application of CCM on real data could be adapted for the investigation of interactions between heart rate and specific EEG components of children with temporal lobe epilepsy.

Region of attraction analysis for nonlinear vehicle lateral dynamics using sum-of-squares programming

NASA Astrophysics Data System (ADS)

Imani Masouleh, Mehdi; Limebeer, David J. N.

2018-07-01

In this study we will estimate the region of attraction (RoA) of the lateral dynamics of a nonlinear single-track vehicle model. The tyre forces are approximated using rational functions that are shown to capture the nonlinearities of tyre curves significantly better than polynomial functions. An existing sum-of-squares (SOS) programming algorithm for estimating regions of attraction is extended to accommodate the use of rational vector fields. This algorithm is then used to find an estimate of the RoA of the vehicle lateral dynamics. The influence of vehicle parameters and driving conditions on the stability region are studied. It is shown that SOS programming techniques can be used to approximate the stability region without resorting to numerical integration. The RoA estimate from the SOS algorithm is compared to the existing results in the literature. The proposed method is shown to obtain significantly better RoA estimates.

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.

Evolutionary optimization with data collocation for reverse engineering of biological networks.

PubMed

Tsai, Kuan-Yao; Wang, Feng-Sheng

2005-04-01

Modern experimental biology is moving away from analyses of single elements to whole-organism measurements. Such measured time-course data contain a wealth of information about the structure and dynamic of the pathway or network. The dynamic modeling of the whole systems is formulated as a reverse problem that requires a well-suited mathematical model and a very efficient computational method to identify the model structure and parameters. Numerical integration for differential equations and finding global parameter values are still two major challenges in this field of the parameter estimation of nonlinear dynamic biological systems. We compare three techniques of parameter estimation for nonlinear dynamic biological systems. In the proposed scheme, the modified collocation method is applied to convert the differential equations to the system of algebraic equations. The observed time-course data are then substituted into the algebraic system equations to decouple system interactions in order to obtain the approximate model profiles. Hybrid differential evolution (HDE) with population size of five is able to find a global solution. The method is not only suited for parameter estimation but also can be applied for structure identification. The solution obtained by HDE is then used as the starting point for a local search method to yield the refined estimates.

Nonparametric identification of nonlinear dynamic systems using a synchronisation-based method

NASA Astrophysics Data System (ADS)

Kenderi, Gábor; Fidlin, Alexander

2014-12-01

The present study proposes an identification method for highly nonlinear mechanical systems that does not require a priori knowledge of the underlying nonlinearities to reconstruct arbitrary restoring force surfaces between degrees of freedom. This approach is based on the master-slave synchronisation between a dynamic model of the system as the slave and the real system as the master using measurements of the latter. As the model synchronises to the measurements, it becomes an observer of the real system. The optimal observer algorithm in a least-squares sense is given by the Kalman filter. Using the well-known state augmentation technique, the Kalman filter can be turned into a dual state and parameter estimator to identify parameters of a priori characterised nonlinearities. The paper proposes an extension of this technique towards nonparametric identification. A general system model is introduced by describing the restoring forces as bilateral spring-dampers with time-variant coefficients, which are estimated as augmented states. The estimation procedure is followed by an a posteriori statistical analysis to reconstruct noise-free restoring force characteristics using the estimated states and their estimated variances. Observability is provided using only one measured mechanical quantity per degree of freedom, which makes this approach less demanding in the number of necessary measurement signals compared with truly nonparametric solutions, which typically require displacement, velocity and acceleration signals. Additionally, due to the statistical rigour of the procedure, it successfully addresses signals corrupted by significant measurement noise. In the present paper, the method is described in detail, which is followed by numerical examples of one degree of freedom (1DoF) and 2DoF mechanical systems with strong nonlinearities of vibro-impact type to demonstrate the effectiveness of the proposed technique.

Flaw characterization through nonlinear ultrasonics and wavelet cross-correlation algorithms

NASA Astrophysics Data System (ADS)

Bunget, Gheorghe; Yee, Andrew; Stewart, Dylan; Rogers, James; Henley, Stanley; Bugg, Chris; Cline, John; Webster, Matthew; Farinholt, Kevin; Friedersdorf, Fritz

2018-04-01

Ultrasonic measurements have become increasingly important non-destructive techniques to characterize flaws found within various in-service industrial components. The prediction of remaining useful life based on fracture analysis depends on the accurate estimation of flaw size and orientation. However, amplitude-based ultrasonic measurements are not able to estimate the plastic zones that exist ahead of crack tips. Estimating the size of the plastic zone is an advantage since some flaws may propagate faster than others. This paper presents a wavelet cross-correlation (WCC) algorithm that was applied to nonlinear analysis of ultrasonically guided waves (GW). By using this algorithm, harmonics present in the waveforms were extracted and nonlinearity parameters were used to indicate both the tip of the cracks and size of the plastic zone. B-scans performed with the quadratic nonlinearities were sensitive to micro-damage specific to plastic zones.

Tuning the control system of a nonlinear inverted pendulum by means of the new method of Lyapunov exponents estimation

NASA Astrophysics Data System (ADS)

Balcerzak, Marek; Dąbrowski, Artur; Pikunov, Danylo

2018-01-01

This paper presents a practical application of a new, simplified method of Lyapunov exponents estimation. The method has been applied to optimization of a real, nonlinear inverted pendulum system. Authors presented how the algorithm of the Largest Lyapunov Exponent (LLE) estimation can be applied to evaluate control systems performance. The new LLE-based control performance index has been proposed. Equations of the inverted pendulum system of the fourth order have been found. The nonlinear friction of the regulation object has been identified by means of the nonlinear least squares method. Three different friction models have been tested: linear, cubic and Coulomb model. The Differential Evolution (DE) algorithm has been used to search for the best set of parameters of the general linear regulator. This work proves that proposed method is efficient and results in faster perturbation rejection, especially when disturbances are significant.

Estimation of Hidden State Variables of the Intracranial System Using Constrained Nonlinear Kalman Filters

PubMed Central

Nenov, Valeriy; Bergsneider, Marvin; Glenn, Thomas C.; Vespa, Paul; Martin, Neil

2007-01-01

Impeded by the rigid skull, assessment of physiological variables of the intracranial system is difficult. A hidden state estimation approach is used in the present work to facilitate the estimation of unobserved variables from available clinical measurements including intracranial pressure (ICP) and cerebral blood flow velocity (CBFV). The estimation algorithm is based on a modified nonlinear intracranial mathematical model, whose parameters are first identified in an offline stage using a nonlinear optimization paradigm. Following the offline stage, an online filtering process is performed using a nonlinear Kalman filter (KF)-like state estimator that is equipped with a new way of deriving the Kalman gain satisfying the physiological constraints on the state variables. The proposed method is then validated by comparing different state estimation methods and input/output (I/O) configurations using simulated data. It is also applied to a set of CBFV, ICP and arterial blood pressure (ABP) signal segments from brain injury patients. The results indicated that the proposed constrained nonlinear KF achieved the best performance among the evaluated state estimators and that the state estimator combined with the I/O configuration that has ICP as the measured output can potentially be used to estimate CBFV continuously. Finally, the state estimator combined with the I/O configuration that has both ICP and CBFV as outputs can potentially estimate the lumped cerebral arterial radii, which are not measurable in a typical clinical environment. PMID:17281533

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models

PubMed Central

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization. PMID:27243005

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

PubMed

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.

State estimation of stochastic non-linear hybrid dynamic system using an interacting multiple model algorithm.

PubMed

Elenchezhiyan, M; Prakash, J

2015-09-01

In this work, state estimation schemes for non-linear hybrid dynamic systems subjected to stochastic state disturbances and random errors in measurements using interacting multiple-model (IMM) algorithms are formulated. In order to compute both discrete modes and continuous state estimates of a hybrid dynamic system either an IMM extended Kalman filter (IMM-EKF) or an IMM based derivative-free Kalman filters is proposed in this study. The efficacy of the proposed IMM based state estimation schemes is demonstrated by conducting Monte-Carlo simulation studies on the two-tank hybrid system and switched non-isothermal continuous stirred tank reactor system. Extensive simulation studies reveal that the proposed IMM based state estimation schemes are able to generate fairly accurate continuous state estimates and discrete modes. In the presence and absence of sensor bias, the simulation studies reveal that the proposed IMM unscented Kalman filter (IMM-UKF) based simultaneous state and parameter estimation scheme outperforms multiple-model UKF (MM-UKF) based simultaneous state and parameter estimation scheme. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in dairy cows with postmilking teat disinfection.

PubMed

White, L J; Evans, N D; Lam, T J G M; Schukken, Y H; Medley, G F; Godfrey, K R; Chappell, M J

2002-01-01

A mathematical model for the transmission of two interacting classes of mastitis causing bacterial pathogens in a herd of dairy cows is presented and applied to a specific data set. The data were derived from a field trial of a specific measure used in the control of these pathogens, where half the individuals were subjected to the control and in the others the treatment was discontinued. The resultant mathematical model (eight non-linear simultaneous ordinary differential equations) therefore incorporates heterogeneity in the host as well as the infectious agent and consequently the effects of control are intrinsic in the model structure. A structural identifiability analysis of the model is presented demonstrating that the scope of the novel method used allows application to high order non-linear systems. The results of a simultaneous estimation of six unknown system parameters are presented. Previous work has only estimated a subset of these either simultaneously or individually. Therefore not only are new estimates provided for the parameters relating to the transmission and control of the classes of pathogens under study, but also information about the relationships between them. We exploit the close link between mathematical modelling, structural identifiability analysis, and parameter estimation to obtain biological insights into the system modelled.

Combining experimental techniques with non-linear numerical models to assess the sorption of pesticides on soils

NASA Astrophysics Data System (ADS)

Magga, Zoi; Tzovolou, Dimitra N.; Theodoropoulou, Maria A.; Tsakiroglou, Christos D.

2012-03-01

The risk assessment of groundwater pollution by pesticides may be based on pesticide sorption and biodegradation kinetic parameters estimated with inverse modeling of datasets from either batch or continuous flow soil column experiments. In the present work, a chemical non-equilibrium and non-linear 2-site sorption model is incorporated into solute transport models to invert the datasets of batch and soil column experiments, and estimate the kinetic sorption parameters for two pesticides: N-phosphonomethyl glycine (glyphosate) and 2,4-dichlorophenoxy-acetic acid (2,4-D). When coupling the 2-site sorption model with the 2-region transport model, except of the kinetic sorption parameters, the soil column datasets enable us to estimate the mass-transfer coefficients associated with solute diffusion between mobile and immobile regions. In order to improve the reliability of models and kinetic parameter values, a stepwise strategy that combines batch and continuous flow tests with adequate true-to-the mechanism analytical of numerical models, and decouples the kinetics of purely reactive steps of sorption from physical mass-transfer processes is required.

Stress evaluation of metallic material under steady state based on nonlinear critically refracted longitudinal wave

NASA Astrophysics Data System (ADS)

Mao, Hanling; Zhang, Yuhua; Mao, Hanying; Li, Xinxin; Huang, Zhenfeng

2018-06-01

This paper presents the study of applying the nonlinear ultrasonic wave to evaluate the stress state of metallic materials under steady state. The pre-stress loading method is applied to guarantee components with steady stress. Three kinds of nonlinear ultrasonic experiments based on critically refracted longitudinal wave are conducted on components which the critically refracted longitudinal wave propagates along x, x1 and x2 direction. Experimental results indicate the second and third order relative nonlinear coefficients monotonically increase with stress, and the normalized relationship is consistent with simplified dislocation models, which indicates the experimental result is logical. The combined ultrasonic nonlinear parameter is proposed, and three stress evaluation models at x direction are established based on three ultrasonic nonlinear parameters, which the estimation error is below 5%. Then two stress detection models at x1 and x2 direction are built based on combined ultrasonic nonlinear parameter, the stress synthesis method is applied to calculate the magnitude and direction of principal stress. The results show the prediction error is within 5% and the angle deviation is within 1.5°. Therefore the nonlinear ultrasonic technique based on LCR wave could be applied to nondestructively evaluate the stress of metallic materials under steady state which the magnitude and direction are included.

A least-squares parameter estimation algorithm for switched hammerstein systems with applications to the VOR

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Kearney, Robert E.; Galiana, Henrietta L.

2005-01-01

A "Multimode" or "switched" system is one that switches between various modes of operation. When a switch occurs from one mode to another, a discontinuity may result followed by a smooth evolution under the new regime. Characterizing the switching behavior of these systems is not well understood and, therefore, identification of multimode systems typically requires a preprocessing step to classify the observed data according to a mode of operation. A further consequence of the switched nature of these systems is that data available for parameter estimation of any subsystem may be inadequate. As such, identification and parameter estimation of multimode systems remains an unresolved problem. In this paper, we 1) show that the NARMAX model structure can be used to describe the impulsive-smooth behavior of switched systems, 2) propose a modified extended least squares (MELS) algorithm to estimate the coefficients of such models, and 3) demonstrate its applicability to simulated and real data from the Vestibulo-Ocular Reflex (VOR). The approach will also allow the identification of other nonlinear bio-systems, suspected of containing "hard" nonlinearities.

Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs

PubMed Central

McFarland, James M.; Cui, Yuwei; Butts, Daniel A.

2013-01-01

The computation represented by a sensory neuron's response to stimuli is constructed from an array of physiological processes both belonging to that neuron and inherited from its inputs. Although many of these physiological processes are known to be nonlinear, linear approximations are commonly used to describe the stimulus selectivity of sensory neurons (i.e., linear receptive fields). Here we present an approach for modeling sensory processing, termed the Nonlinear Input Model (NIM), which is based on the hypothesis that the dominant nonlinearities imposed by physiological mechanisms arise from rectification of a neuron's inputs. Incorporating such ‘upstream nonlinearities’ within the standard linear-nonlinear (LN) cascade modeling structure implicitly allows for the identification of multiple stimulus features driving a neuron's response, which become directly interpretable as either excitatory or inhibitory. Because its form is analogous to an integrate-and-fire neuron receiving excitatory and inhibitory inputs, model fitting can be guided by prior knowledge about the inputs to a given neuron, and elements of the resulting model can often result in specific physiological predictions. Furthermore, by providing an explicit probabilistic model with a relatively simple nonlinear structure, its parameters can be efficiently optimized and appropriately regularized. Parameter estimation is robust and efficient even with large numbers of model components and in the context of high-dimensional stimuli with complex statistical structure (e.g. natural stimuli). We describe detailed methods for estimating the model parameters, and illustrate the advantages of the NIM using a range of example sensory neurons in the visual and auditory systems. We thus present a modeling framework that can capture a broad range of nonlinear response functions while providing physiologically interpretable descriptions of neural computation. PMID:23874185

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.

Nonlinear estimation of parameters in biphasic Arrhenius plots.

PubMed

Puterman, M L; Hrboticky, N; Innis, S M

1988-05-01

This paper presents a formal procedure for the statistical analysis of data on the thermotropic behavior of membrane-bound enzymes generated using the Arrhenius equation and compares the analysis to several alternatives. Data is modeled by a bent hyperbola. Nonlinear regression is used to obtain estimates and standard errors of the intersection of line segments, defined as the transition temperature, and slopes, defined as energies of activation of the enzyme reaction. The methodology allows formal tests of the adequacy of a biphasic model rather than either a single straight line or a curvilinear model. Examples on data concerning the thermotropic behavior of pig brain synaptosomal acetylcholinesterase are given. The data support the biphasic temperature dependence of this enzyme. The methodology represents a formal procedure for statistical validation of any biphasic data and allows for calculation of all line parameters with estimates of precision.

Adaptive Estimation and Heuristic Optimization of Nonlinear Spacecraft Attitude Dynamics

DTIC Science & Technology

2016-09-15

Algorithm GPS Global Positioning System HOUF Higher Order Unscented Filter IC initial conditions IMM Interacting Multiple Model IMU Inertial Measurement Unit ...sources ranging from inertial measurement units to star sensors are used to construct observations for attitude estimation algorithms. The sensor...parameters. A single vector measurement will provide two independent parameters, as a unit vector constraint removes a DOF making the problem underdetermined

Rapid assessment of nonlinear optical propagation effects in dielectrics

PubMed Central

Hoyo, J. del; de la Cruz, A. Ruiz; Grace, E.; Ferrer, A.; Siegel, J.; Pasquazi, A.; Assanto, G.; Solis, J.

2015-01-01

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process. PMID:25564243

Rapid assessment of nonlinear optical propagation effects in dielectrics.

PubMed

del Hoyo, J; de la Cruz, A Ruiz; Grace, E; Ferrer, A; Siegel, J; Pasquazi, A; Assanto, G; Solis, J

2015-01-07

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.

Rapid assessment of nonlinear optical propagation effects in dielectrics

NASA Astrophysics Data System (ADS)

Hoyo, J. Del; de La Cruz, A. Ruiz; Grace, E.; Ferrer, A.; Siegel, J.; Pasquazi, A.; Assanto, G.; Solis, J.

2015-01-01

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.

Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm.

PubMed

Jafari, Masoumeh; Salimifard, Maryam; Dehghani, Maryam

2014-07-01

This paper presents an efficient method for identification of nonlinear Multi-Input Multi-Output (MIMO) systems in the presence of colored noises. The method studies the multivariable nonlinear Hammerstein and Wiener models, in which, the nonlinear memory-less block is approximated based on arbitrary vector-based basis functions. The linear time-invariant (LTI) block is modeled by an autoregressive moving average with exogenous (ARMAX) model which can effectively describe the moving average noises as well as the autoregressive and the exogenous dynamics. According to the multivariable nature of the system, a pseudo-linear-in-the-parameter model is obtained which includes two different kinds of unknown parameters, a vector and a matrix. Therefore, the standard least squares algorithm cannot be applied directly. To overcome this problem, a Hierarchical Least Squares Iterative (HLSI) algorithm is used to simultaneously estimate the vector and the matrix of unknown parameters as well as the noises. The efficiency of the proposed identification approaches are investigated through three nonlinear MIMO case studies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Estimating parameter of influenza transmission using regularized least square

NASA Astrophysics Data System (ADS)

Nuraini, N.; Syukriah, Y.; Indratno, S. W.

2014-02-01

Transmission process of influenza can be presented in a mathematical model as a non-linear differential equations system. In this model the transmission of influenza is determined by the parameter of contact rate of the infected host and susceptible host. This parameter will be estimated using a regularized least square method where the Finite Element Method and Euler Method are used for approximating the solution of the SIR differential equation. The new infected data of influenza from CDC is used to see the effectiveness of the method. The estimated parameter represents the contact rate proportion of transmission probability in a day which can influence the number of infected people by the influenza. Relation between the estimated parameter and the number of infected people by the influenza is measured by coefficient of correlation. The numerical results show positive correlation between the estimated parameters and the infected people.

Ionosphere Profile Estimation Using Ionosonde & GPS Data in an Inverse Refraction Calculation

NASA Astrophysics Data System (ADS)

Psiaki, M. L.

2014-12-01

A method has been developed to assimilate ionosonde virtual heights and GPS slant TEC data to estimate the parameters of a local ionosphere model, including estimates of the topside and of latitude and longitude variations. This effort seeks to better assimilate a variety of remote sensing data in order to characterize local (and eventually regional and global) ionosphere electron density profiles. The core calculations involve a forward refractive ray-tracing solution and a nonlinear optimal estimation algorithm that inverts the forward model. The ray-tracing calculations solve a nonlinear two-point boundary value problem for the curved ionosonde or GPS ray path through a parameterized electron density profile. It implements a full 3D solution that can handle the case of a tilted ionosphere. These calculations use Hamiltonian equivalents of the Appleton-Hartree magneto-plasma refraction index model. The current ionosphere parameterization is a modified Booker profile. It has been augmented to include latitude and longitude dependencies. The forward ray-tracing solution yields a given signal's group delay and beat carrier phase observables. An auxiliary set of boundary value problem solutions determine the sensitivities of the ray paths and observables with respect to the parameters of the augmented Booker profile. The nonlinear estimation algorithm compares the measured ionosonde virtual-altitude observables and GPS slant-TEC observables to the corresponding values from the forward refraction model. It uses the parameter sensitivities of the model to iteratively improve its parameter estimates in a way the reduces the residual errors between the measurements and their modeled values. This method has been applied to data from HAARP in Gakona, AK and has produced good TEC and virtual height fits. It has been extended to characterize electron density perturbations caused by HAARP heating experiments through the use of GPS slant TEC data for an LOS through the heated zone. The next planned extension of the method is to estimate the parameters of a regional ionosphere profile. The input observables will be slant TEC from an array of GPS receivers and group delay and carrier phase observables from an array of high-frequency beacons. The beacon array will function as a sort of multi-static ionosonde.

Inverse models: A necessary next step in ground-water modeling

USGS Publications Warehouse

Poeter, E.P.; Hill, M.C.

1997-01-01

Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares repression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares regression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.

Modeling a multivariable reactor and on-line model predictive control.

PubMed

Yu, D W; Yu, D L

2005-10-01

A nonlinear first principle model is developed for a laboratory-scaled multivariable chemical reactor rig in this paper and the on-line model predictive control (MPC) is implemented to the rig. The reactor has three variables-temperature, pH, and dissolved oxygen with nonlinear dynamics-and is therefore used as a pilot system for the biochemical industry. A nonlinear discrete-time model is derived for each of the three output variables and their model parameters are estimated from the real data using an adaptive optimization method. The developed model is used in a nonlinear MPC scheme. An accurate multistep-ahead prediction is obtained for MPC, where the extended Kalman filter is used to estimate system unknown states. The on-line control is implemented and a satisfactory tracking performance is achieved. The MPC is compared with three decentralized PID controllers and the advantage of the nonlinear MPC over the PID is clearly shown.

A study on nonlinear estimation of submaximal effort tolerance based on the generalized MET concept and the 6MWT in pulmonary rehabilitation

PubMed Central

Szczegielniak, Jan; Łuniewski, Jacek; Stanisławski, Rafał; Bogacz, Katarzyna; Krajczy, Marcin; Rydel, Marek

2018-01-01

Background The six-minute walk test (6MWT) is considered to be a simple and inexpensive tool for the assessment of functional tolerance of submaximal effort. The aim of this work was 1) to background the nonlinear nature of the energy expenditure process due to physical activity, 2) to compare the results/scores of the submaximal treadmill exercise test and those of 6MWT in pulmonary patients and 3) to develop nonlinear mathematical models relating the two. Methods The study group included patients with the COPD. All patients were subjected to a submaximal exercise test and a 6MWT. To develop an optimal mathematical solution and compare the results of the exercise test and the 6MWT, the least squares and genetic algorithms were employed to estimate parameters of polynomial expansion and piecewise linear models. Results Mathematical analysis enabled to construct nonlinear models for estimating the MET result of submaximal exercise test based on average walk velocity (or distance) in the 6MWT. Conclusions Submaximal effort tolerance in COPD patients can be effectively estimated from new, rehabilitation-oriented, nonlinear models based on the generalized MET concept and the 6MWT. PMID:29425213

Performance of nonlinear mixed effects models in the presence of informative dropout.

PubMed

Björnsson, Marcus A; Friberg, Lena E; Simonsson, Ulrika S H

2015-01-01

Informative dropout can lead to bias in statistical analyses if not handled appropriately. The objective of this simulation study was to investigate the performance of nonlinear mixed effects models with regard to bias and precision, with and without handling informative dropout. An efficacy variable and dropout depending on that efficacy variable were simulated and model parameters were reestimated, with or without including a dropout model. The Laplace and FOCE-I estimation methods in NONMEM 7, and the stochastic simulations and estimations (SSE) functionality in PsN, were used in the analysis. For the base scenario, bias was low, less than 5% for all fixed effects parameters, when a dropout model was used in the estimations. When a dropout model was not included, bias increased up to 8% for the Laplace method and up to 21% if the FOCE-I estimation method was applied. The bias increased with decreasing number of observations per subject, increasing placebo effect and increasing dropout rate, but was relatively unaffected by the number of subjects in the study. This study illustrates that ignoring informative dropout can lead to biased parameters in nonlinear mixed effects modeling, but even in cases with few observations or high dropout rate, the bias is relatively low and only translates into small effects on predictions of the underlying effect variable. A dropout model is, however, crucial in the presence of informative dropout in order to make realistic simulations of trial outcomes.

Via generalized function projective synchronization in nonlinear Schrödinger equation for secure communication

NASA Astrophysics Data System (ADS)

Zhao, L. W.; Du, J. G.; Yin, J. L.

2018-05-01

This paper proposes a novel secured communication scheme in a chaotic system by applying generalized function projective synchronization of the nonlinear Schrödinger equation. This phenomenal approach guarantees a secured and convenient communication. Our study applied the Melnikov theorem with an active control strategy to suppress chaos in the system. The transmitted information signal is modulated into the parameter of the nonlinear Schrödinger equation in the transmitter and it is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory and the adaptive control technique, the controllers are designed to make two identical nonlinear Schrödinger equation with the unknown parameter asymptotically synchronized. The numerical simulation results of our study confirmed the validity, effectiveness and the feasibility of the proposed novel synchronization method and error estimate for a secure communication. The Chaos masking signals of the information communication scheme, further guaranteed a safer and secured information communicated via this approach.

NLSCIDNT user's guide maximum likehood parameter identification computer program with nonlinear rotorcraft model

NASA Technical Reports Server (NTRS)

1979-01-01

A nonlinear, maximum likelihood, parameter identification computer program (NLSCIDNT) is described which evaluates rotorcraft stability and control coefficients from flight test data. The optimal estimates of the parameters (stability and control coefficients) are determined (identified) by minimizing the negative log likelihood cost function. The minimization technique is the Levenberg-Marquardt method, which behaves like the steepest descent method when it is far from the minimum and behaves like the modified Newton-Raphson method when it is nearer the minimum. Twenty-one states and 40 measurement variables are modeled, and any subset may be selected. States which are not integrated may be fixed at an input value, or time history data may be substituted for the state in the equations of motion. Any aerodynamic coefficient may be expressed as a nonlinear polynomial function of selected 'expansion variables'.

New non-linear model of groundwater recharge: Inclusion of memory, heterogeneity and visco-elasticity

NASA Astrophysics Data System (ADS)

Spannenberg, Jescica; Atangana, Abdon; Vermeulen, P. D.

2017-09-01

Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.

Estimating the kinetic parameters of activated sludge storage using weighted non-linear least-squares and accelerating genetic algorithm.

PubMed

Fang, Fang; Ni, Bing-Jie; Yu, Han-Qing

2009-06-01

In this study, weighted non-linear least-squares analysis and accelerating genetic algorithm are integrated to estimate the kinetic parameters of substrate consumption and storage product formation of activated sludge. A storage product formation equation is developed and used to construct the objective function for the determination of its production kinetics. The weighted least-squares analysis is employed to calculate the differences in the storage product concentration between the model predictions and the experimental data as the sum of squared weighted errors. The kinetic parameters for the substrate consumption and the storage product formation are estimated to be the maximum heterotrophic growth rate of 0.121/h, the yield coefficient of 0.44 mg CODX/mg CODS (COD, chemical oxygen demand) and the substrate half saturation constant of 16.9 mg/L, respectively, by minimizing the objective function using a real-coding-based accelerating genetic algorithm. Also, the fraction of substrate electrons diverted to the storage product formation is estimated to be 0.43 mg CODSTO/mg CODS. The validity of our approach is confirmed by the results of independent tests and the kinetic parameter values reported in literature, suggesting that this approach could be useful to evaluate the product formation kinetics of mixed cultures like activated sludge. More importantly, as this integrated approach could estimate the kinetic parameters rapidly and accurately, it could be applied to other biological processes.

Linear and Nonlinear Viscoelastic Modeling of Aorta and Carotid Pressure-Area Dynamics under in vivo and ex vivo Conditions

PubMed Central

Valdez-Jasso, Daniela; Bia, Daniel; Zócalo, Yanina; Armentano, Ricardo L.; Haider, Mansoor A.; Olufsen, Mette S.

2013-01-01

A better understanding of the biomechanical properties of the arterial wall provides important insight into arterial vascular biology under normal (healthy) and pathological conditions. This insight has potential to improve tracking of disease progression and to aid in vascular graft design and implementation. In this study, we use linear and nonlinear viscoelastic models to predict biomechanical properties of the thoracic descending aorta and the carotid artery under ex vivo and in vivo conditions in ovine and human arteries. Models analyzed include a four-parameter (linear) Kelvin viscoelastic model and two five-parameter nonlinear viscoelastic models (an arctangent and a sigmoid model) that relate changes in arterial blood pressure to the vessel cross-sectional area (via estimation of vessel strain). These models were developed using the framework of Quasilinear Viscoelasticity (QLV) theory and were validated using measurements from the thoracic descending aorta and the carotid artery obtained from human and ovine arteries. In vivo measurements were obtained from ten ovine aortas and ten human carotid arteries. Ex vivo measurements (from both locations) were made in eleven male Merino sheep. Biomechanical properties were obtained through constrained estimation of model parameters. To further investigate the parameter estimates we computed standard errors and confidence intervals and we used analysis of variance to compare results within and between groups. Overall, our results indicate that optimal model selection depends on the arterial type. Results showed that for the thoracic descending aorta (under both experimental conditions) the best predictions were obtained with the nonlinear sigmoid model, while under healthy physiological pressure loading the carotid arteries nonlinear stiffening with increasing pressure is negligible, and consequently, the linear (Kelvin) viscoelastic model better describes the pressure-area dynamics in this vessel. Results comparing biomechanical properties show that the Kelvin and sigmoid models were able to predict the zero-pressure vessel radius; that under ex vivo conditions vessels are more rigid, and comparatively, that the carotid artery is stiffer than the thoracic descending aorta; and that the viscoelastic gain and relaxation parameters do not differ significantly between vessels or experimental conditions. In conclusion, our study demonstrates that the proposed models can predict pressure-area dynamics and that model parameters can be extracted for further interpretation of biomechanical properties. PMID:21203846

Use of the dispersion ratio in estimating the nonlinear properties of an object of diagnosis

NASA Technical Reports Server (NTRS)

Balitskiy, F. Y.; Genkin, M. D.; Ivanova, M. A.; Kobrinskiy, A. A.; Sokolova, A. G.

1973-01-01

An experimental investigation for estimating the nonlinearity of a diagnostic object was carried out on a single-stage, spur gear reducer. The linearity of the properties of spur gearing (including the linearity of its mode of operation) was tested. Torsional vibrations of the driven wheel and transverse (to the meshing plane) vibrations of the drive wheel on its support were taken as the two outputs of the object to be analyzed. The results of the investigation showed that the degree of nonlinearity of a reducing gear is essentially connected with its operating mode, so that different mathematical models of it can correspond to different values of the system parameters.

Comparison of two non-convex mixed-integer nonlinear programming algorithms applied to autoregressive moving average model structure and parameter estimation

NASA Astrophysics Data System (ADS)

Uilhoorn, F. E.

2016-10-01

In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.

Noniterative estimation of a nonlinear parameter

NASA Technical Reports Server (NTRS)

Bergstroem, A.

1973-01-01

An algorithm is described which solves the parameters X = (x1,x2,...,xm) and p in an approximation problem Ax nearly equal to y(p), where the parameter p occurs nonlinearly in y. Instead of linearization methods, which require an approximate value of p to be supplied as a priori information, and which may lead to the finding of local minima, the proposed algorithm finds the global minimum by permitting the use of series expansions of arbitrary order, exploiting an a priori knowledge that the addition of a particular function, corresponding to a new column in A, will not improve the goodness of the approximation.

Multistage degradation modeling for BLDC motor based on Wiener process

NASA Astrophysics Data System (ADS)

Yuan, Qingyang; Li, Xiaogang; Gao, Yuankai

2018-05-01

Brushless DC motors are widely used, and their working temperatures, regarding as degradation processes, are nonlinear and multistage. It is necessary to establish a nonlinear degradation model. In this research, our study was based on accelerated degradation data of motors, which are their working temperatures. A multistage Wiener model was established by using the transition function to modify linear model. The normal weighted average filter (Gauss filter) was used to improve the results of estimation for the model parameters. Then, to maximize likelihood function for parameter estimation, we used numerical optimization method- the simplex method for cycle calculation. Finally, the modeling results show that the degradation mechanism changes during the degradation of the motor with high speed. The effectiveness and rationality of model are verified by comparison of the life distribution with widely used nonlinear Wiener model, as well as a comparison of QQ plots for residual. Finally, predictions for motor life are gained by life distributions in different times calculated by multistage model.

Validation of Bayesian analysis of compartmental kinetic models in medical imaging.

PubMed

Sitek, Arkadiusz; Li, Quanzheng; El Fakhri, Georges; Alpert, Nathaniel M

2016-10-01

Kinetic compartmental analysis is frequently used to compute physiologically relevant quantitative values from time series of images. In this paper, a new approach based on Bayesian analysis to obtain information about these parameters is presented and validated. The closed-form of the posterior distribution of kinetic parameters is derived with a hierarchical prior to model the standard deviation of normally distributed noise. Markov chain Monte Carlo methods are used for numerical estimation of the posterior distribution. Computer simulations of the kinetics of F18-fluorodeoxyglucose (FDG) are used to demonstrate drawing statistical inferences about kinetic parameters and to validate the theory and implementation. Additionally, point estimates of kinetic parameters and covariance of those estimates are determined using the classical non-linear least squares approach. Posteriors obtained using methods proposed in this work are accurate as no significant deviation from the expected shape of the posterior was found (one-sided P>0.08). It is demonstrated that the results obtained by the standard non-linear least-square methods fail to provide accurate estimation of uncertainty for the same data set (P<0.0001). The results of this work validate new methods for a computer simulations of FDG kinetics. Results show that in situations where the classical approach fails in accurate estimation of uncertainty, Bayesian estimation provides an accurate information about the uncertainties in the parameters. Although a particular example of FDG kinetics was used in the paper, the methods can be extended for different pharmaceuticals and imaging modalities. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Analysis of longitudinal data of beef cattle raised on pasture from northern Brazil using nonlinear models.

PubMed

Lopes, Fernando B; da Silva, Marcelo C; Marques, Ednira G; McManus, Concepta M

2012-12-01

This study was undertaken to aim of estimating the genetic parameters and trends for asymptotic weight (A) and maturity rate (k) of Nellore cattle from northern Brazil. The data set was made available by the Brazilian Association of Zebu Breeders and collected between the years of 1997 and 2007. The Von Bertalanffy, Brody, Gompertz, and logistic nonlinear models were fitted by the Gauss-Newton method to weight-age data of 45,895 animals collected quarterly of the birth to 750 days old. The curve parameters were analyzed using the procedures GLM and CORR. The estimation of (co)variance components and genetic parameters was obtained using the MTDFREML software. The estimated heritability coefficients were 0.21 ± 0.013 and 0.25 ± 0.014 for asymptotic weight and maturity rate, respectively. This indicates that selection for any trait shall results in genetic progress in the herd. The genetic correlation between A and k was negative (-0.57 ± 0.03) and indicated that animals selected for high maturity rate shall result in low asymptotic weight. The Von Bertalanffy function is adequate to establish the mean growth patterns and to predict the adult weight of Nellore cattle. This model is more accurate in predicting the birth weight of these animals and has better overall fit. The prediction of adult weight using nonlinear functions can be accurate when growth curve parameters and their (co)variance components are estimated jointly. The model used in this study can be applied to the prediction of mature weight in herds where a portion of the animals are culled before they reach the adult age.

Nonlinear dynamics applied to the study of cardiovascular effects of stress

NASA Astrophysics Data System (ADS)

Anishchenko, T. G.; Igosheva, N. B.

1998-03-01

We study cardiovascular responses to emotional stresses in humans and rats using traditional physiological parameters and methods of nonlinear dynamics. We found that emotional stress results in significant changes of chaos degree of ECG and blood pressure signals, estimated using a normalized entropy. We demonstrate that the normalized entropy is a more sensitive indicator of the stress-induced changes in cardiovascular systems compared with traditional physiological parameters Using the normalized entropy we discovered the significant individual differences in cardiovascular stress-reactivity that was impossible to obtain by traditional physiological methods.

State and Parameter Estimation for a Coupled Ocean--Atmosphere Model

NASA Astrophysics Data System (ADS)

Ghil, M.; Kondrashov, D.; Sun, C.

2006-12-01

The El-Nino/Southern-Oscillation (ENSO) dominates interannual climate variability and plays, therefore, a key role in seasonal-to-interannual prediction. Much is known by now about the main physical mechanisms that give rise to and modulate ENSO, but the values of several parameters that enter these mechanisms are an important unknown. We apply Extended Kalman Filtering (EKF) for both model state and parameter estimation in an intermediate, nonlinear, coupled ocean--atmosphere model of ENSO. The coupled model consists of an upper-ocean, reduced-gravity model of the Tropical Pacific and a steady-state atmospheric response to the sea surface temperature (SST). The model errors are assumed to be mainly in the atmospheric wind stress, and assimilated data are equatorial Pacific SSTs. Model behavior is very sensitive to two key parameters: (i) μ, the ocean-atmosphere coupling coefficient between SST and wind stress anomalies; and (ii) δs, the surface-layer coefficient. Previous work has shown that δs determines the period of the model's self-sustained oscillation, while μ measures the degree of nonlinearity. Depending on the values of these parameters, the spatio-temporal pattern of model solutions is either that of a delayed oscillator or of a westward propagating mode. Estimation of these parameters is tested first on synthetic data and allows us to recover the delayed-oscillator mode starting from model parameter values that correspond to the westward-propagating case. Assimilation of SST data from the NCEP-NCAR Reanalysis-2 shows that the parameters can vary on fairly short time scales and switch between values that approximate the two distinct modes of ENSO behavior. Rapid adjustments of these parameters occur, in particular, during strong ENSO events. Ways to apply EKF parameter estimation efficiently to state-of-the-art coupled ocean--atmosphere GCMs will be discussed.

Sequential state estimation of nonlinear/non-Gaussian systems with stochastic input for turbine degradation estimation

NASA Astrophysics Data System (ADS)

Hanachi, Houman; Liu, Jie; Banerjee, Avisekh; Chen, Ying

2016-05-01

Health state estimation of inaccessible components in complex systems necessitates effective state estimation techniques using the observable variables of the system. The task becomes much complicated when the system is nonlinear/non-Gaussian and it receives stochastic input. In this work, a novel sequential state estimation framework is developed based on particle filtering (PF) scheme for state estimation of general class of nonlinear dynamical systems with stochastic input. Performance of the developed framework is then validated with simulation on a Bivariate Non-stationary Growth Model (BNGM) as a benchmark. In the next step, three-year operating data of an industrial gas turbine engine (GTE) are utilized to verify the effectiveness of the developed framework. A comprehensive thermodynamic model for the GTE is therefore developed to formulate the relation of the observable parameters and the dominant degradation symptoms of the turbine, namely, loss of isentropic efficiency and increase of the mass flow. The results confirm the effectiveness of the developed framework for simultaneous estimation of multiple degradation symptoms in complex systems with noisy measured inputs.

A New Formulation of the Filter-Error Method for Aerodynamic Parameter Estimation in Turbulence

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2015-01-01

A new formulation of the filter-error method for estimating aerodynamic parameters in nonlinear aircraft dynamic models during turbulence was developed and demonstrated. The approach uses an estimate of the measurement noise covariance to identify the model parameters, their uncertainties, and the process noise covariance, in a relaxation method analogous to the output-error method. Prior information on the model parameters and uncertainties can be supplied, and a post-estimation correction to the uncertainty was included to account for colored residuals not considered in the theory. No tuning parameters, needing adjustment by the analyst, are used in the estimation. The method was demonstrated in simulation using the NASA Generic Transport Model, then applied to the subscale T-2 jet-engine transport aircraft flight. Modeling results in different levels of turbulence were compared with results from time-domain output error and frequency- domain equation error methods to demonstrate the effectiveness of the approach.

Online Estimation of Model Parameters of Lithium-Ion Battery Using the Cubature Kalman Filter

NASA Astrophysics Data System (ADS)

Tian, Yong; Yan, Rusheng; Tian, Jindong; Zhou, Shijie; Hu, Chao

2017-11-01

Online estimation of state variables, including state-of-charge (SOC), state-of-energy (SOE) and state-of-health (SOH) is greatly crucial for the operation safety of lithium-ion battery. In order to improve estimation accuracy of these state variables, a precise battery model needs to be established. As the lithium-ion battery is a nonlinear time-varying system, the model parameters significantly vary with many factors, such as ambient temperature, discharge rate and depth of discharge, etc. This paper presents an online estimation method of model parameters for lithium-ion battery based on the cubature Kalman filter. The commonly used first-order resistor-capacitor equivalent circuit model is selected as the battery model, based on which the model parameters are estimated online. Experimental results show that the presented method can accurately track the parameters variation at different scenarios.

Five parameters for the evaluation of the soil nonlinearity during the Ms8.0 Wenchuan Earthquake using the HVSR method

NASA Astrophysics Data System (ADS)

Ren, Yefei; Wen, Ruizhi; Yao, Xinxin; Ji, Kun

2017-08-01

The consideration of soil nonlinearity is important for the accurate estimation of the site response. To evaluate the soil nonlinearity during the 2008 Ms8.0 Wenchuan Earthquake, 33 strong-motion records obtained from the main shock and 890 records from 157 aftershocks were collected for this study. The horizontal-to-vertical spectral ratio (HVSR) method was used to calculate five parameters: the ratio of predominant frequency (RFp), degree of nonlinearity (DNL), absolute degree of nonlinearity (ADNL), frequency of nonlinearity (fNL), and percentage of nonlinearity (PNL). The purpose of this study was to evaluate the soil nonlinearity level of 33 strong-motion stations and to investigate the characteristics, performance, and effective usage of these five parameters. Their correlations with the peak ground acceleration (PGA), peak ground velocity (PGV), average uppermost 30-m shear-wave velocity ( V S30), and maximum amplitude of HVSR ( A max) were investigated. The results showed that all five parameters correlate well with PGA and PGV. The DNL, ADNL, and PNL also show a good correlation with A max, which means that the degree of soil nonlinearity not only depends on the ground-motion amplitude (e.g., PGA and PGV) but also on the site condition. The fNL correlates with PGA and PGV but shows no correlation with either A max or V S30, implying that the frequency width affected by the soil nonlinearity predominantly depends on the ground-motion amplitude rather than the site condition. At 16 of the 33 stations analyzed in this study, the site response showed evident (i.e., strong and medium) nonlinearity during the main shock of the Wenchuan Earthquake, where the ground-motion level was almost beyond the threshold of PGA > 200 cm/s2 or PGV > 15 cm/s. The site response showed weak and no nonlinearity at the other 14 and 3 stations. These results also confirm that RFp, DNL, ADNL, and PNL are effective in identifying the soil nonlinearity behavior. The identification results vary for different parameters because each parameter has individual features. The performance of the PNL was better than that of DNL and ADNL in this case study. The thresholds of ADNL and PNL are proposed to be 2.0 and 7%, respectively.[Figure not available: see fulltext.

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.

Space-dependent perfusion coefficient estimation in a 2D bioheat transfer problem

NASA Astrophysics Data System (ADS)

Bazán, Fermín S. V.; Bedin, Luciano; Borges, Leonardo S.

2017-05-01

In this work, a method for estimating the space-dependent perfusion coefficient parameter in a 2D bioheat transfer model is presented. In the method, the bioheat transfer model is transformed into a time-dependent semidiscrete system of ordinary differential equations involving perfusion coefficient values as parameters, and the estimation problem is solved through a nonlinear least squares technique. In particular, the bioheat problem is solved by the method of lines based on a highly accurate pseudospectral approach, and perfusion coefficient values are estimated by the regularized Gauss-Newton method coupled with a proper regularization parameter. The performance of the method on several test problems is illustrated numerically.

Estimation of parameters of constant elasticity of substitution production functional model

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi

2017-11-01

Nonlinear model building has become an increasing important powerful tool in mathematical economics. In recent years the popularity of applications of nonlinear models has dramatically been rising up. Several researchers in econometrics are very often interested in the inferential aspects of nonlinear regression models [6]. The present research study gives a distinct method of estimation of more complicated and highly nonlinear model viz Constant Elasticity of Substitution (CES) production functional model. Henningen et.al [5] proposed three solutions to avoid serious problems when estimating CES functions in 2012 and they are i) removing discontinuities by using the limits of the CES function and its derivative. ii) Circumventing large rounding errors by local linear approximations iii) Handling ill-behaved objective functions by a multi-dimensional grid search. Joel Chongeh et.al [7] discussed the estimation of the impact of capital and labour inputs to the gris output agri-food products using constant elasticity of substitution production function in Tanzanian context. Pol Antras [8] presented new estimates of the elasticity of substitution between capital and labour using data from the private sector of the U.S. economy for the period 1948-1998.

An improved swarm optimization for parameter estimation and biological model selection.

PubMed

Abdullah, Afnizanfaizal; Deris, Safaai; Mohamad, Mohd Saberi; Anwar, Sohail

2013-01-01

One of the key aspects of computational systems biology is the investigation on the dynamic biological processes within cells. Computational models are often required to elucidate the mechanisms and principles driving the processes because of the nonlinearity and complexity. The models usually incorporate a set of parameters that signify the physical properties of the actual biological systems. In most cases, these parameters are estimated by fitting the model outputs with the corresponding experimental data. However, this is a challenging task because the available experimental data are frequently noisy and incomplete. In this paper, a new hybrid optimization method is proposed to estimate these parameters from the noisy and incomplete experimental data. The proposed method, called Swarm-based Chemical Reaction Optimization, integrates the evolutionary searching strategy employed by the Chemical Reaction Optimization, into the neighbouring searching strategy of the Firefly Algorithm method. The effectiveness of the method was evaluated using a simulated nonlinear model and two biological models: synthetic transcriptional oscillators, and extracellular protease production models. The results showed that the accuracy and computational speed of the proposed method were better than the existing Differential Evolution, Firefly Algorithm and Chemical Reaction Optimization methods. The reliability of the estimated parameters was statistically validated, which suggests that the model outputs produced by these parameters were valid even when noisy and incomplete experimental data were used. Additionally, Akaike Information Criterion was employed to evaluate the model selection, which highlighted the capability of the proposed method in choosing a plausible model based on the experimental data. In conclusion, this paper presents the effectiveness of the proposed method for parameter estimation and model selection problems using noisy and incomplete experimental data. This study is hoped to provide a new insight in developing more accurate and reliable biological models based on limited and low quality experimental data.

On a Model of a Nonlinear Feedback System for River Flow Prediction

NASA Astrophysics Data System (ADS)

Ozaki, T.

1980-02-01

A nonlinear system with feedback is proposed as a dynamic model for the hydrological system, whose input is the rainfall and whose output is the discharge of river flow. Parameters and orders of the model are estimated using Akaike's information criterion. Its application to the prediction of daily discharges of Kanna River and Bird Creek is discussed.

Development of a shortleaf pine individual-tree growth equation using non-linear mixed modeling techniques

Treesearch

Chakra B. Budhathoki; Thomas B. Lynch; James M. Guldin

2010-01-01

Nonlinear mixed-modeling methods were used to estimate parameters in an individual-tree basal area growth model for shortleaf pine (Pinus echinata Mill.). Shortleaf pine individual-tree growth data were available from over 200 permanently established 0.2-acre fixed-radius plots located in naturally-occurring even-aged shortleaf pine forests on the...

Space Shuttle propulsion parameter estimation using optimal estimation techniques, volume 1

NASA Technical Reports Server (NTRS)

1983-01-01

The mathematical developments and their computer program implementation for the Space Shuttle propulsion parameter estimation project are summarized. The estimation approach chosen is the extended Kalman filtering with a modified Bryson-Frazier smoother. Its use here is motivated by the objective of obtaining better estimates than those available from filtering and to eliminate the lag associated with filtering. The estimation technique uses as the dynamical process the six degree equations-of-motion resulting in twelve state vector elements. In addition to these are mass and solid propellant burn depth as the ""system'' state elements. The ""parameter'' state elements can include aerodynamic coefficient, inertia, center-of-gravity, atmospheric wind, etc. deviations from referenced values. Propulsion parameter state elements have been included not as options just discussed but as the main parameter states to be estimated. The mathematical developments were completed for all these parameters. Since the systems dynamics and measurement processes are non-linear functions of the states, the mathematical developments are taken up almost entirely by the linearization of these equations as required by the estimation algorithms.

Energy spectra of X-ray clusters of galaxies

NASA Technical Reports Server (NTRS)

Avni, Y.

1976-01-01

A procedure for estimating the ranges of parameters that describe the spectra of X-rays from clusters of galaxies is presented. The applicability of the method is proved by statistical simulations of cluster spectra; such a proof is necessary because of the nonlinearity of the spectral functions. Implications for the spectra of the Perseus, Coma, and Virgo clusters are discussed. The procedure can be applied in more general problems of parameter estimation.

NLINEAR - NONLINEAR CURVE FITTING PROGRAM

NASA Technical Reports Server (NTRS)

Everhart, J. L.

1994-01-01

A common method for fitting data is a least-squares fit. In the least-squares method, a user-specified fitting function is utilized in such a way as to minimize the sum of the squares of distances between the data points and the fitting curve. The Nonlinear Curve Fitting Program, NLINEAR, is an interactive curve fitting routine based on a description of the quadratic expansion of the chi-squared statistic. NLINEAR utilizes a nonlinear optimization algorithm that calculates the best statistically weighted values of the parameters of the fitting function and the chi-square that is to be minimized. The inputs to the program are the mathematical form of the fitting function and the initial values of the parameters to be estimated. This approach provides the user with statistical information such as goodness of fit and estimated values of parameters that produce the highest degree of correlation between the experimental data and the mathematical model. In the mathematical formulation of the algorithm, the Taylor expansion of chi-square is first introduced, and justification for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations are derived, which are solved by matrix algebra. To achieve convergence, the algorithm requires meaningful initial estimates for the parameters of the fitting function. NLINEAR is written in Fortran 77 for execution on a CDC Cyber 750 under NOS 2.3. It has a central memory requirement of 5K 60 bit words. Optionally, graphical output of the fitting function can be plotted. Tektronix PLOT-10 routines are required for graphics. NLINEAR was developed in 1987.

Experimental Design for Stochastic Models of Nonlinear Signaling Pathways Using an Interval-Wise Linear Noise Approximation and State Estimation.

PubMed

Zimmer, Christoph

2016-01-01

Computational modeling is a key technique for analyzing models in systems biology. There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE). Experimental design techniques aim at devising experiments that maximize the information encoded in the data. For ODE models there are well established approaches for experimental design and even software tools. However, data from single cell experiments on signaling pathways in systems biology often shows intrinsic stochastic effects prompting the development of specialized methods. While simulation methods have been developed for decades and parameter estimation has been targeted for the last years, only very few articles focus on experimental design for stochastic models. The Fisher information matrix is the central measure for experimental design as it evaluates the information an experiment provides for parameter estimation. This article suggest an approach to calculate a Fisher information matrix for models containing intrinsic stochasticity and high nonlinearity. The approach makes use of a recently suggested multiple shooting for stochastic systems (MSS) objective function. The Fisher information matrix is calculated by evaluating pseudo data with the MSS technique. The performance of the approach is evaluated with simulation studies on an Immigration-Death, a Lotka-Volterra, and a Calcium oscillation model. The Calcium oscillation model is a particularly appropriate case study as it contains the challenges inherent to signaling pathways: high nonlinearity, intrinsic stochasticity, a qualitatively different behavior from an ODE solution, and partial observability. The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models.

Modeling nonlinear responses of DOC transport in boreal catchments in Sweden

NASA Astrophysics Data System (ADS)

Kasurinen, Ville; Alfredsen, Knut; Ojala, Anne; Pumpanen, Jukka; Weyhenmeyer, Gesa A.; Futter, Martyn N.; Laudon, Hjalmar; Berninger, Frank

2016-07-01

Stream water dissolved organic carbon (DOC) concentrations display high spatial and temporal variation in boreal catchments. Understanding and predicting these patterns is a challenge with great implications for water quality projections and carbon balance estimates. Although several biogeochemical models have been used to estimate stream water DOC dynamics, model biases common during both rain and snow melt-driven events. The parsimonious DOC-model, K-DOC, with 10 calibrated parameters, uses a nonlinear discharge and catchment water storage relationship including soil temperature dependencies of DOC release and consumption. K-DOC was used to estimate the stream water DOC concentrations over 5 years for eighteen nested boreal catchments having total area of 68 km2 (varying from 0.04 to 67.9 km2). The model successfully simulated DOC concentrations during base flow conditions, as well as, hydrological events in catchments dominated by organic and mineral soils reaching NSEs from 0.46 to 0.76. Our semimechanistic model was parsimonious enough to have all parameters estimated using statistical methods. We did not find any clear differences between forest and mire-dominated catchments that could be explained by soil type or tree species composition. However, parameters controlling slow release and consumption of DOC from soil water behaved differently for small headwater catchments (less than 2 km2) than for those that integrate larger areas of different ecosystem types (10-68 km2). Our results emphasize that it is important to account for nonlinear dependencies of both, soil temperature, and catchment water storage, when simulating DOC dynamics of boreal catchments.

Influence of nonlinear detuning at plasma wavebreaking threshold on backward Raman compression of non-relativistic laser pulses

NASA Astrophysics Data System (ADS)

Balakin, A. A.; Fraiman, G. M.; Jia, Q.; Fisch, N. J.

2018-06-01

Taking into account the nonlinear dispersion of the plasma wave, the fluid equations for the three-wave (Raman) interaction in plasmas are derived. It is found that, in some parameter regimes, the nonlinear detuning resulting from the plasma wave dispersion during Raman compression limits the plasma wave amplitude to noticeably below the generally recognized wavebreaking threshold. Particle-in-cell simulations confirm the theoretical estimates. For weakly nonlinear dispersion, the detuning effect can be counteracted by pump chirping or, equivalently, by upshifting slightly the pump frequency, so that the frequency-upshifted pump interacts with the seed at the point where the plasma wave enters the nonlinear stage.

Continuous wavelet transform based time-scale and multifractal analysis of the nonlinear oscillations in a hollow cathode glow discharge plasma

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

Nurujjaman, Md.; Narayanan, Ramesh; Iyengar, A. N. Sekar

2009-10-15

Continuous wavelet transform (CWT) based time-scale and multifractal analyses have been carried out on the anode glow related nonlinear floating potential fluctuations in a hollow cathode glow discharge plasma. CWT has been used to obtain the contour and ridge plots. Scale shift (or inversely frequency shift), which is a typical nonlinear behavior, has been detected from the undulating contours. From the ridge plots, we have identified the presence of nonlinearity and degree of chaoticity. Using the wavelet transform modulus maxima technique we have obtained the multifractal spectrum for the fluctuations at different discharge voltages and the spectrum was observed tomore » become a monofractal for periodic signals. These multifractal spectra were also used to estimate different quantities such as the correlation and fractal dimension, degree of multifractality, and complexity parameters. These estimations have been found to be consistent with the nonlinear time series analysis.« less

Cardiovascular oscillations: in search of a nonlinear parametric model

NASA Astrophysics Data System (ADS)

Bandrivskyy, Andriy; Luchinsky, Dmitry; McClintock, Peter V.; Smelyanskiy, Vadim; Stefanovska, Aneta; Timucin, Dogan

2003-05-01

We suggest a fresh approach to the modeling of the human cardiovascular system. Taking advantage of a new Bayesian inference technique, able to deal with stochastic nonlinear systems, we show that one can estimate parameters for models of the cardiovascular system directly from measured time series. We present preliminary results of inference of parameters of a model of coupled oscillators from measured cardiovascular data addressing cardiorespiratory interaction. We argue that the inference technique offers a very promising tool for the modeling, able to contribute significantly towards the solution of a long standing challenge -- development of new diagnostic techniques based on noninvasive measurements.

Desired Accuracy Estimation of Noise Function from ECG Signal by Fuzzy Approach

PubMed Central

Vahabi, Zahra; Kermani, Saeed

2012-01-01

Unknown noise and artifacts present in medical signals with non-linear fuzzy filter will be estimated and then removed. An adaptive neuro-fuzzy interference system which has a non-linear structure presented for the noise function prediction by before Samples. This paper is about a neuro-fuzzy method to estimate unknown noise of Electrocardiogram signal. Adaptive neural combined with Fuzzy System to construct a fuzzy Predictor. For this system setting parameters such as the number of Membership Functions for each input and output, training epochs, type of MFs for each input and output, learning algorithm and etc. is determined by learning data. At the end simulated experimental results are presented for proper validation. PMID:23717810

Neural networks for tracking of unknown SISO discrete-time nonlinear dynamic systems.

PubMed

Aftab, Muhammad Saleheen; Shafiq, Muhammad

2015-11-01

This article presents a Lyapunov function based neural network tracking (LNT) strategy for single-input, single-output (SISO) discrete-time nonlinear dynamic systems. The proposed LNT architecture is composed of two feedforward neural networks operating as controller and estimator. A Lyapunov function based back propagation learning algorithm is used for online adjustment of the controller and estimator parameters. The controller and estimator error convergence and closed-loop system stability analysis is performed by Lyapunov stability theory. Moreover, two simulation examples and one real-time experiment are investigated as case studies. The achieved results successfully validate the controller performance. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis :

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

Adams, Brian M.; Ebeida, Mohamed Salah; Eldred, Michael S.

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components requiredmore » for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.« less

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

Parameter estimation and sensitivity analysis for a mathematical model with time delays of leukemia

NASA Astrophysics Data System (ADS)

Cândea, Doina; Halanay, Andrei; Rǎdulescu, Rodica; Tǎlmaci, Rodica

2017-01-01

We consider a system of nonlinear delay differential equations that describes the interaction between three competing cell populations: healthy, leukemic and anti-leukemia T cells involved in Chronic Myeloid Leukemia (CML) under treatment with Imatinib. The aim of this work is to establish which model parameters are the most important in the success or failure of leukemia remission under treatment using a sensitivity analysis of the model parameters. For the most significant parameters of the model which affect the evolution of CML disease during Imatinib treatment we try to estimate the realistic values using some experimental data. For these parameters, steady states are calculated and their stability is analyzed and biologically interpreted.

Multimodality CT/SPECT Evaluation of Micelle Drug Carriers for Treatment of Breast Tumors

DTIC Science & Technology

2007-07-01

lap diffusion, Dh and Df, were then calculated using non-linear least squares parameter estimation ( Matlab 7.1). Dh and Df were estimated using release... entanglement serves as a much greater impediment to drug transport. 3.4. Mechanism of action of cell death induced by β-lap micelles Growth assays

HIV Model Parameter Estimates from Interruption Trial Data including Drug Efficacy and Reservoir Dynamics

PubMed Central

Luo, Rutao; Piovoso, Michael J.; Martinez-Picado, Javier; Zurakowski, Ryan

2012-01-01

Mathematical models based on ordinary differential equations (ODE) have had significant impact on understanding HIV disease dynamics and optimizing patient treatment. A model that characterizes the essential disease dynamics can be used for prediction only if the model parameters are identifiable from clinical data. Most previous parameter identification studies for HIV have used sparsely sampled data from the decay phase following the introduction of therapy. In this paper, model parameters are identified from frequently sampled viral-load data taken from ten patients enrolled in the previously published AutoVac HAART interruption study, providing between 69 and 114 viral load measurements from 3–5 phases of viral decay and rebound for each patient. This dataset is considerably larger than those used in previously published parameter estimation studies. Furthermore, the measurements come from two separate experimental conditions, which allows for the direct estimation of drug efficacy and reservoir contribution rates, two parameters that cannot be identified from decay-phase data alone. A Markov-Chain Monte-Carlo method is used to estimate the model parameter values, with initial estimates obtained using nonlinear least-squares methods. The posterior distributions of the parameter estimates are reported and compared for all patients. PMID:22815727

On the orthogonalised reverse path method for nonlinear system identification

NASA Astrophysics Data System (ADS)

Muhamad, P.; Sims, N. D.; Worden, K.

2012-09-01

The problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general multi-degree-of-freedom (MDOF) system can be solved using the conditioned reverse path (CRP) method introduced by Richards and Singh (1998 Journal of Sound and Vibration, 213(4): pp. 673-708). The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion. Although the CRP has proved extremely useful in the context of nonlinear system identification, it has a number of small issues associated with it. One of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti-resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors. The first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm. The results are demonstrated on numerically-simulated responses from MDOF systems. In the second part of the paper, a more radical suggestion is made, to replace the conditioned spectral analysis (which is the basis of the CRP method) with an alternative time domain decorrelation method. The suggested approach - the orthogonalised reverse path (ORP) method - is illustrated here using data from simulated single-degree-of-freedom (SDOF) and MDOF systems.

Implementation of an Integrated On-Board Aircraft Engine Diagnostic Architecture

NASA Technical Reports Server (NTRS)

Armstrong, Jeffrey B.; Simon, Donald L.

2012-01-01

An on-board diagnostic architecture for aircraft turbofan engine performance trending, parameter estimation, and gas-path fault detection and isolation has been developed and evaluated in a simulation environment. The architecture incorporates two independent models: a realtime self-tuning performance model providing parameter estimates and a performance baseline model for diagnostic purposes reflecting long-term engine degradation trends. This architecture was evaluated using flight profiles generated from a nonlinear model with realistic fleet engine health degradation distributions and sensor noise. The architecture was found to produce acceptable estimates of engine health and unmeasured parameters, and the integrated diagnostic algorithms were able to perform correct fault isolation in approximately 70 percent of the tested cases

Parameter estimation procedure for complex non-linear systems: calibration of ASM No. 1 for N-removal in a full-scale oxidation ditch.

PubMed

Abusam, A; Keesman, K J; van Straten, G; Spanjers, H; Meinema, K

2001-01-01

When applied to large simulation models, the process of parameter estimation is also called calibration. Calibration of complex non-linear systems, such as activated sludge plants, is often not an easy task. On the one hand, manual calibration of such complex systems is usually time-consuming, and its results are often not reproducible. On the other hand, conventional automatic calibration methods are not always straightforward and often hampered by local minima problems. In this paper a new straightforward and automatic procedure, which is based on the response surface method (RSM) for selecting the best identifiable parameters, is proposed. In RSM, the process response (output) is related to the levels of the input variables in terms of a first- or second-order regression model. Usually, RSM is used to relate measured process output quantities to process conditions. However, in this paper RSM is used for selecting the dominant parameters, by evaluating parameters sensitivity in a predefined region. Good results obtained in calibration of ASM No. 1 for N-removal in a full-scale oxidation ditch proved that the proposed procedure is successful and reliable.

Estimating procedure times for surgeries by determining location parameters for the lognormal model.

PubMed

Spangler, William E; Strum, David P; Vargas, Luis G; May, Jerrold H

2004-05-01

We present an empirical study of methods for estimating the location parameter of the lognormal distribution. Our results identify the best order statistic to use, and indicate that using the best order statistic instead of the median may lead to less frequent incorrect rejection of the lognormal model, more accurate critical value estimates, and higher goodness-of-fit. Using simulation data, we constructed and compared two models for identifying the best order statistic, one based on conventional nonlinear regression and the other using a data mining/machine learning technique. Better surgical procedure time estimates may lead to improved surgical operations.

Linear functional minimization for inverse modeling

DOE PAGES

Barajas-Solano, David A.; Wohlberg, Brendt Egon; Vesselinov, Velimir Valentinov; ...

2015-06-01

In this paper, we present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulicmore » head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Finally, addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.« less

Information measures in nonlinear experimental design

NASA Technical Reports Server (NTRS)

Niple, E.; Shaw, J. H.

1980-01-01

Some different approaches to the problem of designing experiments which estimate the parameters of nonlinear models are discussed. The assumption in these approaches that the information in a set of data can be represented by a scalar is criticized, and the nonscalar discrimination information is proposed as the proper measure to use. The two-step decay example in Box and Lucas (1959) is used to illustrate the main points of the discussion.

Model-based damage evaluation of layered CFRP structures

NASA Astrophysics Data System (ADS)

Munoz, Rafael; Bochud, Nicolas; Rus, Guillermo; Peralta, Laura; Melchor, Juan; Chiachío, Juan; Chiachío, Manuel; Bond, Leonard J.

2015-03-01

An ultrasonic evaluation technique for damage identification of layered CFRP structures is presented. This approach relies on a model-based estimation procedure that combines experimental data and simulation of ultrasonic damage-propagation interactions. The CFPR structure, a [0/90]4s lay-up, has been tested in an immersion through transmission experiment, where a scan has been performed on a damaged specimen. Most ultrasonic techniques in industrial practice consider only a few features of the received signals, namely, time of flight, amplitude, attenuation, frequency contents, and so forth. In this case, once signals are captured, an algorithm is used to reconstruct the complete signal waveform and extract the unknown damage parameters by means of modeling procedures. A linear version of the data processing has been performed, where only Young modulus has been monitored and, in a second nonlinear version, the first order nonlinear coefficient β was incorporated to test the possibility of detection of early damage. The aforementioned physical simulation models are solved by the Transfer Matrix formalism, which has been extended from linear to nonlinear harmonic generation technique. The damage parameter search strategy is based on minimizing the mismatch between the captured and simulated signals in the time domain in an automated way using Genetic Algorithms. Processing all scanned locations, a C-scan of the parameter of each layer can be reconstructed, obtaining the information describing the state of each layer and each interface. Damage can be located and quantified in terms of changes in the selected parameter with a measurable extension. In the case of the nonlinear coefficient of first order, evidence of higher sensitivity to damage than imaging the linearly estimated Young Modulus is provided.

A robust nonlinear position observer for synchronous motors with relaxed excitation conditions

NASA Astrophysics Data System (ADS)

Bobtsov, Alexey; Bazylev, Dmitry; Pyrkin, Anton; Aranovskiy, Stanislav; Ortega, Romeo

2017-04-01

A robust, nonlinear and globally convergent rotor position observer for surface-mounted permanent magnet synchronous motors was recently proposed by the authors. The key feature of this observer is that it requires only the knowledge of the motor's resistance and inductance. Using some particular properties of the mathematical model it is shown that the problem of state observation can be translated into one of estimation of two constant parameters, which is carried out with a standard gradient algorithm. In this work, we propose to replace this estimator with a new one called dynamic regressor extension and mixing, which has the following advantages with respect to gradient estimators: (1) the stringent persistence of excitation (PE) condition of the regressor is not necessary to ensure parameter convergence; (2) the latter is guaranteed requiring instead a non-square-integrability condition that has a clear physical meaning in terms of signal energy; (3) if the regressor is PE, the new observer (like the old one) ensures convergence is exponential, entailing some robustness properties to the observer; (4) the new estimator includes an additional filter that constitutes an additional degree of freedom to satisfy the non-square integrability condition. Realistic simulation results show significant performance improvement of the position observer using the new parameter estimator, with a less oscillatory behaviour and a faster convergence speed.

Power capability evaluation for lithium iron phosphate batteries based on multi-parameter constraints estimation

NASA Astrophysics Data System (ADS)

Wang, Yujie; Pan, Rui; Liu, Chang; Chen, Zonghai; Ling, Qiang

2018-01-01

The battery power capability is intimately correlated with the climbing, braking and accelerating performance of the electric vehicles. Accurate power capability prediction can not only guarantee the safety but also regulate driving behavior and optimize battery energy usage. However, the nonlinearity of the battery model is very complex especially for the lithium iron phosphate batteries. Besides, the hysteresis loop in the open-circuit voltage curve is easy to cause large error in model prediction. In this work, a multi-parameter constraints dynamic estimation method is proposed to predict the battery continuous period power capability. A high-fidelity battery model which considers the battery polarization and hysteresis phenomenon is presented to approximate the high nonlinearity of the lithium iron phosphate battery. Explicit analyses of power capability with multiple constraints are elaborated, specifically the state-of-energy is considered in power capability assessment. Furthermore, to solve the problem of nonlinear system state estimation, and suppress noise interference, the UKF based state observer is employed for power capability prediction. The performance of the proposed methodology is demonstrated by experiments under different dynamic characterization schedules. The charge and discharge power capabilities of the lithium iron phosphate batteries are quantitatively assessed under different time scales and temperatures.

Application of a nonlinear slug test model

USGS Publications Warehouse

McElwee, C.D.

2001-01-01

Knowledge of the hydraulic conductivity distribution is of utmost importance in understanding the dynamics of an aquifer and in planning the consequences of any action taken upon that aquifer. Slug tests have been used extensively to measure hydraulic conductivity in the last 50 years since Hvorslev's (1951) work. A general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the wellbore, and a Hvorslev model for the aquifer has been implemented in this work. The nonlinear model has three parameters: ??, which is related primarily to radius changes in the water column; A, which is related to the nonlinear head losses; and K, the hydraulic conductivity. An additional parameter has been added representing the initial velocity of the water column at slug initiation and is incorporated into an analytical solution to generate the first time step before a sequential numerical solution generates the remainder of the time solution. Corrections are made to the model output for acceleration before it is compared to the experimental data. Sensitivity analysis and least squares fitting are used to estimate the aquifer parameters and produce some diagnostic results, which indicate the accuracy of the fit. Finally, an example of field data has been presented to illustrate the application of the model to data sets that exhibit nonlinear behavior. Multiple slug tests should be taken at a given location to test for nonlinear effects and to determine repeatability.

Evaluation of the site effect with Heuristic Methods

NASA Astrophysics Data System (ADS)

Torres, N. N.; Ortiz-Aleman, C.

2017-12-01

The seismic site response in an area depends mainly on the local geological and topographical conditions. Estimation of variations in ground motion can lead to significant contributions on seismic hazard assessment, in order to reduce human and economic losses. Site response estimation can be posed as a parameterized inversion approach which allows separating source and path effects. The generalized inversion (Field and Jacob, 1995) represents one of the alternative methods to estimate the local seismic response, which involves solving a strongly non-linear multiparametric problem. In this work, local seismic response was estimated using global optimization methods (Genetic Algorithms and Simulated Annealing) which allowed us to increase the range of explored solutions in a nonlinear search, as compared to other conventional linear methods. By using the VEOX Network velocity records, collected from August 2007 to March 2009, source, path and site parameters corresponding to the amplitude spectra of the S wave of the velocity seismic records are estimated. We can establish that inverted parameters resulting from this simultaneous inversion approach, show excellent agreement, not only in terms of adjustment between observed and calculated spectra, but also when compared to previous work from several authors.

Control of AUVs using differential flatness theory and the derivative-free nonlinear Kalman Filter

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Raffo, Guilerme

2015-12-01

The paper proposes nonlinear control and filtering for Autonomous Underwater Vessels (AUVs) based on differential flatness theory and on the use of the Derivative-free nonlinear Kalman Filter. First, it is shown that the 6-DOF dynamic model of the AUV is a differentially flat one. This enables its transformation into the linear canonical (Brunovsky) form and facilitates the design of a state feedback controller. A problem that has to be dealt with is the uncertainty about the parameters of the AUV's dynamic model, as well the external perturbations which affect its motion. To cope with this, it is proposed to use a disturbance observer which is based on the Derivative-free nonlinear Kalman Filter. The considered filtering method consists of the standard Kalman Filter recursion applied on the linearized model of the vessel and of an inverse transformation based on differential flatness theory, which enables to obtain estimates of the state variables of the initial nonlinear model of the vessel. The Kalman Filter-based disturbance observer performs simultaneous estimation of the non-measurable state variables of the AUV and of the perturbation terms that affect its dynamics. By estimating such disturbances, their compensation is also succeeded through suitable modification of the feedback control input. The efficiency of the proposed AUV control and estimation scheme is confirmed through simulation experiments.

Experimental Design for Stochastic Models of Nonlinear Signaling Pathways Using an Interval-Wise Linear Noise Approximation and State Estimation

PubMed Central

Zimmer, Christoph

2016-01-01

Background Computational modeling is a key technique for analyzing models in systems biology. There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE). Experimental design techniques aim at devising experiments that maximize the information encoded in the data. For ODE models there are well established approaches for experimental design and even software tools. However, data from single cell experiments on signaling pathways in systems biology often shows intrinsic stochastic effects prompting the development of specialized methods. While simulation methods have been developed for decades and parameter estimation has been targeted for the last years, only very few articles focus on experimental design for stochastic models. Methods The Fisher information matrix is the central measure for experimental design as it evaluates the information an experiment provides for parameter estimation. This article suggest an approach to calculate a Fisher information matrix for models containing intrinsic stochasticity and high nonlinearity. The approach makes use of a recently suggested multiple shooting for stochastic systems (MSS) objective function. The Fisher information matrix is calculated by evaluating pseudo data with the MSS technique. Results The performance of the approach is evaluated with simulation studies on an Immigration-Death, a Lotka-Volterra, and a Calcium oscillation model. The Calcium oscillation model is a particularly appropriate case study as it contains the challenges inherent to signaling pathways: high nonlinearity, intrinsic stochasticity, a qualitatively different behavior from an ODE solution, and partial observability. The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models. PMID:27583802

Parameters estimation for reactive transport: A way to test the validity of a reactive model

NASA Astrophysics Data System (ADS)

Aggarwal, Mohit; Cheikh Anta Ndiaye, Mame; Carrayrou, Jérôme

The chemical parameters used in reactive transport models are not known accurately due to the complexity and the heterogeneous conditions of a real domain. We will present an efficient algorithm in order to estimate the chemical parameters using Monte-Carlo method. Monte-Carlo methods are very robust for the optimisation of the highly non-linear mathematical model describing reactive transport. Reactive transport of tributyltin (TBT) through natural quartz sand at seven different pHs is taken as the test case. Our algorithm will be used to estimate the chemical parameters of the sorption of TBT onto the natural quartz sand. By testing and comparing three models of surface complexation, we show that the proposed adsorption model cannot explain the experimental data.

Fitting a Structured Juvenile-Adult Model for Green Tree Frogs to Population Estimates from Capture-Mark-Recapture Field Data

USGS Publications Warehouse

Ackleh, A.S.; Carter, J.; Deng, K.; Huang, Q.; Pal, N.; Yang, X.

2012-01-01

We derive point and interval estimates for an urban population of green tree frogs (Hyla cinerea) from capture-mark-recapture field data obtained during the years 2006-2009. We present an infinite-dimensional least-squares approach which compares a mathematical population model to the statistical population estimates obtained from the field data. The model is composed of nonlinear first-order hyperbolic equations describing the dynamics of the amphibian population where individuals are divided into juveniles (tadpoles) and adults (frogs). To solve the least-squares problem, an explicit finite difference approximation is developed. Convergence results for the computed parameters are presented. Parameter estimates for the vital rates of juveniles and adults are obtained, and standard deviations for these estimates are computed. Numerical results for the model sensitivity with respect to these parameters are given. Finally, the above-mentioned parameter estimates are used to illustrate the long-time behavior of the population under investigation. ?? 2011 Society for Mathematical Biology.

Estimation of groundwater recharge parameters by time series analysis

USGS Publications Warehouse

Naff, Richard L.; Gutjahr, Allan L.

1983-01-01

A model is proposed that relates water level fluctuations in a Dupuit aquifer to effective precipitaton at the top of the unsaturated zone. Effective precipitation, defined herein as that portion of precipitation which becomes recharge, is related to precipitation measured in a nearby gage by a two-parameter function. A second-order stationary assumption is used to connect the spectra of effective precipitation and water level fluctuations. Measured precipitation is assumed to be Gaussian, in order to develop a transfer function that relates the spectra of measured and effective precipitation. A nonlinear least squares technique is proposed for estimating parameters of the effective-precipitation function. Although sensitivity analyses indicate difficulties that may be encountered in the estimation procedure, the methods developed did yield convergent estimates for two case studies.

Elbow joint angle and elbow movement velocity estimation using NARX-multiple layer perceptron neural network model with surface EMG time domain parameters.

PubMed

Raj, Retheep; Sivanandan, K S

2017-01-01

Estimation of elbow dynamics has been the object of numerous investigations. In this work a solution is proposed for estimating elbow movement velocity and elbow joint angle from Surface Electromyography (SEMG) signals. Here the Surface Electromyography signals are acquired from the biceps brachii muscle of human hand. Two time-domain parameters, Integrated EMG (IEMG) and Zero Crossing (ZC), are extracted from the Surface Electromyography signal. The relationship between the time domain parameters, IEMG and ZC with elbow angular displacement and elbow angular velocity during extension and flexion of the elbow are studied. A multiple input-multiple output model is derived for identifying the kinematics of elbow. A Nonlinear Auto Regressive with eXogenous inputs (NARX) structure based multiple layer perceptron neural network (MLPNN) model is proposed for the estimation of elbow joint angle and elbow angular velocity. The proposed NARX MLPNN model is trained using Levenberg-marquardt based algorithm. The proposed model is estimating the elbow joint angle and elbow movement angular velocity with appreciable accuracy. The model is validated using regression coefficient value (R). The average regression coefficient value (R) obtained for elbow angular displacement prediction is 0.9641 and for the elbow anglular velocity prediction is 0.9347. The Nonlinear Auto Regressive with eXogenous inputs (NARX) structure based multiple layer perceptron neural networks (MLPNN) model can be used for the estimation of angular displacement and movement angular velocity of the elbow with good accuracy.

Estimation of real-time runway surface contamination using flight data recorder parameters

NASA Astrophysics Data System (ADS)

Curry, Donovan

Within this research effort, the development of an analytic process for friction coefficient estimation is presented. Under static equilibrium, the sum of forces and moments acting on the aircraft, in the aircraft body coordinate system, while on the ground at any instant is equal to zero. Under this premise the longitudinal, lateral and normal forces due to landing are calculated along with the individual deceleration components existent when an aircraft comes to a rest during ground roll. In order to validate this hypothesis a six degree of freedom aircraft model had to be created and landing tests had to be simulated on different surfaces. The simulated aircraft model includes a high fidelity aerodynamic model, thrust model, landing gear model, friction model and antiskid model. Three main surfaces were defined in the friction model; dry, wet and snow/ice. Only the parameters recorded by an FDR are used directly from the aircraft model all others are estimated or known a priori. The estimation of unknown parameters is also presented in the research effort. With all needed parameters a comparison and validation with simulated and estimated data, under different runway conditions, is performed. Finally, this report presents results of a sensitivity analysis in order to provide a measure of reliability of the analytic estimation process. Linear and non-linear sensitivity analysis has been performed in order to quantify the level of uncertainty implicit in modeling estimated parameters and how they can affect the calculation of the instantaneous coefficient of friction. Using the approach of force and moment equilibrium about the CG at landing to reconstruct the instantaneous coefficient of friction appears to be a reasonably accurate estimate when compared to the simulated friction coefficient. This is also true when the FDR and estimated parameters are introduced to white noise and when crosswind is introduced to the simulation. After the linear analysis the results show the minimum frequency at which the algorithm still provides moderately accurate data is at 2Hz. In addition, the linear analysis shows that with estimated parameters increased and decreased up to 25% at random, high priority parameters have to be accurate to within at least +/-5% to have an effect of less than 1% change in the average coefficient of friction. Non-linear analysis results show that the algorithm can be considered reasonably accurate for all simulated cases when inaccuracies in the estimated parameters vary randomly and simultaneously up to +/-27%. At worst-case the maximum percentage change in average coefficient of friction is less than 10% for all surfaces.

Fitting a defect non-linear model with or without prior, distinguishing nuclear reaction products as an example.

PubMed

Helgesson, P; Sjöstrand, H

2017-11-01

Fitting a parametrized function to data is important for many researchers and scientists. If the model is non-linear and/or defect, it is not trivial to do correctly and to include an adequate uncertainty analysis. This work presents how the Levenberg-Marquardt algorithm for non-linear generalized least squares fitting can be used with a prior distribution for the parameters and how it can be combined with Gaussian processes to treat model defects. An example, where three peaks in a histogram are to be distinguished, is carefully studied. In particular, the probability r 1 for a nuclear reaction to end up in one out of two overlapping peaks is studied. Synthetic data are used to investigate effects of linearizations and other assumptions. For perfect Gaussian peaks, it is seen that the estimated parameters are distributed close to the truth with good covariance estimates. This assumes that the method is applied correctly; for example, prior knowledge should be implemented using a prior distribution and not by assuming that some parameters are perfectly known (if they are not). It is also important to update the data covariance matrix using the fit if the uncertainties depend on the expected value of the data (e.g., for Poisson counting statistics or relative uncertainties). If a model defect is added to the peaks, such that their shape is unknown, a fit which assumes perfect Gaussian peaks becomes unable to reproduce the data, and the results for r 1 become biased. It is, however, seen that it is possible to treat the model defect with a Gaussian process with a covariance function tailored for the situation, with hyper-parameters determined by leave-one-out cross validation. The resulting estimates for r 1 are virtually unbiased, and the uncertainty estimates agree very well with the underlying uncertainty.

Fitting a defect non-linear model with or without prior, distinguishing nuclear reaction products as an example

NASA Astrophysics Data System (ADS)

Helgesson, P.; Sjöstrand, H.

2017-11-01

Fitting a parametrized function to data is important for many researchers and scientists. If the model is non-linear and/or defect, it is not trivial to do correctly and to include an adequate uncertainty analysis. This work presents how the Levenberg-Marquardt algorithm for non-linear generalized least squares fitting can be used with a prior distribution for the parameters and how it can be combined with Gaussian processes to treat model defects. An example, where three peaks in a histogram are to be distinguished, is carefully studied. In particular, the probability r1 for a nuclear reaction to end up in one out of two overlapping peaks is studied. Synthetic data are used to investigate effects of linearizations and other assumptions. For perfect Gaussian peaks, it is seen that the estimated parameters are distributed close to the truth with good covariance estimates. This assumes that the method is applied correctly; for example, prior knowledge should be implemented using a prior distribution and not by assuming that some parameters are perfectly known (if they are not). It is also important to update the data covariance matrix using the fit if the uncertainties depend on the expected value of the data (e.g., for Poisson counting statistics or relative uncertainties). If a model defect is added to the peaks, such that their shape is unknown, a fit which assumes perfect Gaussian peaks becomes unable to reproduce the data, and the results for r1 become biased. It is, however, seen that it is possible to treat the model defect with a Gaussian process with a covariance function tailored for the situation, with hyper-parameters determined by leave-one-out cross validation. The resulting estimates for r1 are virtually unbiased, and the uncertainty estimates agree very well with the underlying uncertainty.

Modeling actual evapotranspiration with routine meteorological variables in the data-scarce region of the Tibetan Plateau: Comparisons and implications

NASA Astrophysics Data System (ADS)

Ma, Ning; Zhang, Yinsheng; Xu, Chong-Yu; Szilagyi, Jozsef

2015-08-01

Quantitative estimation of actual evapotranspiration (ETa) by in situ measurements and mathematical modeling is a fundamental task for physical understanding of ETa as well as the feedback mechanisms between land and the ambient atmosphere. However, the ETa information in the Tibetan Plateau (TP) has been greatly impeded by the extremely sparse ground observation network in the region. Approaches for estimating ETa solely from routine meteorological variables are therefore important for investigating spatiotemporal variations of ETa in the data-scarce region of the TP. Motivated by this need, the complementary relationship (CR) and Penman-Monteith approaches were evaluated against in situ measurements of ETa on a daily basis in an alpine steppe region of the TP. The former includes the Nonlinear Complementary Relationship (Nonlinear-CR) as well as the Complementary Relationship Areal Evapotranspiration (CRAE) models, while the latter involves the Katerji-Perrier and the Todorovic models. Results indicate that the Nonlinear-CR, CRAE, and Katerji-Perrier models are all capable of efficiently simulating daily ETa, provided their parameter values were appropriately calibrated. The Katerji-Perrier model performed best since its site-specific parameters take the soil water status into account. The Nonlinear-CR model also performed well with the advantage of not requiring the user to choose between a symmetric and asymmetric CR. The CRAE model, even with a relatively low Nash-Sutcliffe efficiency (NSE) value, is also an acceptable approach in this data-scarce region as it does not need information of wind speed and ground surface conditions. In contrast, application of the Todorovic model was found to be inappropriate in the dry regions of the TP due to its significant overestimation of ETa as it neglects the effect of water stress on the bulk surface resistance. Sensitivity analysis of the parameter values demonstrated the relative importance of each parameter in the corresponding model. Overall, the Nonlinear-CR model is recommended in the absence of measured ETa for local calibration of the model parameter values.

Parameter estimation of a nonlinear Burger's model using nanoindentation and finite element-based inverse analysis

NASA Astrophysics Data System (ADS)

Hamim, Salah Uddin Ahmed

Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain behavior. Thus, theoretically it is possible to extract mechanical properties of a material through nanoindentation. However, due to various nonlinearities associated with nanoindentation the process of interpreting load-displacement data into material properties is difficult. Although, simple elastic behavior can be characterized easily, a method to characterize complicated material behavior such as nonlinear viscoelasticity is still lacking. In this study, a nanoindentation-based material characterization technique is developed to characterize soft materials exhibiting nonlinear viscoelasticity. Nanoindentation experiment was modeled in finite element analysis software (ABAQUS), where a nonlinear viscoelastic behavior was incorporated using user-defined subroutine (UMAT). The model parameters were calibrated using a process called inverse analysis. In this study, a surrogate model-based approach was used for the inverse analysis. The different factors affecting the surrogate model performance are analyzed in order to optimize the performance with respect to the computational cost.

Formation of parametric images using mixed-effects models: a feasibility study.

PubMed

Huang, Husan-Ming; Shih, Yi-Yu; Lin, Chieh

2016-03-01

Mixed-effects models have been widely used in the analysis of longitudinal data. By presenting the parameters as a combination of fixed effects and random effects, mixed-effects models incorporating both within- and between-subject variations are capable of improving parameter estimation. In this work, we demonstrate the feasibility of using a non-linear mixed-effects (NLME) approach for generating parametric images from medical imaging data of a single study. By assuming that all voxels in the image are independent, we used simulation and animal data to evaluate whether NLME can improve the voxel-wise parameter estimation. For testing purposes, intravoxel incoherent motion (IVIM) diffusion parameters including perfusion fraction, pseudo-diffusion coefficient and true diffusion coefficient were estimated using diffusion-weighted MR images and NLME through fitting the IVIM model. The conventional method of non-linear least squares (NLLS) was used as the standard approach for comparison of the resulted parametric images. In the simulated data, NLME provides more accurate and precise estimates of diffusion parameters compared with NLLS. Similarly, we found that NLME has the ability to improve the signal-to-noise ratio of parametric images obtained from rat brain data. These data have shown that it is feasible to apply NLME in parametric image generation, and the parametric image quality can be accordingly improved with the use of NLME. With the flexibility to be adapted to other models or modalities, NLME may become a useful tool to improve the parametric image quality in the future. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1988-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1990-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies.

PubMed

Essa, Khalid S

2014-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values.

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies

PubMed Central

Essa, Khalid S.

2013-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values. PMID:25685472

Multivariate meta-analysis for non-linear and other multi-parameter associations

PubMed Central

Gasparrini, A; Armstrong, B; Kenward, M G

2012-01-01

In this paper, we formalize the application of multivariate meta-analysis and meta-regression to synthesize estimates of multi-parameter associations obtained from different studies. This modelling approach extends the standard two-stage analysis used to combine results across different sub-groups or populations. The most straightforward application is for the meta-analysis of non-linear relationships, described for example by regression coefficients of splines or other functions, but the methodology easily generalizes to any setting where complex associations are described by multiple correlated parameters. The modelling framework of multivariate meta-analysis is implemented in the package mvmeta within the statistical environment R. As an illustrative example, we propose a two-stage analysis for investigating the non-linear exposure–response relationship between temperature and non-accidental mortality using time-series data from multiple cities. Multivariate meta-analysis represents a useful analytical tool for studying complex associations through a two-stage procedure. Copyright © 2012 John Wiley & Sons, Ltd. PMID:22807043

An Improved Swarm Optimization for Parameter Estimation and Biological Model Selection

PubMed Central

Abdullah, Afnizanfaizal; Deris, Safaai; Mohamad, Mohd Saberi; Anwar, Sohail

2013-01-01

One of the key aspects of computational systems biology is the investigation on the dynamic biological processes within cells. Computational models are often required to elucidate the mechanisms and principles driving the processes because of the nonlinearity and complexity. The models usually incorporate a set of parameters that signify the physical properties of the actual biological systems. In most cases, these parameters are estimated by fitting the model outputs with the corresponding experimental data. However, this is a challenging task because the available experimental data are frequently noisy and incomplete. In this paper, a new hybrid optimization method is proposed to estimate these parameters from the noisy and incomplete experimental data. The proposed method, called Swarm-based Chemical Reaction Optimization, integrates the evolutionary searching strategy employed by the Chemical Reaction Optimization, into the neighbouring searching strategy of the Firefly Algorithm method. The effectiveness of the method was evaluated using a simulated nonlinear model and two biological models: synthetic transcriptional oscillators, and extracellular protease production models. The results showed that the accuracy and computational speed of the proposed method were better than the existing Differential Evolution, Firefly Algorithm and Chemical Reaction Optimization methods. The reliability of the estimated parameters was statistically validated, which suggests that the model outputs produced by these parameters were valid even when noisy and incomplete experimental data were used. Additionally, Akaike Information Criterion was employed to evaluate the model selection, which highlighted the capability of the proposed method in choosing a plausible model based on the experimental data. In conclusion, this paper presents the effectiveness of the proposed method for parameter estimation and model selection problems using noisy and incomplete experimental data. This study is hoped to provide a new insight in developing more accurate and reliable biological models based on limited and low quality experimental data. PMID:23593445

Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics.

PubMed

Madi, Mahmoud K; Karameh, Fadi N

2017-01-01

Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate under CD-CKF. In conclusion, and with the CKF recently benchmarked against other advanced Bayesian techniques, the CD-CKF framework could provide significant gains in robustness and accuracy when estimating a variety of biological phenomena models where the underlying process dynamics unfold at time scales faster than those seen in collected measurements.

Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics

PubMed Central

2017-01-01

Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate under CD-CKF. In conclusion, and with the CKF recently benchmarked against other advanced Bayesian techniques, the CD-CKF framework could provide significant gains in robustness and accuracy when estimating a variety of biological phenomena models where the underlying process dynamics unfold at time scales faster than those seen in collected measurements. PMID:28727850

Analysis of the statistical thermodynamic model for nonlinear binary protein adsorption equilibria.

PubMed

Zhou, Xiao-Peng; Su, Xue-Li; Sun, Yan

2007-01-01

The statistical thermodynamic (ST) model was used to study nonlinear binary protein adsorption equilibria on an anion exchanger. Single-component and binary protein adsorption isotherms of bovine hemoglobin (Hb) and bovine serum albumin (BSA) on DEAE Spherodex M were determined by batch adsorption experiments in 10 mM Tris-HCl buffer containing a specific NaCl concentration (0.05, 0.10, and 0.15 M) at pH 7.40. The ST model was found to depict the effect of ionic strength on the single-component equilibria well, with model parameters depending on ionic strength. Moreover, the ST model gave acceptable fitting to the binary adsorption data with the fitted single-component model parameters, leading to the estimation of the binary ST model parameter. The effects of ionic strength on the model parameters are reasonably interpreted by the electrostatic and thermodynamic theories. The effective charge of protein in adsorption phase can be separately calculated from the two categories of the model parameters, and the values obtained from the two methods are consistent. The results demonstrate the utility of the ST model for describing nonlinear binary protein adsorption equilibria.

Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes

DOE PAGES

Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; ...

2015-09-15

Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinearmore » normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.« less

Non-linear Growth Models in Mplus and SAS

PubMed Central

Grimm, Kevin J.; Ram, Nilam

2013-01-01

Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included. PMID:23882134

Missing-value estimation using linear and non-linear regression with Bayesian gene selection.

PubMed

Zhou, Xiaobo; Wang, Xiaodong; Dougherty, Edward R

2003-11-22

Data from microarray experiments are usually in the form of large matrices of expression levels of genes under different experimental conditions. Owing to various reasons, there are frequently missing values. Estimating these missing values is important because they affect downstream analysis, such as clustering, classification and network design. Several methods of missing-value estimation are in use. The problem has two parts: (1) selection of genes for estimation and (2) design of an estimation rule. We propose Bayesian variable selection to obtain genes to be used for estimation, and employ both linear and nonlinear regression for the estimation rule itself. Fast implementation issues for these methods are discussed, including the use of QR decomposition for parameter estimation. The proposed methods are tested on data sets arising from hereditary breast cancer and small round blue-cell tumors. The results compare very favorably with currently used methods based on the normalized root-mean-square error. The appendix is available from http://gspsnap.tamu.edu/gspweb/zxb/missing_zxb/ (user: gspweb; passwd: gsplab).

Robust estimation for partially linear models with large-dimensional covariates

PubMed Central

Zhu, LiPing; Li, RunZe; Cui, HengJian

2014-01-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of o(n), where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures. PMID:24955087

Robust estimation for partially linear models with large-dimensional covariates.

PubMed

Zhu, LiPing; Li, RunZe; Cui, HengJian

2013-10-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of [Formula: see text], where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.

Estimation of Pulse Transit Time as a Function of Blood Pressure Using a Nonlinear Arterial Tube-Load Model.

PubMed

Gao, Mingwu; Cheng, Hao-Min; Sung, Shih-Hsien; Chen, Chen-Huan; Olivier, Nicholas Bari; Mukkamala, Ramakrishna

2017-07-01

pulse transit time (PTT) varies with blood pressure (BP) throughout the cardiac cycle, yet, because of wave reflection, only one PTT value at the diastolic BP level is conventionally estimated from proximal and distal BP waveforms. The objective was to establish a technique to estimate multiple PTT values at different BP levels in the cardiac cycle. a technique was developed for estimating PTT as a function of BP (to indicate the PTT value for every BP level) from proximal and distal BP waveforms. First, a mathematical transformation from one waveform to the other is defined in terms of the parameters of a nonlinear arterial tube-load model accounting for BP-dependent arterial compliance and wave reflection. Then, the parameters are estimated by optimally fitting the waveforms to each other via the model-based transformation. Finally, PTT as a function of BP is specified by the parameters. The technique was assessed in animals and patients in several ways including the ability of its estimated PTT-BP function to serve as a subject-specific curve for calibrating PTT to BP. the calibration curve derived by the technique during a baseline period yielded bias and precision errors in mean BP of 5.1 ± 0.9 and 6.6 ± 1.0 mmHg, respectively, during hemodynamic interventions that varied mean BP widely. the new technique may permit, for the first time, estimation of PTT values throughout the cardiac cycle from proximal and distal waveforms. the technique could potentially be applied to improve arterial stiffness monitoring and help realize cuff-less BP monitoring.

The impact of composite AUC estimates on the prediction of systemic exposure in toxicology experiments.

PubMed

Sahota, Tarjinder; Danhof, Meindert; Della Pasqua, Oscar

2015-06-01

Current toxicity protocols relate measures of systemic exposure (i.e. AUC, Cmax) as obtained by non-compartmental analysis to observed toxicity. A complicating factor in this practice is the potential bias in the estimates defining safe drug exposure. Moreover, it prevents the assessment of variability. The objective of the current investigation was therefore (a) to demonstrate the feasibility of applying nonlinear mixed effects modelling for the evaluation of toxicokinetics and (b) to assess the bias and accuracy in summary measures of systemic exposure for each method. Here, simulation scenarios were evaluated, which mimic toxicology protocols in rodents. To ensure differences in pharmacokinetic properties are accounted for, hypothetical drugs with varying disposition properties were considered. Data analysis was performed using non-compartmental methods and nonlinear mixed effects modelling. Exposure levels were expressed as area under the concentration versus time curve (AUC), peak concentrations (Cmax) and time above a predefined threshold (TAT). Results were then compared with the reference values to assess the bias and precision of parameter estimates. Higher accuracy and precision were observed for model-based estimates (i.e. AUC, Cmax and TAT), irrespective of group or treatment duration, as compared with non-compartmental analysis. Despite the focus of guidelines on establishing safety thresholds for the evaluation of new molecules in humans, current methods neglect uncertainty, lack of precision and bias in parameter estimates. The use of nonlinear mixed effects modelling for the analysis of toxicokinetics provides insight into variability and should be considered for predicting safe exposure in humans.

An offline approach for output-only Bayesian identification of stochastic nonlinear systems using unscented Kalman filtering

NASA Astrophysics Data System (ADS)

Erazo, Kalil; Nagarajaiah, Satish

2017-06-01

In this paper an offline approach for output-only Bayesian identification of stochastic nonlinear systems is presented. The approach is based on a re-parameterization of the joint posterior distribution of the parameters that define a postulated state-space stochastic model class. In the re-parameterization the state predictive distribution is included, marginalized, and estimated recursively in a state estimation step using an unscented Kalman filter, bypassing state augmentation as required by existing online methods. In applications expectations of functions of the parameters are of interest, which requires the evaluation of potentially high-dimensional integrals; Markov chain Monte Carlo is adopted to sample the posterior distribution and estimate the expectations. The proposed approach is suitable for nonlinear systems subjected to non-stationary inputs whose realization is unknown, and that are modeled as stochastic processes. Numerical verification and experimental validation examples illustrate the effectiveness and advantages of the approach, including: (i) an increased numerical stability with respect to augmented-state unscented Kalman filtering, avoiding divergence of the estimates when the forcing input is unmeasured; (ii) the ability to handle arbitrary prior and posterior distributions. The experimental validation of the approach is conducted using data from a large-scale structure tested on a shake table. It is shown that the approach is robust to inherent modeling errors in the description of the system and forcing input, providing accurate prediction of the dynamic response when the excitation history is unknown.

Data Assimilation by Ensemble Kalman Filter during One-Dimensional Nonlinear Consolidation in Randomly Heterogeneous Highly Compressible Aquitards

NASA Astrophysics Data System (ADS)

Zapata Norberto, B.; Morales-Casique, E.; Herrera, G. S.

2017-12-01

Severe land subsidence due to groundwater extraction may occur in multiaquifer systems where highly compressible aquitards are present. The highly compressible nature of the aquitards leads to nonlinear consolidation where the groundwater flow parameters are stress-dependent. The case is further complicated by the heterogeneity of the hydrogeologic and geotechnical properties of the aquitards. We explore the effect of realistic vertical heterogeneity of hydrogeologic and geotechnical parameters on the consolidation of highly compressible aquitards by means of 1-D Monte Carlo numerical simulations. 2000 realizations are generated for each of the following parameters: hydraulic conductivity (K), compression index (Cc) and void ratio (e). The correlation structure, the mean and the variance for each parameter were obtained from a literature review about field studies in the lacustrine sediments of Mexico City. The results indicate that among the parameters considered, random K has the largest effect on the ensemble average behavior of the system. Random K leads to the largest variance (and therefore largest uncertainty) of total settlement, groundwater flux and time to reach steady state conditions. We further propose a data assimilation scheme by means of ensemble Kalman filter to estimate the ensemble mean distribution of K, pore-pressure and total settlement. We consider the case where pore-pressure measurements are available at given time intervals. We test our approach by generating a 1-D realization of K with exponential spatial correlation, and solving the nonlinear flow and consolidation problem. These results are taken as our "true" solution. We take pore-pressure "measurements" at different times from this "true" solution. The ensemble Kalman filter method is then employed to estimate ensemble mean distribution of K, pore-pressure and total settlement based on the sequential assimilation of these pore-pressure measurements. The ensemble-mean estimates from this procedure closely approximate those from the "true" solution. This procedure can be easily extended to other random variables such as compression index and void ratio.

Bowhead whale localization using time-difference-of-arrival data from asynchronous recorders.

PubMed

Warner, Graham A; Dosso, Stan E; Hannay, David E

2017-03-01

This paper estimates bowhead whale locations and uncertainties using nonlinear Bayesian inversion of the time-difference-of-arrival (TDOA) of low-frequency whale calls recorded on onmi-directional asynchronous recorders in the shallow waters of the northeastern Chukchi Sea, Alaska. A Y-shaped cluster of seven autonomous ocean-bottom hydrophones, separated by 0.5-9.2 km, was deployed for several months over which time their clocks drifted out of synchronization. Hundreds of recorded whale calls are manually associated between recorders. The TDOA between hydrophone pairs are calculated from filtered waveform cross correlations and depend on the whale locations, hydrophone locations, relative recorder clock offsets, and effective waveguide sound speed. A nonlinear Bayesian inversion estimates all of these parameters and their uncertainties as well as data error statistics. The problem is highly nonlinear and a linearized inversion did not produce physically realistic results. Whale location uncertainties from nonlinear inversion can be low enough to allow accurate tracking of migrating whales that vocalize repeatedly over several minutes. Estimates of clock drift rates are obtained from inversions of TDOA data over two weeks and agree with corresponding estimates obtained from long-time averaged ambient noise cross correlations. The inversion is suitable for application to large data sets of manually or automatically detected whale calls.

Nonlinear spectral mixture effects for photosynthetic/non-photosynthetic vegetation cover estimates of typical desert vegetation in western China.

PubMed

Ji, Cuicui; Jia, Yonghong; Gao, Zhihai; Wei, Huaidong; Li, Xiaosong

2017-01-01

Desert vegetation plays significant roles in securing the ecological integrity of oasis ecosystems in western China. Timely monitoring of photosynthetic/non-photosynthetic desert vegetation cover is necessary to guide management practices on land desertification and research into the mechanisms driving vegetation recession. In this study, nonlinear spectral mixture effects for photosynthetic/non-photosynthetic vegetation cover estimates are investigated through comparing the performance of linear and nonlinear spectral mixture models with different endmembers applied to field spectral measurements of two types of typical desert vegetation, namely, Nitraria shrubs and Haloxylon. The main results were as follows. (1) The correct selection of endmembers is important for improving the accuracy of vegetation cover estimates, and in particular, shadow endmembers cannot be neglected. (2) For both the Nitraria shrubs and Haloxylon, the Kernel-based Nonlinear Spectral Mixture Model (KNSMM) with nonlinear parameters was the best unmixing model. In consideration of the computational complexity and accuracy requirements, the Linear Spectral Mixture Model (LSMM) could be adopted for Nitraria shrubs plots, but this will result in significant errors for the Haloxylon plots since the nonlinear spectral mixture effects were more obvious for this vegetation type. (3) The vegetation canopy structure (planophile or erectophile) determines the strength of the nonlinear spectral mixture effects. Therefore, no matter for Nitraria shrubs or Haloxylon, the non-linear spectral mixing effects between the photosynthetic / non-photosynthetic vegetation and the bare soil do exist, and its strength is dependent on the three-dimensional structure of the vegetation canopy. The choice of linear or nonlinear spectral mixture models is up to the consideration of computational complexity and the accuracy requirement.

Nonlinear spectral mixture effects for photosynthetic/non-photosynthetic vegetation cover estimates of typical desert vegetation in western China

PubMed Central

Jia, Yonghong; Gao, Zhihai; Wei, Huaidong

2017-01-01

Desert vegetation plays significant roles in securing the ecological integrity of oasis ecosystems in western China. Timely monitoring of photosynthetic/non-photosynthetic desert vegetation cover is necessary to guide management practices on land desertification and research into the mechanisms driving vegetation recession. In this study, nonlinear spectral mixture effects for photosynthetic/non-photosynthetic vegetation cover estimates are investigated through comparing the performance of linear and nonlinear spectral mixture models with different endmembers applied to field spectral measurements of two types of typical desert vegetation, namely, Nitraria shrubs and Haloxylon. The main results were as follows. (1) The correct selection of endmembers is important for improving the accuracy of vegetation cover estimates, and in particular, shadow endmembers cannot be neglected. (2) For both the Nitraria shrubs and Haloxylon, the Kernel-based Nonlinear Spectral Mixture Model (KNSMM) with nonlinear parameters was the best unmixing model. In consideration of the computational complexity and accuracy requirements, the Linear Spectral Mixture Model (LSMM) could be adopted for Nitraria shrubs plots, but this will result in significant errors for the Haloxylon plots since the nonlinear spectral mixture effects were more obvious for this vegetation type. (3) The vegetation canopy structure (planophile or erectophile) determines the strength of the nonlinear spectral mixture effects. Therefore, no matter for Nitraria shrubs or Haloxylon, the non-linear spectral mixing effects between the photosynthetic / non-photosynthetic vegetation and the bare soil do exist, and its strength is dependent on the three-dimensional structure of the vegetation canopy. The choice of linear or nonlinear spectral mixture models is up to the consideration of computational complexity and the accuracy requirement. PMID:29240777

Inversion for Refractivity Parameters Using a Dynamic Adaptive Cuckoo Search with Crossover Operator Algorithm

PubMed Central

Zhang, Zhihua; Sheng, Zheng; Shi, Hanqing; Fan, Zhiqiang

2016-01-01

Using the RFC technique to estimate refractivity parameters is a complex nonlinear optimization problem. In this paper, an improved cuckoo search (CS) algorithm is proposed to deal with this problem. To enhance the performance of the CS algorithm, a parameter dynamic adaptive operation and crossover operation were integrated into the standard CS (DACS-CO). Rechenberg's 1/5 criteria combined with learning factor were used to control the parameter dynamic adaptive adjusting process. The crossover operation of genetic algorithm was utilized to guarantee the population diversity. The new hybrid algorithm has better local search ability and contributes to superior performance. To verify the ability of the DACS-CO algorithm to estimate atmospheric refractivity parameters, the simulation data and real radar clutter data are both implemented. The numerical experiments demonstrate that the DACS-CO algorithm can provide an effective method for near-real-time estimation of the atmospheric refractivity profile from radar clutter. PMID:27212938

Sequential bearings-only-tracking initiation with particle filtering method.

PubMed

Liu, Bin; Hao, Chengpeng

2013-01-01

The tracking initiation problem is examined in the context of autonomous bearings-only-tracking (BOT) of a single appearing/disappearing target in the presence of clutter measurements. In general, this problem suffers from a combinatorial explosion in the number of potential tracks resulted from the uncertainty in the linkage between the target and the measurement (a.k.a the data association problem). In addition, the nonlinear measurements lead to a non-Gaussian posterior probability density function (pdf) in the optimal Bayesian sequential estimation framework. The consequence of this nonlinear/non-Gaussian context is the absence of a closed-form solution. This paper models the linkage uncertainty and the nonlinear/non-Gaussian estimation problem jointly with solid Bayesian formalism. A particle filtering (PF) algorithm is derived for estimating the model's parameters in a sequential manner. Numerical results show that the proposed solution provides a significant benefit over the most commonly used methods, IPDA and IMMPDA. The posterior Cramér-Rao bounds are also involved for performance evaluation.

Gap-filling methods to impute eddy covariance flux data by preserving variance.

NASA Astrophysics Data System (ADS)

Kunwor, S.; Staudhammer, C. L.; Starr, G.; Loescher, H. W.

2015-12-01

To represent carbon dynamics, in terms of exchange of CO2 between the terrestrial ecosystem and the atmosphere, eddy covariance (EC) data has been collected using eddy flux towers from various sites across globe for more than two decades. However, measurements from EC data are missing for various reasons: precipitation, routine maintenance, or lack of vertical turbulence. In order to have estimates of net ecosystem exchange of carbon dioxide (NEE) with high precision and accuracy, robust gap-filling methods to impute missing data are required. While the methods used so far have provided robust estimates of the mean value of NEE, little attention has been paid to preserving the variance structures embodied by the flux data. Preserving the variance of these data will provide unbiased and precise estimates of NEE over time, which mimic natural fluctuations. We used a non-linear regression approach with moving windows of different lengths (15, 30, and 60-days) to estimate non-linear regression parameters for one year of flux data from a long-leaf pine site at the Joseph Jones Ecological Research Center. We used as our base the Michaelis-Menten and Van't Hoff functions. We assessed the potential physiological drivers of these parameters with linear models using micrometeorological predictors. We then used a parameter prediction approach to refine the non-linear gap-filling equations based on micrometeorological conditions. This provides us an opportunity to incorporate additional variables, such as vapor pressure deficit (VPD) and volumetric water content (VWC) into the equations. Our preliminary results indicate that improvements in gap-filling can be gained with a 30-day moving window with additional micrometeorological predictors (as indicated by lower root mean square error (RMSE) of the predicted values of NEE). Our next steps are to use these parameter predictions from moving windows to gap-fill the data with and without incorporation of potential driver variables of the parameters traditionally used. Then, comparisons of the predicted values from these methods and 'traditional' gap-filling methods (using 12 fixed monthly windows) will be assessed to show the scale of preserving variance. Further, this method will be applied to impute artificially created gaps for analyzing if variance is preserved.

New formulations for tsunami runup estimation

NASA Astrophysics Data System (ADS)

Kanoglu, U.; Aydin, B.; Ceylan, N.

2017-12-01

We evaluate shoreline motion and maximum runup in two folds: One, we use linear shallow water-wave equations over a sloping beach and solve as initial-boundary value problem similar to the nonlinear solution of Aydın and Kanoglu (2017, Pure Appl. Geophys., https://doi.org/10.1007/s00024-017-1508-z). Methodology we present here is simple; it involves eigenfunction expansion and, hence, avoids integral transform techniques. We then use several different types of initial wave profiles with and without initial velocity, estimate shoreline properties and confirm classical runup invariance between linear and nonlinear theories. Two, we use the nonlinear shallow water-wave solution of Kanoglu (2004, J. Fluid Mech. 513, 363-372) to estimate maximum runup. Kanoglu (2004) presented a simple integral solution for the nonlinear shallow water-wave equations using the classical Carrier and Greenspan transformation, and further extended shoreline position and velocity to a simpler integral formulation. In addition, Tinti and Tonini (2005, J. Fluid Mech. 535, 33-64) defined initial condition in a very convenient form for near-shore events. We use Tinti and Tonini (2005) type initial condition in Kanoglu's (2004) shoreline integral solution, which leads further simplified estimates for shoreline position and velocity, i.e. algebraic relation. We then use this algebraic runup estimate to investigate effect of earthquake source parameters on maximum runup and present results similar to Sepulveda and Liu (2016, Coast. Eng. 112, 57-68).

Adaptive Elastic Net for Generalized Methods of Moments.

PubMed

Caner, Mehmet; Zhang, Hao Helen

2014-01-30

Model selection and estimation are crucial parts of econometrics. This paper introduces a new technique that can simultaneously estimate and select the model in generalized method of moments (GMM) context. The GMM is particularly powerful for analyzing complex data sets such as longitudinal and panel data, and it has wide applications in econometrics. This paper extends the least squares based adaptive elastic net estimator of Zou and Zhang (2009) to nonlinear equation systems with endogenous variables. The extension is not trivial and involves a new proof technique due to estimators lack of closed form solutions. Compared to Bridge-GMM of Caner (2009), we allow for the number of parameters to diverge to infinity as well as collinearity among a large number of variables, also the redundant parameters set to zero via a data dependent technique. This method has the oracle property, meaning that we can estimate nonzero parameters with their standard limit and the redundant parameters are dropped from the equations simultaneously. Numerical examples are used to illustrate the performance of the new method.

Determining Crack Tip Field Parameters for Elastic-Plastic Materials via an Estimation Scheme

DTIC Science & Technology

1981-07-01

of the Materials Laboratory was the Project Monitor for this study of the application of the Nonlinear Fracture Mechanics (NLFM) parameters to the...fracture mechanics (LEFM) is applicable . If the plastic zone size is large, compared to the case of small scale yielding, LEFM is not applicable . The...above HRR field equations are applicable only for the case of stationary cracks. 2.2 PARAMETER DETERMINATION For elastic-plastic materials, the

Multiparameter Estimation in Networked Quantum Sensors

NASA Astrophysics Data System (ADS)

Proctor, Timothy J.; Knott, Paul A.; Dunningham, Jacob A.

2018-02-01

We introduce a general model for a network of quantum sensors, and we use this model to consider the following question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. This immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or nonlinear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.

Prediction of Unsteady Aerodynamic Coefficients at High Angles of Attack

NASA Technical Reports Server (NTRS)

Pamadi, Bandu N.; Murphy, Patrick C.; Klein, Vladislav; Brandon, Jay M.

2001-01-01

The nonlinear indicial response method is used to model the unsteady aerodynamic coefficients in the low speed longitudinal oscillatory wind tunnel test data of the 0.1 scale model of the F-16XL aircraft. Exponential functions are used to approximate the deficiency function in the indicial response. Using one set of oscillatory wind tunnel data and parameter identification method, the unknown parameters in the exponential functions are estimated. The genetic algorithm is used as a least square minimizing algorithm. The assumed model structures and parameter estimates are validated by comparing the predictions with other sets of available oscillatory wind tunnel test data.

Application of the Generalized Nonlinear Complementary Relationship for Estimating Evaporation in North China

NASA Astrophysics Data System (ADS)

Yu, M.; Wu, B.

2017-12-01

As an important part of the coupled Eco-Hydrological processes, evaporation is the bond for exchange of energy and heat between the surface and the atmosphere. However, the estimation of evaporation remains a challenge compared with other main hydrological factors in water cycle. The complementary relationship which proposed by Bouchet (1963) has laid the foundation for various approaches to estimate evaporation from land surfaces, the essence of the principle is a relationship between three types of evaporation in the environment. It can simply implemented with routine meteorological data without the need for resistance parameters of the vegetation and bare land, which are difficult to observed and complicated to estimate in most surface flux models. On this basis the generalized nonlinear formulation was proposed by Brutsaert (2015). The daily evaporation can be estimated once the potential evaporation (Epo) and apparent potential evaporation (Epa) are known. The new formulation has a strong physical basis and can be expected to perform better under natural water stress conditions, nevertheless, the model has not been widely validated over different climate types and underlying surface patterns. In this study, we attempted to apply the generalized nonlinear complementary relationship in North China, three flux stations in North China are used for testing the universality and accuracy of this model against observed evaporation over different vegetation types, including Guantao Site, Miyun Site and Huailai Site. Guantao Site has double-cropping systems and crop rotations with summer maize and winter wheat; the other two sites are dominated by spring maize. Detailed measurements of meteorological factors at certain heights above ground surface from automatic weather stations offered necessary parameters for daily evaporation estimation. Using the Bowen ratio, the surface energy measured by the eddy covariance systems at the flux stations is adjusted on a daily scale to satisfy the surface energy closure. After calibration the estimated daily evaporation are in good agreement with EC-measured flux data with a mean correlation coefficient in excess of 0.85. The results indicate that the generalized nonlinear complementary relationship can be applied in plant growing and non-growing season in North China.

Nonlinear Directed Interactions Between HRV and EEG Activity in Children With TLE.

PubMed

Schiecke, Karin; Pester, Britta; Piper, Diana; Benninger, Franz; Feucht, Martha; Leistritz, Lutz; Witte, Herbert

2016-12-01

Epileptic seizure activity influences the autonomic nervous system (ANS) in different ways. Heart rate variability (HRV) is used as indicator for alterations of the ANS. It was shown that linear, nondirected interactions between HRV and EEG activity before, during, and after epileptic seizure occur. Accordingly, investigations of directed nonlinear interactions are logical steps to provide, e.g., deeper insight into the development of seizure onsets. Convergent cross mapping (CCM) investigates nonlinear, directed interactions between time series by using nonlinear state space reconstruction. CCM is applied to simulated and clinically relevant data, i.e., interactions between HRV and specific EEG components of children with temporal lobe epilepsy (TLE). In addition, time-variant multivariate Autoregressive model (AR)-based estimation of partial directed coherence (PDC) was performed for the same data. Influence of estimation parameters and time-varying behavior of CCM estimation could be demonstrated by means of simulated data. AR-based estimation of PDC failed for the investigation of our clinical data. Time-varying interval-based application of CCM on these data revealed directed interactions between HRV and delta-related EEG activity. Interactions between HRV and alpha-related EEG activity were visible but less pronounced. EEG components mainly drive HRV. The interaction pattern and directionality clearly changed with onset of seizure. Statistical relevant interactions were quantified by bootstrapping and surrogate data approach. In contrast to AR-based estimation of PDC CCM was able to reveal time-courses and frequency-selective views of nonlinear interactions for the further understanding of complex interactions between the epileptic network and the ANS in children with TLE.

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

Nonlinear viscoelastic characterization of bovine trabecular bone.

PubMed

Manda, Krishnagoud; Wallace, Robert J; Xie, Shuqiao; Levrero-Florencio, Francesc; Pankaj, Pankaj

2017-02-01

The time-independent elastic properties of trabecular bone have been extensively investigated, and several stiffness-density relations have been proposed. Although it is recognized that trabecular bone exhibits time-dependent mechanical behaviour, a property of viscoelastic materials, the characterization of this behaviour has received limited attention. The objective of the present study was to investigate the time-dependent behaviour of bovine trabecular bone through a series of compressive creep-recovery experiments and to identify its nonlinear constitutive viscoelastic material parameters. Uniaxial compressive creep and recovery experiments at multiple loads were performed on cylindrical bovine trabecular bone samples ([Formula: see text]). Creep response was found to be significant and always comprised of recoverable and irrecoverable strains, even at low stress/strain levels. This response was also found to vary nonlinearly with applied stress. A systematic methodology was developed to separate recoverable (nonlinear viscoelastic) and irrecoverable (permanent) strains from the total experimental strain response. We found that Schapery's nonlinear viscoelastic constitutive model describes the viscoelastic response of the trabecular bone, and parameters associated with this model were estimated from the multiple load creep-recovery (MLCR) experiments. Nonlinear viscoelastic recovery compliance was found to have a decreasing and then increasing trend with increasing stress level, indicating possible stiffening and softening behaviour of trabecular bone due to creep. The obtained parameters from MLCR tests, expressed as second-order polynomial functions of stress, showed a similar trend for all the samples, and also demonstrate stiffening-softening behaviour with increasing stress.

Application of parameter estimation to highly unstable aircraft

NASA Technical Reports Server (NTRS)

Maine, R. E.; Murray, J. E.

1986-01-01

This paper discusses the application of parameter estimation to highly unstable aircraft. It includes a discussion of the problems in applying the output error method to such aircraft and demonstrates that the filter error method eliminates these problems. The paper shows that the maximum likelihood estimator with no process noise does not reduce to the output error method when the system is unstable. It also proposes and demonstrates an ad hoc method that is similar in form to the filter error method, but applicable to nonlinear problems. Flight data from the X-29 forward-swept-wing demonstrator is used to illustrate the problems and methods discussed.

Application of parameter estimation to highly unstable aircraft

NASA Technical Reports Server (NTRS)

Maine, R. E.; Murray, J. E.

1986-01-01

The application of parameter estimation to highly unstable aircraft is discussed. Included are a discussion of the problems in applying the output error method to such aircraft and demonstrates that the filter error method eliminates these problems. The paper shows that the maximum likelihood estimator with no process noise does not reduce to the output error method when the system is unstable. It also proposes and demonstrates an ad hoc method that is similar in form to the filter error method, but applicable to nonlinear problems. Flight data from the X-29 forward-swept-wing demonstrator is used to illustrate the problems and methods discussed.

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.

Optimization of Straight Cylindrical Turning Using Artificial Bee Colony (ABC) Algorithm

NASA Astrophysics Data System (ADS)

Prasanth, Rajanampalli Seshasai Srinivasa; Hans Raj, Kandikonda

2017-04-01

Artificial bee colony (ABC) algorithm, that mimics the intelligent foraging behavior of honey bees, is increasingly gaining acceptance in the field of process optimization, as it is capable of handling nonlinearity, complexity and uncertainty. Straight cylindrical turning is a complex and nonlinear machining process which involves the selection of appropriate cutting parameters that affect the quality of the workpiece. This paper presents the estimation of optimal cutting parameters of the straight cylindrical turning process using the ABC algorithm. The ABC algorithm is first tested on four benchmark problems of numerical optimization and its performance is compared with genetic algorithm (GA) and ant colony optimization (ACO) algorithm. Results indicate that, the rate of convergence of ABC algorithm is better than GA and ACO. Then, the ABC algorithm is used to predict optimal cutting parameters such as cutting speed, feed rate, depth of cut and tool nose radius to achieve good surface finish. Results indicate that, the ABC algorithm estimated a comparable surface finish when compared with real coded genetic algorithm and differential evolution algorithm.

Selecting Sensitive Parameter Subsets in Dynamical Models With Application to Biomechanical System Identification.

PubMed

Ramadan, Ahmed; Boss, Connor; Choi, Jongeun; Peter Reeves, N; Cholewicki, Jacek; Popovich, John M; Radcliffe, Clark J

2018-07-01

Estimating many parameters of biomechanical systems with limited data may achieve good fit but may also increase 95% confidence intervals in parameter estimates. This results in poor identifiability in the estimation problem. Therefore, we propose a novel method to select sensitive biomechanical model parameters that should be estimated, while fixing the remaining parameters to values obtained from preliminary estimation. Our method relies on identifying the parameters to which the measurement output is most sensitive. The proposed method is based on the Fisher information matrix (FIM). It was compared against the nonlinear least absolute shrinkage and selection operator (LASSO) method to guide modelers on the pros and cons of our FIM method. We present an application identifying a biomechanical parametric model of a head position-tracking task for ten human subjects. Using measured data, our method (1) reduced model complexity by only requiring five out of twelve parameters to be estimated, (2) significantly reduced parameter 95% confidence intervals by up to 89% of the original confidence interval, (3) maintained goodness of fit measured by variance accounted for (VAF) at 82%, (4) reduced computation time, where our FIM method was 164 times faster than the LASSO method, and (5) selected similar sensitive parameters to the LASSO method, where three out of five selected sensitive parameters were shared by FIM and LASSO methods.

Nonlinear regression method for estimating neutral wind and temperature from Fabry-Perot interferometer data.

PubMed

Harding, Brian J; Gehrels, Thomas W; Makela, Jonathan J

2014-02-01

The Earth's thermosphere plays a critical role in driving electrodynamic processes in the ionosphere and in transferring solar energy to the atmosphere, yet measurements of thermospheric state parameters, such as wind and temperature, are sparse. One of the most popular techniques for measuring these parameters is to use a Fabry-Perot interferometer to monitor the Doppler width and breadth of naturally occurring airglow emissions in the thermosphere. In this work, we present a technique for estimating upper-atmospheric winds and temperatures from images of Fabry-Perot fringes captured by a CCD detector. We estimate instrument parameters from fringe patterns of a frequency-stabilized laser, and we use these parameters to estimate winds and temperatures from airglow fringe patterns. A unique feature of this technique is the model used for the laser and airglow fringe patterns, which fits all fringes simultaneously and attempts to model the effects of optical defects. This technique yields accurate estimates for winds, temperatures, and the associated uncertainties in these parameters, as we show with a Monte Carlo simulation.

UCODE, a computer code for universal inverse modeling

USGS Publications Warehouse

Poeter, E.P.; Hill, M.C.

1999-01-01

This article presents the US Geological Survey computer program UCODE, which was developed in collaboration with the US Army Corps of Engineers Waterways Experiment Station and the International Ground Water Modeling Center of the Colorado School of Mines. UCODE performs inverse modeling, posed as a parameter-estimation problem, using nonlinear regression. Any application model or set of models can be used; the only requirement is that they have numerical (ASCII or text only) input and output files and that the numbers in these files have sufficient significant digits. Application models can include preprocessors and postprocessors as well as models related to the processes of interest (physical, chemical and so on), making UCODE extremely powerful for model calibration. Estimated parameters can be defined flexibly with user-specified functions. Observations to be matched in the regression can be any quantity for which a simulated equivalent value can be produced, thus simulated equivalent values are calculated using values that appear in the application model output files and can be manipulated with additive and multiplicative functions, if necessary. Prior, or direct, information on estimated parameters also can be included in the regression. The nonlinear regression problem is solved by minimizing a weighted least-squares objective function with respect to the parameter values using a modified Gauss-Newton method. Sensitivities needed for the method are calculated approximately by forward or central differences and problems and solutions related to this approximation are discussed. Statistics are calculated and printed for use in (1) diagnosing inadequate data or identifying parameters that probably cannot be estimated with the available data, (2) evaluating estimated parameter values, (3) evaluating the model representation of the actual processes and (4) quantifying the uncertainty of model simulated values. UCODE is intended for use on any computer operating system: it consists of algorithms programmed in perl, a freeware language designed for text manipulation and Fortran90, which efficiently performs numerical calculations.

Comparison of Random Forest and Parametric Imputation Models for Imputing Missing Data Using MICE: A CALIBER Study

PubMed Central

Shah, Anoop D.; Bartlett, Jonathan W.; Carpenter, James; Nicholas, Owen; Hemingway, Harry

2014-01-01

Multivariate imputation by chained equations (MICE) is commonly used for imputing missing data in epidemiologic research. The “true” imputation model may contain nonlinearities which are not included in default imputation models. Random forest imputation is a machine learning technique which can accommodate nonlinearities and interactions and does not require a particular regression model to be specified. We compared parametric MICE with a random forest-based MICE algorithm in 2 simulation studies. The first study used 1,000 random samples of 2,000 persons drawn from the 10,128 stable angina patients in the CALIBER database (Cardiovascular Disease Research using Linked Bespoke Studies and Electronic Records; 2001–2010) with complete data on all covariates. Variables were artificially made “missing at random,” and the bias and efficiency of parameter estimates obtained using different imputation methods were compared. Both MICE methods produced unbiased estimates of (log) hazard ratios, but random forest was more efficient and produced narrower confidence intervals. The second study used simulated data in which the partially observed variable depended on the fully observed variables in a nonlinear way. Parameter estimates were less biased using random forest MICE, and confidence interval coverage was better. This suggests that random forest imputation may be useful for imputing complex epidemiologic data sets in which some patients have missing data. PMID:24589914

Comparison of random forest and parametric imputation models for imputing missing data using MICE: a CALIBER study.

PubMed

Shah, Anoop D; Bartlett, Jonathan W; Carpenter, James; Nicholas, Owen; Hemingway, Harry

2014-03-15

Multivariate imputation by chained equations (MICE) is commonly used for imputing missing data in epidemiologic research. The "true" imputation model may contain nonlinearities which are not included in default imputation models. Random forest imputation is a machine learning technique which can accommodate nonlinearities and interactions and does not require a particular regression model to be specified. We compared parametric MICE with a random forest-based MICE algorithm in 2 simulation studies. The first study used 1,000 random samples of 2,000 persons drawn from the 10,128 stable angina patients in the CALIBER database (Cardiovascular Disease Research using Linked Bespoke Studies and Electronic Records; 2001-2010) with complete data on all covariates. Variables were artificially made "missing at random," and the bias and efficiency of parameter estimates obtained using different imputation methods were compared. Both MICE methods produced unbiased estimates of (log) hazard ratios, but random forest was more efficient and produced narrower confidence intervals. The second study used simulated data in which the partially observed variable depended on the fully observed variables in a nonlinear way. Parameter estimates were less biased using random forest MICE, and confidence interval coverage was better. This suggests that random forest imputation may be useful for imputing complex epidemiologic data sets in which some patients have missing data.

Controlling the non-linear intracavity dynamics of large He-Ne laser gyroscopes

NASA Astrophysics Data System (ADS)

Cuccato, D.; Beghi, A.; Belfi, J.; Beverini, N.; Ortolan, A.; Di Virgilio, A.

2014-02-01

A model based on Lamb's theory of gas lasers is applied to a He-Ne ring laser (RL) gyroscope to estimate and remove the laser dynamics contribution from the rotation measurements. The intensities of the counter-propagating laser beams exiting one cavity mirror are continuously observed together with a monitor of the laser population inversion. These observables, once properly calibrated with a dedicated procedure, allow us to estimate cold cavity and active medium parameters driving the main part of the non-linearities of the system. The quantitative estimation of intrinsic non-reciprocal effects due to cavity and active medium non-linear coupling plays a key role in testing fundamental symmetries of space-time with RLs. The parameter identification and noise subtraction procedure has been verified by means of a Monte Carlo study of the system, and experimentally tested on the G-PISA RL oriented with the normal to the ring plane almost parallel to the Earth's rotation axis. In this configuration the Earth's rotation rate provides the maximum Sagnac effect while the contribution of the orientation error is reduced to a minimum. After the subtraction of laser dynamics by a Kalman filter, the relative systematic errors of G-PISA reduce from 50 to 5 parts in 103 and can be attributed to the residual uncertainties on geometrical scale factor and orientation of the ring.

Dynamic Modeling of Cell-Free Biochemical Networks Using Effective Kinetic Models

DTIC Science & Technology

2015-03-16

sensitivity value was the maximum uncertainty in that value estimated by the Sobol method. 2.4. Global Sensitivity Analysis of the Reduced Order Coagulation...sensitivity analysis, using the variance-based method of Sobol , to estimate which parameters controlled the performance of the reduced order model [69]. We...Environment. Comput. Sci. Eng. 2007, 9, 90–95. 69. Sobol , I. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates

Development of a multi-body nonlinear model for a seat-occupant system

NASA Astrophysics Data System (ADS)

Azizi, Yousof

A car seat is an important component of today's cars, which directly affects ride comfort experienced by occupants. Currently, the process of ride comfort evaluation is subjective. Alternatively, the ride comfort can be evaluated by a series of objective metrics in the dynamic response of the occupant. From previous studies it is well known that the dynamic behavior of a seat-occupant system is greatly affected by soft nonlinear viscoelastic materials used in the seat cushion. Therefore, in this research, especial attention was given to efficiently modeling the behavior of seat cushion. In the first part of this research, a phenomenological nonlinear viscoelastic foam model was proposed and its ability to capture uniaxial behavior of foam was investigated. The model is based on the assumption that the total stress can be decomposed into the sum of a nonlinear elastic component, modeled by a higher order polynomial of strain, and a nonlinear hereditary type viscoelastic component. System identification procedures were developed to estimate the model parameters using uniaxial cyclic compression data from experiments conducted at different rates on two types of low density polyurethane foams and three types of high density CONFOR foams. The performance of the proposed model was compared to that of other traditional continuum models. For each foam type, it was observed that lower order models are sufficient to describe the uniaxial behavior of the foam compressed at different rates. Although, the estimated model parameters were functions of the input strain rate. Alternatively, higher order comprehensive models, with strain independent parameters, were estimated as well. The estimated comprehensive model predicts foam responses under different compression rates. Also, a methodology was proposed to predict the stress-response of a layered foam system using the estimated models of each foam in the layers. Next, the estimated foam model was incorporated into a single-degree of freedom foam-mass model which is also the simplest model of seat-occupant systems. The steady-state response of the system when it is subjected to harmonic base excitation was studied using the incremental harmonic balance method. The incremental harmonic balance method was used to reduce the time required to generate the steady-state response of the system. The incremental harmonic balance method was used to reduce the time required to generate the steady-state response of the system. Experiments are conducted on a single-degree of freedom foam-mass system subjected to harmonic base excitation. Initially, the simulated response predictions were found to deviate from the experimental results. The foam-mass model was then modified to incorporate rate dependency of foam parameters resulting in response predictions that were in good agreement with experimental results. In the second part of this research, the dynamic response of a seat-occupant system was examined through a more realistic planar multi-body seat-occupant model. A constraint Lagrangian formulation was used to derive the governing equations for the seat-occupant model. First, the governing equations were solved numerically to obtain the occupant transient response, the occupant's H-Point location and the interfacial pressure distribution. Variations in the H-Point location and the seat-occupant pressure distribution with changes in the seat-occupant parameters, including the seat geometry and the occupant's characteristics, were studied. The estimated pressure was also investigated experimentally and was found to match with the results obtained using the seat-occupant model. Next, the incremental harmonic balance method was modified and used to obtain the occupant's steady-state response when the seat-occupant system was subjected to harmonic base excitation at different frequencies. The system frequency response and mode shapes at different frequencies were also obtained and compared to the previously measured experimental frequency responses. Finally, variations in the estimated frequency response with changes in the seat-occupant parameters, including the seat geometry and the occupant characteristics, were studied.

The Efficiency of Split Panel Designs in an Analysis of Variance Model

PubMed Central

Wang, Wei-Guo; Liu, Hai-Jun

2016-01-01

We consider split panel design efficiency in analysis of variance models, that is, the determination of the cross-sections series optimal proportion in all samples, to minimize parametric best linear unbiased estimators of linear combination variances. An orthogonal matrix is constructed to obtain manageable expression of variances. On this basis, we derive a theorem for analyzing split panel design efficiency irrespective of interest and budget parameters. Additionally, relative estimator efficiency based on the split panel to an estimator based on a pure panel or a pure cross-section is present. The analysis shows that the gains from split panel can be quite substantial. We further consider the efficiency of split panel design, given a budget, and transform it to a constrained nonlinear integer programming. Specifically, an efficient algorithm is designed to solve the constrained nonlinear integer programming. Moreover, we combine one at time designs and factorial designs to illustrate the algorithm’s efficiency with an empirical example concerning monthly consumer expenditure on food in 1985, in the Netherlands, and the efficient ranges of the algorithm parameters are given to ensure a good solution. PMID:27163447

Fatigue Life Estimation under Cumulative Cyclic Loading Conditions

NASA Technical Reports Server (NTRS)

Kalluri, Sreeramesh; McGaw, Michael A; Halford, Gary R.

1999-01-01

The cumulative fatigue behavior of a cobalt-base superalloy, Haynes 188 was investigated at 760 C in air. Initially strain-controlled tests were conducted on solid cylindrical gauge section specimens of Haynes 188 under fully-reversed, tensile and compressive mean strain-controlled fatigue tests. Fatigue data from these tests were used to establish the baseline fatigue behavior of the alloy with 1) a total strain range type fatigue life relation and 2) the Smith-Wastson-Topper (SWT) parameter. Subsequently, two load-level multi-block fatigue tests were conducted on similar specimens of Haynes 188 at the same temperature. Fatigue lives of the multi-block tests were estimated with 1) the Linear Damage Rule (LDR) and 2) the nonlinear Damage Curve Approach (DCA) both with and without the consideration of mean stresses generated during the cumulative fatigue tests. Fatigue life predictions by the nonlinear DCA were much closer to the experimentally observed lives than those obtained by the LDR. In the presence of mean stresses, the SWT parameter estimated the fatigue lives more accurately under tensile conditions than under compressive conditions.

Simple robust control laws for robot manipulators. Part 2: Adaptive case

NASA Technical Reports Server (NTRS)

Bayard, D. S.; Wen, J. T.

1987-01-01

A new class of asymptotically stable adaptive control laws is introduced for application to the robotic manipulator. Unlike most applications of adaptive control theory to robotic manipulators, this analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and utilizes a parameterization based on physical (time-invariant) quantities. This approach is made possible by using energy-like Lyapunov functions which retain the nonlinear character and structure of the dynamics, rather than simple quadratic forms which are ubiquitous to the adaptive control literature, and which have bound the theory tightly to linear systems with unknown parameters. It is a unique feature of these results that the adaptive forms arise by straightforward certainty equivalence adaptation of their nonadaptive counterparts found in the companion to this paper (i.e., by replacing unknown quantities by their estimates) and that this simple approach leads to asymptotically stable closed-loop adaptive systems. Furthermore, it is emphasized that this approach does not require convergence of the parameter estimates (i.e., via persistent excitation), invertibility of the mass matrix estimate, or measurement of the joint accelerations.

Nonlinear bias compensation of ZiYuan-3 satellite imagery with cubic splines

NASA Astrophysics Data System (ADS)

Cao, Jinshan; Fu, Jianhong; Yuan, Xiuxiao; Gong, Jianya

2017-11-01

Like many high-resolution satellites such as the ALOS, MOMS-2P, QuickBird, and ZiYuan1-02C satellites, the ZiYuan-3 satellite suffers from different levels of attitude oscillations. As a result of such oscillations, the rational polynomial coefficients (RPCs) obtained using a terrain-independent scenario often have nonlinear biases. In the sensor orientation of ZiYuan-3 imagery based on a rational function model (RFM), these nonlinear biases cannot be effectively compensated by an affine transformation. The sensor orientation accuracy is thereby worse than expected. In order to eliminate the influence of attitude oscillations on the RFM-based sensor orientation, a feasible nonlinear bias compensation approach for ZiYuan-3 imagery with cubic splines is proposed. In this approach, no actual ground control points (GCPs) are required to determine the cubic splines. First, the RPCs are calculated using a three-dimensional virtual control grid generated based on a physical sensor model. Second, one cubic spline is used to model the residual errors of the virtual control points in the row direction and another cubic spline is used to model the residual errors in the column direction. Then, the estimated cubic splines are used to compensate the nonlinear biases in the RPCs. Finally, the affine transformation parameters are used to compensate the residual biases in the RPCs. Three ZiYuan-3 images were tested. The experimental results showed that before the nonlinear bias compensation, the residual errors of the independent check points were nonlinearly biased. Even if the number of GCPs used to determine the affine transformation parameters was increased from 4 to 16, these nonlinear biases could not be effectively compensated. After the nonlinear bias compensation with the estimated cubic splines, the influence of the attitude oscillations could be eliminated. The RFM-based sensor orientation accuracies of the three ZiYuan-3 images reached 0.981 pixels, 0.890 pixels, and 1.093 pixels, which were respectively 42.1%, 48.3%, and 54.8% better than those achieved before the nonlinear bias compensation.

Robust control of the DC-DC boost converter based on the uncertainty and disturbance estimator

NASA Astrophysics Data System (ADS)

Oucheriah, Said

2017-11-01

In this paper, a robust non-linear controller based on the uncertainty and disturbance estimator (UDE) scheme is successfully developed and implemented for the output voltage regulation of the DC-DC boost converter. System uncertainties, external disturbances and unknown non-linear dynamics are lumped as a signal that is accurately estimated using a low-pass filter and their effects are cancelled by the controller. This methodology forms the basis of the UDE-based controller. A simple procedure is also developed that systematically determines the parameters of the controller to meet certain specifications. Using simulation, the effectiveness of the proposed controller is compared against the sliding-mode control (SMC). Experimental tests also show that the proposed controller is robust to system uncertainties, large input and load perturbations.

Robust fast controller design via nonlinear fractional differential equations.

PubMed

Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

2017-07-01

A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

The determination of third order linear models from a seventh order nonlinear jet engine model

NASA Technical Reports Server (NTRS)

Lalonde, Rick J.; Hartley, Tom T.; De Abreu-Garcia, J. Alex

1989-01-01

Results are presented that demonstrate how good reduced-order models can be obtained directly by recursive parameter identification using input/output (I/O) data of high-order nonlinear systems. Three different methods of obtaining a third-order linear model from a seventh-order nonlinear turbojet engine model are compared. The first method is to obtain a linear model from the original model and then reduce the linear model by standard reduction techniques such as residualization and balancing. The second method is to identify directly a third-order linear model by recursive least-squares parameter estimation using I/O data of the original model. The third method is to obtain a reduced-order model from the original model and then linearize the reduced model. Frequency responses are used as the performance measure to evaluate the reduced models. The reduced-order models along with their Bode plots are presented for comparison purposes.

Reinforcement learning state estimator.

PubMed

Morimoto, Jun; Doya, Kenji

2007-03-01

In this study, we propose a novel use of reinforcement learning for estimating hidden variables and parameters of nonlinear dynamical systems. A critical issue in hidden-state estimation is that we cannot directly observe estimation errors. However, by defining errors of observable variables as a delayed penalty, we can apply a reinforcement learning frame-work to state estimation problems. Specifically, we derive a method to construct a nonlinear state estimator by finding an appropriate feedback input gain using the policy gradient method. We tested the proposed method on single pendulum dynamics and show that the joint angle variable could be successfully estimated by observing only the angular velocity, and vice versa. In addition, we show that we could acquire a state estimator for the pendulum swing-up task in which a swing-up controller is also acquired by reinforcement learning simultaneously. Furthermore, we demonstrate that it is possible to estimate the dynamics of the pendulum itself while the hidden variables are estimated in the pendulum swing-up task. Application of the proposed method to a two-linked biped model is also presented.

Variations of cosmic large-scale structure covariance matrices across parameter space

NASA Astrophysics Data System (ADS)

Reischke, Robert; Kiessling, Alina; Schäfer, Björn Malte

2017-03-01

The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the non-linear evolution of the cosmic web. As highly non-linear clustering to date has only been described by numerical N-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work, we describe the change of the matter covariance and the weak lensing covariance matrix as a function of cosmological parameters by constructing a suitable basis, where we model the contribution to the covariance from non-linear structure formation using Eulerian perturbation theory at third order. We show that our formalism is capable of dealing with large matrices and reproduces expected degeneracies and scaling with cosmological parameters in a reliable way. Comparing our analytical results to numerical simulations, we find that the method describes the variation of the covariance matrix found in the SUNGLASS weak lensing simulation pipeline within the errors at one-loop and tree-level for the spectrum and the trispectrum, respectively, for multipoles up to ℓ ≤ 1300. We show that it is possible to optimize the sampling of parameter space where numerical simulations should be carried out by minimizing interpolation errors and propose a corresponding method to distribute points in parameter space in an economical way.

Nonlinear System Identification for Aeroelastic Systems with Application to Experimental Data

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

Representation and identification of a nonlinear aeroelastic pitch-plunge system as a model of the Nonlinear AutoRegressive, Moving Average eXogenous (NARMAX) class is considered. A nonlinear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (1) the outputs of the NARMAX model closely match those generated using continuous-time methods, and (2) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

Fisher Scoring Method for Parameter Estimation of Geographically Weighted Ordinal Logistic Regression (GWOLR) Model

NASA Astrophysics Data System (ADS)

Widyaningsih, Purnami; Retno Sari Saputro, Dewi; Nugrahani Putri, Aulia

2017-06-01

GWOLR model combines geographically weighted regression (GWR) and (ordinal logistic reression) OLR models. Its parameter estimation employs maximum likelihood estimation. Such parameter estimation, however, yields difficult-to-solve system of nonlinear equations, and therefore numerical approximation approach is required. The iterative approximation approach, in general, uses Newton-Raphson (NR) method. The NR method has a disadvantage—its Hessian matrix is always the second derivatives of each iteration so it does not always produce converging results. With regard to this matter, NR model is modified by substituting its Hessian matrix into Fisher information matrix, which is termed Fisher scoring (FS). The present research seeks to determine GWOLR model parameter estimation using Fisher scoring method and apply the estimation on data of the level of vulnerability to Dengue Hemorrhagic Fever (DHF) in Semarang. The research concludes that health facilities give the greatest contribution to the probability of the number of DHF sufferers in both villages. Based on the number of the sufferers, IR category of DHF in both villages can be determined.

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

An Iterative Local Updating Ensemble Smoother for Estimation and Uncertainty Assessment of Hydrologic Model Parameters With Multimodal Distributions

NASA Astrophysics Data System (ADS)

Zhang, Jiangjiang; Lin, Guang; Li, Weixuan; Wu, Laosheng; Zeng, Lingzao

2018-03-01

Ensemble smoother (ES) has been widely used in inverse modeling of hydrologic systems. However, for problems where the distribution of model parameters is multimodal, using ES directly would be problematic. One popular solution is to use a clustering algorithm to identify each mode and update the clusters with ES separately. However, this strategy may not be very efficient when the dimension of parameter space is high or the number of modes is large. Alternatively, we propose in this paper a very simple and efficient algorithm, i.e., the iterative local updating ensemble smoother (ILUES), to explore multimodal distributions of model parameters in nonlinear hydrologic systems. The ILUES algorithm works by updating local ensembles of each sample with ES to explore possible multimodal distributions. To achieve satisfactory data matches in nonlinear problems, we adopt an iterative form of ES to assimilate the measurements multiple times. Numerical cases involving nonlinearity and multimodality are tested to illustrate the performance of the proposed method. It is shown that overall the ILUES algorithm can well quantify the parametric uncertainties of complex hydrologic models, no matter whether the multimodal distribution exists.

Adaptive fuzzy predictive sliding control of uncertain nonlinear systems with bound-known input delay.

PubMed

Khazaee, Mostafa; Markazi, Amir H D; Omidi, Ehsan

2015-11-01

In this paper, a new Adaptive Fuzzy Predictive Sliding Mode Control (AFP-SMC) is presented for nonlinear systems with uncertain dynamics and unknown input delay. The control unit consists of a fuzzy inference system to approximate the ideal linearization control, together with a switching strategy to compensate for the estimation errors. Also, an adaptive fuzzy predictor is used to estimate the future values of the system states to compensate for the time delay. The adaptation laws are used to tune the controller and predictor parameters, which guarantee the stability based on a Lyapunov-Krasovskii functional. To evaluate the method effectiveness, the simulation and experiment on an overhead crane system are presented. According to the obtained results, AFP-SMC can effectively control the uncertain nonlinear systems, subject to input delays of known bound. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Solid-State Thermionic Power Generators: An Analytical Analysis in the Nonlinear Regime

NASA Astrophysics Data System (ADS)

Zebarjadi, M.

2017-07-01

Solid-state thermionic power generators are an alternative to thermoelectric modules. In this paper, we develop an analytical model to investigate the performance of these generators in the nonlinear regime. We identify dimensionless parameters determining their performance and provide measures to estimate an acceptable range of thermal and electrical resistances of thermionic generators. We find the relation between the optimum load resistance and the internal resistance and suggest guidelines for the design of thermionic power generators. Finally, we show that in the nonlinear regime, thermionic power generators can have efficiency values higher than the state-of-the-art thermoelectric modules.

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.

HRV analysis and blood pressure monitoring on weighing scale using BCG.

PubMed

Shin, Jae Hyuk; Park, Kwang Suk

2012-01-01

Using the Ballistocardiogram(BCG) measured on weighing scale, heart rate variability(HRV) and blood pressure were estimated. BCG was measured while subjects were on weighing scale in resting state and under the Valsalva maneuver and static exercise condition to induce the change in cardiac autonomic rhythm. Time domain, frequency domain and nonlinear HRV parameters were estimated from the measured BCG and compared with the ones calculated from ECG measured simultaneously. For blood pressure(BP) estimation, ECG was measured additionally on the feet using dry electrodes simultaneously installed on weighing scale and R-J intervals were extracted as a BP correlated parameter at every beat cycle. HRV estimation results shows the correlation higher than 0.97, and the estimated BP was similar to the measured BP with a reliable correlations.

Numerical Problem Solving Using Mathcad in Undergraduate Reaction Engineering

ERIC Educational Resources Information Center

Parulekar, Satish J.

2006-01-01

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

Non-linear identification of a squeeze-film damper

NASA Technical Reports Server (NTRS)

Stanway, Roger; Mottershead, John; Firoozian, Riaz

1987-01-01

Described is an experimental study to identify the damping laws associated with a squeeze-film vibration damper. This is achieved by using a non-linear filtering algorithm to process displacement responses of the damper ring to synchronous excitation and thus to estimate the parameters in an nth-power velocity model. The experimental facility is described in detail and a representative selection of results is included. The identified models are validated through the prediction of damper-ring orbits and comparison with observed responses.

Estimation on nonlinear damping in second order distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1989-01-01

An approximation and convergence theory for the identification of nonlinear damping in abstract wave equations is developed. It is assumed that the unknown dissipation mechanism to be identified can be described by a maximal monotone operator acting on the generalized velocity. The stiffness is assumed to be linear and symmetric. Functional analytic techniques are used to establish that solutions to a sequence of finite dimensional (Galerkin) approximating identification problems in some sense approximate a solution to the original infinite dimensional inverse problem.

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).

Aerodynamic parameter estimation via Fourier modulating function techniques

NASA Technical Reports Server (NTRS)

Pearson, A. E.

1995-01-01

Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models.

Non-linear motions in reprocessed GPS station position time series

NASA Astrophysics Data System (ADS)

Rudenko, Sergei; Gendt, Gerd

2010-05-01

Global Positioning System (GPS) data of about 400 globally distributed stations obtained at time span from 1998 till 2007 were reprocessed using GFZ Potsdam EPOS (Earth Parameter and Orbit System) software within International GNSS Service (IGS) Tide Gauge Benchmark Monitoring (TIGA) Pilot Project and IGS Data Reprocessing Campaign with the purpose to determine weekly precise coordinates of GPS stations located at or near tide gauges. Vertical motions of these stations are used to correct the vertical motions of tide gauges for local motions and to tie tide gauge measurements to the geocentric reference frame. Other estimated parameters include daily values of the Earth rotation parameters and their rates, as well as satellite antenna offsets. The solution GT1 derived is based on using absolute phase center variation model, ITRF2005 as a priori reference frame, and other new models. The solution contributed also to ITRF2008. The time series of station positions are analyzed to identify non-linear motions caused by different effects. The paper presents the time series of GPS station coordinates and investigates apparent non-linear motions and their influence on GPS station height rates.

Identification and control of plasma vertical position using neural network in Damavand tokamak.

PubMed

Rasouli, H; Rasouli, C; Koohi, A

2013-02-01

In this work, a nonlinear model is introduced to determine the vertical position of the plasma column in Damavand tokamak. Using this model as a simulator, a nonlinear neural network controller has been designed. In the first stage, the electronic drive and sensory circuits of Damavand tokamak are modified. These circuits can control the vertical position of the plasma column inside the vacuum vessel. Since the vertical position of plasma is an unstable parameter, a direct closed loop system identification algorithm is performed. In the second stage, a nonlinear model is identified for plasma vertical position, based on the multilayer perceptron (MLP) neural network (NN) structure. Estimation of simulator parameters has been performed by back-propagation error algorithm using Levenberg-Marquardt gradient descent optimization technique. The model is verified through simulation of the whole closed loop system using both simulator and actual plant in similar conditions. As the final stage, a MLP neural network controller is designed for simulator model. In the last step, online training is performed to tune the controller parameters. Simulation results justify using of the NN controller for the actual plant.

Estimation of dynamic stability parameters from drop model flight tests

NASA Technical Reports Server (NTRS)

Chambers, J. R.; Iliff, K. W.

1981-01-01

A recent NASA application of a remotely-piloted drop model to studies of the high angle-of-attack and spinning characteristics of a fighter configuration has provided an opportunity to evaluate and develop parameter estimation methods for the complex aerodynamic environment associated with high angles of attack. The paper discusses the overall drop model operation including descriptions of the model, instrumentation, launch and recovery operations, piloting concept, and parameter identification methods used. Static and dynamic stability derivatives were obtained for an angle-of-attack range from -20 deg to 53 deg. The results of the study indicated that the variations of the estimates with angle of attack were consistent for most of the static derivatives, and the effects of configuration modifications to the model (such as nose strakes) were apparent in the static derivative estimates. The dynamic derivatives exhibited greater uncertainty levels than the static derivatives, possibly due to nonlinear aerodynamics, model response characteristics, or additional derivatives.

Estimation variance bounds of importance sampling simulations in digital communication systems

NASA Technical Reports Server (NTRS)

Lu, D.; Yao, K.

1991-01-01

In practical applications of importance sampling (IS) simulation, two basic problems are encountered, that of determining the estimation variance and that of evaluating the proper IS parameters needed in the simulations. The authors derive new upper and lower bounds on the estimation variance which are applicable to IS techniques. The upper bound is simple to evaluate and may be minimized by the proper selection of the IS parameter. Thus, lower and upper bounds on the improvement ratio of various IS techniques relative to the direct Monte Carlo simulation are also available. These bounds are shown to be useful and computationally simple to obtain. Based on the proposed technique, one can readily find practical suboptimum IS parameters. Numerical results indicate that these bounding techniques are useful for IS simulations of linear and nonlinear communication systems with intersymbol interference in which bit error rate and IS estimation variances cannot be obtained readily using prior techniques.

libSRES: a C library for stochastic ranking evolution strategy for parameter estimation.

PubMed

Ji, Xinglai; Xu, Ying

2006-01-01

Estimation of kinetic parameters in a biochemical pathway or network represents a common problem in systems studies of biological processes. We have implemented a C library, named libSRES, to facilitate a fast implementation of computer software for study of non-linear biochemical pathways. This library implements a (mu, lambda)-ES evolutionary optimization algorithm that uses stochastic ranking as the constraint handling technique. Considering the amount of computing time it might require to solve a parameter-estimation problem, an MPI version of libSRES is provided for parallel implementation, as well as a simple user interface. libSRES is freely available and could be used directly in any C program as a library function. We have extensively tested the performance of libSRES on various pathway parameter-estimation problems and found its performance to be satisfactory. The source code (in C) is free for academic users at http://csbl.bmb.uga.edu/~jix/science/libSRES/

Predicting Loss-of-Control Boundaries Toward a Piloting Aid

NASA Technical Reports Server (NTRS)

Barlow, Jonathan; Stepanyan, Vahram; Krishnakumar, Kalmanje

2012-01-01

This work presents an approach to predicting loss-of-control with the goal of providing the pilot a decision aid focused on maintaining the pilot's control action within predicted loss-of-control boundaries. The predictive architecture combines quantitative loss-of-control boundaries, a data-based predictive control boundary estimation algorithm and an adaptive prediction method to estimate Markov model parameters in real-time. The data-based loss-of-control boundary estimation algorithm estimates the boundary of a safe set of control inputs that will keep the aircraft within the loss-of-control boundaries for a specified time horizon. The adaptive prediction model generates estimates of the system Markov Parameters, which are used by the data-based loss-of-control boundary estimation algorithm. The combined algorithm is applied to a nonlinear generic transport aircraft to illustrate the features of the architecture.

Analysis of blood pressure signal in patients with different ventricular ejection fraction using linear and non-linear methods.

PubMed

Arcentales, Andres; Rivera, Patricio; Caminal, Pere; Voss, Andreas; Bayes-Genis, Antonio; Giraldo, Beatriz F

2016-08-01

Changes in the left ventricle function produce alternans in the hemodynamic and electric behavior of the cardiovascular system. A total of 49 cardiomyopathy patients have been studied based on the blood pressure signal (BP), and were classified according to the left ventricular ejection fraction (LVEF) in low risk (LR: LVEF>35%, 17 patients) and high risk (HR: LVEF≤35, 32 patients) groups. We propose to characterize these patients using a linear and a nonlinear methods, based on the spectral estimation and the recurrence plot, respectively. From BP signal, we extracted each systolic time interval (STI), upward systolic slope (BPsl), and the difference between systolic and diastolic BP, defined as pulse pressure (PP). After, the best subset of parameters were obtained through the sequential feature selection (SFS) method. According to the results, the best classification was obtained using a combination of linear and nonlinear features from STI and PP parameters. For STI, the best combination was obtained considering the frequency peak and the diagonal structures of RP, with an area under the curve (AUC) of 79%. The same results were obtained when comparing PP values. Consequently, the use of combined linear and nonlinear parameters could improve the risk stratification of cardiomyopathy patients.

Nonlinear parameters of surface EMG in schizophrenia patients depend on kind of antipsychotic therapy

PubMed Central

Meigal, Alexander Yu.; Miroshnichenko, German G.; Kuzmina, Anna P.; Rissanen, Saara M.; Georgiadis, Stefanos D.; Karjalainen, Pasi A.

2015-01-01

We compared a set of surface EMG (sEMG) parameters in several groups of schizophrenia (SZ, n = 74) patients and healthy controls (n = 11) and coupled them with the clinical data. sEMG records were quantified with spectral, mutual information (MI) based and recurrence quantification analysis (RQA) parameters, and with approximate and sample entropies (ApEn and SampEn). Psychotic deterioration was estimated with Positive and Negative Syndrome Scale (PANSS) and with the positive subscale of PANSS. Neuroleptic-induced parkinsonism (NIP) motor symptoms were estimated with Simpson-Angus Scale (SAS). Dyskinesia was measured with Abnormal Involuntary Movement Scale (AIMS). We found that there was no difference in values of sEMG parameters between healthy controls and drug-naïve SZ patients. The most specific group was formed of SZ patients who were administered both typical and atypical antipsychotics (AP). Their sEMG parameters were significantly different from those of SZ patients taking either typical or atypical AP or taking no AP. This may represent a kind of synergistic effect of these two classes of AP. For the clinical data we found that PANSS, SAS, and AIMS were not correlated to any of the sEMG parameters. Conclusion: with nonlinear parameters of sEMG it is possible to reveal NIP in SZ patients, and it may help to discriminate between different clinical groups of SZ patients. Combined typical and atypical AP therapy has stronger effect on sEMG than a therapy with AP of only one class. PMID:26217236

Nonlinear parameters of surface EMG in schizophrenia patients depend on kind of antipsychotic therapy.

PubMed

Meigal, Alexander Yu; Miroshnichenko, German G; Kuzmina, Anna P; Rissanen, Saara M; Georgiadis, Stefanos D; Karjalainen, Pasi A

2015-01-01

We compared a set of surface EMG (sEMG) parameters in several groups of schizophrenia (SZ, n = 74) patients and healthy controls (n = 11) and coupled them with the clinical data. sEMG records were quantified with spectral, mutual information (MI) based and recurrence quantification analysis (RQA) parameters, and with approximate and sample entropies (ApEn and SampEn). Psychotic deterioration was estimated with Positive and Negative Syndrome Scale (PANSS) and with the positive subscale of PANSS. Neuroleptic-induced parkinsonism (NIP) motor symptoms were estimated with Simpson-Angus Scale (SAS). Dyskinesia was measured with Abnormal Involuntary Movement Scale (AIMS). We found that there was no difference in values of sEMG parameters between healthy controls and drug-naïve SZ patients. The most specific group was formed of SZ patients who were administered both typical and atypical antipsychotics (AP). Their sEMG parameters were significantly different from those of SZ patients taking either typical or atypical AP or taking no AP. This may represent a kind of synergistic effect of these two classes of AP. For the clinical data we found that PANSS, SAS, and AIMS were not correlated to any of the sEMG parameters. with nonlinear parameters of sEMG it is possible to reveal NIP in SZ patients, and it may help to discriminate between different clinical groups of SZ patients. Combined typical and atypical AP therapy has stronger effect on sEMG than a therapy with AP of only one class.

MTPA control of mechanical sensorless IPMSM based on adaptive nonlinear control.

PubMed

Najjar-Khodabakhsh, Abbas; Soltani, Jafar

2016-03-01

In this paper, an adaptive nonlinear control scheme has been proposed for implementing maximum torque per ampere (MTPA) control strategy corresponding to interior permanent magnet synchronous motor (IPMSM) drive. This control scheme is developed in the rotor d-q axis reference frame using adaptive input-output state feedback linearization (AIOFL) method. The drive system control stability is supported by Lyapunov theory. The motor inductances are online estimated by an estimation law obtained by AIOFL. The estimation errors of these parameters are proved to be asymptotically converged to zero. Based on minimizing the motor current amplitude, the MTPA control strategy is performed by using the nonlinear optimization technique while considering the online reference torque. The motor reference torque is generated by a conventional rotor speed PI controller. By performing MTPA control strategy, the generated online motor d-q reference currents were used in AIOFL controller to obtain the SV-PWM reference voltages and the online estimation of the motor d-q inductances. In addition, the stator resistance is online estimated using a conventional PI controller. Moreover, the rotor position is detected using the online estimation of the stator flux and online estimation of the motor q-axis inductance. Simulation and experimental results obtained prove the effectiveness and the capability of the proposed control method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

A new adaptive estimation method of spacecraft thermal mathematical model with an ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Akita, T.; Takaki, R.; Shima, E.

2012-04-01

An adaptive estimation method of spacecraft thermal mathematical model is presented. The method is based on the ensemble Kalman filter, which can effectively handle the nonlinearities contained in the thermal model. The state space equations of the thermal mathematical model is derived, where both temperature and uncertain thermal characteristic parameters are considered as the state variables. In the method, the thermal characteristic parameters are automatically estimated as the outputs of the filtered state variables, whereas, in the usual thermal model correlation, they are manually identified by experienced engineers using trial-and-error approach. A numerical experiment of a simple small satellite is provided to verify the effectiveness of the presented method.

Frequency-domain full-waveform inversion with non-linear descent directions

NASA Astrophysics Data System (ADS)

Geng, Yu; Pan, Wenyong; Innanen, Kristopher A.

2018-05-01

Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. We examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss-Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s0 is, in our scheme, proportional to at most (Δs/s0)3 in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss-Newton FWI update is proportional to (Δs/s0)2. For numerical implementation of more complex cases, we introduce a non-linear frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. The inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a benchmark FWI approach involving the standard gradient.

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

PubMed

Frey Law, Laura A; Shields, Richard K

2006-03-01

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

Uncertainty in simulated groundwater-quality trends in transient flow

USGS Publications Warehouse

Starn, J. Jeffrey; Bagtzoglou, Amvrossios; Robbins, Gary A.

2013-01-01

In numerical modeling of groundwater flow, the result of a given solution method is affected by the way in which transient flow conditions and geologic heterogeneity are simulated. An algorithm is demonstrated that simulates breakthrough curves at a pumping well by convolution-based particle tracking in a transient flow field for several synthetic basin-scale aquifers. In comparison to grid-based (Eulerian) methods, the particle (Lagrangian) method is better able to capture multimodal breakthrough caused by changes in pumping at the well, although the particle method may be apparently nonlinear because of the discrete nature of particle arrival times. Trial-and-error choice of number of particles and release times can perhaps overcome the apparent nonlinearity. Heterogeneous aquifer properties tend to smooth the effects of transient pumping, making it difficult to separate their effects in parameter estimation. Porosity, a new parameter added for advective transport, can be accurately estimated using both grid-based and particle-based methods, but predictions can be highly uncertain, even in the simple, nonreactive case.

Parameter estimation of a pulp digester model with derivative-free optimization strategies

NASA Astrophysics Data System (ADS)

Seiça, João C.; Romanenko, Andrey; Fernandes, Florbela P.; Santos, Lino O.; Fernandes, Natércia C. P.

2017-07-01

The work concerns the parameter estimation in the context of the mechanistic modelling of a pulp digester. The problem is cast as a box bounded nonlinear global optimization problem in order to minimize the mismatch between the model outputs with the experimental data observed at a real pulp and paper plant. MCSFilter and Simulated Annealing global optimization methods were used to solve the optimization problem. While the former took longer to converge to the global minimum, the latter terminated faster at a significantly higher value of the objective function and, thus, failed to find the global solution.

STATEQ: a nonlinear least-squares code for obtaining Martin thermodynamic representations of fluids in the gaseous and dense gaseous regions

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

Milora, S. L.

1976-02-01

The use of the code NLIN (IBM Share Program No. 1428) to obtain empirical thermodynamic pressure-volume-temperature (P-V-T) relationships for substances in the gaseous and dense gaseous states is described. When sufficient experimental data exist, the code STATEQ will provide least-squares estimates for the 21 parameters of the Martin model. Another code, APPROX, is described which also obtains parameter estimates for the model by making use of the approximate generalized behavior of fluids. Use of the codes is illustrated in obtaining thermodynamic representations for isobutane. (auth)

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

Multiparameter Estimation in Networked Quantum Sensors

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

Proctor, Timothy J.; Knott, Paul A.; Dunningham, Jacob A.

We introduce a general model for a network of quantum sensors, and we use this model to consider the question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. Thismore » immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or non-linear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.« less

Multiparameter Estimation in Networked Quantum Sensors

DOE PAGES

Proctor, Timothy J.; Knott, Paul A.; Dunningham, Jacob A.

2018-02-21

We introduce a general model for a network of quantum sensors, and we use this model to consider the question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. Thismore » immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or non-linear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.« less

Accurate determination of electronic transport properties of silicon wafers by nonlinear photocarrier radiometry with multiple pump beam sizes

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

Wang, Qian; University of the Chinese Academy of Sciences, Beijing 100039; Li, Bincheng, E-mail: bcli@uestc.ac.cn

2015-12-07

In this paper, photocarrier radiometry (PCR) technique with multiple pump beam sizes is employed to determine simultaneously the electronic transport parameters (the carrier lifetime, the carrier diffusion coefficient, and the front surface recombination velocity) of silicon wafers. By employing the multiple pump beam sizes, the influence of instrumental frequency response on the multi-parameter estimation is totally eliminated. A nonlinear PCR model is developed to interpret the PCR signal. Theoretical simulations are performed to investigate the uncertainties of the estimated parameter values by investigating the dependence of a mean square variance on the corresponding transport parameters and compared to that obtainedmore » by the conventional frequency-scan method, in which only the frequency dependences of the PCR amplitude and phase are recorded at single pump beam size. Simulation results show that the proposed multiple-pump-beam-size method can improve significantly the accuracy of the determination of the electronic transport parameters. Comparative experiments with a p-type silicon wafer with resistivity 0.1–0.2 Ω·cm are performed, and the electronic transport properties are determined simultaneously. The estimated uncertainties of the carrier lifetime, diffusion coefficient, and front surface recombination velocity are approximately ±10.7%, ±8.6%, and ±35.4% by the proposed multiple-pump-beam-size method, which is much improved than ±15.9%, ±29.1%, and >±50% by the conventional frequency-scan method. The transport parameters determined by the proposed multiple-pump-beam-size PCR method are in good agreement with that obtained by a steady-state PCR imaging technique.« less

Azimuthal Seismic Amplitude Variation with Offset and Azimuth Inversion in Weakly Anisotropic Media with Orthorhombic Symmetry

NASA Astrophysics Data System (ADS)

Pan, Xinpeng; Zhang, Guangzhi; Yin, Xingyao

2018-01-01

Seismic amplitude variation with offset and azimuth (AVOaz) inversion is well known as a popular and pragmatic tool utilized to estimate fracture parameters. A single set of vertical fractures aligned along a preferred horizontal direction embedded in a horizontally layered medium can be considered as an effective long-wavelength orthorhombic medium. Estimation of Thomsen's weak-anisotropy (WA) parameters and fracture weaknesses plays an important role in characterizing the orthorhombic anisotropy in a weakly anisotropic medium. Our goal is to demonstrate an orthorhombic anisotropic AVOaz inversion approach to describe the orthorhombic anisotropy utilizing the observable wide-azimuth seismic reflection data in a fractured reservoir with the assumption of orthorhombic symmetry. Combining Thomsen's WA theory and linear-slip model, we first derive a perturbation in stiffness matrix of a weakly anisotropic medium with orthorhombic symmetry under the assumption of small WA parameters and fracture weaknesses. Using the perturbation matrix and scattering function, we then derive an expression for linearized PP-wave reflection coefficient in terms of P- and S-wave moduli, density, Thomsen's WA parameters, and fracture weaknesses in such an orthorhombic medium, which avoids the complicated nonlinear relationship between the orthorhombic anisotropy and azimuthal seismic reflection data. Incorporating azimuthal seismic data and Bayesian inversion theory, the maximum a posteriori solutions of Thomsen's WA parameters and fracture weaknesses in a weakly anisotropic medium with orthorhombic symmetry are reasonably estimated with the constraints of Cauchy a priori probability distribution and smooth initial models of model parameters to enhance the inversion resolution and the nonlinear iteratively reweighted least squares strategy. The synthetic examples containing a moderate noise demonstrate the feasibility of the derived orthorhombic anisotropic AVOaz inversion method, and the real data illustrate the inversion stabilities of orthorhombic anisotropy in a fractured reservoir.

Analysis of pumping tests: Significance of well diameter, partial penetration, and noise

USGS Publications Warehouse

Heidari, M.; Ghiassi, K.; Mehnert, E.

1999-01-01

The nonlinear least squares (NLS) method was applied to pumping and recovery aquifer test data in confined and unconfined aquifers with finite diameter and partially penetrating pumping wells, and with partially penetrating piezometers or observation wells. It was demonstrated that noiseless and moderately noisy drawdown data from observation points located less than two saturated thicknesses of the aquifer from the pumping well produced an exact or acceptable set of parameters when the diameter of the pumping well was included in the analysis. The accuracy of the estimated parameters, particularly that of specific storage, decreased with increases in the noise level in the observed drawdown data. With consideration of the well radii, the noiseless drawdown data from the pumping well in an unconfined aquifer produced good estimates of horizontal and vertical hydraulic conductivities and specific yield, but the estimated specific storage was unacceptable. When noisy data from the pumping well were used, an acceptable set of parameters was not obtained. Further experiments with noisy drawdown data in an unconfined aquifer revealed that when the well diameter was included in the analysis, hydraulic conductivity, specific yield and vertical hydraulic conductivity may be estimated rather effectively from piezometers located over a range of distances from the pumping well. Estimation of specific storage became less reliable for piezemeters located at distances greater than the initial saturated thickness of the aquifer. Application of the NLS to field pumping and recovery data from a confined aquifer showed that the estimated parameters from the two tests were in good agreement only when the well diameter was included in the analysis. Without consideration of well radii, the estimated values of hydraulic conductivity from the pumping and recovery tests were off by a factor of four.The nonlinear least squares method was applied to pumping and recovery aquifer test data in confined and unconfined aquifers with finite diameter and partially penetrating piezometers and observation wells. Noiseless and moderately noisy drawdown data from observation points located less than two saturated thicknesses of the aquifer from the pumping well produced a set of parameters that agrees very well with piezometer test data when the diameter of the pumping well was included in the analysis. The accuracy of the estimated parameters decreased with increasing noise level.

Gas Path On-line Fault Diagnostics Using a Nonlinear Integrated Model for Gas Turbine Engines

NASA Astrophysics Data System (ADS)

Lu, Feng; Huang, Jin-quan; Ji, Chun-sheng; Zhang, Dong-dong; Jiao, Hua-bin

2014-08-01

Gas turbine engine gas path fault diagnosis is closely related technology that assists operators in managing the engine units. However, the performance gradual degradation is inevitable due to the usage, and it result in the model mismatch and then misdiagnosis by the popular model-based approach. In this paper, an on-line integrated architecture based on nonlinear model is developed for gas turbine engine anomaly detection and fault diagnosis over the course of the engine's life. These two engine models have different performance parameter update rate. One is the nonlinear real-time adaptive performance model with the spherical square-root unscented Kalman filter (SSR-UKF) producing performance estimates, and the other is a nonlinear baseline model for the measurement estimates. The fault detection and diagnosis logic is designed to discriminate sensor fault and component fault. This integration architecture is not only aware of long-term engine health degradation but also effective to detect gas path performance anomaly shifts while the engine continues to degrade. Compared to the existing architecture, the proposed approach has its benefit investigated in the experiment and analysis.

Nonlinear system identification based on Takagi-Sugeno fuzzy modeling and unscented Kalman filter.

PubMed

Vafamand, Navid; Arefi, Mohammad Mehdi; Khayatian, Alireza

2018-03-01

This paper proposes two novel Kalman-based learning algorithms for an online Takagi-Sugeno (TS) fuzzy model identification. The proposed approaches are designed based on the unscented Kalman filter (UKF) and the concept of dual estimation. Contrary to the extended Kalman filter (EKF) which utilizes derivatives of nonlinear functions, the UKF employs the unscented transformation. Consequently, non-differentiable membership functions can be considered in the structure of the TS models. This makes the proposed algorithms to be applicable for the online parameter calculation of wider classes of TS models compared to the recently published papers concerning the same issue. Furthermore, because of the great capability of the UKF in handling severe nonlinear dynamics, the proposed approaches can effectively approximate the nonlinear systems. Finally, numerical and practical examples are provided to show the advantages of the proposed approaches. Simulation results reveal the effectiveness of the proposed methods and performance improvement based on the root mean square (RMS) of the estimation error compared to the existing results. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear aeroacoustic characterization of Helmholtz resonators with a local-linear neuro-fuzzy network model

NASA Astrophysics Data System (ADS)

Förner, K.; Polifke, W.

2017-10-01

The nonlinear acoustic behavior of Helmholtz resonators is characterized by a data-based reduced-order model, which is obtained by a combination of high-resolution CFD simulation and system identification. It is shown that even in the nonlinear regime, a linear model is capable of describing the reflection behavior at a particular amplitude with quantitative accuracy. This observation motivates to choose a local-linear model structure for this study, which consists of a network of parallel linear submodels. A so-called fuzzy-neuron layer distributes the input signal over the linear submodels, depending on the root mean square of the particle velocity at the resonator surface. The resulting model structure is referred to as an local-linear neuro-fuzzy network. System identification techniques are used to estimate the free parameters of this model from training data. The training data are generated by CFD simulations of the resonator, with persistent acoustic excitation over a wide range of frequencies and sound pressure levels. The estimated nonlinear, reduced-order models show good agreement with CFD and experimental data over a wide range of amplitudes for several test cases.

Nonlinear Optical Properties and Subpicosecond Dynamics of Excitons and Electron-Hole Plasmas in Multiple Quantum Well Structures.

DTIC Science & Technology

1987-12-01

estimated from 10 S Ee 0.916 O(Pe) (7)rs Vel / y 7 where ve is the valley degeneracy factor, and $ is an anisotropy factor 10 1/6 sin- [(I Pe)l 124O...nergy, an potential, (2V,), have been deduced from the bro adening parameters of the jt structure The growth parameters with n-i p-i 498 having

Model-Based Engine Control Architecture with an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Csank, Jeffrey T.; Connolly, Joseph W.

2016-01-01

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The non-linear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

Model-Based Engine Control Architecture with an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Csank, Jeffrey T.; Connolly, Joseph W.

2016-01-01

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The nonlinear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

Modern control concepts in hydrology. [parameter identification in adaptive stochastic control approach

NASA Technical Reports Server (NTRS)

Duong, N.; Winn, C. B.; Johnson, G. R.

1975-01-01

Two approaches to an identification problem in hydrology are presented, based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time-invariant or time-dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and confirm the results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.

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.

New methods of testing nonlinear hypothesis using iterative NLLS estimator

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper discusses the method of testing nonlinear hypothesis using iterative Nonlinear Least Squares (NLLS) estimator. Takeshi Amemiya [1] explained this method. However in the present research paper, a modified Wald test statistic due to Engle, Robert [6] is proposed to test the nonlinear hypothesis using iterative NLLS estimator. An alternative method for testing nonlinear hypothesis using iterative NLLS estimator based on nonlinear hypothesis using iterative NLLS estimator based on nonlinear studentized residuals has been proposed. In this research article an innovative method of testing nonlinear hypothesis using iterative restricted NLLS estimator is derived. Pesaran and Deaton [10] explained the methods of testing nonlinear hypothesis. This paper uses asymptotic properties of nonlinear least squares estimator proposed by Jenrich [8]. The main purpose of this paper is to provide very innovative methods of testing nonlinear hypothesis using iterative NLLS estimator, iterative NLLS estimator based on nonlinear studentized residuals and iterative restricted NLLS estimator. Eakambaram et al. [12] discussed least absolute deviation estimations versus nonlinear regression model with heteroscedastic errors and also they studied the problem of heteroscedasticity with reference to nonlinear regression models with suitable illustration. William Grene [13] examined the interaction effect in nonlinear models disused by Ai and Norton [14] and suggested ways to examine the effects that do not involve statistical testing. Peter [15] provided guidelines for identifying composite hypothesis and addressing the probability of false rejection for multiple hypotheses.

The contribution of NOAA/CMDL ground-based measurements to understanding long-term stratospheric changes

NASA Astrophysics Data System (ADS)

Montzka, S. A.; Butler, J. H.; Dutton, G.; Thompson, T. M.; Hall, B.; Mondeel, D. J.; Elkins, J. W.

2005-05-01

The El-Nino/Southern-Oscillation (ENSO) dominates interannual climate variability and plays, therefore, a key role in seasonal-to-interannual prediction. Much is known by now about the main physical mechanisms that give rise to and modulate ENSO, but the values of several parameters that enter these mechanisms are an important unknown. We apply Extended Kalman Filtering (EKF) for both model state and parameter estimation in an intermediate, nonlinear, coupled ocean--atmosphere model of ENSO. The coupled model consists of an upper-ocean, reduced-gravity model of the Tropical Pacific and a steady-state atmospheric response to the sea surface temperature (SST). The model errors are assumed to be mainly in the atmospheric wind stress, and assimilated data are equatorial Pacific SSTs. Model behavior is very sensitive to two key parameters: (i) μ, the ocean-atmosphere coupling coefficient between SST and wind stress anomalies; and (ii) δs, the surface-layer coefficient. Previous work has shown that δs determines the period of the model's self-sustained oscillation, while μ measures the degree of nonlinearity. Depending on the values of these parameters, the spatio-temporal pattern of model solutions is either that of a delayed oscillator or of a westward propagating mode. Estimation of these parameters is tested first on synthetic data and allows us to recover the delayed-oscillator mode starting from model parameter values that correspond to the westward-propagating case. Assimilation of SST data from the NCEP-NCAR Reanalysis-2 shows that the parameters can vary on fairly short time scales and switch between values that approximate the two distinct modes of ENSO behavior. Rapid adjustments of these parameters occur, in particular, during strong ENSO events. Ways to apply EKF parameter estimation efficiently to state-of-the-art coupled ocean--atmosphere GCMs will be discussed.

VBA: A Probabilistic Treatment of Nonlinear Models for Neurobiological and Behavioural Data

PubMed Central

Daunizeau, Jean; Adam, Vincent; Rigoux, Lionel

2014-01-01

This work is in line with an on-going effort tending toward a computational (quantitative and refutable) understanding of human neuro-cognitive processes. Many sophisticated models for behavioural and neurobiological data have flourished during the past decade. Most of these models are partly unspecified (i.e. they have unknown parameters) and nonlinear. This makes them difficult to peer with a formal statistical data analysis framework. In turn, this compromises the reproducibility of model-based empirical studies. This work exposes a software toolbox that provides generic, efficient and robust probabilistic solutions to the three problems of model-based analysis of empirical data: (i) data simulation, (ii) parameter estimation/model selection, and (iii) experimental design optimization. PMID:24465198

Adaptive control of servo system based on LuGre model

NASA Astrophysics Data System (ADS)

Jin, Wang; Niancong, Liu; Jianlong, Chen; Weitao, Geng

2018-03-01

This paper established a mechanical model of feed system based on LuGre model. In order to solve the influence of nonlinear factors on the system running stability, a nonlinear single observer is designed to estimate the parameter z in the LuGre model and an adaptive friction compensation controller is designed. Simulink simulation results show that the control method can effectively suppress the adverse effects of friction and external disturbances. The simulation show that the adaptive parameter kz is between 0.11-0.13, and the value of gamma1 is between 1.9-2.1. Position tracking error reaches level 10-3 and is stabilized near 0 values within 0.3 seconds, the compensation method has better tracking accuracy and robustness.

DUAL STATE-PARAMETER UPDATING SCHEME ON A CONCEPTUAL HYDROLOGIC MODEL USING SEQUENTIAL MONTE CARLO FILTERS

NASA Astrophysics Data System (ADS)

Noh, Seong Jin; Tachikawa, Yasuto; Shiiba, Michiharu; Kim, Sunmin

Applications of data assimilation techniques have been widely used to improve upon the predictability of hydrologic modeling. Among various data assimilation techniques, sequential Monte Carlo (SMC) filters, known as "particle filters" provide the capability to handle non-linear and non-Gaussian state-space models. This paper proposes a dual state-parameter updating scheme (DUS) based on SMC methods to estimate both state and parameter variables of a hydrologic model. We introduce a kernel smoothing method for the robust estimation of uncertain model parameters in the DUS. The applicability of the dual updating scheme is illustrated using the implementation of the storage function model on a middle-sized Japanese catchment. We also compare performance results of DUS combined with various SMC methods, such as SIR, ASIR and RPF.

An adaptive control scheme for a flexible manipulator

NASA Technical Reports Server (NTRS)

Yang, T. C.; Yang, J. C. S.; Kudva, P.

1987-01-01

The problem of controlling a single link flexible manipulator is considered. A self-tuning adaptive control scheme is proposed which consists of a least squares on-line parameter identification of an equivalent linear model followed by a tuning of the gains of a pole placement controller using the parameter estimates. Since the initial parameter values for this model are assumed unknown, the use of arbitrarily chosen initial parameter estimates in the adaptive controller would result in undesirable transient effects. Hence, the initial stage control is carried out with a PID controller. Once the identified parameters have converged, control is transferred to the adaptive controller. Naturally, the relevant issues in this scheme are tests for parameter convergence and minimization of overshoots during control switch-over. To demonstrate the effectiveness of the proposed scheme, simulation results are presented with an analytical nonlinear dynamic model of a single link flexible manipulator.

Estimation of hysteretic damping of structures by stochastic subspace identification

NASA Astrophysics Data System (ADS)

Bajrić, Anela; Høgsberg, Jan

2018-05-01

Output-only system identification techniques can estimate modal parameters of structures represented by linear time-invariant systems. However, the extension of the techniques to structures exhibiting non-linear behavior has not received much attention. This paper presents an output-only system identification method suitable for random response of dynamic systems with hysteretic damping. The method applies the concept of Stochastic Subspace Identification (SSI) to estimate the model parameters of a dynamic system with hysteretic damping. The restoring force is represented by the Bouc-Wen model, for which an equivalent linear relaxation model is derived. Hysteretic properties can be encountered in engineering structures exposed to severe cyclic environmental loads, as well as in vibration mitigation devices, such as Magneto-Rheological (MR) dampers. The identification technique incorporates the equivalent linear damper model in the estimation procedure. Synthetic data, representing the random vibrations of systems with hysteresis, validate the estimated system parameters by the presented identification method at low and high-levels of excitation amplitudes.

Digital signal processing and control and estimation theory -- Points of tangency, area of intersection, and parallel directions

NASA Technical Reports Server (NTRS)

Willsky, A. S.

1976-01-01

A number of current research directions in the fields of digital signal processing and modern control and estimation theory were studied. Topics such as stability theory, linear prediction and parameter identification, system analysis and implementation, two-dimensional filtering, decentralized control and estimation, image processing, and nonlinear system theory were examined in order to uncover some of the basic similarities and differences in the goals, techniques, and philosophy of the two disciplines. An extensive bibliography is included.

On estimating the phase of a periodic waveform in additive Gaussian noise, part 3

NASA Technical Reports Server (NTRS)

Rauch, L. L.

1991-01-01

Motivated by advances in signal processing technology that support more complex algorithms, researchers have taken a new look at the problem of estimating the phase and other parameters of a nearly periodic waveform in additive Gaussian noise, based on observation during a given time interval. Parts 1 and 2 are very briefly reviewed. In part 3, the actual performances of some of the highly nonlinear estimation algorithms of parts 1 and 2 are evaluated by numerical simulation using Monte Carlo techniques.

DAISY: a new software tool to test global identifiability of biological and physiological systems.

PubMed

Bellu, Giuseppina; Saccomani, Maria Pia; Audoly, Stefania; D'Angiò, Leontina

2007-10-01

A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a differential algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/.

Simulation of broadband ground motion including nonlinear soil effects for a magnitude 6.5 earthquake on the Seattle fault, Seattle, Washington

USGS Publications Warehouse

Hartzell, S.; Leeds, A.; Frankel, A.; Williams, R.A.; Odum, J.; Stephenson, W.; Silva, W.

2002-01-01

The Seattle fault poses a significant seismic hazard to the city of Seattle, Washington. A hybrid, low-frequency, high-frequency method is used to calculate broadband (0-20 Hz) ground-motion time histories for a M 6.5 earthquake on the Seattle fault. Low frequencies (1 Hz) are calculated by a stochastic method that uses a fractal subevent size distribution to give an ω-2 displacement spectrum. Time histories are calculated for a grid of stations and then corrected for the local site response using a classification scheme based on the surficial geology. Average shear-wave velocity profiles are developed for six surficial geologic units: artificial fill, modified land, Esperance sand, Lawton clay, till, and Tertiary sandstone. These profiles together with other soil parameters are used to compare linear, equivalent-linear, and nonlinear predictions of ground motion in the frequency band 0-15 Hz. Linear site-response corrections are found to yield unreasonably large ground motions. Equivalent-linear and nonlinear calculations give peak values similar to the 1994 Northridge, California, earthquake and those predicted by regression relationships. Ground-motion variance is estimated for (1) randomization of the velocity profiles, (2) variation in source parameters, and (3) choice of nonlinear model. Within the limits of the models tested, the results are found to be most sensitive to the nonlinear model and soil parameters, notably the over consolidation ratio.

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.

Non-Linear System Identification for Aeroelastic Systems with Application to Experimental Data

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

Representation and identification of a non-linear aeroelastic pitch-plunge system as a model of the NARMAX class is considered. A non-linear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (i) the outputs of the NARMAX model match closely those generated using continuous-time methods and (ii) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

Artificial Neural Networks applied to estimate permeability, porosity and intrinsic attenuation using seismic attributes and well-log data

NASA Astrophysics Data System (ADS)

Iturrarán-Viveros, Ursula; Parra, Jorge O.

2014-08-01

Permeability and porosity are two fundamental reservoir properties which relate to the amount of fluid contained in a reservoir and its ability to flow. The intrinsic attenuation is another important parameter since it is related to porosity, permeability, oil and gas saturation and these parameters significantly affect the seismic signature of a reservoir. We apply Artificial Neural Network (ANN) models to predict permeability (k) and porosity (ϕ) for a carbonate aquifer in southeastern Florida and to predict intrinsic attenuation (1/Q) for a sand-shale oil reservoir in northeast Texas. In this study, the Gamma test (a revolutionary estimator of the noise in a data set) has been used as a mathematically non-parametric nonlinear smooth modeling tool to choose the best input combination of seismic attributes to estimate k and ϕ, and the best combination of well-logs to estimate 1/Q. This saves time during the construction and training of ANN models and also sets a lower bound for the mean squared error to prevent over-training. The Neural Network method successfully delineates a highly permeable zone that corresponds to a high water production in the aquifer. The Gamma test found nonlinear relations that were not visible to linear regression allowing us to generalize the ANN estimations of k, ϕ and 1/Q for their respective sets of patterns that were not used during the learning phase.

Effect of correlated observation error on parameters, predictions, and uncertainty

USGS Publications Warehouse

Tiedeman, Claire; Green, Christopher T.

2013-01-01

Correlations among observation errors are typically omitted when calculating observation weights for model calibration by inverse methods. We explore the effects of omitting these correlations on estimates of parameters, predictions, and uncertainties. First, we develop a new analytical expression for the difference in parameter variance estimated with and without error correlations for a simple one-parameter two-observation inverse model. Results indicate that omitting error correlations from both the weight matrix and the variance calculation can either increase or decrease the parameter variance, depending on the values of error correlation (ρ) and the ratio of dimensionless scaled sensitivities (rdss). For small ρ, the difference in variance is always small, but for large ρ, the difference varies widely depending on the sign and magnitude of rdss. Next, we consider a groundwater reactive transport model of denitrification with four parameters and correlated geochemical observation errors that are computed by an error-propagation approach that is new for hydrogeologic studies. We compare parameter estimates, predictions, and uncertainties obtained with and without the error correlations. Omitting the correlations modestly to substantially changes parameter estimates, and causes both increases and decreases of parameter variances, consistent with the analytical expression. Differences in predictions for the models calibrated with and without error correlations can be greater than parameter differences when both are considered relative to their respective confidence intervals. These results indicate that including observation error correlations in weighting for nonlinear regression can have important effects on parameter estimates, predictions, and their respective uncertainties.

Analytical flow duration curves for summer streamflow in Switzerland

NASA Astrophysics Data System (ADS)

Santos, Ana Clara; Portela, Maria Manuela; Rinaldo, Andrea; Schaefli, Bettina

2018-04-01

This paper proposes a systematic assessment of the performance of an analytical modeling framework for streamflow probability distributions for a set of 25 Swiss catchments. These catchments show a wide range of hydroclimatic regimes, including namely snow-influenced streamflows. The model parameters are calculated from a spatially averaged gridded daily precipitation data set and from observed daily discharge time series, both in a forward estimation mode (direct parameter calculation from observed data) and in an inverse estimation mode (maximum likelihood estimation). The performance of the linear and the nonlinear model versions is assessed in terms of reproducing observed flow duration curves and their natural variability. Overall, the nonlinear model version outperforms the linear model for all regimes, but the linear model shows a notable performance increase with catchment elevation. More importantly, the obtained results demonstrate that the analytical model performs well for summer discharge for all analyzed streamflow regimes, ranging from rainfall-driven regimes with summer low flow to snow and glacier regimes with summer high flow. These results suggest that the model's encoding of discharge-generating events based on stochastic soil moisture dynamics is more flexible than previously thought. As shown in this paper, the presence of snowmelt or ice melt is accommodated by a relative increase in the discharge-generating frequency, a key parameter of the model. Explicit quantification of this frequency increase as a function of mean catchment meteorological conditions is left for future research.

Estimating Tree Height-Diameter Models with the Bayesian Method

PubMed Central

Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the “best” model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2. PMID:24711733

Estimating tree height-diameter models with the Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the "best" model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2.

Understanding the Percolation Characteristics of Nonlinear Composite Dielectrics

PubMed Central

Yang, Xiao; Hu, Jun; Chen, Shuiming; He, Jinliang

2016-01-01

Nonlinear composite dielectrics can function as smart materials for stress control and field grading in all fields of electrical insulations. The percolation process is a significant issue of composite dielectrics. However, the classic percolation theory mainly deals with traditional composites in which the electrical parameters of both insulation matrix and conducting fillers are independent of the applied electric field. This paper measured the nonlinear V-I characteristics of ZnO microvaristors/silicone rubber composites with several filler concentrations around an estimated percolation threshold. For the comparison with the experiment, a new microstructural model is proposed to simulate the nonlinear conducting behavior of the composite dielectrics modified by metal oxide fillers, which is based on the Voronoi network and considers the breakdown feature of the insulation matrix for near percolated composites. Through both experiment and simulation, the interior conducting mechanism and percolation process of the nonlinear composites were presented and a specific percolation threshold was determined as 33%. This work has provided a solution to better understand the characteristics of nonlinear composite dielectrics. PMID:27476998

Understanding the Percolation Characteristics of Nonlinear Composite Dielectrics

NASA Astrophysics Data System (ADS)

Yang, Xiao; Hu, Jun; Chen, Shuiming; He, Jinliang

2016-08-01

Nonlinear composite dielectrics can function as smart materials for stress control and field grading in all fields of electrical insulations. The percolation process is a significant issue of composite dielectrics. However, the classic percolation theory mainly deals with traditional composites in which the electrical parameters of both insulation matrix and conducting fillers are independent of the applied electric field. This paper measured the nonlinear V-I characteristics of ZnO microvaristors/silicone rubber composites with several filler concentrations around an estimated percolation threshold. For the comparison with the experiment, a new microstructural model is proposed to simulate the nonlinear conducting behavior of the composite dielectrics modified by metal oxide fillers, which is based on the Voronoi network and considers the breakdown feature of the insulation matrix for near percolated composites. Through both experiment and simulation, the interior conducting mechanism and percolation process of the nonlinear composites were presented and a specific percolation threshold was determined as 33%. This work has provided a solution to better understand the characteristics of nonlinear composite dielectrics.

Adaptive Neural Networks Prescribed Performance Control Design for Switched Interconnected Uncertain Nonlinear Systems.

PubMed

Li, Yongming; Tong, Shaocheng

2017-06-28

In this paper, an adaptive neural networks (NNs)-based decentralized control scheme with the prescribed performance is proposed for uncertain switched nonstrict-feedback interconnected nonlinear systems. It is assumed that nonlinear interconnected terms and nonlinear functions of the concerned systems are unknown, and also the switching signals are unknown and arbitrary. A linear state estimator is constructed to solve the problem of unmeasured states. The NNs are employed to approximate unknown interconnected terms and nonlinear functions. A new output feedback decentralized control scheme is developed by using the adaptive backstepping design technique. The control design problem of nonlinear interconnected switched systems with unknown switching signals can be solved by the proposed scheme, and only a tuning parameter is needed for each subsystem. The proposed scheme can ensure that all variables of the control systems are semi-globally uniformly ultimately bounded and the tracking errors converge to a small residual set with the prescribed performance bound. The effectiveness of the proposed control approach is verified by some simulation results.

Disentangling Redshift-Space Distortions and Nonlinear Bias using the 2D Power Spectrum

DOE PAGES

Jennings, Elise; Wechsler, Risa H.

2015-08-07

We present the nonlinear 2D galaxy power spectrum, P(k, µ), in redshift space, measured from the Dark Sky simulations, using galaxy catalogs constructed with both halo occupation distribution and subhalo abundance matching methods, chosen to represent an intermediate redshift sample of luminous red galaxies. We find that the information content in individual µ (cosine of the angle to the line of sight) bins is substantially richer then multipole moments, and show that this can be used to isolate the impact of nonlinear growth and redshift space distortion (RSD) effects. Using the µ < 0.2 simulation data, which we show ismore » not impacted by RSD effects, we can successfully measure the nonlinear bias to an accuracy of ~ 5% at k < 0.6hMpc-1 . This use of individual µ bins to extract the nonlinear bias successfully removes a large parameter degeneracy when constraining the linear growth rate of structure. We carry out a joint parameter estimation, using the low µ simulation data to constrain the nonlinear bias, and µ > 0.2 to constrain the growth rate and show that f can be constrained to ~ 26(22)% to a kmax < 0.4(0.6)hMpc-1 from clustering alone using a simple dispersion model, for a range of galaxy models. Our analysis of individual µ bins also reveals interesting physical effects which arise simply from different methods of populating halos with galaxies. We also find a prominent turnaround scale, at which RSD damping effects are greater then the nonlinear growth, which differs not only for each µ bin but also for each galaxy model. These features may provide unique signatures which could be used to shed light on the galaxy–dark matter connection. Furthermore, the idea of separating nonlinear growth and RSD effects making use of the full information in the 2D galaxy power spectrum yields significant improvements in constraining cosmological parameters and may be a promising probe of galaxy formation models.« less

Inverse Analysis of Irradiated NuclearMaterial Gamma Spectra via Nonlinear Optimization

NASA Astrophysics Data System (ADS)

Dean, Garrett James

Nuclear forensics is the collection of technical methods used to identify the provenance of nuclear material interdicted outside of regulatory control. Techniques employed in nuclear forensics include optical microscopy, gas chromatography, mass spectrometry, and alpha, beta, and gamma spectrometry. This dissertation focuses on the application of inverse analysis to gamma spectroscopy to estimate the history of pulse irradiated nuclear material. Previous work in this area has (1) utilized destructive analysis techniques to supplement the nondestructive gamma measurements, and (2) been applied to samples composed of spent nuclear fuel with long irradiation and cooling times. Previous analyses have employed local nonlinear solvers, simple empirical models of gamma spectral features, and simple detector models of gamma spectral features. The algorithm described in this dissertation uses a forward model of the irradiation and measurement process within a global nonlinear optimizer to estimate the unknown irradiation history of pulse irradiated nuclear material. The forward model includes a detector response function for photopeaks only. The algorithm uses a novel hybrid global and local search algorithm to quickly estimate the irradiation parameters, including neutron fluence, cooling time and original composition. Sequential, time correlated series of measurements are used to reduce the uncertainty in the estimated irradiation parameters. This algorithm allows for in situ measurements of interdicted irradiated material. The increase in analysis speed comes with a decrease in information that can be determined, but the sample fluence, cooling time, and composition can be determined within minutes of a measurement. Furthermore, pulse irradiated nuclear material has a characteristic feature that irradiation time and flux cannot be independently estimated. The algorithm has been tested against pulse irradiated samples of pure special nuclear material with cooling times of four minutes to seven hours. The algorithm described is capable of determining the cooling time and fluence the sample was exposed to within 10% as well as roughly estimating the relative concentrations of nuclides present in the original composition.

Using the nonlinear aquifer storage-discharge relationship to simulate the base flow of glacier- and snowmelt-dominated basins in northwest China

NASA Astrophysics Data System (ADS)

Gan, R.; Luo, Y.

2013-09-01

Base flow is an important component in hydrological modeling. This process is usually modeled by using the linear aquifer storage-discharge relation approach, although the outflow from groundwater aquifers is nonlinear. To identify the accuracy of base flow estimates in rivers dominated by snowmelt and/or glacier melt in arid and cold northwestern China, a nonlinear storage-discharge relationship for use in SWAT (Soil Water Assessment Tool) modeling was developed and applied to the Manas River basin in the Tian Shan Mountains. Linear reservoir models and a digital filter program were used for comparisons. Meanwhile, numerical analysis of recession curves from 78 river gauge stations revealed variation in the parameters of the nonlinear relationship. It was found that the nonlinear reservoir model can improve the streamflow simulation, especially for low-flow period. The higher Nash-Sutcliffe efficiency, logarithmic efficiency, and volumetric efficiency, and lower percent bias were obtained when compared to the one-linear reservoir approach. The parameter b of the aquifer storage-discharge function varied mostly between 0.0 and 0.1, which is much smaller than the suggested value of 0.5. The coefficient a of the function is related to catchment properties, primarily the basin and glacier areas.

Optimization of CW Fiber Lasers With Strong Nonlinear Cavity Dynamics

NASA Astrophysics Data System (ADS)

Shtyrina, O. V.; Efremov, S. A.; Yarutkina, I. A.; Skidin, A. S.; Fedoruk, M. P.

2018-04-01

In present work the equation for the saturated gain is derived from one-level gain equations describing the energy evolution inside the laser cavity. It is shown how to derive the parameters of the mathematical model from the experimental results. The numerically-estimated energy and spectrum of the signal are in good agreement with the experiment. Also, the optimization of the output energy is performed for a given set of model parameters.

Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

NASA Astrophysics Data System (ADS)

Fukuda, Jun'ichi; Johnson, Kaj M.

2010-06-01

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework. In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

INDES User's guide multistep input design with nonlinear rotorcraft modeling

NASA Technical Reports Server (NTRS)

1979-01-01

The INDES computer program, a multistep input design program used as part of a data processing technique for rotorcraft systems identification, is described. Flight test inputs base on INDES improve the accuracy of parameter estimates. The input design algorithm, program input, and program output are presented.

Parameter Estimation Versus Homogenization Techniques in Time-Domain Characterization of Composite Dielectrics

DTIC Science & Technology

2006-08-22

H. T. Banks, V. A. Bokil, D. Cioranescu, N. L. Gibson, G. Griso, and B. Miara , Homogeniza- tion of periodically varying coefficients in...Terahertz signals, Nonlinear Analysis: Real World Applications, 6 (2005), 381–416. [6] A. Bossavit, G. Griso, and B. Miara , Modeling of periodic

Individual tree growth models for natural even-aged shortleaf pine

Treesearch

Chakra B. Budhathoki; Thomas B. Lynch; James M. Guldin

2006-01-01

Shortleaf pine (Pinus echinata Mill.) measurements were available from permanent plots established in even-aged stands of the Ouachita Mountains for studying growth. Annual basal area growth was modeled with a least-squares nonlinear regression method utilizing three measurements. The analysis showed that the parameter estimates were in agreement...

Housing price prediction: parametric versus semi-parametric spatial hedonic models

NASA Astrophysics Data System (ADS)

Montero, José-María; Mínguez, Román; Fernández-Avilés, Gema

2018-01-01

House price prediction is a hot topic in the economic literature. House price prediction has traditionally been approached using a-spatial linear (or intrinsically linear) hedonic models. It has been shown, however, that spatial effects are inherent in house pricing. This article considers parametric and semi-parametric spatial hedonic model variants that account for spatial autocorrelation, spatial heterogeneity and (smooth and nonparametrically specified) nonlinearities using penalized splines methodology. The models are represented as a mixed model that allow for the estimation of the smoothing parameters along with the other parameters of the model. To assess the out-of-sample performance of the models, the paper uses a database containing the price and characteristics of 10,512 homes in Madrid, Spain (Q1 2010). The results obtained suggest that the nonlinear models accounting for spatial heterogeneity and flexible nonlinear relationships between some of the individual or areal characteristics of the houses and their prices are the best strategies for house price prediction.

Fast nonlinear gravity inversion in spherical coordinates with application to the South American Moho

NASA Astrophysics Data System (ADS)

Uieda, Leonardo; Barbosa, Valéria C. F.

2017-01-01

Estimating the relief of the Moho from gravity data is a computationally intensive nonlinear inverse problem. What is more, the modelling must take the Earths curvature into account when the study area is of regional scale or greater. We present a regularized nonlinear gravity inversion method that has a low computational footprint and employs a spherical Earth approximation. To achieve this, we combine the highly efficient Bott's method with smoothness regularization and a discretization of the anomalous Moho into tesseroids (spherical prisms). The computational efficiency of our method is attained by harnessing the fact that all matrices involved are sparse. The inversion results are controlled by three hyperparameters: the regularization parameter, the anomalous Moho density-contrast, and the reference Moho depth. We estimate the regularization parameter using the method of hold-out cross-validation. Additionally, we estimate the density-contrast and the reference depth using knowledge of the Moho depth at certain points. We apply the proposed method to estimate the Moho depth for the South American continent using satellite gravity data and seismological data. The final Moho model is in accordance with previous gravity-derived models and seismological data. The misfit to the gravity and seismological data is worse in the Andes and best in oceanic areas, central Brazil and Patagonia, and along the Atlantic coast. Similarly to previous results, the model suggests a thinner crust of 30-35 km under the Andean foreland basins. Discrepancies with the seismological data are greatest in the Guyana Shield, the central Solimões and Amazonas Basins, the Paraná Basin, and the Borborema province. These differences suggest the existence of crustal or mantle density anomalies that were unaccounted for during gravity data processing.

Model-Based Estimation of Ankle Joint Stiffness

PubMed Central

Misgeld, Berno J. E.; Zhang, Tony; Lüken, Markus J.; Leonhardt, Steffen

2017-01-01

We address the estimation of biomechanical parameters with wearable measurement technologies. In particular, we focus on the estimation of sagittal plane ankle joint stiffness in dorsiflexion/plantar flexion. For this estimation, a novel nonlinear biomechanical model of the lower leg was formulated that is driven by electromyographic signals. The model incorporates a two-dimensional kinematic description in the sagittal plane for the calculation of muscle lever arms and torques. To reduce estimation errors due to model uncertainties, a filtering algorithm is necessary that employs segmental orientation sensor measurements. Because of the model’s inherent nonlinearities and nonsmooth dynamics, a square-root cubature Kalman filter was developed. The performance of the novel estimation approach was evaluated in silico and in an experimental procedure. The experimental study was conducted with body-worn sensors and a test-bench that was specifically designed to obtain reference angle and torque measurements for a single joint. Results show that the filter is able to reconstruct joint angle positions, velocities and torque, as well as, joint stiffness during experimental test bench movements. PMID:28353683

Thermal Property Parameter Estimation of TPS Materials

NASA Technical Reports Server (NTRS)

Maddren, Jesse

1998-01-01

Accurate knowledge of the thermophysical properties of TPS (thermal protection system) materials is necessary for pre-flight design and post-flight data analysis. Thermal properties, such as thermal conductivity and the volumetric specific heat, can be estimated from transient temperature measurements using non-linear parameter estimation methods. Property values are derived by minimizing a functional of the differences between measured and calculated temperatures. High temperature thermal response testing of TPS materials is usually done in arc-jet or radiant heating facilities which provide a quasi one-dimensional heating environment. Last year, under the NASA-ASEE-Stanford Fellowship Program, my work focused on developing a radiant heating apparatus. This year, I have worked on increasing the fidelity of the experimental measurements, optimizing the experimental procedures and interpreting the data.

State and parameter estimation of spatiotemporally chaotic systems illustrated by an application to Rayleigh-Bénard convection.

PubMed

Cornick, Matthew; Hunt, Brian; Ott, Edward; Kurtuldu, Huseyin; Schatz, Michael F

2009-03-01

Data assimilation refers to the process of estimating a system's state from a time series of measurements (which may be noisy or incomplete) in conjunction with a model for the system's time evolution. Here we demonstrate the applicability of a recently developed data assimilation method, the local ensemble transform Kalman filter, to nonlinear, high-dimensional, spatiotemporally chaotic flows in Rayleigh-Bénard convection experiments. Using this technique we are able to extract the full temperature and velocity fields from a time series of shadowgraph measurements. In addition, we describe extensions of the algorithm for estimating model parameters. Our results suggest the potential usefulness of our data assimilation technique to a broad class of experimental situations exhibiting spatiotemporal chaos.

Nonlinear PP and PS joint inversion based on the exact Zoeppritz equations: a two-stage procedure

NASA Astrophysics Data System (ADS)

Zhi, Lixia; Chen, Shuangquan; Song, Baoshan; Li, Xiang-yang

2018-04-01

S-velocity and density are very important parameters in distinguishing lithology and estimating other petrophysical properties. A reliable estimate of S-velocity and density is very difficult to obtain, even from long-offset gather data. Joint inversion of PP and PS data provides a promising strategy for stabilizing and improving the results of inversion in estimating elastic parameters and density. For 2D or 3D inversion, the trace-by-trace strategy is still the most widely used method although it often suffers from a lack of clarity because of its high efficiency, which is due to parallel computing. This paper describes a two-stage inversion method for nonlinear PP and PS joint inversion based on the exact Zoeppritz equations. There are several advantages for our proposed methods as follows: (1) Thanks to the exact Zoeppritz equation, our joint inversion method is applicable for wide angle amplitude-versus-angle inversion; (2) The use of both P- and S-wave information can further enhance the stability and accuracy of parameter estimation, especially for the S-velocity and density; (3) The two-stage inversion procedure proposed in this paper can achieve a good compromise between efficiency and precision. On the one hand, the trace-by-trace strategy used in the first stage can be processed in parallel so that it has high computational efficiency. On the other hand, to deal with the indistinctness of and undesired disturbances to the inversion results obtained from the first stage, we apply the second stage—total variation (TV) regularization. By enforcing spatial and temporal constraints, the TV regularization stage deblurs the inversion results and leads to parameter estimation with greater precision. Notably, the computation consumption of the TV regularization stage can be ignored compared to the first stage because it is solved using the fast split Bregman iterations. Numerical examples using a well log and the Marmousi II model show that the proposed joint inversion is a reliable method capable of accurately estimating the density parameter as well as P-wave velocity and S-wave velocity, even when the seismic data is noisy with signal-to-noise ratio of 5.

Dynamic Modeling of the Human Coagulation Cascade Using Reduced Order Effective Kinetic Models (Open Access)

DTIC Science & Technology

2015-03-16

shaded region around each total sensitivity value was the maximum uncertainty in that value estimated by the Sobol method. 2.4. Global Sensitivity...Performance We conducted a global sensitivity analysis, using the variance-based method of Sobol , to estimate which parameters controlled the...Hunter, J.D. Matplotlib: A 2D Graphics Environment. Comput. Sci. Eng. 2007, 9, 90–95. 69. Sobol , I. Global sensitivity indices for nonlinear

Novel Estimation of Pilot Performance Characteristics

NASA Technical Reports Server (NTRS)

Bachelder, Edward N.; Aponso, Bimal

2017-01-01

Two mechanisms internal to the pilot that affect performance during a tracking task are: 1) Pilot equalization (i.e. lead/lag); and 2) Pilot gain (i.e. sensitivity to the error signal). For some applications McRuer's Crossover Model can be used to anticipate what equalization will be employed to control a vehicle's dynamics. McRuer also established approximate time delays associated with different types of equalization - the more cognitive processing that is required due to equalization difficulty, the larger the time delay. However, the Crossover Model does not predict what the pilot gain will be. A nonlinear pilot control technique, observed and coined by the authors as 'amplitude clipping', is shown to improve stability, performance, and reduce workload when employed with vehicle dynamics that require high lead compensation by the pilot. Combining linear and nonlinear methods a novel approach is used to measure the pilot control parameters when amplitude clipping is present, allowing precise measurement in real time of key pilot control parameters. Based on the results of an experiment which was designed to probe workload primary drivers, a method is developed that estimates pilot spare capacity from readily observable measures and is tested for generality using multi-axis flight data. This paper documents the initial steps to developing a novel, simple objective metric for assessing pilot workload and its variation over time across a wide variety of tasks. Additionally, it offers a tangible, easily implementable methodology for anticipating a pilot's operating parameters and workload, and an effective design tool. The model shows promise in being able to precisely predict the actual pilot settings and workload, and observed tolerance of pilot parameter variation over the course of operation. Finally, an approach is proposed for generating Cooper-Harper ratings based on the workload and parameter estimation methodology.

Model selection and parameter estimation in structural dynamics using approximate Bayesian computation

NASA Astrophysics Data System (ADS)

Ben Abdessalem, Anis; Dervilis, Nikolaos; Wagg, David; Worden, Keith

2018-01-01

This paper will introduce the use of the approximate Bayesian computation (ABC) algorithm for model selection and parameter estimation in structural dynamics. ABC is a likelihood-free method typically used when the likelihood function is either intractable or cannot be approached in a closed form. To circumvent the evaluation of the likelihood function, simulation from a forward model is at the core of the ABC algorithm. The algorithm offers the possibility to use different metrics and summary statistics representative of the data to carry out Bayesian inference. The efficacy of the algorithm in structural dynamics is demonstrated through three different illustrative examples of nonlinear system identification: cubic and cubic-quintic models, the Bouc-Wen model and the Duffing oscillator. The obtained results suggest that ABC is a promising alternative to deal with model selection and parameter estimation issues, specifically for systems with complex behaviours.

ARMA models for earthquake ground motions. Seismic safety margins research program

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

Chang, M. K.; Kwiatkowski, J. W.; Nau, R. F.

1981-02-01

Four major California earthquake records were analyzed by use of a class of discrete linear time-domain processes commonly referred to as ARMA (Autoregressive/Moving-Average) models. It was possible to analyze these different earthquakes, identify the order of the appropriate ARMA model(s), estimate parameters, and test the residuals generated by these models. It was also possible to show the connections, similarities, and differences between the traditional continuous models (with parameter estimates based on spectral analyses) and the discrete models with parameters estimated by various maximum-likelihood techniques applied to digitized acceleration data in the time domain. The methodology proposed is suitable for simulatingmore » earthquake ground motions in the time domain, and appears to be easily adapted to serve as inputs for nonlinear discrete time models of structural motions. 60 references, 19 figures, 9 tables.« less

Period Estimation for Sparsely-sampled Quasi-periodic Light Curves Applied to Miras

NASA Astrophysics Data System (ADS)

He, Shiyuan; Yuan, Wenlong; Huang, Jianhua Z.; Long, James; Macri, Lucas M.

2016-12-01

We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequency parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period-luminosity relations.

Improvements in aircraft extraction programs

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.; Maine, R. E.

1976-01-01

Flight data from an F-8 Corsair and a Cessna 172 was analyzed to demonstrate specific improvements in the LRC parameter extraction computer program. The Cramer-Rao bounds were shown to provide a satisfactory relative measure of goodness of parameter estimates. It was not used as an absolute measure due to an inherent uncertainty within a multiplicative factor, traced in turn to the uncertainty in the noise bandwidth in the statistical theory of parameter estimation. The measure was also derived on an entirely nonstatistical basis, yielding thereby also an interpretation of the significance of off-diagonal terms in the dispersion matrix. The distinction between coefficients as linear and non-linear was shown to be important in its implication to a recommended order of parameter iteration. Techniques of improving convergence generally, were developed, and tested out on flight data. In particular, an easily implemented modification incorporating a gradient search was shown to improve initial estimates and thus remove a common cause for lack of convergence.

Parameter Estimation of Actuators for Benchmark Active Control Technology (BACT) Wind Tunnel Model with Analysis of Wear and Aerodynamic Loading Effects

NASA Technical Reports Server (NTRS)

Waszak, Martin R.; Fung, Jimmy

1998-01-01

This report describes the development of transfer function models for the trailing-edge and upper and lower spoiler actuators of the Benchmark Active Control Technology (BACT) wind tunnel model for application to control system analysis and design. A simple nonlinear least-squares parameter estimation approach is applied to determine transfer function parameters from frequency response data. Unconstrained quasi-Newton minimization of weighted frequency response error was employed to estimate the transfer function parameters. An analysis of the behavior of the actuators over time to assess the effects of wear and aerodynamic load by using the transfer function models is also presented. The frequency responses indicate consistent actuator behavior throughout the wind tunnel test and only slight degradation in effectiveness due to aerodynamic hinge loading. The resulting actuator models have been used in design, analysis, and simulation of controllers for the BACT to successfully suppress flutter over a wide range of conditions.

A combined reconstruction-classification method for diffuse optical tomography.

PubMed

Hiltunen, P; Prince, S J D; Arridge, S

2009-11-07

We present a combined classification and reconstruction algorithm for diffuse optical tomography (DOT). DOT is a nonlinear ill-posed inverse problem. Therefore, some regularization is needed. We present a mixture of Gaussians prior, which regularizes the DOT reconstruction step. During each iteration, the parameters of a mixture model are estimated. These associate each reconstructed pixel with one of several classes based on the current estimate of the optical parameters. This classification is exploited to form a new prior distribution to regularize the reconstruction step and update the optical parameters. The algorithm can be described as an iteration between an optimization scheme with zeroth-order variable mean and variance Tikhonov regularization and an expectation-maximization scheme for estimation of the model parameters. We describe the algorithm in a general Bayesian framework. Results from simulated test cases and phantom measurements show that the algorithm enhances the contrast of the reconstructed images with good spatial accuracy. The probabilistic classifications of each image contain only a few misclassified pixels.

Modern control concepts in hydrology

NASA Technical Reports Server (NTRS)

Duong, N.; Johnson, G. R.; Winn, C. B.

1974-01-01

Two approaches to an identification problem in hydrology are presented based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time invariant or time dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and conform with results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second, by using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.

Structural identifiability analyses of candidate models for in vitro Pitavastatin hepatic uptake.

PubMed

Grandjean, Thomas R B; Chappell, Michael J; Yates, James W T; Evans, Neil D

2014-05-01

In this paper a review of the application of four different techniques (a version of the similarity transformation approach for autonomous uncontrolled systems, a non-differential input/output observable normal form approach, the characteristic set differential algebra and a recent algebraic input/output relationship approach) to determine the structural identifiability of certain in vitro nonlinear pharmacokinetic models is provided. The Organic Anion Transporting Polypeptide (OATP) substrate, Pitavastatin, is used as a probe on freshly isolated animal and human hepatocytes. Candidate pharmacokinetic non-linear compartmental models have been derived to characterise the uptake process of Pitavastatin. As a prerequisite to parameter estimation, structural identifiability analyses are performed to establish that all unknown parameters can be identified from the experimental observations available. Copyright © 2013. Published by Elsevier Ireland Ltd.

Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats.

PubMed

Leander, Jacob; Almquist, Joachim; Ahlström, Christine; Gabrielsson, Johan; Jirstrand, Mats

2015-05-01

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

Further comments on sensitivities, parameter estimation, and sampling design in one-dimensional analysis of solute transport in porous media

USGS Publications Warehouse

Knopman, Debra S.; Voss, Clifford I.

1988-01-01

Sensitivities of solute concentration to parameters associated with first-order chemical decay, boundary conditions, initial conditions, and multilayer transport are examined in one-dimensional analytical models of transient solute transport in porous media. A sensitivity is a change in solute concentration resulting from a change in a model parameter. Sensitivity analysis is important because minimum information required in regression on chemical data for the estimation of model parameters by regression is expressed in terms of sensitivities. Nonlinear regression models of solute transport were tested on sets of noiseless observations from known models that exceeded the minimum sensitivity information requirements. Results demonstrate that the regression models consistently converged to the correct parameters when the initial sets of parameter values substantially deviated from the correct parameters. On the basis of the sensitivity analysis, several statements may be made about design of sampling for parameter estimation for the models examined: (1) estimation of parameters associated with solute transport in the individual layers of a multilayer system is possible even when solute concentrations in the individual layers are mixed in an observation well; (2) when estimating parameters in a decaying upstream boundary condition, observations are best made late in the passage of the front near a time chosen by adding the inverse of an hypothesized value of the source decay parameter to the estimated mean travel time at a given downstream location; (3) estimation of a first-order chemical decay parameter requires observations to be made late in the passage of the front, preferably near a location corresponding to a travel time of √2 times the half-life of the solute; and (4) estimation of a parameter relating to spatial variability in an initial condition requires observations to be made early in time relative to passage of the solute front.

Utilizing High-Performance Computing to Investigate Parameter Sensitivity of an Inversion Model for Vadose Zone Flow and Transport

NASA Astrophysics Data System (ADS)

Fang, Z.; Ward, A. L.; Fang, Y.; Yabusaki, S.

2011-12-01

High-resolution geologic models have proven effective in improving the accuracy of subsurface flow and transport predictions. However, many of the parameters in subsurface flow and transport models cannot be determined directly at the scale of interest and must be estimated through inverse modeling. A major challenge, particularly in vadose zone flow and transport, is the inversion of the highly-nonlinear, high-dimensional problem as current methods are not readily scalable for large-scale, multi-process models. In this paper we describe the implementation of a fully automated approach for addressing complex parameter optimization and sensitivity issues on massively parallel multi- and many-core systems. The approach is based on the integration of PNNL's extreme scale Subsurface Transport Over Multiple Phases (eSTOMP) simulator, which uses the Global Array toolkit, with the Beowulf-Cluster inspired parallel nonlinear parameter estimation software, BeoPEST in the MPI mode. In the eSTOMP/BeoPEST implementation, a pre-processor generates all of the PEST input files based on the eSTOMP input file. Simulation results for comparison with observations are extracted automatically at each time step eliminating the need for post-process data extractions. The inversion framework was tested with three different experimental data sets: one-dimensional water flow at Hanford Grass Site; irrigation and infiltration experiment at the Andelfingen Site; and a three-dimensional injection experiment at Hanford's Sisson and Lu Site. Good agreements are achieved in all three applications between observations and simulations in both parameter estimates and water dynamics reproduction. Results show that eSTOMP/BeoPEST approach is highly scalable and can be run efficiently with hundreds or thousands of processors. BeoPEST is fault tolerant and new nodes can be dynamically added and removed. A major advantage of this approach is the ability to use high-resolution geologic models to preserve the spatial structure in the inverse model, which leads to better parameter estimates and improved predictions when using the inverse-conditioned realizations of parameter fields.

Fast estimation of diffusion tensors under Rician noise by the EM algorithm.

PubMed

Liu, Jia; Gasbarra, Dario; Railavo, Juha

2016-01-15

Diffusion tensor imaging (DTI) is widely used to characterize, in vivo, the white matter of the central nerve system (CNS). This biological tissue contains much anatomic, structural and orientational information of fibers in human brain. Spectral data from the displacement distribution of water molecules located in the brain tissue are collected by a magnetic resonance scanner and acquired in the Fourier domain. After the Fourier inversion, the noise distribution is Gaussian in both real and imaginary parts and, as a consequence, the recorded magnitude data are corrupted by Rician noise. Statistical estimation of diffusion leads a non-linear regression problem. In this paper, we present a fast computational method for maximum likelihood estimation (MLE) of diffusivities under the Rician noise model based on the expectation maximization (EM) algorithm. By using data augmentation, we are able to transform a non-linear regression problem into the generalized linear modeling framework, reducing dramatically the computational cost. The Fisher-scoring method is used for achieving fast convergence of the tensor parameter. The new method is implemented and applied using both synthetic and real data in a wide range of b-amplitudes up to 14,000s/mm(2). Higher accuracy and precision of the Rician estimates are achieved compared with other log-normal based methods. In addition, we extend the maximum likelihood (ML) framework to the maximum a posteriori (MAP) estimation in DTI under the aforementioned scheme by specifying the priors. We will describe how close numerically are the estimators of model parameters obtained through MLE and MAP estimation. Copyright © 2015 Elsevier B.V. All rights reserved.

Nonparametric Transfer Function Models

PubMed Central

Liu, Jun M.; Chen, Rong; Yao, Qiwei

2009-01-01

In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between ‘input’ and ‘output’ time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modeling the correlation in the noise, the transfer function can be estimated more efficiently. The parsimonious ARMA structure improves the estimation efficiency in finite samples. The asymptotic properties of the estimators are investigated. The finite-sample properties are illustrated through simulations and one empirical example. PMID:20628584

DAISY: a new software tool to test global identifiability of biological and physiological systems

PubMed Central

Bellu, Giuseppina; Saccomani, Maria Pia; Audoly, Stefania; D’Angiò, Leontina

2009-01-01

A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a differential algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/. PMID:17707944

A Bayesian estimation of a stochastic predator-prey model of economic fluctuations

NASA Astrophysics Data System (ADS)

Dibeh, Ghassan; Luchinsky, Dmitry G.; Luchinskaya, Daria D.; Smelyanskiy, Vadim N.

2007-06-01

In this paper, we develop a Bayesian framework for the empirical estimation of the parameters of one of the best known nonlinear models of the business cycle: The Marx-inspired model of a growth cycle introduced by R. M. Goodwin. The model predicts a series of closed cycles representing the dynamics of labor's share and the employment rate in the capitalist economy. The Bayesian framework is used to empirically estimate a modified Goodwin model. The original model is extended in two ways. First, we allow for exogenous periodic variations of the otherwise steady growth rates of the labor force and productivity per worker. Second, we allow for stochastic variations of those parameters. The resultant modified Goodwin model is a stochastic predator-prey model with periodic forcing. The model is then estimated using a newly developed Bayesian estimation method on data sets representing growth cycles in France and Italy during the years 1960-2005. Results show that inference of the parameters of the stochastic Goodwin model can be achieved. The comparison of the dynamics of the Goodwin model with the inferred values of parameters demonstrates quantitative agreement with the growth cycle empirical data.

Structural Identifiability of Dynamic Systems Biology Models

PubMed Central

Villaverde, Alejandro F.

2016-01-01

A powerful way of gaining insight into biological systems is by creating a nonlinear differential equation model, which usually contains many unknown parameters. Such a model is called structurally identifiable if it is possible to determine the values of its parameters from measurements of the model outputs. Structural identifiability is a prerequisite for parameter estimation, and should be assessed before exploiting a model. However, this analysis is seldom performed due to the high computational cost involved in the necessary symbolic calculations, which quickly becomes prohibitive as the problem size increases. In this paper we show how to analyse the structural identifiability of a very general class of nonlinear models by extending methods originally developed for studying observability. We present results about models whose identifiability had not been previously determined, report unidentifiabilities that had not been found before, and show how to modify those unidentifiable models to make them identifiable. This method helps prevent problems caused by lack of identifiability analysis, which can compromise the success of tasks such as experiment design, parameter estimation, and model-based optimization. The procedure is called STRIKE-GOLDD (STRuctural Identifiability taKen as Extended-Generalized Observability with Lie Derivatives and Decomposition), and it is implemented in a MATLAB toolbox which is available as open source software. The broad applicability of this approach facilitates the analysis of the increasingly complex models used in systems biology and other areas. PMID:27792726

Rapid determination of vial heat transfer parameters using tunable diode laser absorption spectroscopy (TDLAS) in response to step-changes in pressure set-point during freeze-drying.

PubMed

Kuu, Wei Y; Nail, Steven L; Sacha, Gregory

2009-03-01

The purpose of this study was to perform a rapid determination of vial heat transfer parameters, that is, the contact parameter K(cs) and the separation distance l(v), using the sublimation rate profiles measured by tunable diode laser absorption spectroscopy (TDLAS). In this study, each size of vial was filled with pure water followed by a freeze-drying cycle using a LyoStar II dryer (FTS Systems) with step-changes of the chamber pressure set-point at to 25, 50, 100, 200, 300, and 400 mTorr. K(cs) was independently determined by nonlinear parameter estimation using the sublimation rates measured at the pressure set-point of 25 mTorr. After obtaining K(cs), the l(v) value for each vial size was determined by nonlinear parameter estimation using the pooled sublimation rate profiles obtained at 25 to 400 mTorr. The vial heat transfer coefficient K(v), as a function of the chamber pressure, was readily calculated, using the obtained K(cs) and l(v) values. It is interesting to note the significant difference in K(v) of two similar types of 10 mL Schott tubing vials, primary due to the geometry of the vial-bottom, as demonstrated by the images of the contact areas of the vial-bottom. (c) 2008 Wiley-Liss, Inc. and the American Pharmacists Association

Study of Heart Rate Variability in Bipolar Disorder: Linear and Non-Linear Parameters during Sleep

PubMed Central

Migliorini, Matteo; Mendez, Martin O.; Bianchi, Anna M.

2012-01-01

The aim of the study is to define physiological parameters and vital signs that may be related to the mood and mental status in patients affected by bipolar disorder. In particular we explored the autonomic nervous system through the analysis of the heart rate variability. Many different parameters, in the time and in the frequency domain, linear and non-linear were evaluated during the sleep in a group of normal subject and in one patient in four different conditions. The recording of the signals was performed through a wearable sensorized T-shirt. Heart rate variability (HRV) signal and movement analysis allowed also obtaining sleep staging and the estimation of REM sleep percentage over the total sleep time. A group of eight normal females constituted the control group, on which normality ranges were estimated. The pathologic subject was recorded during four different nights, at time intervals of at least 1 week, and during different phases of the disturbance. Some of the examined parameters (MEANNN, SDNN, RMSSD) confirmed reduced HRV in depression and bipolar disorder. REM sleep percentage was found to be increased. Lempel–Ziv complexity and sample entropy, on the other hand, seem to correlate with the depression level. Even if the number of examined subjects is still small, and the results need further validation, the proposed methodology and the calculated parameters seem promising tools for the monitoring of mood changes in psychiatric disorders. PMID:22291638

The ice age cycle and the deglaciations: an application of nonlinear regression modelling

NASA Astrophysics Data System (ADS)

Dalgleish, A. N.; Boulton, G. S.; Renshaw, E.

2000-03-01

We have applied the nonlinear regression technique known as additivity and variance stabilisation (AVAS) to time series which reflect Earth's climate over the last 600 ka. AVAS estimates a smooth, nonlinear transform for each variable, under the assumption of an additive model. The Earth's orbital parameters and insolation variations have been used as regression variables. Analysis of the contribution of each variable shows that the deglaciations are characterised by periods of increasing obliquity and perihelion approaching the vernal equinox, but not by any systematic change in eccentricity. The magnitude of insolation changes also plays no role. By approximating the transforms we can obtain a future prediction, with a glacial maximum at 60 ka AP, and a subsequent obliquity and precession forced deglaciation.

Sustainable Mining Land Use for Lignite Based Energy Projects

NASA Astrophysics Data System (ADS)

Dudek, Michal; Krysa, Zbigniew

2017-12-01

This research aims to discuss complex lignite based energy projects economic viability and its impact on sustainable land use with respect to project risk and uncertainty, economics, optimisation (e.g. Lerchs and Grossmann) and importance of lignite as fuel that may be expressed in situ as deposit of energy. Sensitivity analysis and simulation consist of estimated variable land acquisition costs, geostatistics, 3D deposit block modelling, electricity price considered as project product price, power station efficiency and power station lignite processing unit cost, CO2 allowance costs, mining unit cost and also lignite availability treated as lignite reserves kriging estimation error. Investigated parameters have nonlinear influence on results so that economically viable amount of lignite in optimal pit varies having also nonlinear impact on land area required for mining operation.

Suspension parameter estimation in the frequency domain using a matrix inversion approach

NASA Astrophysics Data System (ADS)

Thite, A. N.; Banvidi, S.; Ibicek, T.; Bennett, L.

2011-12-01

The dynamic lumped parameter models used to optimise the ride and handling of a vehicle require base values of the suspension parameters. These parameters are generally experimentally identified. The accuracy of identified parameters can depend on the measurement noise and the validity of the model used. The existing publications on suspension parameter identification are generally based on the time domain and use a limited degree of freedom. Further, the data used are either from a simulated 'experiment' or from a laboratory test on an idealised quarter or a half-car model. In this paper, a method is developed in the frequency domain which effectively accounts for the measurement noise. Additional dynamic constraining equations are incorporated and the proposed formulation results in a matrix inversion approach. The nonlinearities in damping are estimated, however, using a time-domain approach. Full-scale 4-post rig test data of a vehicle are used. The variations in the results are discussed using the modal resonant behaviour. Further, a method is implemented to show how the results can be improved when the matrix inverted is ill-conditioned. The case study shows a good agreement between the estimates based on the proposed frequency-domain approach and measurable physical parameters.

The nonlinear Galerkin method: A multi-scale method applied to the simulation of homogeneous turbulent flows

NASA Technical Reports Server (NTRS)

Debussche, A.; Dubois, T.; Temam, R.

1993-01-01

Using results of Direct Numerical Simulation (DNS) in the case of two-dimensional homogeneous isotropic flows, the behavior of the small and large scales of Kolmogorov like flows at moderate Reynolds numbers are first analyzed in detail. Several estimates on the time variations of the small eddies and the nonlinear interaction terms were derived; those terms play the role of the Reynolds stress tensor in the case of LES. Since the time step of a numerical scheme is determined as a function of the energy-containing eddies of the flow, the variations of the small scales and of the nonlinear interaction terms over one iteration can become negligible by comparison with the accuracy of the computation. Based on this remark, a multilevel scheme which treats differently the small and the large eddies was proposed. Using mathematical developments, estimates of all the parameters involved in the algorithm, which then becomes a completely self-adaptive procedure were derived. Finally, realistic simulations of (Kolmorov like) flows over several eddy-turnover times were performed. The results are analyzed in detail and a parametric study of the nonlinear Galerkin method is performed.

Nonlinear Bayesian filtering and learning: a neuronal dynamics for perception.

PubMed

Kutschireiter, Anna; Surace, Simone Carlo; Sprekeler, Henning; Pfister, Jean-Pascal

2017-08-18

The robust estimation of dynamical hidden features, such as the position of prey, based on sensory inputs is one of the hallmarks of perception. This dynamical estimation can be rigorously formulated by nonlinear Bayesian filtering theory. Recent experimental and behavioral studies have shown that animals' performance in many tasks is consistent with such a Bayesian statistical interpretation. However, it is presently unclear how a nonlinear Bayesian filter can be efficiently implemented in a network of neurons that satisfies some minimum constraints of biological plausibility. Here, we propose the Neural Particle Filter (NPF), a sampling-based nonlinear Bayesian filter, which does not rely on importance weights. We show that this filter can be interpreted as the neuronal dynamics of a recurrently connected rate-based neural network receiving feed-forward input from sensory neurons. Further, it captures properties of temporal and multi-sensory integration that are crucial for perception, and it allows for online parameter learning with a maximum likelihood approach. The NPF holds the promise to avoid the 'curse of dimensionality', and we demonstrate numerically its capability to outperform weighted particle filters in higher dimensions and when the number of particles is limited.

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

A Process Dynamics and Control Experiment for the Undergraduate Laboratory

ERIC Educational Resources Information Center

Spencer, Jordan L.

2009-01-01

This paper describes a process control experiment. The apparatus includes a three-vessel glass flow system with a variable flow configuration, means for feeding dye solution controlled by a stepper-motor driven valve, and a flow spectrophotometer. Students use impulse response data and nonlinear regression to estimate three parameters of a model…

SigrafW: An easy-to-use program for fitting enzyme kinetic data.

PubMed

Leone, Francisco Assis; Baranauskas, José Augusto; Furriel, Rosa Prazeres Melo; Borin, Ivana Aparecida

2005-11-01

SigrafW is Windows-compatible software developed using the Microsoft® Visual Basic Studio program that uses the simplified Hill equation for fitting kinetic data from allosteric and Michaelian enzymes. SigrafW uses a modified Fibonacci search to calculate maximal velocity (V), the Hill coefficient (n), and the enzyme-substrate apparent dissociation constant (K). The estimation of V, K, and the sum of the squares of residuals is performed using a Wilkinson nonlinear regression at any Hill coefficient (n). In contrast to many currently available kinetic analysis programs, SigrafW shows several advantages for the determination of kinetic parameters of both hyperbolic and nonhyperbolic saturation curves. No initial estimates of the kinetic parameters are required, a measure of the goodness-of-the-fit for each calculation performed is provided, the nonlinear regression used for calculations eliminates the statistical bias inherent in linear transformations, and the software can be used for enzyme kinetic simulations either for educational or research purposes. Persons interested in receiving a free copy of the software should contact Dr. F. A. Leone. Copyright © 2005 International Union of Biochemistry and Molecular Biology, Inc.

Fully probabilistic control for stochastic nonlinear control systems with input dependent noise.

PubMed

Herzallah, Randa

2015-03-01

Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained. Copyright © 2014 Elsevier Ltd. All rights reserved.

Electrostatic interaction between stereocilia: I. Its role in supporting the structure of the hair bundle.

PubMed

Dolgobrodov, S G; Lukashkin, A N; Russell, I J

2000-12-01

This paper provides theoretical estimates for the forces of electrostatic interaction between adjacent stereocilia in auditory and vestibular hair cells. Estimates are given for parameters within the measured physiological range using constraints appropriate for the known geometry of the hair bundle. Stereocilia are assumed to possess an extended, negatively charged surface coat, the glycocalyx. Different charge distribution profiles within the glycocalyx are analysed. It is shown that charged glycocalices on the apical surface of the hair cells can support spatial separation between adjacent stereocilia in the hair bundles through electrostatic repulsion between stereocilia. The charge density profile within the glycocalyx is a crucial parameter. In fact, attraction instead of repulsion between adjacent stereocilia will be observed if the charge of the glycocalyx is concentrated near the membrane of the stereocilia, thereby making this type of charge distribution unlikely. The forces of electrostatic interaction between stereocilia may influence the mechanical properties of the hair bundle and, being strongly non-linear, contribute to the non-linear phenomena that have been recorded from the periphery of the auditory and vestibular systems.

An exponential decay model for mediation.

PubMed

Fritz, Matthew S

2014-10-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, address many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed.

An Exponential Decay Model for Mediation

PubMed Central

Fritz, Matthew S.

2013-01-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, addresses many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed. PMID:23625557

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

Jennings, Elise; Wechsler, Risa H.

We present the nonlinear 2D galaxy power spectrum, P(k, µ), in redshift space, measured from the Dark Sky simulations, using galaxy catalogs constructed with both halo occupation distribution and subhalo abundance matching methods, chosen to represent an intermediate redshift sample of luminous red galaxies. We find that the information content in individual µ (cosine of the angle to the line of sight) bins is substantially richer then multipole moments, and show that this can be used to isolate the impact of nonlinear growth and redshift space distortion (RSD) effects. Using the µ < 0.2 simulation data, which we show ismore » not impacted by RSD effects, we can successfully measure the nonlinear bias to an accuracy of ~ 5% at k < 0.6hMpc-1 . This use of individual µ bins to extract the nonlinear bias successfully removes a large parameter degeneracy when constraining the linear growth rate of structure. We carry out a joint parameter estimation, using the low µ simulation data to constrain the nonlinear bias, and µ > 0.2 to constrain the growth rate and show that f can be constrained to ~ 26(22)% to a kmax < 0.4(0.6)hMpc-1 from clustering alone using a simple dispersion model, for a range of galaxy models. Our analysis of individual µ bins also reveals interesting physical effects which arise simply from different methods of populating halos with galaxies. We also find a prominent turnaround scale, at which RSD damping effects are greater then the nonlinear growth, which differs not only for each µ bin but also for each galaxy model. These features may provide unique signatures which could be used to shed light on the galaxy–dark matter connection. Furthermore, the idea of separating nonlinear growth and RSD effects making use of the full information in the 2D galaxy power spectrum yields significant improvements in constraining cosmological parameters and may be a promising probe of galaxy formation models.« less

Three Least-Squares Minimization Approaches to Interpret Gravity Data Due to Dipping Faults

NASA Astrophysics Data System (ADS)

Abdelrahman, E. M.; Essa, K. S.

2015-02-01

We have developed three different least-squares minimization approaches to determine, successively, the depth, dip angle, and amplitude coefficient related to the thickness and density contrast of a buried dipping fault from first moving average residual gravity anomalies. By defining the zero-anomaly distance and the anomaly value at the origin of the moving average residual profile, the problem of depth determination is transformed into a constrained nonlinear gravity inversion. After estimating the depth of the fault, the dip angle is estimated by solving a nonlinear inverse problem. Finally, after estimating the depth and dip angle, the amplitude coefficient is determined using a linear equation. This method can be applied to residuals as well as to measured gravity data because it uses the moving average residual gravity anomalies to estimate the model parameters of the faulted structure. The proposed method was tested on noise-corrupted synthetic and real gravity data. In the case of the synthetic data, good results are obtained when errors are given in the zero-anomaly distance and the anomaly value at the origin, and even when the origin is determined approximately. In the case of practical data (Bouguer anomaly over Gazal fault, south Aswan, Egypt), the fault parameters obtained are in good agreement with the actual ones and with those given in the published literature.

Optimization and uncertainty assessment of strongly nonlinear groundwater models with high parameter dimensionality

NASA Astrophysics Data System (ADS)

Keating, Elizabeth H.; Doherty, John; Vrugt, Jasper A.; Kang, Qinjun

2010-10-01

Highly parameterized and CPU-intensive groundwater models are increasingly being used to understand and predict flow and transport through aquifers. Despite their frequent use, these models pose significant challenges for parameter estimation and predictive uncertainty analysis algorithms, particularly global methods which usually require very large numbers of forward runs. Here we present a general methodology for parameter estimation and uncertainty analysis that can be utilized in these situations. Our proposed method includes extraction of a surrogate model that mimics key characteristics of a full process model, followed by testing and implementation of a pragmatic uncertainty analysis technique, called null-space Monte Carlo (NSMC), that merges the strengths of gradient-based search and parameter dimensionality reduction. As part of the surrogate model analysis, the results of NSMC are compared with a formal Bayesian approach using the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm. Such a comparison has never been accomplished before, especially in the context of high parameter dimensionality. Despite the highly nonlinear nature of the inverse problem, the existence of multiple local minima, and the relatively large parameter dimensionality, both methods performed well and results compare favorably with each other. Experiences gained from the surrogate model analysis are then transferred to calibrate the full highly parameterized and CPU intensive groundwater model and to explore predictive uncertainty of predictions made by that model. The methodology presented here is generally applicable to any highly parameterized and CPU-intensive environmental model, where efficient methods such as NSMC provide the only practical means for conducting predictive uncertainty analysis.

The multiple complex exponential model and its application to EEG analysis

NASA Astrophysics Data System (ADS)

Chen, Dao-Mu; Petzold, J.

The paper presents a novel approach to the analysis of the EEG signal, which is based on a multiple complex exponential (MCE) model. Parameters of the model are estimated using a nonharmonic Fourier expansion algorithm. The central idea of the algorithm is outlined, and the results, estimated on the basis of simulated data, are presented and compared with those obtained by the conventional methods of signal analysis. Preliminary work on various application possibilities of the MCE model in EEG data analysis is described. It is shown that the parameters of the MCE model reflect the essential information contained in an EEG segment. These parameters characterize the EEG signal in a more objective way because they are closer to the recent supposition of the nonlinear character of the brain's dynamic behavior.

An extended harmonic balance method based on incremental nonlinear control parameters

NASA Astrophysics Data System (ADS)

Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.

2017-02-01

A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.

3D non-linear inversion of magnetic anomalies caused by prismatic bodies using differential evolution algorithm

NASA Astrophysics Data System (ADS)

Balkaya, Çağlayan; Ekinci, Yunus Levent; Göktürkler, Gökhan; Turan, Seçil

2017-01-01

3D non-linear inversion of total field magnetic anomalies caused by vertical-sided prismatic bodies has been achieved by differential evolution (DE), which is one of the population-based evolutionary algorithms. We have demonstrated the efficiency of the algorithm on both synthetic and field magnetic anomalies by estimating horizontal distances from the origin in both north and east directions, depths to the top and bottom of the bodies, inclination and declination angles of the magnetization, and intensity of magnetization of the causative bodies. In the synthetic anomaly case, we have considered both noise-free and noisy data sets due to two vertical-sided prismatic bodies in a non-magnetic medium. For the field case, airborne magnetic anomalies originated from intrusive granitoids at the eastern part of the Biga Peninsula (NW Turkey) which is composed of various kinds of sedimentary, metamorphic and igneous rocks, have been inverted and interpreted. Since the granitoids are the outcropped rocks in the field, the estimations for the top depths of two prisms representing the magnetic bodies were excluded during inversion studies. Estimated bottom depths are in good agreement with the ones obtained by a different approach based on 3D modelling of pseudogravity anomalies. Accuracy of the estimated parameters from both cases has been also investigated via probability density functions. Based on the tests in the present study, it can be concluded that DE is a useful tool for the parameter estimation of source bodies using magnetic anomalies.

Asymmetrical effects of mesophyll conductance on fundamental photosynthetic parameters and their relationships estimated from leaf gas exchange measurements.

PubMed

Sun, Ying; Gu, Lianhong; Dickinson, Robert E; Pallardy, Stephen G; Baker, John; Cao, Yonghui; DaMatta, Fábio Murilo; Dong, Xuejun; Ellsworth, David; Van Goethem, Davina; Jensen, Anna M; Law, Beverly E; Loos, Rodolfo; Martins, Samuel C Vitor; Norby, Richard J; Warren, Jeffrey; Weston, David; Winter, Klaus

2014-04-01

Worldwide measurements of nearly 130 C3 species covering all major plant functional types are analysed in conjunction with model simulations to determine the effects of mesophyll conductance (g(m)) on photosynthetic parameters and their relationships estimated from A/Ci curves. We find that an assumption of infinite g(m) results in up to 75% underestimation for maximum carboxylation rate V(cmax), 60% for maximum electron transport rate J(max), and 40% for triose phosphate utilization rate T(u) . V(cmax) is most sensitive, J(max) is less sensitive, and T(u) has the least sensitivity to the variation of g(m). Because of this asymmetrical effect of g(m), the ratios of J(max) to V(cmax), T(u) to V(cmax) and T(u) to J(max) are all overestimated. An infinite g(m) assumption also limits the freedom of variation of estimated parameters and artificially constrains parameter relationships to stronger shapes. These findings suggest the importance of quantifying g(m) for understanding in situ photosynthetic machinery functioning. We show that a nonzero resistance to CO2 movement in chloroplasts has small effects on estimated parameters. A non-linear function with gm as input is developed to convert the parameters estimated under an assumption of infinite gm to proper values. This function will facilitate gm representation in global carbon cycle models. © 2013 John Wiley & Sons Ltd.

Stochastic control system parameter identifiability

NASA Technical Reports Server (NTRS)

Lee, C. H.; Herget, C. J.

1975-01-01

The parameter identification problem of general discrete time, nonlinear, multiple input/multiple output dynamic systems with Gaussian white distributed measurement errors is considered. The knowledge of the system parameterization was assumed to be known. Concepts of local parameter identifiability and local constrained maximum likelihood parameter identifiability were established. A set of sufficient conditions for the existence of a region of parameter identifiability was derived. A computation procedure employing interval arithmetic was provided for finding the regions of parameter identifiability. If the vector of the true parameters is locally constrained maximum likelihood (CML) identifiable, then with probability one, the vector of true parameters is a unique maximal point of the maximum likelihood function in the region of parameter identifiability and the constrained maximum likelihood estimation sequence will converge to the vector of true parameters.

Adaptive Jacobian Fuzzy Attitude Control for Flexible Spacecraft Combined Attitude and Sun Tracking System

NASA Astrophysics Data System (ADS)

Chak, Yew-Chung; Varatharajoo, Renuganth

2016-07-01

Many spacecraft attitude control systems today use reaction wheels to deliver precise torques to achieve three-axis attitude stabilization. However, irrecoverable mechanical failure of reaction wheels could potentially lead to mission interruption or total loss. The electrically-powered Solar Array Drive Assemblies (SADA) are usually installed in the pitch axis which rotate the solar arrays to track the Sun, can produce torques to compensate for the pitch-axis wheel failure. In addition, the attitude control of a flexible spacecraft poses a difficult problem. These difficulties include the strong nonlinear coupled dynamics between the rigid hub and flexible solar arrays, and the imprecisely known system parameters, such as inertia matrix, damping ratios, and flexible mode frequencies. In order to overcome these drawbacks, the adaptive Jacobian tracking fuzzy control is proposed for the combined attitude and sun-tracking control problem of a flexible spacecraft during attitude maneuvers in this work. For the adaptation of kinematic and dynamic uncertainties, the proposed scheme uses an adaptive sliding vector based on estimated attitude velocity via approximate Jacobian matrix. The unknown nonlinearities are approximated by deriving the fuzzy models with a set of linguistic If-Then rules using the idea of sector nonlinearity and local approximation in fuzzy partition spaces. The uncertain parameters of the estimated nonlinearities and the Jacobian matrix are being adjusted online by an adaptive law to realize feedback control. The attitude of the spacecraft can be directly controlled with the Jacobian feedback control when the attitude pointing trajectory is designed with respect to the spacecraft coordinate frame itself. A significant feature of this work is that the proposed adaptive Jacobian tracking scheme will result in not only the convergence of angular position and angular velocity tracking errors, but also the convergence of estimated angular velocity to the actual angular velocity. Numerical results are presented to demonstrate the effectiveness of the proposed scheme in tracking the desired attitude, as well as suppressing the elastic deflection effects of solar arrays during maneuver.

Modeling and comparative study of linear and nonlinear controllers for rotary inverted pendulum

NASA Astrophysics Data System (ADS)

Lima, Byron; Cajo, Ricardo; Huilcapi, Víctor; Agila, Wilton

2017-01-01

The rotary inverted pendulum (RIP) is a problem difficult to control, several studies have been conducted where different control techniques have been applied. Literature reports that, although problem is nonlinear, classical PID controllers presents appropriate performances when applied to the system. In this paper, a comparative study of the performances of linear and nonlinear PID structures is carried out. The control algorithms are evaluated in the RIP system, using indices of performance and power consumption, which allow the categorization of control strategies according to their performance. This article also presents the modeling system, which has been estimated some of the parameters involved in the RIP system, using computer-aided design tools (CAD) and experimental methods or techniques proposed by several authors attended. The results indicate a better performance of the nonlinear controller with an increase in the robustness and faster response than the linear controller.

Regions of attraction and ultimate boundedness for linear quadratic regulators with nonlinearities

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1984-01-01

The closed-loop stability of multivariable linear time-invariant systems controlled by optimal linear quadratic (LQ) regulators is investigated for the case when the feedback loops have nonlinearities N(sigma) that violate the standard stability condition, sigma N(sigma) or = 0.5 sigma(2). The violations of the condition are assumed to occur either (1) for values of sigma away from the origin (sigma = 0) or (2) for values of sigma in a neighborhood of the origin. It is proved that there exists a region of attraction for case (1) and a region of ultimate boundedness for case (2), and estimates are obtained for these regions. The results provide methods for selecting the performance function parameters to design LQ regulators with better tolerance to nonlinearities. The results are demonstrated by application to the problem of attitude and vibration control of a large, flexible space antenna in the presence of actuator nonlinearities.

Estimating cosmic velocity fields from density fields and tidal tensors

NASA Astrophysics Data System (ADS)

Kitaura, Francisco-Shu; Angulo, Raul E.; Hoffman, Yehuda; Gottlöber, Stefan

2012-10-01

In this work we investigate the non-linear and non-local relation between cosmological density and peculiar velocity fields. Our goal is to provide an algorithm for the reconstruction of the non-linear velocity field from the fully non-linear density. We find that including the gravitational tidal field tensor using second-order Lagrangian perturbation theory based upon an estimate of the linear component of the non-linear density field significantly improves the estimate of the cosmic flow in comparison to linear theory not only in the low density, but also and more dramatically in the high-density regions. In particular we test two estimates of the linear component: the lognormal model and the iterative Lagrangian linearization. The present approach relies on a rigorous higher order Lagrangian perturbation theory analysis which incorporates a non-local relation. It does not require additional fitting from simulations being in this sense parameter free, it is independent of statistical-geometrical optimization and it is straightforward and efficient to compute. The method is demonstrated to yield an unbiased estimator of the velocity field on scales ≳5 h-1 Mpc with closely Gaussian distributed errors. Moreover, the statistics of the divergence of the peculiar velocity field is extremely well recovered showing a good agreement with the true one from N-body simulations. The typical errors of about 10 km s-1 (1σ confidence intervals) are reduced by more than 80 per cent with respect to linear theory in the scale range between 5 and 10 h-1 Mpc in high-density regions (δ > 2). We also find that iterative Lagrangian linearization is significantly superior in the low-density regime with respect to the lognormal model.

Estimation of sum-to-one constrained parameters with non-Gaussian extensions of ensemble-based Kalman filters: application to a 1D ocean biogeochemical model

NASA Astrophysics Data System (ADS)

Simon, E.; Bertino, L.; Samuelsen, A.

2011-12-01

Combined state-parameter estimation in ocean biogeochemical models with ensemble-based Kalman filters is a challenging task due to the non-linearity of the models, the constraints of positiveness that apply to the variables and parameters, and the non-Gaussian distribution of the variables in which they result. Furthermore, these models are sensitive to numerous parameters that are poorly known. Previous works [1] demonstrated that the Gaussian anamorphosis extensions of ensemble-based Kalman filters were relevant tools to perform combined state-parameter estimation in such non-Gaussian framework. In this study, we focus on the estimation of the grazing preferences parameters of zooplankton species. These parameters are introduced to model the diet of zooplankton species among phytoplankton species and detritus. They are positive values and their sum is equal to one. Because the sum-to-one constraint cannot be handled by ensemble-based Kalman filters, a reformulation of the parameterization is proposed. We investigate two types of changes of variables for the estimation of sum-to-one constrained parameters. The first one is based on Gelman [2] and leads to the estimation of normal distributed parameters. The second one is based on the representation of the unit sphere in spherical coordinates and leads to the estimation of parameters with bounded distributions (triangular or uniform). These formulations are illustrated and discussed in the framework of twin experiments realized in the 1D coupled model GOTM-NORWECOM with Gaussian anamorphosis extensions of the deterministic ensemble Kalman filter (DEnKF). [1] Simon E., Bertino L. : Gaussian anamorphosis extension of the DEnKF for combined state and parameter estimation : application to a 1D ocean ecosystem model. Journal of Marine Systems, 2011. doi :10.1016/j.jmarsys.2011.07.007 [2] Gelman A. : Method of Moments Using Monte Carlo Simulation. Journal of Computational and Graphical Statistics, 4, 1, 36-54, 1995.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

PubMed

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models

PubMed Central

Xing, W. W.; Triantafyllidis, V.

2017-01-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach. PMID:28484327

Evaluation of confidence intervals for a steady-state leaky aquifer model

USGS Publications Warehouse

Christensen, S.; Cooley, R.L.

1999-01-01

The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley [Vecchia, A.V. and Cooley, R.L., Water Resources Research, 1987, 23(7), 1237-1250] was used to calculate nonlinear Scheffe-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km2 of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley was used to calculate nonlinear Scheffe-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km2 of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.

Estimating rainfall time series and model parameter distributions using model data reduction and inversion techniques

NASA Astrophysics Data System (ADS)

Wright, Ashley J.; Walker, Jeffrey P.; Pauwels, Valentijn R. N.

2017-08-01

Floods are devastating natural hazards. To provide accurate, precise, and timely flood forecasts, there is a need to understand the uncertainties associated within an entire rainfall time series, even when rainfall was not observed. The estimation of an entire rainfall time series and model parameter distributions from streamflow observations in complex dynamic catchments adds skill to current areal rainfall estimation methods, allows for the uncertainty of entire rainfall input time series to be considered when estimating model parameters, and provides the ability to improve rainfall estimates from poorly gauged catchments. Current methods to estimate entire rainfall time series from streamflow records are unable to adequately invert complex nonlinear hydrologic systems. This study aims to explore the use of wavelets in the estimation of rainfall time series from streamflow records. Using the Discrete Wavelet Transform (DWT) to reduce rainfall dimensionality for the catchment of Warwick, Queensland, Australia, it is shown that model parameter distributions and an entire rainfall time series can be estimated. Including rainfall in the estimation process improves streamflow simulations by a factor of up to 1.78. This is achieved while estimating an entire rainfall time series, inclusive of days when none was observed. It is shown that the choice of wavelet can have a considerable impact on the robustness of the inversion. Combining the use of a likelihood function that considers rainfall and streamflow errors with the use of the DWT as a model data reduction technique allows the joint inference of hydrologic model parameters along with rainfall.

Quantifying lost information due to covariance matrix estimation in parameter inference

NASA Astrophysics Data System (ADS)

Sellentin, Elena; Heavens, Alan F.

2017-02-01

Parameter inference with an estimated covariance matrix systematically loses information due to the remaining uncertainty of the covariance matrix. Here, we quantify this loss of precision and develop a framework to hypothetically restore it, which allows to judge how far away a given analysis is from the ideal case of a known covariance matrix. We point out that it is insufficient to estimate this loss by debiasing the Fisher matrix as previously done, due to a fundamental inequality that describes how biases arise in non-linear functions. We therefore develop direct estimators for parameter credibility contours and the figure of merit, finding that significantly fewer simulations than previously thought are sufficient to reach satisfactory precisions. We apply our results to DES Science Verification weak lensing data, detecting a 10 per cent loss of information that increases their credibility contours. No significant loss of information is found for KiDS. For a Euclid-like survey, with about 10 nuisance parameters we find that 2900 simulations are sufficient to limit the systematically lost information to 1 per cent, with an additional uncertainty of about 2 per cent. Without any nuisance parameters, 1900 simulations are sufficient to only lose 1 per cent of information. We further derive estimators for all quantities needed for forecasting with estimated covariance matrices. Our formalism allows to determine the sweetspot between running sophisticated simulations to reduce the number of nuisance parameters, and running as many fast simulations as possible.

Temporal rainfall estimation using input data reduction and model inversion

NASA Astrophysics Data System (ADS)

Wright, A. J.; Vrugt, J. A.; Walker, J. P.; Pauwels, V. R. N.

2016-12-01

Floods are devastating natural hazards. To provide accurate, precise and timely flood forecasts there is a need to understand the uncertainties associated with temporal rainfall and model parameters. The estimation of temporal rainfall and model parameter distributions from streamflow observations in complex dynamic catchments adds skill to current areal rainfall estimation methods, allows for the uncertainty of rainfall input to be considered when estimating model parameters and provides the ability to estimate rainfall from poorly gauged catchments. Current methods to estimate temporal rainfall distributions from streamflow are unable to adequately explain and invert complex non-linear hydrologic systems. This study uses the Discrete Wavelet Transform (DWT) to reduce rainfall dimensionality for the catchment of Warwick, Queensland, Australia. The reduction of rainfall to DWT coefficients allows the input rainfall time series to be simultaneously estimated along with model parameters. The estimation process is conducted using multi-chain Markov chain Monte Carlo simulation with the DREAMZS algorithm. The use of a likelihood function that considers both rainfall and streamflow error allows for model parameter and temporal rainfall distributions to be estimated. Estimation of the wavelet approximation coefficients of lower order decomposition structures was able to estimate the most realistic temporal rainfall distributions. These rainfall estimates were all able to simulate streamflow that was superior to the results of a traditional calibration approach. It is shown that the choice of wavelet has a considerable impact on the robustness of the inversion. The results demonstrate that streamflow data contains sufficient information to estimate temporal rainfall and model parameter distributions. The extent and variance of rainfall time series that are able to simulate streamflow that is superior to that simulated by a traditional calibration approach is a demonstration of equifinality. The use of a likelihood function that considers both rainfall and streamflow error combined with the use of the DWT as a model data reduction technique allows the joint inference of hydrologic model parameters along with rainfall.

Temperature profile retrievals with extended Kalman-Bucy filters

NASA Technical Reports Server (NTRS)

Ledsham, W. H.; Staelin, D. H.

1979-01-01

The Extended Kalman-Bucy Filter is a powerful technique for estimating non-stationary random parameters in situations where the received signal is a noisy non-linear function of those parameters. A practical causal filter for retrieving atmospheric temperature profiles from radiances observed at a single scan angle by the Scanning Microwave Spectrometer (SCAMS) carried on the Nimbus 6 satellite typically shows approximately a 10-30% reduction in rms error about the mean at almost all levels below 70 mb when compared with a regression inversion.

Physics issues in diffraction limited storage ring design

NASA Astrophysics Data System (ADS)

Fan, Wei; Bai, ZhengHe; Gao, WeiWei; Feng, GuangYao; Li, WeiMin; Wang, Lin; He, DuoHui

2012-05-01

Diffraction limited electron storage ring is considered a promising candidate for future light sources, whose main characteristics are higher brilliance, better transverse coherence and better stability. The challenge of diffraction limited storage ring design is how to achieve the ultra low beam emittance with acceptable nonlinear performance. Effective linear and nonlinear parameter optimization methods based on Artificial Intelligence were developed for the storage ring physical design. As an example of application, partial physical design of HALS (Hefei Advanced Light Source), which is a diffraction limited VUV and soft X-ray light source, was introduced. Severe emittance growth due to the Intra Beam Scattering effect, which is the main obstacle to achieve ultra low emittance, was estimated quantitatively and possible cures were discussed. It is inspiring that better performance of diffraction limited storage ring can be achieved in principle with careful parameter optimization.

Global identifiability of linear compartmental models--a computer algebra algorithm.

PubMed

Audoly, S; D'Angiò, L; Saccomani, M P; Cobelli, C

1998-01-01

A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.

Modeling Nonlinear Site Response Uncertainty in Broadband Ground Motion Simulations for the Los Angeles Basin

NASA Astrophysics Data System (ADS)

Assimaki, D.; Li, W.; Steidl, J. M.; Schmedes, J.

2007-12-01

The assessment of strong motion site response is of great significance, both for mitigating seismic hazard and for performing detailed analyses of earthquake source characteristics. There currently exists, however, large degree of uncertainty concerning the mathematical model to be employed for the computationally efficient evaluation of local site effects, and the site investigation program necessary to evaluate the nonlinear input model parameters and ensure cost-effective predictions; and while site response observations may provide critical constraints on interpretation methods, the lack of a statistically significant number of in-situ strong motion records prohibits statistical analyses to be conducted and uncertainties to be quantified based entirely on field data. In this paper, we combine downhole observations and broadband ground motion synthetics for characteristic site conditions the Los Angeles Basin, and investigate the variability in ground motion estimation introduced by the site response assessment methodology. In particular, site-specific regional velocity and attenuation structures are initially compiled using near-surface geotechnical data collected at downhole geotechnical arrays, inverse low-strain velocity and attenuation profiles at these sites obtained by inversion of weak motion records and the crustal velocity structure at the corresponding locations obtained from the Southern California Earthquake Centre Community Velocity Model. Successively, broadband ground motions are simulated by means of a hybrid low/high-frequency finite source model with correlated random parameters for rupture scenaria of weak, medium and large magnitude events (M =3.5-7.5). Observed estimates of site response at the stations of interest are first compared to the ensemble of approximate and incremental nonlinear site response models. Parametric studies are next conducted for each fixed magnitude (fault geometry) scenario by varying the source-to-site distance and source parameters for the ensemble of site conditions. Elastic, equivalent linear and nonlinear simulations are implemented for the deterministic description of the base-model velocity and attenuation structures and nonlinear soil properties, to examine the variability in ground motion predictions as a function of ground motion amplitude and frequency content, and nonlinear site response methodology. The modeling site response uncertainty introduced in the broadband ground motion predictions is reported by means of the COV of site amplification, defined as the ratio of the predicted peak ground acceleration (PGA) and spectral acceleration (SA) at short and long periods to the corresponding intensity measure on the ground surface of a typical NEHRP BC boundary profile (Vs30=760m/s), for the ensemble of approximate and incremental nonlinear models implemented. A frequency index is developed to describe the frequency content of incident ground motion. In conjunction with the rock-outcrop acceleration level, this index is used to identify the site and ground motion conditions where incremental nonlinear analyses should be employed in lieu of approximate methodologies. Finally, the effects of modeling uncertainty in ground response analysis is evaluated in the estimation of site amplification factors, which are successively compared to recently published factors of the New Generation Attenuation Relations (NGA) and the currently employed Seismic Code Provisions (NEHRP).

Nonlinear method for including the mass uncertainty of standards and the system measurement errors in the fitting of calibration curves

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

Pickles, W.L.; McClure, J.W.; Howell, R.H.

1978-01-01

A sophisticated non-linear multiparameter fitting program has been used to produce a best fit calibration curve for the response of an x-ray fluorescence analyzer to uranium nitrate, freeze dried, 0.2% accurate, gravimetric standards. The program is based on unconstrained minimization subroutine, VA02A. The program considers the mass values of the gravimetric standards as parameters to be fit along with the normal calibration curve parameters. The fitting procedure weights with the system errors and the mass errors in a consistent way. The resulting best fit calibration curve parameters reflect the fact that the masses of the standard samples are measured quantitiesmore » with a known error. Error estimates for the calibration curve parameters can be obtined from the curvature of the Chi-Squared Matrix or from error relaxation techniques. It has been shown that non-dispersive x-ray fluorescence analysis of 0.1 to 1 mg freeze-dried UNO/sub 3/ can have an accuracy of 0.2% in 1000 sec.« less

Use of a non-linear method for including the mass uncertainty of gravimetric standards and system measurement errors in the fitting of calibration curves for XRFA freeze-dried UNO/sub 3/ standards

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

Pickles, W.L.; McClure, J.W.; Howell, R.H.

1978-05-01

A sophisticated nonlinear multiparameter fitting program was used to produce a best fit calibration curve for the response of an x-ray fluorescence analyzer to uranium nitrate, freeze dried, 0.2% accurate, gravimetric standards. The program is based on unconstrained minimization subroutine, VA02A. The program considers the mass values of the gravimetric standards as parameters to be fit along with the normal calibration curve parameters. The fitting procedure weights with the system errors and the mass errors in a consistent way. The resulting best fit calibration curve parameters reflect the fact that the masses of the standard samples are measured quantities withmore » a known error. Error estimates for the calibration curve parameters can be obtained from the curvature of the ''Chi-Squared Matrix'' or from error relaxation techniques. It was shown that nondispersive XRFA of 0.1 to 1 mg freeze-dried UNO/sub 3/ can have an accuracy of 0.2% in 1000 s.« less

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.

Magnetohydrodynamic dissipative flow across the slendering stretching sheet with temperature dependent variable viscosity

NASA Astrophysics Data System (ADS)

Jayachandra Babu, M.; Sandeep, N.; Ali, M. E.; Nuhait, Abdullah O.

The boundary layer flow across a slendering stretching sheet has gotten awesome consideration due to its inexhaustible pragmatic applications in nuclear reactor technology, acoustical components, chemical and manufacturing procedures, for example, polymer extrusion, and machine design. By keeping this in view, we analyzed the two-dimensional MHD flow across a slendering stretching sheet within the sight of variable viscosity and viscous dissipation. The sheet is thought to be convectively warmed. Convective boundary conditions through heat and mass are employed. Similarity transformations used to change over the administering nonlinear partial differential equations as a group of nonlinear ordinary differential equations. Runge-Kutta based shooting technique is utilized to solve the converted equations. Numerical estimations of the physical parameters involved in the problem are calculated for the friction factor, local Nusselt and Sherwood numbers. Viscosity variation parameter and chemical reaction parameter shows the opposite impact to each other on the concentration profile. Heat and mass transfer Biot numbers are helpful to enhance the temperature and concentration respectively.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

PubMed

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

PubMed Central

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems. PMID:25811858

A DERATING METHOD FOR THERAPEUTIC APPLICATIONS OF HIGH INTENSITY FOCUSED ULTRASOUND

PubMed Central

Bessonova, O.V.; Khokhlova, V.A.; Canney, M.S.; Bailey, M.R.; Crum, L.A.

2010-01-01

Current methods of determining high intensity focused ultrasound (HIFU) fields in tissue rely on extrapolation of measurements in water assuming linear wave propagation both in water and in tissue. Neglecting nonlinear propagation effects in the derating process can result in significant errors. In this work, a new method based on scaling the source amplitude is introduced to estimate focal parameters of nonlinear HIFU fields in tissue. Focal values of acoustic field parameters in absorptive tissue are obtained from a numerical solution to a KZK-type equation and are compared to those simulated for propagation in water. Focal waveforms, peak pressures, and intensities are calculated over a wide range of source outputs and linear focusing gains. Our modeling indicates, that for the high gain sources which are typically used in therapeutic medical applications, the focal field parameters derated with our method agree well with numerical simulation in tissue. The feasibility of the derating method is demonstrated experimentally in excised bovine liver tissue. PMID:20582159

A derating method for therapeutic applications of high intensity focused ultrasound

NASA Astrophysics Data System (ADS)

Bessonova, O. V.; Khokhlova, V. A.; Canney, M. S.; Bailey, M. R.; Crum, L. A.

2010-05-01

Current methods of determining high intensity focused ultrasound (HIFU) fields in tissue rely on extrapolation of measurements in water assuming linear wave propagation both in water and in tissue. Neglecting nonlinear propagation effects in the derating process can result in significant errors. A new method based on scaling the source amplitude is introduced to estimate focal parameters of nonlinear HIFU fields in tissue. Focal values of acoustic field parameters in absorptive tissue are obtained from a numerical solution to a KZK-type equation and are compared to those simulated for propagation in water. Focal wave-forms, peak pressures, and intensities are calculated over a wide range of source outputs and linear focusing gains. Our modeling indicates, that for the high gain sources which are typically used in therapeutic medical applications, the focal field parameters derated with our method agree well with numerical simulation in tissue. The feasibility of the derating method is demonstrated experimentally in excised bovine liver tissue.

A DERATING METHOD FOR THERAPEUTIC APPLICATIONS OF HIGH INTENSITY FOCUSED ULTRASOUND.

PubMed

Bessonova, O V; Khokhlova, V A; Canney, M S; Bailey, M R; Crum, L A

2010-01-01

Current methods of determining high intensity focused ultrasound (HIFU) fields in tissue rely on extrapolation of measurements in water assuming linear wave propagation both in water and in tissue. Neglecting nonlinear propagation effects in the derating process can result in significant errors. In this work, a new method based on scaling the source amplitude is introduced to estimate focal parameters of nonlinear HIFU fields in tissue. Focal values of acoustic field parameters in absorptive tissue are obtained from a numerical solution to a KZK-type equation and are compared to those simulated for propagation in water. Focal waveforms, peak pressures, and intensities are calculated over a wide range of source outputs and linear focusing gains. Our modeling indicates, that for the high gain sources which are typically used in therapeutic medical applications, the focal field parameters derated with our method agree well with numerical simulation in tissue. The feasibility of the derating method is demonstrated experimentally in excised bovine liver tissue.

A python framework for environmental model uncertainty analysis

USGS Publications Warehouse

White, Jeremy; Fienen, Michael N.; Doherty, John E.

2016-01-01

We have developed pyEMU, a python framework for Environmental Modeling Uncertainty analyses, open-source tool that is non-intrusive, easy-to-use, computationally efficient, and scalable to highly-parameterized inverse problems. The framework implements several types of linear (first-order, second-moment (FOSM)) and non-linear uncertainty analyses. The FOSM-based analyses can also be completed prior to parameter estimation to help inform important modeling decisions, such as parameterization and objective function formulation. Complete workflows for several types of FOSM-based and non-linear analyses are documented in example notebooks implemented using Jupyter that are available in the online pyEMU repository. Example workflows include basic parameter and forecast analyses, data worth analyses, and error-variance analyses, as well as usage of parameter ensemble generation and management capabilities. These workflows document the necessary steps and provides insights into the results, with the goal of educating users not only in how to apply pyEMU, but also in the underlying theory of applied uncertainty quantification.

Nonlinear Prediction As A Tool For Determining Parameters For Phase Space Reconstruction In Meteorology

NASA Astrophysics Data System (ADS)

Miksovsky, J.; Raidl, A.

Time delays phase space reconstruction represents one of useful tools of nonlinear time series analysis, enabling number of applications. Its utilization requires the value of time delay to be known, as well as the value of embedding dimension. There are sev- eral methods how to estimate both these parameters. Typically, time delay is computed first, followed by embedding dimension. Our presented approach is slightly different - we reconstructed phase space for various combinations of mentioned parameters and used it for prediction by means of the nearest neighbours in the phase space. Then some measure of prediction's success was computed (correlation or RMSE, e.g.). The position of its global maximum (minimum) should indicate the suitable combination of time delay and embedding dimension. Several meteorological (particularly clima- tological) time series were used for the computations. We have also created a MS- Windows based program in order to implement this approach - its basic features will be presented as well.

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.

Ultra-large nonlinear parameter in graphene-silicon waveguide structures.

PubMed

Donnelly, Christine; Tan, Dawn T H

2014-09-22

Mono-layer graphene integrated with optical waveguides is studied for the purpose of maximizing E-field interaction with the graphene layer, for the generation of ultra-large nonlinear parameters. It is shown that the common approach used to minimize the waveguide effective modal area does not accurately predict the configuration with the maximum nonlinear parameter. Both photonic and plasmonic waveguide configurations and graphene integration techniques realizable with today's fabrication tools are studied. Importantly, nonlinear parameters exceeding 10(4) W(-1)/m, two orders of magnitude larger than that in silicon on insulator waveguides without graphene, are obtained for the quasi-TE mode in silicon waveguides incorporating mono-layer graphene in the evanescent part of the optical field. Dielectric loaded surface plasmon polariton waveguides incorporating mono-layer graphene are observed to generate nonlinear parameters as large as 10(5) W(-1)/m, three orders of magnitude larger than that in silicon on insulator waveguides without graphene. The ultra-large nonlinear parameters make such waveguides promising platforms for nonlinear integrated optics at ultra-low powers, and for previously unobserved nonlinear optical effects to be studied in a waveguide platform.

Inverse problems and optimal experiment design in unsteady heat transfer processes identification

NASA Technical Reports Server (NTRS)

Artyukhin, Eugene A.

1991-01-01

Experimental-computational methods for estimating characteristics of unsteady heat transfer processes are analyzed. The methods are based on the principles of distributed parameter system identification. The theoretical basis of such methods is the numerical solution of nonlinear ill-posed inverse heat transfer problems and optimal experiment design problems. Numerical techniques for solving problems are briefly reviewed. The results of the practical application of identification methods are demonstrated when estimating effective thermophysical characteristics of composite materials and thermal contact resistance in two-layer systems.

Algorithm Estimates Microwave Water-Vapor Delay

NASA Technical Reports Server (NTRS)

Robinson, Steven E.

1989-01-01

Accuracy equals or exceeds conventional linear algorithms. "Profile" algorithm improved algorithm using water-vapor-radiometer data to produce estimates of microwave delays caused by water vapor in troposphere. Does not require site-specific and weather-dependent empirical parameters other than standard meteorological data, latitude, and altitude for use in conjunction with published standard atmospheric data. Basic premise of profile algorithm, wet-path delay approximated closely by solution to simplified version of nonlinear delay problem and generated numerically from each radiometer observation and simultaneous meteorological data.

Stability region maximization by decomposition-aggregation method. [Skylab stability

NASA Technical Reports Server (NTRS)

Siljak, D. D.; Cuk, S. M.

1974-01-01

This work is to improve the estimates of the stability regions by formulating and resolving a proper maximization problem. The solution of the problem provides the best estimate of the maximal value of the structural parameter and at the same time yields the optimum comparison system, which can be used to determine the degree of stability of the Skylab. The analysis procedure is completely computerized, resulting in a flexible and powerful tool for stability considerations of large-scale linear as well as nonlinear systems.

Estimation of Handling Qualities Parameters of the Tu-144 Supersonic Transport Aircraft from Flight Test Data

NASA Technical Reports Server (NTRS)

Curry, Timothy J.; Batterson, James G. (Technical Monitor)

2000-01-01

Low order equivalent system (LOES) models for the Tu-144 supersonic transport aircraft were identified from flight test data. The mathematical models were given in terms of transfer functions with a time delay by the military standard MIL-STD-1797A, "Flying Qualities of Piloted Aircraft," and the handling qualities were predicted from the estimated transfer function coefficients. The coefficients and the time delay in the transfer functions were estimated using a nonlinear equation error formulation in the frequency domain. Flight test data from pitch, roll, and yaw frequency sweeps at various flight conditions were used for parameter estimation. Flight test results are presented in terms of the estimated parameter values, their standard errors, and output fits in the time domain. Data from doublet maneuvers at the same flight conditions were used to assess the predictive capabilities of the identified models. The identified transfer function models fit the measured data well and demonstrated good prediction capabilities. The Tu-144 was predicted to be between level 2 and 3 for all longitudinal maneuvers and level I for all lateral maneuvers. High estimates of the equivalent time delay in the transfer function model caused the poor longitudinal rating.

Genomic data assimilation for estimating hybrid functional Petri net from time-course gene expression data.

PubMed

Nagasaki, Masao; Yamaguchi, Rui; Yoshida, Ryo; Imoto, Seiya; Doi, Atsushi; Tamada, Yoshinori; Matsuno, Hiroshi; Miyano, Satoru; Higuchi, Tomoyuki

2006-01-01

We propose an automatic construction method of the hybrid functional Petri net as a simulation model of biological pathways. The problems we consider are how we choose the values of parameters and how we set the network structure. Usually, we tune these unknown factors empirically so that the simulation results are consistent with biological knowledge. Obviously, this approach has the limitation in the size of network of interest. To extend the capability of the simulation model, we propose the use of data assimilation approach that was originally established in the field of geophysical simulation science. We provide genomic data assimilation framework that establishes a link between our simulation model and observed data like microarray gene expression data by using a nonlinear state space model. A key idea of our genomic data assimilation is that the unknown parameters in simulation model are converted as the parameter of the state space model and the estimates are obtained as the maximum a posteriori estimators. In the parameter estimation process, the simulation model is used to generate the system model in the state space model. Such a formulation enables us to handle both the model construction and the parameter tuning within a framework of the Bayesian statistical inferences. In particular, the Bayesian approach provides us a way of controlling overfitting during the parameter estimations that is essential for constructing a reliable biological pathway. We demonstrate the effectiveness of our approach using synthetic data. As a result, parameter estimation using genomic data assimilation works very well and the network structure is suitably selected.

Evaluation of Available Software for Reconstruction of a Structure from its Imagery

DTIC Science & Technology

2017-04-01

Math . 2, 164–168. Lowe, D. G. (1999) Object recognition from local scale-invariant features, in Proc. Int. Conf. Computer Vision, Vol. 2, pp. 1150–1157...Marquardt, D. (1963) An algorithm for least-squares estimation of nonlinear parameters, SIAM J. Appl. Math . 11(2), 431–441. UNCLASSIFIED 11 DST-Group–TR

Estimation of Saxophone Control Parameters by Convex Optimization.

PubMed

Wang, Cheng-I; Smyth, Tamara; Lipton, Zachary C

2014-12-01

In this work, an approach to jointly estimating the tone hole configuration (fingering) and reed model parameters of a saxophone is presented. The problem isn't one of merely estimating pitch as one applied fingering can be used to produce several different pitches by bugling or overblowing. Nor can a fingering be estimated solely by the spectral envelope of the produced sound (as it might for estimation of vocal tract shape in speech) since one fingering can produce markedly different spectral envelopes depending on the player's embouchure and control of the reed. The problem is therefore addressed by jointly estimating both the reed (source) parameters and the fingering (filter) of a saxophone model using convex optimization and 1) a bank of filter frequency responses derived from measurement of the saxophone configured with all possible fingerings and 2) sample recordings of notes produced using all possible fingerings, played with different overblowing, dynamics and timbre. The saxophone model couples one of several possible frequency response pairs (corresponding to the applied fingering), and a quasi-static reed model generating input pressure at the mouthpiece, with control parameters being blowing pressure and reed stiffness. Applied fingering and reed parameters are estimated for a given recording by formalizing a minimization problem, where the cost function is the error between the recording and the synthesized sound produced by the model having incremental parameter values for blowing pressure and reed stiffness. The minimization problem is nonlinear and not differentiable and is made solvable using convex optimization. The performance of the fingering identification is evaluated with better accuracy than previous reported value.

A unified perspective on robot control - The energy Lyapunov function approach

NASA Technical Reports Server (NTRS)

Wen, John T.

1990-01-01

A unified framework for the stability analysis of robot tracking control is presented. By using an energy-motivated Lyapunov function candidate, the closed-loop stability is shown for a large family of control laws sharing a common structure of proportional and derivative feedback and a model-based feedforward. The feedforward can be zero, partial or complete linearized dynamics, partial or complete nonlinear dynamics, or linearized or nonlinear dynamics with parameter adaptation. As result, the dichotomous approaches to the robot control problem based on the open-loop linearization and nonlinear Lyapunov analysis are both included in this treatment. Furthermore, quantitative estimates of the trade-offs between different schemes in terms of the tracking performance, steady state error, domain of convergence, realtime computation load and required a prior model information are derived.

Fast Generation of Ensembles of Cosmological N-Body Simulations via Mode-Resampling

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

Schneider, M D; Cole, S; Frenk, C S

2011-02-14

We present an algorithm for quickly generating multiple realizations of N-body simulations to be used, for example, for cosmological parameter estimation from surveys of large-scale structure. Our algorithm uses a new method to resample the large-scale (Gaussian-distributed) Fourier modes in a periodic N-body simulation box in a manner that properly accounts for the nonlinear mode-coupling between large and small scales. We find that our method for adding new large-scale mode realizations recovers the nonlinear power spectrum to sub-percent accuracy on scales larger than about half the Nyquist frequency of the simulation box. Using 20 N-body simulations, we obtain a powermore » spectrum covariance matrix estimate that matches the estimator from Takahashi et al. (from 5000 simulations) with < 20% errors in all matrix elements. Comparing the rates of convergence, we determine that our algorithm requires {approx}8 times fewer simulations to achieve a given error tolerance in estimates of the power spectrum covariance matrix. The degree of success of our algorithm indicates that we understand the main physical processes that give rise to the correlations in the matter power spectrum. Namely, the large-scale Fourier modes modulate both the degree of structure growth through the variation in the effective local matter density and also the spatial frequency of small-scale perturbations through large-scale displacements. We expect our algorithm to be useful for noise modeling when constraining cosmological parameters from weak lensing (cosmic shear) and galaxy surveys, rescaling summary statistics of N-body simulations for new cosmological parameter values, and any applications where the influence of Fourier modes larger than the simulation size must be accounted for.« less

Financial market dynamics: superdiffusive or not?

NASA Astrophysics Data System (ADS)

Devi, Sandhya

2017-08-01

The behavior of stock market returns over a period of 1-60 d has been investigated for S&P 500 and Nasdaq within the framework of nonextensive Tsallis statistics. Even for such long terms, the distributions of the returns are non-Gaussian. They have fat tails indicating that the stock returns do not follow a random walk model. In this work, a good fit to a Tsallis q-Gaussian distribution is obtained for the distributions of all the returns using the method of Maximum Likelihood Estimate. For all the regions of data considered, the values of the scaling parameter q, estimated from 1 d returns, lie in the range 1.4-1.65. The estimated inverse mean square deviations (beta) show a power law behavior in time with exponent values between  -0.91 and  -1.1 indicating normal to mildly subdiffusive behavior. Quite often, the dynamics of market return distributions is modelled by a Fokker-Plank (FP) equation either with a linear drift and a nonlinear diffusion term or with just a nonlinear diffusion term. Both of these cases support a q-Gaussian distribution as a solution. The distributions obtained from current estimated parameters are compared with the solutions of the FP equations. For negligible drift term, the inverse mean square deviations (betaFP) from the FP model follow a power law with exponent values between  -1.25 and  -1.48 indicating superdiffusion. When the drift term is non-negligible, the corresponding betaFP do not follow a power law and become stationary after certain characteristic times that depend on the values of the drift parameter and q. Neither of these behaviors is supported by the results of the empirical fit.

Calculation of the confidence intervals for transformation parameters in the registration of medical images

PubMed Central

Bansal, Ravi; Staib, Lawrence H.; Laine, Andrew F.; Xu, Dongrong; Liu, Jun; Posecion, Lainie F.; Peterson, Bradley S.

2010-01-01

Images from different individuals typically cannot be registered precisely because anatomical features within the images differ across the people imaged and because the current methods for image registration have inherent technological limitations that interfere with perfect registration. Quantifying the inevitable error in image registration is therefore of crucial importance in assessing the effects that image misregistration may have on subsequent analyses in an imaging study. We have developed a mathematical framework for quantifying errors in registration by computing the confidence intervals of the estimated parameters (3 translations, 3 rotations, and 1 global scale) for the similarity transformation. The presence of noise in images and the variability in anatomy across individuals ensures that estimated registration parameters are always random variables. We assume a functional relation among intensities across voxels in the images, and we use the theory of nonlinear, least-squares estimation to show that the parameters are multivariate Gaussian distributed. We then use the covariance matrix of this distribution to compute the confidence intervals of the transformation parameters. These confidence intervals provide a quantitative assessment of the registration error across the images. Because transformation parameters are nonlinearly related to the coordinates of landmark points in the brain, we subsequently show that the coordinates of those landmark points are also multivariate Gaussian distributed. Using these distributions, we then compute the confidence intervals of the coordinates for landmark points in the image. Each of these confidence intervals in turn provides a quantitative assessment of the registration error at a particular landmark point. Because our method is computationally intensive, however, its current implementation is limited to assessing the error of the parameters in the similarity transformation across images. We assessed the performance of our method in computing the error in estimated similarity parameters by applying that method to real world dataset. Our results showed that the size of the confidence intervals computed using our method decreased – i.e. our confidence in the registration of images from different individuals increased – for increasing amounts of blur in the images. Moreover, the size of the confidence intervals increased for increasing amounts of noise, misregistration, and differing anatomy. Thus, our method precisely quantified confidence in the registration of images that contain varying amounts of misregistration and varying anatomy across individuals. PMID:19138877

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.

Direct and accelerated parameter mapping using the unscented Kalman filter.

PubMed

Zhao, Li; Feng, Xue; Meyer, Craig H

2016-05-01

To accelerate parameter mapping using a new paradigm that combines image reconstruction and model regression as a parameter state-tracking problem. In T2 mapping, the T2 map is first encoded in parameter space by multi-TE measurements and then encoded by Fourier transformation with readout/phase encoding gradients. Using a state transition function and a measurement function, the unscented Kalman filter can describe T2 mapping as a dynamic system and directly estimate the T2 map from the k-space data. The proposed method was validated with a numerical brain phantom and volunteer experiments with a multiple-contrast spin echo sequence. Its performance was compared with a conjugate-gradient nonlinear inversion method at undersampling factors of 2 to 8. An accelerated pulse sequence was developed based on this method to achieve prospective undersampling. Compared with the nonlinear inversion reconstruction, the proposed method had higher precision, improved structural similarity and reduced normalized root mean squared error, with acceleration factors up to 8 in numerical phantom and volunteer studies. This work describes a new perspective on parameter mapping by state tracking. The unscented Kalman filter provides a highly accelerated and efficient paradigm for T2 mapping. © 2015 Wiley Periodicals, Inc.

PERIOD ESTIMATION FOR SPARSELY SAMPLED QUASI-PERIODIC LIGHT CURVES APPLIED TO MIRAS

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

He, Shiyuan; Huang, Jianhua Z.; Long, James

2016-12-01

We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequencymore » parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period–luminosity relations.« less

A gap-filling model for eddy covariance latent heat flux: Estimating evapotranspiration of a subtropical seasonal evergreen broad-leaved forest as an example

NASA Astrophysics Data System (ADS)

Chen, Yi-Ying; Chu, Chia-Ren; Li, Ming-Hsu

2012-10-01

SummaryIn this paper we present a semi-parametric multivariate gap-filling model for tower-based measurement of latent heat flux (LE). Two statistical techniques, the principal component analysis (PCA) and a nonlinear interpolation approach were integrated into this LE gap-filling model. The PCA was first used to resolve the multicollinearity relationships among various environmental variables, including radiation, soil moisture deficit, leaf area index, wind speed, etc. Two nonlinear interpolation methods, multiple regressions (MRS) and the K-nearest neighbors (KNNs) were examined with random selected flux gaps for both clear sky and nighttime/cloudy data to incorporate into this LE gap-filling model. Experimental results indicated that the KNN interpolation approach is able to provide consistent LE estimations while MRS presents over estimations during nighttime/cloudy. Rather than using empirical regression parameters, the KNN approach resolves the nonlinear relationship between the gap-filled LE flux and principal components with adaptive K values under different atmospheric states. The developed LE gap-filling model (PCA with KNN) works with a RMSE of 2.4 W m-2 (˜0.09 mm day-1) at a weekly time scale by adding 40% artificial flux gaps into original dataset. Annual evapotranspiration at this study site were estimated at 736 mm (1803 MJ) and 728 mm (1785 MJ) for year 2008 and 2009, respectively.

Linear and non-linear regression analysis for the sorption kinetics of methylene blue onto activated carbon.

PubMed

Kumar, K Vasanth

2006-10-11

Batch kinetic experiments were carried out for the sorption of methylene blue onto activated carbon. The experimental kinetics were fitted to the pseudo first-order and pseudo second-order kinetics by linear and a non-linear method. The five different types of Ho pseudo second-order expression have been discussed. A comparison of linear least-squares method and a trial and error non-linear method of estimating the pseudo second-order rate kinetic parameters were examined. The sorption process was found to follow a both pseudo first-order kinetic and pseudo second-order kinetic model. Present investigation showed that it is inappropriate to use a type 1 and type pseudo second-order expressions as proposed by Ho and Blanachard et al. respectively for predicting the kinetic rate constants and the initial sorption rate for the studied system. Three correct possible alternate linear expressions (type 2 to type 4) to better predict the initial sorption rate and kinetic rate constants for the studied system (methylene blue/activated carbon) was proposed. Linear method was found to check only the hypothesis instead of verifying the kinetic model. Non-linear regression method was found to be the more appropriate method to determine the rate kinetic parameters.

Optimal design of stimulus experiments for robust discrimination of biochemical reaction networks.

PubMed

Flassig, R J; Sundmacher, K

2012-12-01

Biochemical reaction networks in the form of coupled ordinary differential equations (ODEs) provide a powerful modeling tool for understanding the dynamics of biochemical processes. During the early phase of modeling, scientists have to deal with a large pool of competing nonlinear models. At this point, discrimination experiments can be designed and conducted to obtain optimal data for selecting the most plausible model. Since biological ODE models have widely distributed parameters due to, e.g. biologic variability or experimental variations, model responses become distributed. Therefore, a robust optimal experimental design (OED) for model discrimination can be used to discriminate models based on their response probability distribution functions (PDFs). In this work, we present an optimal control-based methodology for designing optimal stimulus experiments aimed at robust model discrimination. For estimating the time-varying model response PDF, which results from the nonlinear propagation of the parameter PDF under the ODE dynamics, we suggest using the sigma-point approach. Using the model overlap (expected likelihood) as a robust discrimination criterion to measure dissimilarities between expected model response PDFs, we benchmark the proposed nonlinear design approach against linearization with respect to prediction accuracy and design quality for two nonlinear biological reaction networks. As shown, the sigma-point outperforms the linearization approach in the case of widely distributed parameter sets and/or existing multiple steady states. Since the sigma-point approach scales linearly with the number of model parameter, it can be applied to large systems for robust experimental planning. An implementation of the method in MATLAB/AMPL is available at http://www.uni-magdeburg.de/ivt/svt/person/rf/roed.html. flassig@mpi-magdeburg.mpg.de Supplementary data are are available at Bioinformatics online.

Alpha models for rotating Navier-Stokes equations in geophysics with nonlinear dispersive regularization

NASA Astrophysics Data System (ADS)

Kim, Bong-Sik

Three dimensional (3D) Navier-Stokes-alpha equations are considered for uniformly rotating geophysical fluid flows (large Coriolis parameter f = 2O). The Navier-Stokes-alpha equations are a nonlinear dispersive regularization of usual Navier-Stokes equations obtained by Lagrangian averaging. The focus is on the existence and global regularity of solutions of the 3D rotating Navier-Stokes-alpha equations and the uniform convergence of these solutions to those of the original 3D rotating Navier-Stokes equations for large Coriolis parameters f as alpha → 0. Methods are based on fast singular oscillating limits and results are obtained for periodic boundary conditions for all domain aspect ratios, including the case of three wave resonances which yields nonlinear "2½-dimensional" limit resonant equations for f → 0. The existence and global regularity of solutions of limit resonant equations is established, uniformly in alpha. Bootstrapping from global regularity of the limit equations, the existence of a regular solution of the full 3D rotating Navier-Stokes-alpha equations for large f for an infinite time is established. Then, the uniform convergence of a regular solution of the 3D rotating Navier-Stokes-alpha equations (alpha ≠ 0) to the one of the original 3D rotating NavierStokes equations (alpha = 0) for f large but fixed as alpha → 0 follows; this implies "shadowing" of trajectories of the limit dynamical systems by those of the perturbed alpha-dynamical systems. All the estimates are uniform in alpha, in contrast with previous estimates in the literature which blow up as alpha → 0. Finally, the existence of global attractors as well as exponential attractors is established for large f and the estimates are uniform in alpha.

Centralized Multi-Sensor Square Root Cubature Joint Probabilistic Data Association

PubMed Central

Liu, Jun; Li, Gang; Qi, Lin; Li, Yaowen; He, You

2017-01-01

This paper focuses on the tracking problem of multiple targets with multiple sensors in a nonlinear cluttered environment. To avoid Jacobian matrix computation and scaling parameter adjustment, improve numerical stability, and acquire more accurate estimated results for centralized nonlinear tracking, a novel centralized multi-sensor square root cubature joint probabilistic data association algorithm (CMSCJPDA) is proposed. Firstly, the multi-sensor tracking problem is decomposed into several single-sensor multi-target tracking problems, which are sequentially processed during the estimation. Then, in each sensor, the assignment of its measurements to target tracks is accomplished on the basis of joint probabilistic data association (JPDA), and a weighted probability fusion method with square root version of a cubature Kalman filter (SRCKF) is utilized to estimate the targets’ state. With the measurements in all sensors processed CMSCJPDA is derived and the global estimated state is achieved. Experimental results show that CMSCJPDA is superior to the state-of-the-art algorithms in the aspects of tracking accuracy, numerical stability, and computational cost, which provides a new idea to solve multi-sensor tracking problems. PMID:29113085

Centralized Multi-Sensor Square Root Cubature Joint Probabilistic Data Association.

PubMed

Liu, Yu; Liu, Jun; Li, Gang; Qi, Lin; Li, Yaowen; He, You

2017-11-05

This paper focuses on the tracking problem of multiple targets with multiple sensors in a nonlinear cluttered environment. To avoid Jacobian matrix computation and scaling parameter adjustment, improve numerical stability, and acquire more accurate estimated results for centralized nonlinear tracking, a novel centralized multi-sensor square root cubature joint probabilistic data association algorithm (CMSCJPDA) is proposed. Firstly, the multi-sensor tracking problem is decomposed into several single-sensor multi-target tracking problems, which are sequentially processed during the estimation. Then, in each sensor, the assignment of its measurements to target tracks is accomplished on the basis of joint probabilistic data association (JPDA), and a weighted probability fusion method with square root version of a cubature Kalman filter (SRCKF) is utilized to estimate the targets' state. With the measurements in all sensors processed CMSCJPDA is derived and the global estimated state is achieved. Experimental results show that CMSCJPDA is superior to the state-of-the-art algorithms in the aspects of tracking accuracy, numerical stability, and computational cost, which provides a new idea to solve multi-sensor tracking problems.

Delineating parameter unidentifiabilities in complex models

NASA Astrophysics Data System (ADS)

Raman, Dhruva V.; Anderson, James; Papachristodoulou, Antonis

2017-03-01

Scientists use mathematical modeling as a tool for understanding and predicting the properties of complex physical systems. In highly parametrized models there often exist relationships between parameters over which model predictions are identical, or nearly identical. These are known as structural or practical unidentifiabilities, respectively. They are hard to diagnose and make reliable parameter estimation from data impossible. They furthermore imply the existence of an underlying model simplification. We describe a scalable method for detecting unidentifiabilities, as well as the functional relations defining them, for generic models. This allows for model simplification, and appreciation of which parameters (or functions thereof) cannot be estimated from data. Our algorithm can identify features such as redundant mechanisms and fast time-scale subsystems, as well as the regimes in parameter space over which such approximations are valid. We base our algorithm on a quantification of regional parametric sensitivity that we call `multiscale sloppiness'. Traditionally, the link between parametric sensitivity and the conditioning of the parameter estimation problem is made locally, through the Fisher information matrix. This is valid in the regime of infinitesimal measurement uncertainty. We demonstrate the duality between multiscale sloppiness and the geometry of confidence regions surrounding parameter estimates made where measurement uncertainty is non-negligible. Further theoretical relationships are provided linking multiscale sloppiness to the likelihood-ratio test. From this, we show that a local sensitivity analysis (as typically done) is insufficient for determining the reliability of parameter estimation, even with simple (non)linear systems. Our algorithm can provide a tractable alternative. We finally apply our methods to a large-scale, benchmark systems biology model of necrosis factor (NF)-κ B , uncovering unidentifiabilities.

A comparison of Monte Carlo-based Bayesian parameter estimation methods for stochastic models of genetic networks

PubMed Central

Zaikin, Alexey; Míguez, Joaquín

2017-01-01

We compare three state-of-the-art Bayesian inference methods for the estimation of the unknown parameters in a stochastic model of a genetic network. In particular, we introduce a stochastic version of the paradigmatic synthetic multicellular clock model proposed by Ullner et al., 2007. By introducing dynamical noise in the model and assuming that the partial observations of the system are contaminated by additive noise, we enable a principled mechanism to represent experimental uncertainties in the synthesis of the multicellular system and pave the way for the design of probabilistic methods for the estimation of any unknowns in the model. Within this setup, we tackle the Bayesian estimation of a subset of the model parameters. Specifically, we compare three Monte Carlo based numerical methods for the approximation of the posterior probability density function of the unknown parameters given a set of partial and noisy observations of the system. The schemes we assess are the particle Metropolis-Hastings (PMH) algorithm, the nonlinear population Monte Carlo (NPMC) method and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) scheme. We present an extensive numerical simulation study, which shows that while the three techniques can effectively solve the problem there are significant differences both in estimation accuracy and computational efficiency. PMID:28797087

Fast Quantitative Susceptibility Mapping with L1-Regularization and Automatic Parameter Selection

PubMed Central

Bilgic, Berkin; Fan, Audrey P.; Polimeni, Jonathan R.; Cauley, Stephen F.; Bianciardi, Marta; Adalsteinsson, Elfar; Wald, Lawrence L.; Setsompop, Kawin

2014-01-01

Purpose To enable fast reconstruction of quantitative susceptibility maps with Total Variation penalty and automatic regularization parameter selection. Methods ℓ1-regularized susceptibility mapping is accelerated by variable-splitting, which allows closed-form evaluation of each iteration of the algorithm by soft thresholding and FFTs. This fast algorithm also renders automatic regularization parameter estimation practical. A weighting mask derived from the magnitude signal can be incorporated to allow edge-aware regularization. Results Compared to the nonlinear Conjugate Gradient (CG) solver, the proposed method offers 20× speed-up in reconstruction time. A complete pipeline including Laplacian phase unwrapping, background phase removal with SHARP filtering and ℓ1-regularized dipole inversion at 0.6 mm isotropic resolution is completed in 1.2 minutes using Matlab on a standard workstation compared to 22 minutes using the Conjugate Gradient solver. This fast reconstruction allows estimation of regularization parameters with the L-curve method in 13 minutes, which would have taken 4 hours with the CG algorithm. Proposed method also permits magnitude-weighted regularization, which prevents smoothing across edges identified on the magnitude signal. This more complicated optimization problem is solved 5× faster than the nonlinear CG approach. Utility of the proposed method is also demonstrated in functional BOLD susceptibility mapping, where processing of the massive time-series dataset would otherwise be prohibitive with the CG solver. Conclusion Online reconstruction of regularized susceptibility maps may become feasible with the proposed dipole inversion. PMID:24259479

System IDentification Programs for AirCraft (SIDPAC)

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

2002-01-01

A collection of computer programs for aircraft system identification is described and demonstrated. The programs, collectively called System IDentification Programs for AirCraft, or SIDPAC, were developed in MATLAB as m-file functions. SIDPAC has been used successfully at NASA Langley Research Center with data from many different flight test programs and wind tunnel experiments. SIDPAC includes routines for experiment design, data conditioning, data compatibility analysis, model structure determination, equation-error and output-error parameter estimation in both the time and frequency domains, real-time and recursive parameter estimation, low order equivalent system identification, estimated parameter error calculation, linear and nonlinear simulation, plotting, and 3-D visualization. An overview of SIDPAC capabilities is provided, along with a demonstration of the use of SIDPAC with real flight test data from the NASA Glenn Twin Otter aircraft. The SIDPAC software is available without charge to U.S. citizens by request to the author, contingent on the requestor completing a NASA software usage agreement.

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

PubMed

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

2015-12-18

An approach that is commonly used for calculating the retention time of a compound in GC departs from the thermodynamic properties ΔH, ΔS and ΔCp of phase change (from mobile to stationary). Such properties can be estimated by using experimental retention time data, which results in a non-linear regression problem for non-isothermal temperature programs. As shown in this work, the surface of the objective function (approximation error criterion) on the basis of thermodynamic parameters can be divided into three clearly defined regions, and solely in one of them there is a possibility for the global optimum to be found. The main contribution of this study was the development of an algorithm that distinguishes the different regions of the error surface and its use in the robust initialization of the estimation of parameters ΔH, ΔS and ΔCp. Copyright © 2015 Elsevier B.V. All rights reserved.

Fast myopic 2D-SIM super resolution microscopy with joint modulation pattern estimation

NASA Astrophysics Data System (ADS)

Orieux, François; Loriette, Vincent; Olivo-Marin, Jean-Christophe; Sepulveda, Eduardo; Fragola, Alexandra

2017-12-01

Super-resolution in structured illumination microscopy (SIM) is obtained through de-aliasing of modulated raw images, in which high frequencies are measured indirectly inside the optical transfer function. Usual approaches that use 9 or 15 images are often too slow for dynamic studies. Moreover, as experimental conditions change with time, modulation parameters must be estimated within the images. This paper tackles the problem of image reconstruction for fast super resolution in SIM, where the number of available raw images is reduced to four instead of nine or fifteen. Within an optimization framework, the solution is inferred via a joint myopic criterion for image and modulation (or acquisition) parameters, leading to what is frequently called a myopic or semi-blind inversion problem. The estimate is chosen as the minimizer of the nonlinear criterion, numerically calculated by means of a block coordinate optimization algorithm. The effectiveness of the proposed method is demonstrated for simulated and experimental examples. The results show precise estimation of the modulation parameters jointly with the reconstruction of the super resolution image. The method also shows its effectiveness for thick biological samples.

Estimation of Unsteady Aerodynamic Models from Dynamic Wind Tunnel Data

NASA Technical Reports Server (NTRS)

Murphy, Patrick; Klein, Vladislav

2011-01-01

Demanding aerodynamic modelling requirements for military and civilian aircraft have motivated researchers to improve computational and experimental techniques and to pursue closer collaboration in these areas. Model identification and validation techniques are key components for this research. This paper presents mathematical model structures and identification techniques that have been used successfully to model more general aerodynamic behaviours in single-degree-of-freedom dynamic testing. Model parameters, characterizing aerodynamic properties, are estimated using linear and nonlinear regression methods in both time and frequency domains. Steps in identification including model structure determination, parameter estimation, and model validation, are addressed in this paper with examples using data from one-degree-of-freedom dynamic wind tunnel and water tunnel experiments. These techniques offer a methodology for expanding the utility of computational methods in application to flight dynamics, stability, and control problems. Since flight test is not always an option for early model validation, time history comparisons are commonly made between computational and experimental results and model adequacy is inferred by corroborating results. An extension is offered to this conventional approach where more general model parameter estimates and their standard errors are compared.

Ensemble Kalman filter inference of spatially-varying Manning's n coefficients in the coastal ocean

NASA Astrophysics Data System (ADS)

Siripatana, Adil; Mayo, Talea; Knio, Omar; Dawson, Clint; Maître, Olivier Le; Hoteit, Ibrahim

2018-07-01

Ensemble Kalman (EnKF) filtering is an established framework for large scale state estimation problems. EnKFs can also be used for state-parameter estimation, using the so-called "Joint-EnKF" approach. The idea is simply to augment the state vector with the parameters to be estimated and assign invariant dynamics for the time evolution of the parameters. In this contribution, we investigate the efficiency of the Joint-EnKF for estimating spatially-varying Manning's n coefficients used to define the bottom roughness in the Shallow Water Equations (SWEs) of a coastal ocean model. Observation System Simulation Experiments (OSSEs) are conducted using the ADvanced CIRCulation (ADCIRC) model, which solves a modified form of the Shallow Water Equations. A deterministic EnKF, the Singular Evolutive Interpolated Kalman (SEIK) filter, is used to estimate a vector of Manning's n coefficients defined at the model nodal points by assimilating synthetic water elevation data. It is found that with reasonable ensemble size (O (10)) , the filter's estimate converges to the reference Manning's field. To enhance performance, we have further reduced the dimension of the parameter search space through a Karhunen-Loéve (KL) expansion. We have also iterated on the filter update step to better account for the nonlinearity of the parameter estimation problem. We study the sensitivity of the system to the ensemble size, localization scale, dimension of retained KL modes, and number of iterations. The performance of the proposed framework in term of estimation accuracy suggests that a well-tuned Joint-EnKF provides a promising robust approach to infer spatially varying seabed roughness parameters in the context of coastal ocean modeling.

Volcano deformation source parameters estimated from InSAR: Sensitivities to uncertainties in seismic tomography

USGS Publications Warehouse

Masterlark, Timothy; Donovan, Theodore; Feigl, Kurt L.; Haney, Matt; Thurber, Clifford H.; Tung, Sui

2016-01-01

The eruption cycle of a volcano is controlled in part by the upward migration of magma. The characteristics of the magma flux produce a deformation signature at the Earth's surface. Inverse analyses use geodetic data to estimate strategic controlling parameters that describe the position and pressurization of a magma chamber at depth. The specific distribution of material properties controls how observed surface deformation translates to source parameter estimates. Seismic tomography models describe the spatial distributions of material properties that are necessary for accurate models of volcano deformation. This study investigates how uncertainties in seismic tomography models propagate into variations in the estimates of volcano deformation source parameters inverted from geodetic data. We conduct finite element model-based nonlinear inverse analyses of interferometric synthetic aperture radar (InSAR) data for Okmok volcano, Alaska, as an example. We then analyze the estimated parameters and their uncertainties to characterize the magma chamber. Analyses are performed separately for models simulating a pressurized chamber embedded in a homogeneous domain as well as for a domain having a heterogeneous distribution of material properties according to seismic tomography. The estimated depth of the source is sensitive to the distribution of material properties. The estimated depths for the homogeneous and heterogeneous domains are 2666 ± 42 and 3527 ± 56 m below mean sea level, respectively (99% confidence). A Monte Carlo analysis indicates that uncertainties of the seismic tomography cannot account for this discrepancy at the 99% confidence level. Accounting for the spatial distribution of elastic properties according to seismic tomography significantly improves the fit of the deformation model predictions and significantly influences estimates for parameters that describe the location of a pressurized magma chamber.

ConvAn: a convergence analyzing tool for optimization of biochemical networks.

PubMed

Kostromins, Andrejs; Mozga, Ivars; Stalidzans, Egils

2012-01-01

Dynamic models of biochemical networks usually are described as a system of nonlinear differential equations. In case of optimization of models for purpose of parameter estimation or design of new properties mainly numerical methods are used. That causes problems of optimization predictability as most of numerical optimization methods have stochastic properties and the convergence of the objective function to the global optimum is hardly predictable. Determination of suitable optimization method and necessary duration of optimization becomes critical in case of evaluation of high number of combinations of adjustable parameters or in case of large dynamic models. This task is complex due to variety of optimization methods, software tools and nonlinearity features of models in different parameter spaces. A software tool ConvAn is developed to analyze statistical properties of convergence dynamics for optimization runs with particular optimization method, model, software tool, set of optimization method parameters and number of adjustable parameters of the model. The convergence curves can be normalized automatically to enable comparison of different methods and models in the same scale. By the help of the biochemistry adapted graphical user interface of ConvAn it is possible to compare different optimization methods in terms of ability to find the global optima or values close to that as well as the necessary computational time to reach them. It is possible to estimate the optimization performance for different number of adjustable parameters. The functionality of ConvAn enables statistical assessment of necessary optimization time depending on the necessary optimization accuracy. Optimization methods, which are not suitable for a particular optimization task, can be rejected if they have poor repeatability or convergence properties. The software ConvAn is freely available on www.biosystems.lv/convan. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

A Non-linear Geodetic Data Inversion Using ABIC for Slip Distribution on a Fault With an Unknown dip Angle

NASA Astrophysics Data System (ADS)

Fukahata, Y.; Wright, T. J.

2006-12-01

We developed a method of geodetic data inversion for slip distribution on a fault with an unknown dip angle. When fault geometry is unknown, the problem of geodetic data inversion is non-linear. A common strategy for obtaining slip distribution is to first determine the fault geometry by minimizing the square misfit under the assumption of a uniform slip on a rectangular fault, and then apply the usual linear inversion technique to estimate a slip distribution on the determined fault. It is not guaranteed, however, that the fault determined under the assumption of a uniform slip gives the best fault geometry for a spatially variable slip distribution. In addition, in obtaining a uniform slip fault model, we have to simultaneously determine the values of the nine mutually dependent parameters, which is a highly non-linear, complicated process. Although the inverse problem is non-linear for cases with unknown fault geometries, the non-linearity of the problems is actually weak, when we can assume the fault surface to be flat. In particular, when a clear fault trace is observed on the EarthOs surface after an earthquake, we can precisely estimate the strike and the location of the fault. In this case only the dip angle has large ambiguity. In geodetic data inversion we usually need to introduce smoothness constraints in order to compromise reciprocal requirements for model resolution and estimation errors in a natural way. Strictly speaking, the inverse problem with smoothness constraints is also non-linear, even if the fault geometry is known. The non-linearity has been dissolved by introducing AkaikeOs Bayesian Information Criterion (ABIC), with which the optimal value of the relative weight of observed data to smoothness constraints is objectively determined. In this study, using ABIC in determining the optimal dip angle, we dissolved the non-linearity of the inverse problem. We applied the method to the InSAR data of the 1995 Dinar, Turkey earthquake and obtained a much shallower dip angle than before.

Experimental and theoretical simulation studies on picosecond closed-aperture Z-scan profiles of N,N‧-Bis(2,5,-di-tert-butylphenyl)-3,4,9,10-perylenedicarboximide (DBPI)

NASA Astrophysics Data System (ADS)

Tripathy, Umakanta; Rallabandi, Sailaja; Bisht, Prem B.

2017-10-01

The optical nonlinear refractive and absorptive parameters of the dye N,N‧-Bis(2,5,-di-tert-butylphenyl)-3,4,9,10-perylenedicarboximide (DBPI) in 96% sulphuric acid have been obtained by a single closed-aperture (CA) Z-scan technique with picosecond pulses at the wavelength of 532 nm. Here a theoretical model was used to deduce both the refractive and absorptive optical nonlinearity present simultaneously in the CA Z-scan profile. Under the range of concentrations and energies studied here, we found that the effect of saturable absorption (SA) is dominating at higher concentrations (i.e. 1.0 × 10-3 M), whereas the reverse saturable absorption (RSA) effect was taken over at dilute concentrations (i.e. 1.0 × 10-4 M and 1.0 × 10-5 M). The dominance of absorptive nonlinearity over the refractive nonlinearity results in a low value of the refractive cross-section (σr). A relative increase in the value of σr is observed with decrease in the dye concentration. Mathematical modeling of CA Z-scan profiles of DBPI shows the existence of peak-valley or valley-peak structure depending upon the contribution of nonlinear absorption. The optical nonlinear parameters have also been estimated by theoretical simulation studies as a function of wavelength and compared with the experimental results. The dye DBPI has been found to be suitable as an important highly photostable molecule for photonic devices in the visible region (400-630 nm).

Estimating Ω from Galaxy Redshifts: Linear Flow Distortions and Nonlinear Clustering

NASA Astrophysics Data System (ADS)

Bromley, B. C.; Warren, M. S.; Zurek, W. H.

1997-02-01

We propose a method to determine the cosmic mass density Ω from redshift-space distortions induced by large-scale flows in the presence of nonlinear clustering. Nonlinear structures in redshift space, such as fingers of God, can contaminate distortions from linear flows on scales as large as several times the small-scale pairwise velocity dispersion σv. Following Peacock & Dodds, we work in the Fourier domain and propose a model to describe the anisotropy in the redshift-space power spectrum; tests with high-resolution numerical data demonstrate that the model is robust for both mass and biased galaxy halos on translinear scales and above. On the basis of this model, we propose an estimator of the linear growth parameter β = Ω0.6/b, where b measures bias, derived from sampling functions that are tuned to eliminate distortions from nonlinear clustering. The measure is tested on the numerical data and found to recover the true value of β to within ~10%. An analysis of IRAS 1.2 Jy galaxies yields β=0.8+0.4-0.3 at a scale of 1000 km s-1, which is close to optimal given the shot noise and finite size of the survey. This measurement is consistent with dynamical estimates of β derived from both real-space and redshift-space information. The importance of the method presented here is that nonlinear clustering effects are removed to enable linear correlation anisotropy measurements on scales approaching the translinear regime. We discuss implications for analyses of forthcoming optical redshift surveys in which the dispersion is more than a factor of 2 greater than in the IRAS data.

Quantifying rainfall-derived inflow and infiltration in sanitary sewer systems based on conductivity monitoring

NASA Astrophysics Data System (ADS)

Zhang, Mingkai; Liu, Yanchen; Cheng, Xun; Zhu, David Z.; Shi, Hanchang; Yuan, Zhiguo

2018-03-01

Quantifying rainfall-derived inflow and infiltration (RDII) in a sanitary sewer is difficult when RDII and overflow occur simultaneously. This study proposes a novel conductivity-based method for estimating RDII. The method separately decomposes rainfall-derived inflow (RDI) and rainfall-induced infiltration (RII) on the basis of conductivity data. Fast Fourier transform was adopted to analyze variations in the flow and water quality during dry weather. Nonlinear curve fitting based on the least squares algorithm was used to optimize parameters in the proposed RDII model. The method was successfully applied to real-life case studies, in which inflow and infiltration were successfully estimated for three typical rainfall events with total rainfall volumes of 6.25 mm (light), 28.15 mm (medium), and 178 mm (heavy). Uncertainties of model parameters were estimated using the generalized likelihood uncertainty estimation (GLUE) method and were found to be acceptable. Compared with traditional flow-based methods, the proposed approach exhibits distinct advantages in estimating RDII and overflow, particularly when the two processes happen simultaneously.

Estimation and Identifiability of Model Parameters in Human Nociceptive Processing Using Yes-No Detection Responses to Electrocutaneous Stimulation.

PubMed

Yang, Huan; Meijer, Hil G E; Buitenweg, Jan R; van Gils, Stephan A

2016-01-01

Healthy or pathological states of nociceptive subsystems determine different stimulus-response relations measured from quantitative sensory testing. In turn, stimulus-response measurements may be used to assess these states. In a recently developed computational model, six model parameters characterize activation of nerve endings and spinal neurons. However, both model nonlinearity and limited information in yes-no detection responses to electrocutaneous stimuli challenge to estimate model parameters. Here, we address the question whether and how one can overcome these difficulties for reliable parameter estimation. First, we fit the computational model to experimental stimulus-response pairs by maximizing the likelihood. To evaluate the balance between model fit and complexity, i.e., the number of model parameters, we evaluate the Bayesian Information Criterion. We find that the computational model is better than a conventional logistic model regarding the balance. Second, our theoretical analysis suggests to vary the pulse width among applied stimuli as a necessary condition to prevent structural non-identifiability. In addition, the numerically implemented profile likelihood approach reveals structural and practical non-identifiability. Our model-based approach with integration of psychophysical measurements can be useful for a reliable assessment of states of the nociceptive system.

Direct reconstruction of pharmacokinetic parameters in dynamic fluorescence molecular tomography by the augmented Lagrangian method

NASA Astrophysics Data System (ADS)

Zhu, Dianwen; Zhang, Wei; Zhao, Yue; Li, Changqing

2016-03-01

Dynamic fluorescence molecular tomography (FMT) has the potential to quantify physiological or biochemical information, known as pharmacokinetic parameters, which are important for cancer detection, drug development and delivery etc. To image those parameters, there are indirect methods, which are easier to implement but tend to provide images with low signal-to-noise ratio, and direct methods, which model all the measurement noises together and are statistically more efficient. The direct reconstruction methods in dynamic FMT have attracted a lot of attention recently. However, the coupling of tomographic image reconstruction and nonlinearity of kinetic parameter estimation due to the compartment modeling has imposed a huge computational burden to the direct reconstruction of the kinetic parameters. In this paper, we propose to take advantage of both the direct and indirect reconstruction ideas through a variable splitting strategy under the augmented Lagrangian framework. Each iteration of the direct reconstruction is split into two steps: the dynamic FMT image reconstruction and the node-wise nonlinear least squares fitting of the pharmacokinetic parameter images. Through numerical simulation studies, we have found that the proposed algorithm can achieve good reconstruction results within a small amount of time. This will be the first step for a combined dynamic PET and FMT imaging in the future.

On the bistable zone of milling processes

PubMed Central

Dombovari, Zoltan; Stepan, Gabor

2015-01-01

A modal-based model of milling machine tools subjected to time-periodic nonlinear cutting forces is introduced. The model describes the phenomenon of bistability for certain cutting parameters. In engineering, these parameter domains are referred to as unsafe zones, where steady-state milling may switch to chatter for certain perturbations. In mathematical terms, these are the parameter domains where the periodic solution of the corresponding nonlinear, time-periodic delay differential equation is linearly stable, but its domain of attraction is limited due to the existence of an unstable quasi-periodic solution emerging from a secondary Hopf bifurcation. A semi-numerical method is presented to identify the borders of these bistable zones by tracking the motion of the milling tool edges as they might leave the surface of the workpiece during the cutting operation. This requires the tracking of unstable quasi-periodic solutions and the checking of their grazing to a time-periodic switching surface in the infinite-dimensional phase space. As the parameters of the linear structural behaviour of the tool/machine tool system can be obtained by means of standard modal testing, the developed numerical algorithm provides efficient support for the design of milling processes with quick estimates of those parameter domains where chatter can still appear in spite of setting the parameters into linearly stable domains. PMID:26303918

Exploration of DGVM Parameter Solution Space Using Simulated Annealing: Implications for Forecast Uncertainties

NASA Astrophysics Data System (ADS)

Wells, J. R.; Kim, J. B.

2011-12-01

Parameters in dynamic global vegetation models (DGVMs) are thought to be weakly constrained and can be a significant source of errors and uncertainties. DGVMs use between 5 and 26 plant functional types (PFTs) to represent the average plant life form in each simulated plot, and each PFT typically has a dozen or more parameters that define the way it uses resource and responds to the simulated growing environment. Sensitivity analysis explores how varying parameters affects the output, but does not do a full exploration of the parameter solution space. The solution space for DGVM parameter values are thought to be complex and non-linear; and multiple sets of acceptable parameters may exist. In published studies, PFT parameters are estimated from published literature, and often a parameter value is estimated from a single published value. Further, the parameters are "tuned" using somewhat arbitrary, "trial-and-error" methods. BIOMAP is a new DGVM created by fusing MAPSS biogeography model with Biome-BGC. It represents the vegetation of North America using 26 PFTs. We are using simulated annealing, a global search method, to systematically and objectively explore the solution space for the BIOMAP PFTs and system parameters important for plant water use. We defined the boundaries of the solution space by obtaining maximum and minimum values from published literature, and where those were not available, using +/-20% of current values. We used stratified random sampling to select a set of grid cells representing the vegetation of the conterminous USA. Simulated annealing algorithm is applied to the parameters for spin-up and a transient run during the historical period 1961-1990. A set of parameter values is considered acceptable if the associated simulation run produces a modern potential vegetation distribution map that is as accurate as one produced by trial-and-error calibration. We expect to confirm that the solution space is non-linear and complex, and that multiple acceptable parameter sets exist. Further we expect to demonstrate that the multiple parameter sets produce significantly divergent future forecasts in NEP, C storage, and ET and runoff; and thereby identify a highly important source of DGVM uncertainty

Simultaneous Intrinsic and Extrinsic Parameter Identification of a Hand-Mounted Laser-Vision Sensor

PubMed Central

Lee, Jong Kwang; Kim, Kiho; Lee, Yongseok; Jeong, Taikyeong

2011-01-01

In this paper, we propose a simultaneous intrinsic and extrinsic parameter identification of a hand-mounted laser-vision sensor (HMLVS). A laser-vision sensor (LVS), consisting of a camera and a laser stripe projector, is used as a sensor component of the robotic measurement system, and it measures the range data with respect to the robot base frame using the robot forward kinematics and the optical triangulation principle. For the optimal estimation of the model parameters, we applied two optimization techniques: a nonlinear least square optimizer and a particle swarm optimizer. Best-fit parameters, including both the intrinsic and extrinsic parameters of the HMLVS, are simultaneously obtained based on the least-squares criterion. From the simulation and experimental results, it is shown that the parameter identification problem considered was characterized by a highly multimodal landscape; thus, the global optimization technique such as a particle swarm optimization can be a promising tool to identify the model parameters for a HMLVS, while the nonlinear least square optimizer often failed to find an optimal solution even when the initial candidate solutions were selected close to the true optimum. The proposed optimization method does not require good initial guesses of the system parameters to converge at a very stable solution and it could be applied to a kinematically dissimilar robot system without loss of generality. PMID:22164104

Nonlinear-regression groundwater flow modeling of a deep regional aquifer system

USGS Publications Warehouse

Cooley, Richard L.; Konikow, Leonard F.; Naff, Richard L.

1986-01-01

A nonlinear regression groundwater flow model, based on a Galerkin finite-element discretization, was used to analyze steady state two-dimensional groundwater flow in the areally extensive Madison aquifer in a 75,000 mi2 area of the Northern Great Plains. Regression parameters estimated include intrinsic permeabilities of the main aquifer and separate lineament zones, discharges from eight major springs surrounding the Black Hills, and specified heads on the model boundaries. Aquifer thickness and temperature variations were included as specified functions. The regression model was applied using sequential F testing so that the fewest number and simplest zonation of intrinsic permeabilities, combined with the simplest overall model, were evaluated initially; additional complexities (such as subdivisions of zones and variations in temperature and thickness) were added in stages to evaluate the subsequent degree of improvement in the model results. It was found that only the eight major springs, a single main aquifer intrinsic permeability, two separate lineament intrinsic permeabilities of much smaller values, and temperature variations are warranted by the observed data (hydraulic heads and prior information on some parameters) for inclusion in a model that attempts to explain significant controls on groundwater flow. Addition of thickness variations did not significantly improve model results; however, thickness variations were included in the final model because they are fairly well defined. Effects on the observed head distribution from other features, such as vertical leakage and regional variations in intrinsic permeability, apparently were overshadowed by measurement errors in the observed heads. Estimates of the parameters correspond well to estimates obtained from other independent sources.

Nonlinear-Regression Groundwater Flow Modeling of a Deep Regional Aquifer System

NASA Astrophysics Data System (ADS)

Cooley, Richard L.; Konikow, Leonard F.; Naff, Richard L.

1986-12-01

A nonlinear regression groundwater flow model, based on a Galerkin finite-element discretization, was used to analyze steady state two-dimensional groundwater flow in the areally extensive Madison aquifer in a 75,000 mi2 area of the Northern Great Plains. Regression parameters estimated include intrinsic permeabilities of the main aquifer and separate lineament zones, discharges from eight major springs surrounding the Black Hills, and specified heads on the model boundaries. Aquifer thickness and temperature variations were included as specified functions. The regression model was applied using sequential F testing so that the fewest number and simplest zonation of intrinsic permeabilities, combined with the simplest overall model, were evaluated initially; additional complexities (such as subdivisions of zones and variations in temperature and thickness) were added in stages to evaluate the subsequent degree of improvement in the model results. It was found that only the eight major springs, a single main aquifer intrinsic permeability, two separate lineament intrinsic permeabilities of much smaller values, and temperature variations are warranted by the observed data (hydraulic heads and prior information on some parameters) for inclusion in a model that attempts to explain significant controls on groundwater flow. Addition of thickness variations did not significantly improve model results; however, thickness variations were included in the final model because they are fairly well defined. Effects on the observed head distribution from other features, such as vertical leakage and regional variations in intrinsic permeability, apparently were overshadowed by measurement errors in the observed heads. Estimates of the parameters correspond well to estimates obtained from other independent sources.

Optimal estimation and scheduling in aquifer management using the rapid feedback control method

NASA Astrophysics Data System (ADS)

Ghorbanidehno, Hojat; Kokkinaki, Amalia; Kitanidis, Peter K.; Darve, Eric

2017-12-01

Management of water resources systems often involves a large number of parameters, as in the case of large, spatially heterogeneous aquifers, and a large number of "noisy" observations, as in the case of pressure observation in wells. Optimizing the operation of such systems requires both searching among many possible solutions and utilizing new information as it becomes available. However, the computational cost of this task increases rapidly with the size of the problem to the extent that textbook optimization methods are practically impossible to apply. In this paper, we present a new computationally efficient technique as a practical alternative for optimally operating large-scale dynamical systems. The proposed method, which we term Rapid Feedback Controller (RFC), provides a practical approach for combined monitoring, parameter estimation, uncertainty quantification, and optimal control for linear and nonlinear systems with a quadratic cost function. For illustration, we consider the case of a weakly nonlinear uncertain dynamical system with a quadratic objective function, specifically a two-dimensional heterogeneous aquifer management problem. To validate our method, we compare our results with the linear quadratic Gaussian (LQG) method, which is the basic approach for feedback control. We show that the computational cost of the RFC scales only linearly with the number of unknowns, a great improvement compared to the basic LQG control with a computational cost that scales quadratically. We demonstrate that the RFC method can obtain the optimal control values at a greatly reduced computational cost compared to the conventional LQG algorithm with small and controllable losses in the accuracy of the state and parameter estimation.

Weibull Modulus Estimated by the Non-linear Least Squares Method: A Solution to Deviation Occurring in Traditional Weibull Estimation

NASA Astrophysics Data System (ADS)

Li, T.; Griffiths, W. D.; Chen, J.

2017-11-01

The Maximum Likelihood method and the Linear Least Squares (LLS) method have been widely used to estimate Weibull parameters for reliability of brittle and metal materials. In the last 30 years, many researchers focused on the bias of Weibull modulus estimation, and some improvements have been achieved, especially in the case of the LLS method. However, there is a shortcoming in these methods for a specific type of data, where the lower tail deviates dramatically from the well-known linear fit in a classic LLS Weibull analysis. This deviation can be commonly found from the measured properties of materials, and previous applications of the LLS method on this kind of dataset present an unreliable linear regression. This deviation was previously thought to be due to physical flaws ( i.e., defects) contained in materials. However, this paper demonstrates that this deviation can also be caused by the linear transformation of the Weibull function, occurring in the traditional LLS method. Accordingly, it may not be appropriate to carry out a Weibull analysis according to the linearized Weibull function, and the Non-linear Least Squares method (Non-LS) is instead recommended for the Weibull modulus estimation of casting properties.

Dark localized structures in a cavity filled with a left-handed material

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

Tlidi, Mustapha; Kockaert, Pascal; Gelens, Lendert

2011-07-15

We consider a nonlinear passive optical cavity filled with left-handed and right-handed materials and driven by a coherent injected beam. We assume that both left-handed and right-handed materials possess a Kerr focusing type of nonlinearity. We show that close to the zero-diffraction regime, high-order diffraction allows us to stabilize dark localized structures in this device. These structures consist of dips in the transverse profile of the intracavity field and do not exist without high-order diffraction. We analyze the snaking bifurcation diagram associated with these structures. Finally, a realistic estimation of the model parameters is provided.

Numerical experience with a class of algorithms for nonlinear optimization using inexact function and gradient information

NASA Technical Reports Server (NTRS)

Carter, Richard G.

1989-01-01

For optimization problems associated with engineering design, parameter estimation, image reconstruction, and other optimization/simulation applications, low accuracy function and gradient values are frequently much less expensive to obtain than high accuracy values. Here, researchers investigate the computational performance of trust region methods for nonlinear optimization when high accuracy evaluations are unavailable or prohibitively expensive, and confirm earlier theoretical predictions when the algorithm is convergent even with relative gradient errors of 0.5 or more. The proper choice of the amount of accuracy to use in function and gradient evaluations can result in orders-of-magnitude savings in computational cost.

Optimal non-linear health insurance.

PubMed

Blomqvist, A

1997-06-01

Most theoretical and empirical work on efficient health insurance has been based on models with linear insurance schedules (a constant co-insurance parameter). In this paper, dynamic optimization techniques are used to analyse the properties of optimal non-linear insurance schedules in a model similar to one originally considered by Spence and Zeckhauser (American Economic Review, 1971, 61, 380-387) and reminiscent of those that have been used in the literature on optimal income taxation. The results of a preliminary numerical example suggest that the welfare losses from the implicit subsidy to employer-financed health insurance under US tax law may be a good deal smaller than previously estimated using linear models.

Controller design for a class of nonlinear MIMO coupled system using multiple models and second level adaptation.

PubMed

Pandey, Vinay Kumar; Kar, Indrani; Mahanta, Chitralekha

2017-07-01

In this paper, an adaptive control method using multiple models with second level adaptation is proposed for a class of nonlinear multi-input multi-output (MIMO) coupled systems. Multiple estimation models are used to tune the unknown parameters at the first level. The second level adaptation provides a single parameter vector for the controller. A feedback linearization technique is used to design a state feedback control. The efficacy of the designed controller is validated by conducting real time experiment on a laboratory setup of twin rotor MIMO system (TRMS). The TRMS setup is discussed in detail and the experiments were performed for regulation and tracking problem for pitch and yaw control using different reference signals. An Extended Kalman Filter (EKF) has been used to observe the unavailable states of the TRMS. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Intelligent, Robust Control of Deteriorated Turbofan Engines via Linear Parameter Varying Quadratic Lyapunov Function Design

NASA Technical Reports Server (NTRS)

Turso, James A.; Litt, Jonathan S.

2004-01-01

A method for accommodating engine deterioration via a scheduled Linear Parameter Varying Quadratic Lyapunov Function (LPVQLF)-Based controller is presented. The LPVQLF design methodology provides a means for developing unconditionally stable, robust control of Linear Parameter Varying (LPV) systems. The controller is scheduled on the Engine Deterioration Index, a function of estimated parameters that relate to engine health, and is computed using a multilayer feedforward neural network. Acceptable thrust response and tight control of exhaust gas temperature (EGT) is accomplished by adjusting the performance weights on these parameters for different levels of engine degradation. Nonlinear simulations demonstrate that the controller achieves specified performance objectives while being robust to engine deterioration as well as engine-to-engine variations.

Crown area equations for 13 species of trees and shrubs in northern California and southwestern Oregon

Treesearch

Fabian C.C. Uzoh; Martin W. Ritchie

1996-01-01

The equations presented predict crown area for 13 species of trees and shrubs which may be found growing in competition with commercial conifers during early stages of stand development. The equations express crown area as a function of basal area and height. Parameters were estimated for each species individually using weighted nonlinear least square regression.

Enhancing Data Assimilation by Evolutionary Particle Filter and Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Moradkhani, H.; Abbaszadeh, P.; Yan, H.

2016-12-01

Particle Filters (PFs) have received increasing attention by the researchers from different disciplines in hydro-geosciences as an effective method to improve model predictions in nonlinear and non-Gaussian dynamical systems. The implication of dual state and parameter estimation by means of data assimilation in hydrology and geoscience has evolved since 2005 from SIR-PF to PF-MCMC and now to the most effective and robust framework through evolutionary PF approach based on Genetic Algorithm (GA) and Markov Chain Monte Carlo (MCMC), the so-called EPF-MCMC. In this framework, the posterior distribution undergoes an evolutionary process to update an ensemble of prior states that more closely resemble realistic posterior probability distribution. The premise of this approach is that the particles move to optimal position using the GA optimization coupled with MCMC increasing the number of effective particles, hence the particle degeneracy is avoided while the particle diversity is improved. The proposed algorithm is applied on a conceptual and highly nonlinear hydrologic model and the effectiveness, robustness and reliability of the method in jointly estimating the states and parameters and also reducing the uncertainty is demonstrated for few river basins across the United States.