Theoretical and experimental studies of error in square-law detector circuits

NASA Technical Reports Server (NTRS)

Stanley, W. D.; Hearn, C. P.; Williams, J. B.

1984-01-01

Square law detector circuits to determine errors from the ideal input/output characteristic function were investigated. The nonlinear circuit response is analyzed by a power series expansion containing terms through the fourth degree, from which the significant deviation from square law can be predicted. Both fixed bias current and flexible bias current configurations are considered. The latter case corresponds with the situation where the mean current can change with the application of a signal. Experimental investigations of the circuit arrangements are described. Agreement between the analytical models and the experimental results are established. Factors which contribute to differences under certain conditions are outlined.

LOGISTIC FUNCTION PROFILE FIT: A least-squares program for fitting interface profiles to an extended logistic function

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

Kirchhoff, William H.

2012-09-15

The extended logistic function provides a physically reasonable description of interfaces such as depth profiles or line scans of surface topological or compositional features. It describes these interfaces with the minimum number of parameters, namely, position, width, and asymmetry. Logistic Function Profile Fit (LFPF) is a robust, least-squares fitting program in which the nonlinear extended logistic function is linearized by a Taylor series expansion (equivalent to a Newton-Raphson approach) with no apparent introduction of bias in the analysis. The program provides reliable confidence limits for the parameters when systematic errors are minimal and provides a display of the residuals frommore » the fit for the detection of systematic errors. The program will aid researchers in applying ASTM E1636-10, 'Standard practice for analytically describing sputter-depth-profile and linescan-profile data by an extended logistic function,' and may also prove useful in applying ISO 18516: 2006, 'Surface chemical analysis-Auger electron spectroscopy and x-ray photoelectron spectroscopy-determination of lateral resolution.' Examples are given of LFPF fits to a secondary ion mass spectrometry depth profile, an Auger surface line scan, and synthetic data generated to exhibit known systematic errors for examining the significance of such errors to the extrapolation of partial profiles.« less

Hazard Function Estimation with Cause-of-Death Data Missing at Random.

PubMed

Wang, Qihua; Dinse, Gregg E; Liu, Chunling

2012-04-01

Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random. Specifically, we present a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator. All three estimators are uniformly strongly consistent and asymptotically normal. We derive asymptotic representations of the mean squared error and the mean integrated squared error for these estimators and we discuss a data-driven bandwidth selection method. A simulation study, conducted to assess finite sample behavior, demonstrates that the proposed hazard estimators perform relatively well. We illustrate our methods with an analysis of some vascular disease data.

A Bayesian approach to parameter and reliability estimation in the Poisson distribution.

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1972-01-01

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.

Optimal estimation of large structure model errors. [in Space Shuttle controller design

NASA Technical Reports Server (NTRS)

Rodriguez, G.

1979-01-01

In-flight estimation of large structure model errors is usually required as a means of detecting inevitable deficiencies in large structure controller/estimator models. The present paper deals with a least-squares formulation which seeks to minimize a quadratic functional of the model errors. The properties of these error estimates are analyzed. It is shown that an arbitrary model error can be decomposed as the sum of two components that are orthogonal in a suitably defined function space. Relations between true and estimated errors are defined. The estimates are found to be approximations that retain many of the significant dynamics of the true model errors. Current efforts are directed toward application of the analytical results to a reference large structure model.

Ambiguity resolution for satellite Doppler positioning systems

NASA Technical Reports Server (NTRS)

Argentiero, P. D.; Marini, J. W.

1977-01-01

A test for ambiguity resolution was derived which was the most powerful in the sense that it maximized the probability of a correct decision. When systematic error sources were properly included in the least squares reduction process to yield an optimal solution, the test reduced to choosing the solution which provided the smaller valuation of the least squares loss function. When systematic error sources were ignored in the least squares reduction, the most powerful test was a quadratic form comparison with the weighting matrix of the quadratic form obtained by computing the pseudo-inverse of a reduced rank square matrix. A formula is presented for computing the power of the most powerful test. A numerical example is included in which the power of the test is computed for a situation which may occur during an actual satellite aided search and rescue mission.

A Canonical Ensemble Correlation Prediction Model for Seasonal Precipitation Anomaly

NASA Technical Reports Server (NTRS)

Shen, Samuel S. P.; Lau, William K. M.; Kim, Kyu-Myong; Li, Guilong

2001-01-01

This report describes an optimal ensemble forecasting model for seasonal precipitation and its error estimation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. This new CCA model includes the following features: (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States precipitation field. The predictor is the sea surface temperature.

Hazard Function Estimation with Cause-of-Death Data Missing at Random

PubMed Central

Wang, Qihua; Dinse, Gregg E.; Liu, Chunling

2010-01-01

Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random. Specifically, we present a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator. All three estimators are uniformly strongly consistent and asymptotically normal. We derive asymptotic representations of the mean squared error and the mean integrated squared error for these estimators and we discuss a data-driven bandwidth selection method. A simulation study, conducted to assess finite sample behavior, demonstrates that the proposed hazard estimators perform relatively well. We illustrate our methods with an analysis of some vascular disease data. PMID:22267874

{lambda} elements for singular problems in CFD: Viscoelastic fluids

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

Wong, K.K.; Surana, K.S.

1996-10-01

This paper presents two dimensional {lambda} element formulation for viscoelastic fluid flow containing point singularities in the flow field. The flow of viscoelastic fluid even without singularities are a difficult class of problems for increasing Deborah number or Weissenburg number due to increased dominance of convective terms and thus increased hyperbolicity. In the present work the equations of fluid motion and the constitutive laws are recast in the form of a first order system of coupled equations with the use of auxiliary variables. The velocity, pressure and stresses are interpolated using equal order C{sup 0} {lambda} element approximations. The Leastmore » Squares Finite Element Method (LSFEM) is used to construct the integral form (error functional I) corresponding to these equations. The error functional is constructed by taking the integrated sum of the squares of the errors or residuals (over the whole discretization) resulting when the element approximation is substituted into these equations. The conditions resulting from the minimization of the error functional are satisfied by using Newton`s method with line search. LSFEM has much superior performance when dealing with non-linear and convection dominated problems.« less

Regression-assisted deconvolution.

PubMed

McIntyre, Julie; Stefanski, Leonard A

2011-06-30

We present a semi-parametric deconvolution estimator for the density function of a random variable biX that is measured with error, a common challenge in many epidemiological studies. Traditional deconvolution estimators rely only on assumptions about the distribution of X and the error in its measurement, and ignore information available in auxiliary variables. Our method assumes the availability of a covariate vector statistically related to X by a mean-variance function regression model, where regression errors are normally distributed and independent of the measurement errors. Simulations suggest that the estimator achieves a much lower integrated squared error than the observed-data kernel density estimator when models are correctly specified and the assumption of normal regression errors is met. We illustrate the method using anthropometric measurements of newborns to estimate the density function of newborn length. Copyright © 2011 John Wiley & Sons, Ltd.

Selection of neural network structure for system error correction of electro-optical tracker system with horizontal gimbal

NASA Astrophysics Data System (ADS)

Liu, Xing-fa; Cen, Ming

2007-12-01

Neural Network system error correction method is more precise than lest square system error correction method and spheric harmonics function system error correction method. The accuracy of neural network system error correction method is mainly related to the frame of Neural Network. Analysis and simulation prove that both BP neural network system error correction method and RBF neural network system error correction method have high correction accuracy; it is better to use RBF Network system error correction method than BP Network system error correction method for little studying stylebook considering training rate and neural network scale.

Identification and compensation of the temperature influences in a miniature three-axial accelerometer based on the least squares method

NASA Astrophysics Data System (ADS)

Grigorie, Teodor Lucian; Corcau, Ileana Jenica; Tudosie, Alexandru Nicolae

2017-06-01

The paper presents a way to obtain an intelligent miniaturized three-axial accelerometric sensor, based on the on-line estimation and compensation of the sensor errors generated by the environmental temperature variation. Taking into account that this error's value is a strongly nonlinear complex function of the values of environmental temperature and of the acceleration exciting the sensor, its correction may not be done off-line and it requires the presence of an additional temperature sensor. The proposed identification methodology for the error model is based on the least square method which process off-line the numerical values obtained from the accelerometer experimental testing for different values of acceleration applied to its axes of sensitivity and for different values of operating temperature. A final analysis of the error level after the compensation highlights the best variant for the matrix in the error model. In the sections of the paper are shown the results of the experimental testing of the accelerometer on all the three sensitivity axes, the identification of the error models on each axis by using the least square method, and the validation of the obtained models with experimental values. For all of the three detection channels was obtained a reduction by almost two orders of magnitude of the acceleration absolute maximum error due to environmental temperature variation.

Discrete Tchebycheff orthonormal polynomials and applications

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

GDF v2.0, an enhanced version of GDF

NASA Astrophysics Data System (ADS)

Tsoulos, Ioannis G.; Gavrilis, Dimitris; Dermatas, Evangelos

2007-12-01

An improved version of the function estimation program GDF is presented. The main enhancements of the new version include: multi-output function estimation, capability of defining custom functions in the grammar and selection of the error function. The new version has been evaluated on a series of classification and regression datasets, that are widely used for the evaluation of such methods. It is compared to two known neural networks and outperforms them in 5 (out of 10) datasets. Program summaryTitle of program: GDF v2.0 Catalogue identifier: ADXC_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXC_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 98 147 No. of bytes in distributed program, including test data, etc.: 2 040 684 Distribution format: tar.gz Programming language: GNU C++ Computer: The program is designed to be portable in all systems running the GNU C++ compiler Operating system: Linux, Solaris, FreeBSD RAM: 200000 bytes Classification: 4.9 Does the new version supersede the previous version?: Yes Nature of problem: The technique of function estimation tries to discover from a series of input data a functional form that best describes them. This can be performed with the use of parametric models, whose parameters can adapt according to the input data. Solution method: Functional forms are being created by genetic programming which are approximations for the symbolic regression problem. Reasons for new version: The GDF package was extended in order to be more flexible and user customizable than the old package. The user can extend the package by defining his own error functions and he can extend the grammar of the package by adding new functions to the function repertoire. Also, the new version can perform function estimation of multi-output functions and it can be used for classification problems. Summary of revisions: The following features have been added to the package GDF: Multi-output function approximation. The package can now approximate any function f:R→R. This feature gives also to the package the capability of performing classification and not only regression. User defined function can be added to the repertoire of the grammar, extending the regression capabilities of the package. This feature is limited to 3 functions, but easily this number can be increased. Capability of selecting the error function. The package offers now to the user apart from the mean square error other error functions such as: mean absolute square error, maximum square error. Also, user defined error functions can be added to the set of error functions. More verbose output. The main program displays more information to the user as well as the default values for the parameters. Also, the package gives to the user the capability to define an output file, where the output of the gdf program for the testing set will be stored after the termination of the process. Additional comments: A technical report describing the revisions, experiments and test runs is packaged with the source code. Running time: Depending on the train data.

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

NASA Technical Reports Server (NTRS)

Manteuffel, Thomas A.; McCormick, Stephen F.; Starke, Gerhard

1996-01-01

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

Adaptively combined FIR and functional link artificial neural network equalizer for nonlinear communication channel.

PubMed

Zhao, Haiquan; Zhang, Jiashu

2009-04-01

This paper proposes a novel computational efficient adaptive nonlinear equalizer based on combination of finite impulse response (FIR) filter and functional link artificial neural network (CFFLANN) to compensate linear and nonlinear distortions in nonlinear communication channel. This convex nonlinear combination results in improving the speed while retaining the lower steady-state error. In addition, since the CFFLANN needs not the hidden layers, which exist in conventional neural-network-based equalizers, it exhibits a simpler structure than the traditional neural networks (NNs) and can require less computational burden during the training mode. Moreover, appropriate adaptation algorithm for the proposed equalizer is derived by the modified least mean square (MLMS). Results obtained from the simulations clearly show that the proposed equalizer using the MLMS algorithm can availably eliminate various intensity linear and nonlinear distortions, and be provided with better anti-jamming performance. Furthermore, comparisons of the mean squared error (MSE), the bit error rate (BER), and the effect of eigenvalue ratio (EVR) of input correlation matrix are presented.

Rapid estimation of frequency response functions by close-range photogrammetry

NASA Technical Reports Server (NTRS)

Tripp, J. S.

1985-01-01

The accuracy of a rapid method which estimates the frequency response function from stereoscopic dynamic data is computed. It is shown that reversal of the order of the operations of coordinate transformation and Fourier transformation, which provides a significant increase in computational speed, introduces error. A portion of the error, proportional to the perturbation components normal to the camera focal planes, cannot be eliminated. The remaining error may be eliminated by proper scaling of frequency data prior to coordinate transformation. Methods are developed for least squares estimation of the full 3x3 frequency response matrix for a three dimensional structure.

Modelling of the batch biosorption system: study on exchange of protons with cell wall-bound mineral ions.

PubMed

Mishra, Vishal

2015-01-01

The interchange of the protons with the cell wall-bound calcium and magnesium ions at the interface of solution/bacterial cell surface in the biosorption system at various concentrations of protons has been studied in the present work. A mathematical model for establishing the correlation between concentration of protons and active sites was developed and optimized. The sporadic limited residence time reactor was used to titrate the calcium and magnesium ions at the individual data point. The accuracy of the proposed mathematical model was estimated using error functions such as nonlinear regression, adjusted nonlinear regression coefficient, the chi-square test, P-test and F-test. The values of the chi-square test (0.042-0.017), P-test (<0.001-0.04), sum of square errors (0.061-0.016), root mean square error (0.01-0.04) and F-test (2.22-19.92) reported in the present research indicated the suitability of the model over a wide range of proton concentrations. The zeta potential of the bacterium surface at various concentrations of protons was observed to validate the denaturation of active sites.

Using Least Squares for Error Propagation

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2015-01-01

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

Adaptive optics system performance approximations for atmospheric turbulence correction

NASA Astrophysics Data System (ADS)

Tyson, Robert K.

1990-10-01

Analysis of adaptive optics system behavior often can be reduced to a few approximations and scaling laws. For atmospheric turbulence correction, the deformable mirror (DM) fitting error is most often used to determine a priori the interactuator spacing and the total number of correction zones required. This paper examines the mirror fitting error in terms of its most commonly used exponential form. The explicit constant in the error term is dependent on deformable mirror influence function shape and actuator geometry. The method of least squares fitting of discrete influence functions to the turbulent wavefront is compared to the linear spatial filtering approximation of system performance. It is found that the spatial filtering method overstimates the correctability of the adaptive optics system by a small amount. By evaluating fitting error for a number of DM configurations, actuator geometries, and influence functions, fitting error constants verify some earlier investigations.

Least-Squares, Continuous Sensitivity Analysis for Nonlinear Fluid-Structure Interaction

DTIC Science & Technology

2009-08-20

Tangential stress optimization convergence to uniform value  1.797  as a function of eccentric anomaly   E and Objective function value as a...up to the domain dimension, domainn . Equation (3.7) expands as truncation error round-off error decreasing step size FD e rr or 54...force, and E is Young’s modulus. Equations (3.31) and (3.32) may be directly integrated to yield the stress and displacement solutions, which, for no

Quantized kernel least mean square algorithm.

PubMed

Chen, Badong; Zhao, Songlin; Zhu, Pingping; Príncipe, José C

2012-01-01

In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.

A Monte Carlo comparison of the recovery of winds near upwind and downwind from the SASS-1 model function by means of the sum of squares algorithm and a maximum likelihood estimator

NASA Technical Reports Server (NTRS)

Pierson, W. J., Jr.

1984-01-01

Backscatter measurements at upwind and crosswind are simulated for five incidence angles by means of the SASS-1 model function. The effects of communication noise and attitude errors are simulated by Monte Carlo methods, and the winds are recovered by both the Sum of Square (SOS) algorithm and a Maximum Likelihood Estimater (MLE). The SOS algorithm is shown to fail for light enough winds at all incidence angles and to fail to show areas of calm because backscatter estimates that were negative or that produced incorrect values of K sub p greater than one were discarded. The MLE performs well for all input backscatter estimates and returns calm when both are negative. The use of the SOS algorithm is shown to have introduced errors in the SASS-1 model function that, in part, cancel out the errors that result from using it, but that also cause disagreement with other data sources such as the AAFE circle flight data at light winds. Implications for future scatterometer systems are given.

The theory precision analyse of RFM localization of satellite remote sensing imagery

NASA Astrophysics Data System (ADS)

Zhang, Jianqing; Xv, Biao

2009-11-01

The tradition method of detecting precision of Rational Function Model(RFM) is to make use of a great deal check points, and it calculates mean square error through comparing calculational coordinate with known coordinate. This method is from theory of probability, through a large number of samples to statistic estimate value of mean square error, we can think its estimate value approaches in its true when samples are well enough. This paper is from angle of survey adjustment, take law of propagation of error as the theory basis, and it calculates theory precision of RFM localization. Then take the SPOT5 three array imagery as experiment data, and the result of traditional method and narrated method in the paper are compared, while has confirmed tradition method feasible, and answered its theory precision question from the angle of survey adjustment.

Demand Forecasting: An Evaluation of DODs Accuracy Metric and Navys Procedures

DTIC Science & Technology

2016-06-01

inventory management improvement plan, mean of absolute scaled error, lead time adjusted squared error, forecast accuracy, benchmarking, naïve method...Manager JASA Journal of the American Statistical Association LASE Lead-time Adjusted Squared Error LCI Life Cycle Indicator MA Moving Average MAE...Mean Squared Error xvi NAVSUP Naval Supply Systems Command NDAA National Defense Authorization Act NIIN National Individual Identification Number

Measurement System Characterization in the Presence of Measurement Errors

NASA Technical Reports Server (NTRS)

Commo, Sean A.

2012-01-01

In the calibration of a measurement system, data are collected in order to estimate a mathematical model between one or more factors of interest and a response. Ordinary least squares is a method employed to estimate the regression coefficients in the model. The method assumes that the factors are known without error; yet, it is implicitly known that the factors contain some uncertainty. In the literature, this uncertainty is known as measurement error. The measurement error affects both the estimates of the model coefficients and the prediction, or residual, errors. There are some methods, such as orthogonal least squares, that are employed in situations where measurement errors exist, but these methods do not directly incorporate the magnitude of the measurement errors. This research proposes a new method, known as modified least squares, that combines the principles of least squares with knowledge about the measurement errors. This knowledge is expressed in terms of the variance ratio - the ratio of response error variance to measurement error variance.

Comparison of various error functions in predicting the optimum isotherm by linear and non-linear regression analysis for the sorption of basic red 9 by activated carbon.

PubMed

Kumar, K Vasanth; Porkodi, K; Rocha, F

2008-01-15

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of basic red 9 sorption by activated carbon. The r(2) was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions namely coefficient of determination (r(2)), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), the average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. Non-linear regression was found to be a better way to obtain the parameters involved in the isotherms and also the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r(2) was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K(2) was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

Nonparametric probability density estimation by optimization theoretic techniques

NASA Technical Reports Server (NTRS)

Scott, D. W.

1976-01-01

Two nonparametric probability density estimators are considered. The first is the kernel estimator. The problem of choosing the kernel scaling factor based solely on a random sample is addressed. An interactive mode is discussed and an algorithm proposed to choose the scaling factor automatically. The second nonparametric probability estimate uses penalty function techniques with the maximum likelihood criterion. A discrete maximum penalized likelihood estimator is proposed and is shown to be consistent in the mean square error. A numerical implementation technique for the discrete solution is discussed and examples displayed. An extensive simulation study compares the integrated mean square error of the discrete and kernel estimators. The robustness of the discrete estimator is demonstrated graphically.

Discrete-time state estimation for stochastic polynomial systems over polynomial observations

NASA Astrophysics Data System (ADS)

Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.

2018-07-01

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

Robustness study of the pseudo open-loop controller for multiconjugate adaptive optics.

PubMed

Piatrou, Piotr; Gilles, Luc

2005-02-20

Robustness of the recently proposed "pseudo open-loop control" algorithm against various system errors has been investigated for the representative example of the Gemini-South 8-m telescope multiconjugate adaptive-optics system. The existing model to represent the adaptive-optics system with pseudo open-loop control has been modified to account for misalignments, noise and calibration errors in deformable mirrors, and wave-front sensors. Comparison with the conventional least-squares control model has been done. We show with the aid of both transfer-function pole-placement analysis and Monte Carlo simulations that POLC remains remarkably stable and robust against very large levels of system errors and outperforms in this respect least-squares control. Approximate stability margins as well as performance metrics such as Strehl ratios and rms wave-front residuals averaged over a 1-arc min field of view have been computed for different types and levels of system errors to quantify the expected performance degradation.

Functional Mixed Effects Model for Small Area Estimation.

PubMed

Maiti, Tapabrata; Sinha, Samiran; Zhong, Ping-Shou

2016-09-01

Functional data analysis has become an important area of research due to its ability of handling high dimensional and complex data structures. However, the development is limited in the context of linear mixed effect models, and in particular, for small area estimation. The linear mixed effect models are the backbone of small area estimation. In this article, we consider area level data, and fit a varying coefficient linear mixed effect model where the varying coefficients are semi-parametrically modeled via B-splines. We propose a method of estimating the fixed effect parameters and consider prediction of random effects that can be implemented using a standard software. For measuring prediction uncertainties, we derive an analytical expression for the mean squared errors, and propose a method of estimating the mean squared errors. The procedure is illustrated via a real data example, and operating characteristics of the method are judged using finite sample simulation studies.

Least square regularized regression in sum space.

PubMed

Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu

2013-04-01

This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.

Two Enhancements of the Logarithmic Least-Squares Method for Analyzing Subjective Comparisons

DTIC Science & Technology

1989-03-25

error term. 1 For this model, the total sum of squares ( SSTO ), defined as n 2 SSTO = E (yi y) i=1 can be partitioned into error and regression sums...of the regression line around the mean value. Mathematically, for the model given by equation A.4, SSTO = SSE + SSR (A.6) A-4 where SSTO is the total...sum of squares (i.e., the variance of the yi’s), SSE is error sum of squares, and SSR is the regression sum of squares. SSTO , SSE, and SSR are given

An algebraic aspect of Pareto mixture parameter estimation using censored sample: A Bayesian approach.

PubMed

Saleem, Muhammad; Sharif, Kashif; Fahmi, Aliya

2018-04-27

Applications of Pareto distribution are common in reliability, survival and financial studies. In this paper, A Pareto mixture distribution is considered to model a heterogeneous population comprising of two subgroups. Each of two subgroups is characterized by the same functional form with unknown distinct shape and scale parameters. Bayes estimators have been derived using flat and conjugate priors using squared error loss function. Standard errors have also been derived for the Bayes estimators. An interesting feature of this study is the preparation of components of Fisher Information matrix.

AKLSQF - LEAST SQUARES CURVE FITTING

NASA Technical Reports Server (NTRS)

Kantak, A. V.

1994-01-01

The Least Squares Curve Fitting program, AKLSQF, computes the polynomial which will least square fit uniformly spaced data easily and efficiently. The program allows the user to specify the tolerable least squares error in the fitting or allows the user to specify the polynomial degree. In both cases AKLSQF returns the polynomial and the actual least squares fit error incurred in the operation. The data may be supplied to the routine either by direct keyboard entry or via a file. AKLSQF produces the least squares polynomial in two steps. First, the data points are least squares fitted using the orthogonal factorial polynomials. The result is then reduced to a regular polynomial using Sterling numbers of the first kind. If an error tolerance is specified, the program starts with a polynomial of degree 1 and computes the least squares fit error. The degree of the polynomial used for fitting is then increased successively until the error criterion specified by the user is met. At every step the polynomial as well as the least squares fitting error is printed to the screen. In general, the program can produce a curve fitting up to a 100 degree polynomial. All computations in the program are carried out under Double Precision format for real numbers and under long integer format for integers to provide the maximum accuracy possible. AKLSQF was written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler. It has been implemented under DOS 3.2.1 using 23K of RAM. AKLSQF was developed in 1989.

Ambiguity resolution for satellite Doppler positioning systems

NASA Technical Reports Server (NTRS)

Argentiero, P.; Marini, J.

1979-01-01

The implementation of satellite-based Doppler positioning systems frequently requires the recovery of transmitter position from a single pass of Doppler data. The least-squares approach to the problem yields conjugate solutions on either side of the satellite subtrack. It is important to develop a procedure for choosing the proper solution which is correct in a high percentage of cases. A test for ambiguity resolution which is the most powerful in the sense that it maximizes the probability of a correct decision is derived. When systematic error sources are properly included in the least-squares reduction process to yield an optimal solution the test reduces to choosing the solution which provides the smaller valuation of the least-squares loss function. When systematic error sources are ignored in the least-squares reduction, the most powerful test is a quadratic form comparison with the weighting matrix of the quadratic form obtained by computing the pseudoinverse of a reduced-rank square matrix. A formula for computing the power of the most powerful test is provided. Numerical examples are included in which the power of the test is computed for situations that are relevant to the design of a satellite-aided search and rescue system.

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

NASA Technical Reports Server (NTRS)

Alvarez, L. S.

1991-01-01

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

A Temperature Compensation Method for Piezo-Resistive Pressure Sensor Utilizing Chaotic Ions Motion Algorithm Optimized Hybrid Kernel LSSVM.

PubMed

Li, Ji; Hu, Guoqing; Zhou, Yonghong; Zou, Chong; Peng, Wei; Alam Sm, Jahangir

2016-10-14

A piezo-resistive pressure sensor is made of silicon, the nature of which is considerably influenced by ambient temperature. The effect of temperature should be eliminated during the working period in expectation of linear output. To deal with this issue, an approach consists of a hybrid kernel Least Squares Support Vector Machine (LSSVM) optimized by a chaotic ions motion algorithm presented. To achieve the learning and generalization for excellent performance, a hybrid kernel function, constructed by a local kernel as Radial Basis Function (RBF) kernel, and a global kernel as polynomial kernel is incorporated into the Least Squares Support Vector Machine. The chaotic ions motion algorithm is introduced to find the best hyper-parameters of the Least Squares Support Vector Machine. The temperature data from a calibration experiment is conducted to validate the proposed method. With attention on algorithm robustness and engineering applications, the compensation result shows the proposed scheme outperforms other compared methods on several performance measures as maximum absolute relative error, minimum absolute relative error mean and variance of the averaged value on fifty runs. Furthermore, the proposed temperature compensation approach lays a foundation for more extensive research.

Testing the Hypothesis of a Homoscedastic Error Term in Simple, Nonparametric Regression

ERIC Educational Resources Information Center

Wilcox, Rand R.

2006-01-01

Consider the nonparametric regression model Y = m(X)+ [tau](X)[epsilon], where X and [epsilon] are independent random variables, [epsilon] has a median of zero and variance [sigma][squared], [tau] is some unknown function used to model heteroscedasticity, and m(X) is an unknown function reflecting some conditional measure of location associated…

Model-based mean square error estimators for k-nearest neighbour predictions and applications using remotely sensed data for forest inventories

Treesearch

Steen Magnussen; Ronald E. McRoberts; Erkki O. Tomppo

2009-01-01

New model-based estimators of the uncertainty of pixel-level and areal k-nearest neighbour (knn) predictions of attribute Y from remotely-sensed ancillary data X are presented. Non-parametric functions predict Y from scalar 'Single Index Model' transformations of X. Variance functions generated...

Convergence and objective functions of some fault/noise-injection-based online learning algorithms for RBF networks.

PubMed

Ho, Kevin I-J; Leung, Chi-Sing; Sum, John

2010-06-01

In the last two decades, many online fault/noise injection algorithms have been developed to attain a fault tolerant neural network. However, not much theoretical works related to their convergence and objective functions have been reported. This paper studies six common fault/noise-injection-based online learning algorithms for radial basis function (RBF) networks, namely 1) injecting additive input noise, 2) injecting additive/multiplicative weight noise, 3) injecting multiplicative node noise, 4) injecting multiweight fault (random disconnection of weights), 5) injecting multinode fault during training, and 6) weight decay with injecting multinode fault. Based on the Gladyshev theorem, we show that the convergence of these six online algorithms is almost sure. Moreover, their true objective functions being minimized are derived. For injecting additive input noise during training, the objective function is identical to that of the Tikhonov regularizer approach. For injecting additive/multiplicative weight noise during training, the objective function is the simple mean square training error. Thus, injecting additive/multiplicative weight noise during training cannot improve the fault tolerance of an RBF network. Similar to injective additive input noise, the objective functions of other fault/noise-injection-based online algorithms contain a mean square error term and a specialized regularization term.

Bivariate least squares linear regression: Towards a unified analytic formalism. I. Functional models

NASA Astrophysics Data System (ADS)

Caimmi, R.

2011-08-01

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts ( York, 1966, 1969) is reviewed using a new formalism in terms of deviation (matrix) traces which, for unweighted data, reduce to usual quantities leaving aside an unessential (but dimensional) multiplicative factor. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. The classes of linear models considered are regression lines in the general case of correlated errors in X and in Y for weighted data, and in the opposite limiting situations of (i) uncorrelated errors in X and in Y, and (ii) completely correlated errors in X and in Y. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases, namely: (Y) errors in X negligible (ideally null) with respect to errors in Y; (X) errors in Y negligible (ideally null) with respect to errors in X; (O) genuine orthogonal regression; (R) reduced major-axis regression. In the limit of unweighted data, the results determined for functional models are compared with their counterparts related to extreme structural models i.e. the instrumental scatter is negligible (ideally null) with respect to the intrinsic scatter ( Isobe et al., 1990; Feigelson and Babu, 1992). While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with the exception of Y models. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors (∓ σ) for both heteroscedastic and homoscedastic data. Conversely, samples related to different methods produce discrepant results, due to the presence of (still undetected) systematic errors, which implies no definitive statement can be made at present. A comparison is also made between different expressions of regression line slope and intercept variance estimators, where fractional discrepancies are found to be not exceeding a few percent, which grows up to about 20% in the presence of large dispersion data. An extension of the formalism to structural models is left to a forthcoming paper.

Response Surface Analysis of Experiments with Random Blocks

DTIC Science & Technology

1988-09-01

partitioned into a lack of fit sum of squares, SSLOF, and a pure error sum of squares, SSPE . The latter is obtained by pooling the pure error sums of squares...from the blocks. Tests concerning the polynomial effects can then proceed using SSPE as the error term in the denominators of the F test statistics. 3.2...the center point in each of the three blocks is equal to SSPE = 2.0127 with 5 degrees of freedom. Hence, the lack of fit sum of squares is SSLoF

Least-Squares Curve-Fitting Program

NASA Technical Reports Server (NTRS)

Kantak, Anil V.

1990-01-01

Least Squares Curve Fitting program, AKLSQF, easily and efficiently computes polynomial providing least-squares best fit to uniformly spaced data. Enables user to specify tolerable least-squares error in fit or degree of polynomial. AKLSQF returns polynomial and actual least-squares-fit error incurred in operation. Data supplied to routine either by direct keyboard entry or via file. Written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler.

Dependence of the compensation error on the error of a sensor and corrector in an adaptive optics phase-conjugating system

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

Kiyko, V V; Kislov, V I; Ofitserov, E N

2015-08-31

In the framework of a statistical model of an adaptive optics system (AOS) of phase conjugation, three algorithms based on an integrated mathematical approach are considered, each of them intended for minimisation of one of the following characteristics: the sensor error (in the case of an ideal corrector), the corrector error (in the case of ideal measurements) and the compensation error (with regard to discreteness and measurement noises and to incompleteness of a system of response functions of the corrector actuators). Functional and statistical relationships between the algorithms are studied and a relation is derived to ensure calculation of themore » mean-square compensation error as a function of the errors of the sensor and corrector with an accuracy better than 10%. Because in adjusting the AOS parameters, it is reasonable to proceed from the equality of the sensor and corrector errors, in the case the Hartmann sensor is used as a wavefront sensor, the required number of actuators in the absence of the noise component in the sensor error turns out 1.5 – 2.5 times less than the number of counts, and that difference grows with increasing measurement noise. (adaptive optics)« less

Temperature dependence of emission measure in solar X-ray plasmas. 1: Non-flaring active regions

NASA Technical Reports Server (NTRS)

Phillips, K. J. H.

1974-01-01

X-ray and ultraviolet line emission from hot, optically thin material forming coronal active regions on the sun may be described in terms of an emission measure distribution function, Phi (T). A relationship is developed between line flux and Phi (T), a theory which assumes that the electron density is a single-valued function of temperature. The sources of error involved in deriving Phi (T) from a set of line fluxes are examined in some detail. These include errors in atomic data (collisional excitation rates, assessment of other mechanisms for populating excited states of transitions, element abundances, ion concentrations, oscillator strengths) and errors in observed line fluxes arising from poorly - known instrumental responses. Two previous analyses are discussed in which Phi (T) for a non-flaring active region is derived. A least squares method of Batstone uses X-ray data of low statistical significance, a fact which appears to influence the results considerably. Two methods for finding Phi (T) ab initio are developed. The coefficients are evaluated by least squares. These two methods should have application not only to active-region plasmas, but also to hot, flare-produced plasmas.

Estimators of The Magnitude-Squared Spectrum and Methods for Incorporating SNR Uncertainty

PubMed Central

Lu, Yang; Loizou, Philipos C.

2011-01-01

Statistical estimators of the magnitude-squared spectrum are derived based on the assumption that the magnitude-squared spectrum of the noisy speech signal can be computed as the sum of the (clean) signal and noise magnitude-squared spectra. Maximum a posterior (MAP) and minimum mean square error (MMSE) estimators are derived based on a Gaussian statistical model. The gain function of the MAP estimator was found to be identical to the gain function used in the ideal binary mask (IdBM) that is widely used in computational auditory scene analysis (CASA). As such, it was binary and assumed the value of 1 if the local SNR exceeded 0 dB, and assumed the value of 0 otherwise. By modeling the local instantaneous SNR as an F-distributed random variable, soft masking methods were derived incorporating SNR uncertainty. The soft masking method, in particular, which weighted the noisy magnitude-squared spectrum by the a priori probability that the local SNR exceeds 0 dB was shown to be identical to the Wiener gain function. Results indicated that the proposed estimators yielded significantly better speech quality than the conventional MMSE spectral power estimators, in terms of yielding lower residual noise and lower speech distortion. PMID:21886543

Contrast improvement of continuous wave diffuse optical tomography reconstruction by hybrid approach using least square and genetic algorithm

NASA Astrophysics Data System (ADS)

Patra, Rusha; Dutta, Pranab K.

2015-07-01

Reconstruction of the absorption coefficient of tissue with good contrast is of key importance in functional diffuse optical imaging. A hybrid approach using model-based iterative image reconstruction and a genetic algorithm is proposed to enhance the contrast of the reconstructed image. The proposed method yields an observed contrast of 98.4%, mean square error of 0.638×10-3, and object centroid error of (0.001 to 0.22) mm. Experimental validation of the proposed method has also been provided with tissue-like phantoms which shows a significant improvement in image quality and thus establishes the potential of the method for functional diffuse optical tomography reconstruction with continuous wave setup. A case study of finger joint imaging is illustrated as well to show the prospect of the proposed method in clinical diagnosis. The method can also be applied to the concentration measurement of a region of interest in a turbid medium.

A novel beamformer design method for medical ultrasound. Part I: Theory.

PubMed

Ranganathan, Karthik; Walker, William F

2003-01-01

The design of transmit and receive aperture weightings is a critical step in the development of ultrasound imaging systems. Current design methods are generally iterative, and consequently time consuming and inexact. We describe a new and general ultrasound beamformer design method, the minimum sum squared error (MSSE) technique. The MSSE technique enables aperture design for arbitrary beam patterns (within fundamental limitations imposed by diffraction). It uses a linear algebra formulation to describe the system point spread function (psf) as a function of the aperture weightings. The sum squared error (SSE) between the system psf and the desired or goal psf is minimized, yielding the optimal aperture weightings. We present detailed analysis for continuous wave (CW) and broadband systems. We also discuss several possible applications of the technique, such as the design of aperture weightings that improve the system depth of field, generate limited diffraction transmit beams, and improve the correlation depth of field in translated aperture system geometries. Simulation results are presented in an accompanying paper.

Explicit least squares system parameter identification for exact differential input/output models

NASA Technical Reports Server (NTRS)

Pearson, A. E.

1993-01-01

The equation error for a class of systems modeled by input/output differential operator equations has the potential to be integrated exactly, given the input/output data on a finite time interval, thereby opening up the possibility of using an explicit least squares estimation technique for system parameter identification. The paper delineates the class of models for which this is possible and shows how the explicit least squares cost function can be obtained in a way that obviates dealing with unknown initial and boundary conditions. The approach is illustrated by two examples: a second order chemical kinetics model and a third order system of Lorenz equations.

Error propagation of partial least squares for parameters optimization in NIR modeling.

PubMed

Du, Chenzhao; Dai, Shengyun; Qiao, Yanjiang; Wu, Zhisheng

2018-03-05

A novel methodology is proposed to determine the error propagation of partial least-square (PLS) for parameters optimization in near-infrared (NIR) modeling. The parameters include spectral pretreatment, latent variables and variable selection. In this paper, an open source dataset (corn) and a complicated dataset (Gardenia) were used to establish PLS models under different modeling parameters. And error propagation of modeling parameters for water quantity in corn and geniposide quantity in Gardenia were presented by both type І and type II error. For example, when variable importance in the projection (VIP), interval partial least square (iPLS) and backward interval partial least square (BiPLS) variable selection algorithms were used for geniposide in Gardenia, compared with synergy interval partial least squares (SiPLS), the error weight varied from 5% to 65%, 55% and 15%. The results demonstrated how and what extent the different modeling parameters affect error propagation of PLS for parameters optimization in NIR modeling. The larger the error weight, the worse the model. Finally, our trials finished a powerful process in developing robust PLS models for corn and Gardenia under the optimal modeling parameters. Furthermore, it could provide a significant guidance for the selection of modeling parameters of other multivariate calibration models. Copyright © 2017. Published by Elsevier B.V.

Error propagation of partial least squares for parameters optimization in NIR modeling

NASA Astrophysics Data System (ADS)

Du, Chenzhao; Dai, Shengyun; Qiao, Yanjiang; Wu, Zhisheng

2018-03-01

A novel methodology is proposed to determine the error propagation of partial least-square (PLS) for parameters optimization in near-infrared (NIR) modeling. The parameters include spectral pretreatment, latent variables and variable selection. In this paper, an open source dataset (corn) and a complicated dataset (Gardenia) were used to establish PLS models under different modeling parameters. And error propagation of modeling parameters for water quantity in corn and geniposide quantity in Gardenia were presented by both type І and type II error. For example, when variable importance in the projection (VIP), interval partial least square (iPLS) and backward interval partial least square (BiPLS) variable selection algorithms were used for geniposide in Gardenia, compared with synergy interval partial least squares (SiPLS), the error weight varied from 5% to 65%, 55% and 15%. The results demonstrated how and what extent the different modeling parameters affect error propagation of PLS for parameters optimization in NIR modeling. The larger the error weight, the worse the model. Finally, our trials finished a powerful process in developing robust PLS models for corn and Gardenia under the optimal modeling parameters. Furthermore, it could provide a significant guidance for the selection of modeling parameters of other multivariate calibration models.

On the robustness of a Bayes estimate. [in reliability theory

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1974-01-01

This paper examines the robustness of a Bayes estimator with respect to the assigned prior distribution. A Bayesian analysis for a stochastic scale parameter of a Weibull failure model is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by the Monte Carlo method in which, although an inverted gamma is the assigned prior, realizations are generated using distribution functions of varying shape. For several distributional forms and even for some fixed values of the parameter, simulated mean squared errors of Bayes and minimum variance unbiased estimators are determined and compared. Results indicate that the Bayes estimator remains squared-error superior and appears to be largely robust to the form of the assigned prior distribution.

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

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

Zhou, Ping; Wang, Chenyu; Li, Mingjie

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

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

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

Zhou, Ping; Wang, Chenyu; Li, Mingjie

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

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

DOE PAGES

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

2018-01-31

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

Uncertainties in extracted parameters of a Gaussian emission line profile with continuum background.

PubMed

Minin, Serge; Kamalabadi, Farzad

2009-12-20

We derive analytical equations for uncertainties in parameters extracted by nonlinear least-squares fitting of a Gaussian emission function with an unknown continuum background component in the presence of additive white Gaussian noise. The derivation is based on the inversion of the full curvature matrix (equivalent to Fisher information matrix) of the least-squares error, chi(2), in a four-variable fitting parameter space. The derived uncertainty formulas (equivalent to Cramer-Rao error bounds) are found to be in good agreement with the numerically computed uncertainties from a large ensemble of simulated measurements. The derived formulas can be used for estimating minimum achievable errors for a given signal-to-noise ratio and for investigating some aspects of measurement setup trade-offs and optimization. While the intended application is Fabry-Perot spectroscopy for wind and temperature measurements in the upper atmosphere, the derivation is generic and applicable to other spectroscopy problems with a Gaussian line shape.

Comparison of genetic algorithm and imperialist competitive algorithms in predicting bed load transport in clean pipe.

PubMed

Ebtehaj, Isa; Bonakdari, Hossein

2014-01-01

The existence of sediments in wastewater greatly affects the performance of the sewer and wastewater transmission systems. Increased sedimentation in wastewater collection systems causes problems such as reduced transmission capacity and early combined sewer overflow. The article reviews the performance of the genetic algorithm (GA) and imperialist competitive algorithm (ICA) in minimizing the target function (mean square error of observed and predicted Froude number). To study the impact of bed load transport parameters, using four non-dimensional groups, six different models have been presented. Moreover, the roulette wheel selection method is used to select the parents. The ICA with root mean square error (RMSE) = 0.007, mean absolute percentage error (MAPE) = 3.5% show better results than GA (RMSE = 0.007, MAPE = 5.6%) for the selected model. All six models return better results than the GA. Also, the results of these two algorithms were compared with multi-layer perceptron and existing equations.

Some Modified Integrated Squared Error Procedures for Multivariate Normal Data.

DTIC Science & Technology

1982-06-01

p-dimensional Gaussian. There are a number of measures of qualitative robustness but the most important is the influence function . Most of the other...measures are derived from the influence function . The influence function is simply proportional to the score function (Huber, 1981, p. 45 ). The... influence function at the p-variate Gaussian distribution Np (UV) is as -1P IC(x; ,N) = IE&) ;-") sD=XV = (I+c) (p+2)(x-p) exp(- ! (x-p) TV-.1-)) (3.6

Kinetic modelling for zinc (II) ions biosorption onto Luffa cylindrica

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

Oboh, I., E-mail: innocentoboh@uniuyo.edu.ng; Aluyor, E.; Audu, T.

The biosorption of Zinc (II) ions onto a biomaterial - Luffa cylindrica has been studied. This biomaterial was characterized by elemental analysis, surface area, pore size distribution, scanning electron microscopy, and the biomaterial before and after sorption, was characterized by Fourier Transform Infra Red (FTIR) spectrometer. The kinetic nonlinear models fitted were Pseudo-first order, Pseudo-second order and Intra-particle diffusion. A comparison of non-linear regression method in selecting the kinetic model was made. Four error functions, namely coefficient of determination (R{sup 2}), hybrid fractional error function (HYBRID), average relative error (ARE), and sum of the errors squared (ERRSQ), were used tomore » predict the parameters of the kinetic models. The strength of this study is that a biomaterial with wide distribution particularly in the tropical world and which occurs as waste material could be put into effective utilization as a biosorbent to address a crucial environmental problem.« less

Kinetic modelling for zinc (II) ions biosorption onto Luffa cylindrica

NASA Astrophysics Data System (ADS)

Oboh, I.; Aluyor, E.; Audu, T.

2015-03-01

The biosorption of Zinc (II) ions onto a biomaterial - Luffa cylindrica has been studied. This biomaterial was characterized by elemental analysis, surface area, pore size distribution, scanning electron microscopy, and the biomaterial before and after sorption, was characterized by Fourier Transform Infra Red (FTIR) spectrometer. The kinetic nonlinear models fitted were Pseudo-first order, Pseudo-second order and Intra-particle diffusion. A comparison of non-linear regression method in selecting the kinetic model was made. Four error functions, namely coefficient of determination (R2), hybrid fractional error function (HYBRID), average relative error (ARE), and sum of the errors squared (ERRSQ), were used to predict the parameters of the kinetic models. The strength of this study is that a biomaterial with wide distribution particularly in the tropical world and which occurs as waste material could be put into effective utilization as a biosorbent to address a crucial environmental problem.

Linearised and non-linearised isotherm models optimization analysis by error functions and statistical means

PubMed Central

2014-01-01

In adsorption study, to describe sorption process and evaluation of best-fitting isotherm model is a key analysis to investigate the theoretical hypothesis. Hence, numerous statistically analysis have been extensively used to estimate validity of the experimental equilibrium adsorption values with the predicted equilibrium values. Several statistical error analysis were carried out. In the present study, the following statistical analysis were carried out to evaluate the adsorption isotherm model fitness, like the Pearson correlation, the coefficient of determination and the Chi-square test, have been used. The ANOVA test was carried out for evaluating significance of various error functions and also coefficient of dispersion were evaluated for linearised and non-linearised models. The adsorption of phenol onto natural soil (Local name Kalathur soil) was carried out, in batch mode at 30 ± 20 C. For estimating the isotherm parameters, to get a holistic view of the analysis the models were compared between linear and non-linear isotherm models. The result reveled that, among above mentioned error functions and statistical functions were designed to determine the best fitting isotherm. PMID:25018878

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

NASA Technical Reports Server (NTRS)

Whitmore, Stephen A.; Moes, Timothy R.

1994-01-01

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

Moments and Root-Mean-Square Error of the Bayesian MMSE Estimator of Classification Error in the Gaussian Model.

PubMed

Zollanvari, Amin; Dougherty, Edward R

2014-06-01

The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because the error must be estimated using the same data from which the classifier has been designed. Use of prior knowledge, in the form of a prior distribution on an uncertainty class of feature-label distributions to which the true, but unknown, feature-distribution belongs, can facilitate accurate error estimation (in the mean-square sense) in circumstances where accurate completely model-free error estimation is impossible. This paper provides analytic asymptotically exact finite-sample approximations for various performance metrics of the resulting Bayesian Minimum Mean-Square-Error (MMSE) error estimator in the case of linear discriminant analysis (LDA) in the multivariate Gaussian model. These performance metrics include the first, second, and cross moments of the Bayesian MMSE error estimator with the true error of LDA, and therefore, the Root-Mean-Square (RMS) error of the estimator. We lay down the theoretical groundwork for Kolmogorov double-asymptotics in a Bayesian setting, which enables us to derive asymptotic expressions of the desired performance metrics. From these we produce analytic finite-sample approximations and demonstrate their accuracy via numerical examples. Various examples illustrate the behavior of these approximations and their use in determining the necessary sample size to achieve a desired RMS. The Supplementary Material contains derivations for some equations and added figures.

Network Adjustment of Orbit Errors in SAR Interferometry

NASA Astrophysics Data System (ADS)

Bahr, Hermann; Hanssen, Ramon

2010-03-01

Orbit errors can induce significant long wavelength error signals in synthetic aperture radar (SAR) interferograms and thus bias estimates of wide-scale deformation phenomena. The presented approach aims for correcting orbit errors in a preprocessing step to deformation analysis by modifying state vectors. Whereas absolute errors in the orbital trajectory are negligible, the influence of relative errors (baseline errors) is parametrised by their parallel and perpendicular component as a linear function of time. As the sensitivity of the interferometric phase is only significant with respect to the perpendicular base-line and the rate of change of the parallel baseline, the algorithm focuses on estimating updates to these two parameters. This is achieved by a least squares approach, where the unwrapped residual interferometric phase is observed and atmospheric contributions are considered to be stochastic with constant mean. To enhance reliability, baseline errors are adjusted in an overdetermined network of interferograms, yielding individual orbit corrections per acquisition.

Discordance between net analyte signal theory and practical multivariate calibration.

PubMed

Brown, Christopher D

2004-08-01

Lorber's concept of net analyte signal is reviewed in the context of classical and inverse least-squares approaches to multivariate calibration. It is shown that, in the presence of device measurement error, the classical and inverse calibration procedures have radically different theoretical prediction objectives, and the assertion that the popular inverse least-squares procedures (including partial least squares, principal components regression) approximate Lorber's net analyte signal vector in the limit is disproved. Exact theoretical expressions for the prediction error bias, variance, and mean-squared error are given under general measurement error conditions, which reinforce the very discrepant behavior between these two predictive approaches, and Lorber's net analyte signal theory. Implications for multivariate figures of merit and numerous recently proposed preprocessing treatments involving orthogonal projections are also discussed.

Photogrammetric Method and Software for Stream Planform Identification

NASA Astrophysics Data System (ADS)

Stonedahl, S. H.; Stonedahl, F.; Lohberg, M. M.; Lusk, K.; Miller, D.

2013-12-01

Accurately characterizing the planform of a stream is important for many purposes, including recording measurement and sampling locations, monitoring change due to erosion or volumetric discharge, and spatial modeling of stream processes. While expensive surveying equipment or high resolution aerial photography can be used to obtain planform data, our research focused on developing a close-range photogrammetric method (and accompanying free/open-source software) to serve as a cost-effective alternative. This method involves securing and floating a wooden square frame on the stream surface at several locations, taking photographs from numerous angles at each location, and then post-processing and merging data from these photos using the corners of the square for reference points, unit scale, and perspective correction. For our test field site we chose a ~35m reach along Black Hawk Creek in Sunderbruch Park (Davenport, IA), a small, slow-moving stream with overhanging trees. To quantify error we measured 88 distances between 30 marked control points along the reach. We calculated error by comparing these 'ground truth' distances to the corresponding distances extracted from our photogrammetric method. We placed the square at three locations along our reach and photographed it from multiple angles. The square corners, visible control points, and visible stream outline were hand-marked in these photos using the GIMP (open-source image editor). We wrote an open-source GUI in Java (hosted on GitHub), which allows the user to load marked-up photos, designate square corners and label control points. The GUI also extracts the marked pixel coordinates from the images. We also wrote several scripts (currently in MATLAB) that correct the pixel coordinates for radial distortion using Brown's lens distortion model, correct for perspective by forcing the four square corner pixels to form a parallelogram in 3-space, and rotate the points in order to correctly orient all photos of the same square location. Planform data from multiple photos (and multiple square locations) are combined using weighting functions that mitigate the error stemming from the markup-process, imperfect camera calibration, etc. We have used our (beta) software to mark and process over 100 photos, yielding an average error of only 1.5% relative to our 88 measured lengths. Next we plan to translate the MATLAB scripts into Python and release their source code, at which point only free software, consumer-grade digital cameras, and inexpensive building materials will be needed for others to replicate this method at new field sites. Three sample photographs of the square with the created planform and control points

Closed-loop carrier phase synchronization techniques motivated by likelihood functions

NASA Technical Reports Server (NTRS)

Tsou, H.; Hinedi, S.; Simon, M.

1994-01-01

This article reexamines the notion of closed-loop carrier phase synchronization motivated by the theory of maximum a posteriori phase estimation with emphasis on the development of new structures based on both maximum-likelihood and average-likelihood functions. The criterion of performance used for comparison of all the closed-loop structures discussed is the mean-squared phase error for a fixed-loop bandwidth.

Augmented GNSS Differential Corrections Minimum Mean Square Error Estimation Sensitivity to Spatial Correlation Modeling Errors

PubMed Central

Kassabian, Nazelie; Presti, Letizia Lo; Rispoli, Francesco

2014-01-01

Railway signaling is a safety system that has evolved over the last couple of centuries towards autonomous functionality. Recently, great effort is being devoted in this field, towards the use and exploitation of Global Navigation Satellite System (GNSS) signals and GNSS augmentation systems in view of lower railway track equipments and maintenance costs, that is a priority to sustain the investments for modernizing the local and regional lines most of which lack automatic train protection systems and are still manually operated. The objective of this paper is to assess the sensitivity of the Linear Minimum Mean Square Error (LMMSE) algorithm to modeling errors in the spatial correlation function that characterizes true pseudorange Differential Corrections (DCs). This study is inspired by the railway application; however, it applies to all transportation systems, including the road sector, that need to be complemented by an augmentation system in order to deliver accurate and reliable positioning with integrity specifications. A vector of noisy pseudorange DC measurements are simulated, assuming a Gauss-Markov model with a decay rate parameter inversely proportional to the correlation distance that exists between two points of a certain environment. The LMMSE algorithm is applied on this vector to estimate the true DC, and the estimation error is compared to the noise added during simulation. The results show that for large enough correlation distance to Reference Stations (RSs) distance separation ratio values, the LMMSE brings considerable advantage in terms of estimation error accuracy and precision. Conversely, the LMMSE algorithm may deteriorate the quality of the DC measurements whenever the ratio falls below a certain threshold. PMID:24922454

The mean-square error optimal linear discriminant function and its application to incomplete data vectors

NASA Technical Reports Server (NTRS)

Walker, H. F.

1979-01-01

In many pattern recognition problems, data vectors are classified although one or more of the data vector elements are missing. This problem occurs in remote sensing when the ground is obscured by clouds. Optimal linear discrimination procedures for classifying imcomplete data vectors are discussed.

Research on error control and compensation in magnetorheological finishing.

PubMed

Dai, Yifan; Hu, Hao; Peng, Xiaoqiang; Wang, Jianmin; Shi, Feng

2011-07-01

Although magnetorheological finishing (MRF) is a deterministic finishing technology, the machining results always fall short of simulation precision in the actual process, and it cannot meet the precision requirements just through a single treatment but after several iterations. We investigate the reasons for this problem through simulations and experiments. Through controlling and compensating the chief errors in the manufacturing procedure, such as removal function calculation error, positioning error of the removal function, and dynamic performance limitation of the CNC machine, the residual error convergence ratio (ratio of figure error before and after processing) in a single process is obviously increased, and higher figure precision is achieved. Finally, an improved technical process is presented based on these researches, and the verification experiment is accomplished on the experimental device we developed. The part is a circular plane mirror of fused silica material, and the surface figure error is improved from the initial λ/5 [peak-to-valley (PV) λ=632.8 nm], λ/30 [root-mean-square (rms)] to the final λ/40 (PV), λ/330 (rms) just through one iteration in 4.4 min. Results show that a higher convergence ratio and processing precision can be obtained by adopting error control and compensation techniques in MRF.

Online Removal of Baseline Shift with a Polynomial Function for Hemodynamic Monitoring Using Near-Infrared Spectroscopy.

PubMed

Zhao, Ke; Ji, Yaoyao; Li, Yan; Li, Ting

2018-01-21

Near-infrared spectroscopy (NIRS) has become widely accepted as a valuable tool for noninvasively monitoring hemodynamics for clinical and diagnostic purposes. Baseline shift has attracted great attention in the field, but there has been little quantitative study on baseline removal. Here, we aimed to study the baseline characteristics of an in-house-built portable medical NIRS device over a long time (>3.5 h). We found that the measured baselines all formed perfect polynomial functions on phantom tests mimicking human bodies, which were identified by recent NIRS studies. More importantly, our study shows that the fourth-order polynomial function acted to distinguish performance with stable and low-computation-burden fitting calibration (R-square >0.99 for all probes) among second- to sixth-order polynomials, evaluated by the parameters R-square, sum of squares due to error, and residual. This study provides a straightforward, efficient, and quantitatively evaluated solution for online baseline removal for hemodynamic monitoring using NIRS devices.

Very-short-term wind power prediction by a hybrid model with single- and multi-step approaches

NASA Astrophysics Data System (ADS)

Mohammed, E.; Wang, S.; Yu, J.

2017-05-01

Very-short-term wind power prediction (VSTWPP) has played an essential role for the operation of electric power systems. This paper aims at improving and applying a hybrid method of VSTWPP based on historical data. The hybrid method is combined by multiple linear regressions and least square (MLR&LS), which is intended for reducing prediction errors. The predicted values are obtained through two sub-processes:1) transform the time-series data of actual wind power into the power ratio, and then predict the power ratio;2) use the predicted power ratio to predict the wind power. Besides, the proposed method can include two prediction approaches: single-step prediction (SSP) and multi-step prediction (MSP). WPP is tested comparatively by auto-regressive moving average (ARMA) model from the predicted values and errors. The validity of the proposed hybrid method is confirmed in terms of error analysis by using probability density function (PDF), mean absolute percent error (MAPE) and means square error (MSE). Meanwhile, comparison of the correlation coefficients between the actual values and the predicted values for different prediction times and window has confirmed that MSP approach by using the hybrid model is the most accurate while comparing to SSP approach and ARMA. The MLR&LS is accurate and promising for solving problems in WPP.

Rapid Detection of Volatile Oil in Mentha haplocalyx by Near-Infrared Spectroscopy and Chemometrics.

PubMed

Yan, Hui; Guo, Cheng; Shao, Yang; Ouyang, Zhen

2017-01-01

Near-infrared spectroscopy combined with partial least squares regression (PLSR) and support vector machine (SVM) was applied for the rapid determination of chemical component of volatile oil content in Mentha haplocalyx . The effects of data pre-processing methods on the accuracy of the PLSR calibration models were investigated. The performance of the final model was evaluated according to the correlation coefficient ( R ) and root mean square error of prediction (RMSEP). For PLSR model, the best preprocessing method combination was first-order derivative, standard normal variate transformation (SNV), and mean centering, which had of 0.8805, of 0.8719, RMSEC of 0.091, and RMSEP of 0.097, respectively. The wave number variables linking to volatile oil are from 5500 to 4000 cm-1 by analyzing the loading weights and variable importance in projection (VIP) scores. For SVM model, six LVs (less than seven LVs in PLSR model) were adopted in model, and the result was better than PLSR model. The and were 0.9232 and 0.9202, respectively, with RMSEC and RMSEP of 0.084 and 0.082, respectively, which indicated that the predicted values were accurate and reliable. This work demonstrated that near infrared reflectance spectroscopy with chemometrics could be used to rapidly detect the main content volatile oil in M. haplocalyx . The quality of medicine directly links to clinical efficacy, thus, it is important to control the quality of Mentha haplocalyx . Near-infrared spectroscopy combined with partial least squares regression (PLSR) and support vector machine (SVM) was applied for the rapid determination of chemical component of volatile oil content in Mentha haplocalyx . For SVM model, 6 LVs (less than 7 LVs in PLSR model) were adopted in model, and the result was better than PLSR model. It demonstrated that near infrared reflectance spectroscopy with chemometrics could be used to rapidly detect the main content volatile oil in Mentha haplocalyx . Abbreviations used: 1 st der: First-order derivative; 2 nd der: Second-order derivative; LOO: Leave-one-out; LVs: Latent variables; MC: Mean centering, NIR: Near-infrared; NIRS: Near infrared spectroscopy; PCR: Principal component regression, PLSR: Partial least squares regression; RBF: Radial basis function; RMSEC: Root mean square error of cross validation, RMSEC: Root mean square error of calibration; RMSEP: Root mean square error of prediction; SNV: Standard normal variate transformation; SVM: Support vector machine; VIP: Variable Importance in projection.

Weight Vector Fluctuations in Adaptive Antenna Arrays Tuned Using the Least-Mean-Square Error Algorithm with Quadratic Constraint

NASA Astrophysics Data System (ADS)

Zimina, S. V.

2015-06-01

We present the results of statistical analysis of an adaptive antenna array tuned using the least-mean-square error algorithm with quadratic constraint on the useful-signal amplification with allowance for the weight-coefficient fluctuations. Using the perturbation theory, the expressions for the correlation function and power of the output signal of the adaptive antenna array, as well as the formula for the weight-vector covariance matrix are obtained in the first approximation. The fluctuations are shown to lead to the signal distortions at the antenna-array output. The weight-coefficient fluctuations result in the appearance of additional terms in the statistical characteristics of the antenna array. It is also shown that the weight-vector fluctuations are isotropic, i.e., identical in all directions of the weight-coefficient space.

Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression

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

Verdoolaege, G., E-mail: geert.verdoolaege@ugent.be; Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels; Shabbir, A.

Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standardmore » least squares.« less

Study of the convergence behavior of the complex kernel least mean square algorithm.

PubMed

Paul, Thomas K; Ogunfunmi, Tokunbo

2013-09-01

The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.

Landsat-4 (TDRSS-user) orbit determination using batch least-squares and sequential methods

NASA Technical Reports Server (NTRS)

Oza, D. H.; Jones, T. L.; Hakimi, M.; Samii, M. V.; Doll, C. E.; Mistretta, G. D.; Hart, R. C.

1992-01-01

TDRSS user orbit determination is analyzed using a batch least-squares method and a sequential estimation method. It was found that in the batch least-squares method analysis, the orbit determination consistency for Landsat-4, which was heavily tracked by TDRSS during January 1991, was about 4 meters in the rms overlap comparisons and about 6 meters in the maximum position differences in overlap comparisons. The consistency was about 10 to 30 meters in the 3 sigma state error covariance function in the sequential method analysis. As a measure of consistency, the first residual of each pass was within the 3 sigma bound in the residual space.

Testing the Concept of Quark-Hadron Duality with the ALEPH τ Decay Data

NASA Astrophysics Data System (ADS)

Magradze, B. A.

2010-12-01

We propose a modified procedure for extracting the numerical value for the strong coupling constant α s from the τ lepton hadronic decay rate into non-strange particles in the vector channel. We employ the concept of the quark-hadron duality specifically, introducing a boundary energy squared s p > 0, the onset of the perturbative QCD continuum in Minkowski space (Bertlmann et al. in Nucl Phys B 250:61, 1985; de Rafael in An introduction to sum rules in QCD. In: Lectures at the Les Houches Summer School. arXiv: 9802448 [hep-ph], 1997; Peris et al. in JHEP 9805:011, 1998). To approximate the hadronic spectral function in the region s > s p, we use analytic perturbation theory (APT) up to the fifth order. A new feature of our procedure is that it enables us to extract from the data simultaneously the QCD scale parameter {Λ_{overlineMS}} and the boundary energy squared s p. We carefully determine the experimental errors on these parameters which come from the errors on the invariant mass squared distribution. For the {overlineMS} scheme coupling constant, we obtain {α_s(m2_{tau})=0.3204± 0.0159_{exp.}}. We show that our numerical analysis is much more stable against higher-order corrections than the standard one. Additionally, we recalculate the “experimental” Adler function in the infrared region using final ALEPH results. The uncertainty on this function is also determined.

Performance of statistical models to predict mental health and substance abuse cost.

PubMed

Montez-Rath, Maria; Christiansen, Cindy L; Ettner, Susan L; Loveland, Susan; Rosen, Amy K

2006-10-26

Providers use risk-adjustment systems to help manage healthcare costs. Typically, ordinary least squares (OLS) models on either untransformed or log-transformed cost are used. We examine the predictive ability of several statistical models, demonstrate how model choice depends on the goal for the predictive model, and examine whether building models on samples of the data affects model choice. Our sample consisted of 525,620 Veterans Health Administration patients with mental health (MH) or substance abuse (SA) diagnoses who incurred costs during fiscal year 1999. We tested two models on a transformation of cost: a Log Normal model and a Square-root Normal model, and three generalized linear models on untransformed cost, defined by distributional assumption and link function: Normal with identity link (OLS); Gamma with log link; and Gamma with square-root link. Risk-adjusters included age, sex, and 12 MH/SA categories. To determine the best model among the entire dataset, predictive ability was evaluated using root mean square error (RMSE), mean absolute prediction error (MAPE), and predictive ratios of predicted to observed cost (PR) among deciles of predicted cost, by comparing point estimates and 95% bias-corrected bootstrap confidence intervals. To study the effect of analyzing a random sample of the population on model choice, we re-computed these statistics using random samples beginning with 5,000 patients and ending with the entire sample. The Square-root Normal model had the lowest estimates of the RMSE and MAPE, with bootstrap confidence intervals that were always lower than those for the other models. The Gamma with square-root link was best as measured by the PRs. The choice of best model could vary if smaller samples were used and the Gamma with square-root link model had convergence problems with small samples. Models with square-root transformation or link fit the data best. This function (whether used as transformation or as a link) seems to help deal with the high comorbidity of this population by introducing a form of interaction. The Gamma distribution helps with the long tail of the distribution. However, the Normal distribution is suitable if the correct transformation of the outcome is used.

Selective Weighted Least Squares Method for Fourier Transform Infrared Quantitative Analysis.

PubMed

Wang, Xin; Li, Yan; Wei, Haoyun; Chen, Xia

2017-06-01

Classical least squares (CLS) regression is a popular multivariate statistical method used frequently for quantitative analysis using Fourier transform infrared (FT-IR) spectrometry. Classical least squares provides the best unbiased estimator for uncorrelated residual errors with zero mean and equal variance. However, the noise in FT-IR spectra, which accounts for a large portion of the residual errors, is heteroscedastic. Thus, if this noise with zero mean dominates in the residual errors, the weighted least squares (WLS) regression method described in this paper is a better estimator than CLS. However, if bias errors, such as the residual baseline error, are significant, WLS may perform worse than CLS. In this paper, we compare the effect of noise and bias error in using CLS and WLS in quantitative analysis. Results indicated that for wavenumbers with low absorbance, the bias error significantly affected the error, such that the performance of CLS is better than that of WLS. However, for wavenumbers with high absorbance, the noise significantly affected the error, and WLS proves to be better than CLS. Thus, we propose a selective weighted least squares (SWLS) regression that processes data with different wavenumbers using either CLS or WLS based on a selection criterion, i.e., lower or higher than an absorbance threshold. The effects of various factors on the optimal threshold value (OTV) for SWLS have been studied through numerical simulations. These studies reported that: (1) the concentration and the analyte type had minimal effect on OTV; and (2) the major factor that influences OTV is the ratio between the bias error and the standard deviation of the noise. The last part of this paper is dedicated to quantitative analysis of methane gas spectra, and methane/toluene mixtures gas spectra as measured using FT-IR spectrometry and CLS, WLS, and SWLS. The standard error of prediction (SEP), bias of prediction (bias), and the residual sum of squares of the errors (RSS) from the three quantitative analyses were compared. In methane gas analysis, SWLS yielded the lowest SEP and RSS among the three methods. In methane/toluene mixture gas analysis, a modification of the SWLS has been presented to tackle the bias error from other components. The SWLS without modification presents the lowest SEP in all cases but not bias and RSS. The modification of SWLS reduced the bias, which showed a lower RSS than CLS, especially for small components.

Microwave Photonic Architecture for Direction Finding of LPI Emitters: Post-Processing for Angle of Arrival Estimation

DTIC Science & Technology

2016-09-01

mean- square (RMS) error of 0.29° at ə° resolution. For a P4 coded signal, the RMS error in estimating the AOA is 0.32° at 1° resolution. 14...FMCW signal, it was demonstrated that the system is capable of estimating the AOA with a root-mean- square (RMS) error of 0.29° at ə° resolution. For a...Modulator PCB printed circuit board PD photodetector RF radio frequency RMS root-mean- square xvi THIS PAGE INTENTIONALLY LEFT BLANK xvii

Single-Event Effect Performance of a Conductive-Bridge Memory EEPROM

NASA Technical Reports Server (NTRS)

Chen, Dakai; Wilcox, Edward; Berg, Melanie; Kim, Hak; Phan, Anthony; Figueiredo, Marco; Seidleck, Christina; LaBel, Kenneth

2015-01-01

We investigated the heavy ion single-event effect (SEE) susceptibility of the industry’s first stand-alone memory based on conductive-bridge memory (CBRAM) technology. The device is available as an electrically erasable programmable read-only memory (EEPROM). We found that single-event functional interrupt (SEFI) is the dominant SEE type for each operational mode (standby, dynamic read, and dynamic write/read). SEFIs occurred even while the device is statically biased in standby mode. Worst case SEFIs resulted in errors that filled the entire memory space. Power cycle did not always clear the errors. Thus the corrupted cells had to be reprogrammed in some cases. The device is also vulnerable to bit upsets during dynamic write/read tests, although the frequency of the upsets are relatively low. The linear energy transfer threshold for cell upset is between 10 and 20 megaelectron volts per square centimeter per milligram, with an upper limit cross section of 1.6 times 10(sup -11) square centimeters per bit (95 percent confidence level) at 10 megaelectronvolts per square centimeter per milligram. In standby mode, the CBRAM array appears invulnerable to bit upsets.

Robust Least-Squares Support Vector Machine With Minimization of Mean and Variance of Modeling Error.

PubMed

Lu, Xinjiang; Liu, Wenbo; Zhou, Chuang; Huang, Minghui

2017-06-13

The least-squares support vector machine (LS-SVM) is a popular data-driven modeling method and has been successfully applied to a wide range of applications. However, it has some disadvantages, including being ineffective at handling non-Gaussian noise as well as being sensitive to outliers. In this paper, a robust LS-SVM method is proposed and is shown to have more reliable performance when modeling a nonlinear system under conditions where Gaussian or non-Gaussian noise is present. The construction of a new objective function allows for a reduction of the mean of the modeling error as well as the minimization of its variance, and it does not constrain the mean of the modeling error to zero. This differs from the traditional LS-SVM, which uses a worst-case scenario approach in order to minimize the modeling error and constrains the mean of the modeling error to zero. In doing so, the proposed method takes the modeling error distribution information into consideration and is thus less conservative and more robust in regards to random noise. A solving method is then developed in order to determine the optimal parameters for the proposed robust LS-SVM. An additional analysis indicates that the proposed LS-SVM gives a smaller weight to a large-error training sample and a larger weight to a small-error training sample, and is thus more robust than the traditional LS-SVM. The effectiveness of the proposed robust LS-SVM is demonstrated using both artificial and real life cases.

Feasibility study on the least square method for fitting non-Gaussian noise data

NASA Astrophysics Data System (ADS)

Xu, Wei; Chen, Wen; Liang, Yingjie

2018-02-01

This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, Lévy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. Lévy and stretched Gaussian distributions have many applications in fractional and fractal calculus. It is observed that the non-Gaussian noises are less accurately fitted than the Gaussian noise, but the stretched Gaussian cases appear to perform better than the Lévy noise cases. It is stressed that the least-squares method is inapplicable to the non-Gaussian noise cases when the noise level is larger than 5%.

Hybrid online sensor error detection and functional redundancy for systems with time-varying parameters.

PubMed

Feng, Jianyuan; Turksoy, Kamuran; Samadi, Sediqeh; Hajizadeh, Iman; Littlejohn, Elizabeth; Cinar, Ali

2017-12-01

Supervision and control systems rely on signals from sensors to receive information to monitor the operation of a system and adjust manipulated variables to achieve the control objective. However, sensor performance is often limited by their working conditions and sensors may also be subjected to interference by other devices. Many different types of sensor errors such as outliers, missing values, drifts and corruption with noise may occur during process operation. A hybrid online sensor error detection and functional redundancy system is developed to detect errors in online signals, and replace erroneous or missing values detected with model-based estimates. The proposed hybrid system relies on two techniques, an outlier-robust Kalman filter (ORKF) and a locally-weighted partial least squares (LW-PLS) regression model, which leverage the advantages of automatic measurement error elimination with ORKF and data-driven prediction with LW-PLS. The system includes a nominal angle analysis (NAA) method to distinguish between signal faults and large changes in sensor values caused by real dynamic changes in process operation. The performance of the system is illustrated with clinical data continuous glucose monitoring (CGM) sensors from people with type 1 diabetes. More than 50,000 CGM sensor errors were added to original CGM signals from 25 clinical experiments, then the performance of error detection and functional redundancy algorithms were analyzed. The results indicate that the proposed system can successfully detect most of the erroneous signals and substitute them with reasonable estimated values computed by functional redundancy system.

The multicategory case of the sequential Bayesian pixel selection and estimation procedure

NASA Technical Reports Server (NTRS)

Pore, M. D.; Dennis, T. B. (Principal Investigator)

1980-01-01

A Bayesian technique for stratified proportion estimation and a sampling based on minimizing the mean squared error of this estimator were developed and tested on LANDSAT multispectral scanner data using the beta density function to model the prior distribution in the two-class case. An extention of this procedure to the k-class case is considered. A generalization of the beta function is shown to be a density function for the general case which allows the procedure to be extended.

Application of least-squares fitting of ellipse and hyperbola for two dimensional data

NASA Astrophysics Data System (ADS)

Lawiyuniarti, M. P.; Rahmadiantri, E.; Alamsyah, I. M.; Rachmaputri, G.

2018-01-01

Application of the least-square method of ellipse and hyperbola for two-dimensional data has been applied to analyze the spatial continuity of coal deposits in the mining field, by using the fitting method introduced by Fitzgibbon, Pilu, and Fisher in 1996. This method uses 4{a_0}{a_2} - a_12 = 1 as a constrain function. Meanwhile, in 1994, Gander, Golub and Strebel have introduced ellipse and hyperbola fitting methods using the singular value decomposition approach. This SVD approach can be generalized into a three-dimensional fitting. In this research we, will discuss about those two fitting methods and apply it to four data content of coal that is in the form of ash, calorific value, sulfur and thickness of seam so as to produce form of ellipse or hyperbola. In addition, we compute the error difference resulting from each method and from that calculation, we conclude that although the errors are not much different, the error of the method introduced by Fitzgibbon et al is smaller than the fitting method that introduced by Golub et al.

Determination of suitable drying curve model for bread moisture loss during baking

NASA Astrophysics Data System (ADS)

Soleimani Pour-Damanab, A. R.; Jafary, A.; Rafiee, S.

2013-03-01

This study presents mathematical modelling of bread moisture loss or drying during baking in a conventional bread baking process. In order to estimate and select the appropriate moisture loss curve equation, 11 different models, semi-theoretical and empirical, were applied to the experimental data and compared according to their correlation coefficients, chi-squared test and root mean square error which were predicted by nonlinear regression analysis. Consequently, of all the drying models, a Page model was selected as the best one, according to the correlation coefficients, chi-squared test, and root mean square error values and its simplicity. Mean absolute estimation error of the proposed model by linear regression analysis for natural and forced convection modes was 2.43, 4.74%, respectively.

a New Method for Calculating the Fractal Dimension of Surface Topography

NASA Astrophysics Data System (ADS)

Zuo, Xue; Zhu, Hua; Zhou, Yuankai; Li, Yan

2015-06-01

A new method termed as three-dimensional root-mean-square (3D-RMS) method, is proposed to calculate the fractal dimension (FD) of machined surfaces. The measure of this method is the root-mean-square value of surface data, and the scale is the side length of square in the projection plane. In order to evaluate the calculation accuracy of the proposed method, the isotropic surfaces with deterministic FD are generated based on the fractional Brownian function and Weierstrass-Mandelbrot (WM) fractal function, and two kinds of anisotropic surfaces are generated by stretching or rotating a WM fractal curve. Their FDs are estimated by the proposed method, as well as differential boxing-counting (DBC) method, triangular prism surface area (TPSA) method and variation method (VM). The results show that the 3D-RMS method performs better than the other methods with a lower relative error for both isotropic and anisotropic surfaces, especially for the surfaces with dimensions higher than 2.5, since the relative error between the estimated value and its theoretical value decreases with theoretical FD. Finally, the electrodeposited surface, end-turning surface and grinding surface are chosen as examples to illustrate the application of 3D-RMS method on the real machined surfaces. This method gives a new way to accurately calculate the FD from the surface topographic data.

Correcting Four Similar Correlational Measures for Attenuation Due to Errors of Measurement in the Dependent Variable: Eta, Epsilon, Omega, and Intraclass r.

ERIC Educational Resources Information Center

Stanley, Julian C.; Livingston, Samuel A.

Besides the ubiquitous Pearson product-moment r, there are a number of other measures of relationship that are attenuated by errors of measurement and for which the relationship between true measures can be estimated. Among these are the correlation ratio (eta squared), Kelley's unbiased correlation ratio (epsilon squared), Hays' omega squared,…

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

NASA Technical Reports Server (NTRS)

Blerman, Gregory S.

1995-01-01

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

Propagation of error from parameter constraints in quantitative MRI: Example application of multiple spin echo T2 mapping.

PubMed

Lankford, Christopher L; Does, Mark D

2018-02-01

Quantitative MRI may require correcting for nuisance parameters which can or must be constrained to independently measured or assumed values. The noise and/or bias in these constraints propagate to fitted parameters. For example, the case of refocusing pulse flip angle constraint in multiple spin echo T 2 mapping is explored. An analytical expression for the mean-squared error of a parameter of interest was derived as a function of the accuracy and precision of an independent estimate of a nuisance parameter. The expression was validated by simulations and then used to evaluate the effects of flip angle (θ) constraint on the accuracy and precision of T⁁2 for a variety of multi-echo T 2 mapping protocols. Constraining θ improved T⁁2 precision when the θ-map signal-to-noise ratio was greater than approximately one-half that of the first spin echo image. For many practical scenarios, constrained fitting was calculated to reduce not just the variance but the full mean-squared error of T⁁2, for bias in θ⁁≲6%. The analytical expression derived in this work can be applied to inform experimental design in quantitative MRI. The example application to T 2 mapping provided specific cases, depending on θ⁁ accuracy and precision, in which θ⁁ measurement and constraint would be beneficial to T⁁2 variance or mean-squared error. Magn Reson Med 79:673-682, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Study on the Rationality and Validity of Probit Models of Domino Effect to Chemical Process Equipment caused by Overpressure

NASA Astrophysics Data System (ADS)

Sun, Dongliang; Huang, Guangtuan; Jiang, Juncheng; Zhang, Mingguang; Wang, Zhirong

2013-04-01

Overpressure is one important cause of domino effect in accidents of chemical process equipments. Some models considering propagation probability and threshold values of the domino effect caused by overpressure have been proposed in previous study. In order to prove the rationality and validity of the models reported in the reference, two boundary values of three damage degrees reported were considered as random variables respectively in the interval [0, 100%]. Based on the overpressure data for damage to the equipment and the damage state, and the calculation method reported in the references, the mean square errors of the four categories of damage probability models of overpressure were calculated with random boundary values, and then a relationship of mean square error vs. the two boundary value was obtained, the minimum of mean square error was obtained, compared with the result of the present work, mean square error decreases by about 3%. Therefore, the error was in the acceptable range of engineering applications, the models reported can be considered reasonable and valid.

System identification and model reduction using modulating function techniques

NASA Technical Reports Server (NTRS)

Shen, Yan

1993-01-01

Weighted least squares (WLS) and adaptive weighted least squares (AWLS) algorithms are initiated for continuous-time system identification using Fourier type modulating function techniques. Two stochastic signal models are examined using the mean square properties of the stochastic calculus: an equation error signal model with white noise residuals, and a more realistic white measurement noise signal model. The covariance matrices in each model are shown to be banded and sparse, and a joint likelihood cost function is developed which links the real and imaginary parts of the modulated quantities. The superior performance of above algorithms is demonstrated by comparing them with the LS/MFT and popular predicting error method (PEM) through 200 Monte Carlo simulations. A model reduction problem is formulated with the AWLS/MFT algorithm, and comparisons are made via six examples with a variety of model reduction techniques, including the well-known balanced realization method. Here the AWLS/MFT algorithm manifests higher accuracy in almost all cases, and exhibits its unique flexibility and versatility. Armed with this model reduction, the AWLS/MFT algorithm is extended into MIMO transfer function system identification problems. The impact due to the discrepancy in bandwidths and gains among subsystem is explored through five examples. Finally, as a comprehensive application, the stability derivatives of the longitudinal and lateral dynamics of an F-18 aircraft are identified using physical flight data provided by NASA. A pole-constrained SIMO and MIMO AWLS/MFT algorithm is devised and analyzed. Monte Carlo simulations illustrate its high-noise rejecting properties. Utilizing the flight data, comparisons among different MFT algorithms are tabulated and the AWLS is found to be strongly favored in almost all facets.

Integrating Map Algebra and Statistical Modeling for Spatio- Temporal Analysis of Monthly Mean Daily Incident Photosynthetically Active Radiation (PAR) over a Complex Terrain.

PubMed

Evrendilek, Fatih

2007-12-12

This study aims at quantifying spatio-temporal dynamics of monthly mean dailyincident photosynthetically active radiation (PAR) over a vast and complex terrain such asTurkey. The spatial interpolation method of universal kriging, and the combination ofmultiple linear regression (MLR) models and map algebra techniques were implemented togenerate surface maps of PAR with a grid resolution of 500 x 500 m as a function of fivegeographical and 14 climatic variables. Performance of the geostatistical and MLR modelswas compared using mean prediction error (MPE), root-mean-square prediction error(RMSPE), average standard prediction error (ASE), mean standardized prediction error(MSPE), root-mean-square standardized prediction error (RMSSPE), and adjustedcoefficient of determination (R² adj. ). The best-fit MLR- and universal kriging-generatedmodels of monthly mean daily PAR were validated against an independent 37-year observeddataset of 35 climate stations derived from 160 stations across Turkey by the Jackknifingmethod. The spatial variability patterns of monthly mean daily incident PAR were moreaccurately reflected in the surface maps created by the MLR-based models than in thosecreated by the universal kriging method, in particular, for spring (May) and autumn(November). The MLR-based spatial interpolation algorithms of PAR described in thisstudy indicated the significance of the multifactor approach to understanding and mappingspatio-temporal dynamics of PAR for a complex terrain over meso-scales.

An Empirical State Error Covariance Matrix for the Weighted Least Squares Estimation Method

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2011-01-01

State estimation techniques effectively provide mean state estimates. However, the theoretical state error covariance matrices provided as part of these techniques often suffer from a lack of confidence in their ability to describe the un-certainty in the estimated states. By a reinterpretation of the equations involved in the weighted least squares algorithm, it is possible to directly arrive at an empirical state error covariance matrix. This proposed empirical state error covariance matrix will contain the effect of all error sources, known or not. Results based on the proposed technique will be presented for a simple, two observer, measurement error only problem.

[Application of wavelet transform-radial basis function neural network in NIRS for determination of rifampicin and isoniazide tablets].

PubMed

Lu, Jia-hui; Zhang, Yi-bo; Zhang, Zhuo-yong; Meng, Qing-fan; Guo, Wei-liang; Teng, Li-rong

2008-06-01

A calibration model (WT-RBFNN) combination of wavelet transform (WT) and radial basis function neural network (RBFNN) was proposed for synchronous and rapid determination of rifampicin and isoniazide in Rifampicin and Isoniazide tablets by near infrared reflectance spectroscopy (NIRS). The approximation coefficients were used for input data in RBFNN. The network parameters including the number of hidden layer neurons and spread constant (SC) were investigated. WT-RBFNN model which compressed the original spectra data, removed the noise and the interference of background, and reduced the randomness, the capabilities of prediction were well optimized. The root mean square errors of prediction (RMSEP) for the determination of rifampicin and isoniazide obtained from the optimum WT-RBFNN model are 0.00639 and 0.00587, and the root mean square errors of cross-calibration (RMSECV) for them are 0.00604 and 0.00457, respectively which are superior to those obtained by the optimum RBFNN and PLS models. Regression coefficient (R) between NIRS predicted values and RP-HPLC values for rifampicin and isoniazide are 0.99522 and 0.99392, respectively and the relative error is lower than 2.300%. It was verified that WT-RBFNN model is a suitable approach to dealing with NIRS. The proposed WT-RBFNN model is convenient, and rapid and with no pollution for the determination of rifampicin and isoniazide tablets.

A family of chaotic pure analog coding schemes based on baker's map function

NASA Astrophysics Data System (ADS)

Liu, Yang; Li, Jing; Lu, Xuanxuan; Yuen, Chau; Wu, Jun

2015-12-01

This paper considers a family of pure analog coding schemes constructed from dynamic systems which are governed by chaotic functions—baker's map function and its variants. Various decoding methods, including maximum likelihood (ML), minimum mean square error (MMSE), and mixed ML-MMSE decoding algorithms, have been developed for these novel encoding schemes. The proposed mirrored baker's and single-input baker's analog codes perform a balanced protection against the fold error (large distortion) and weak distortion and outperform the classical chaotic analog coding and analog joint source-channel coding schemes in literature. Compared to the conventional digital communication system, where quantization and digital error correction codes are used, the proposed analog coding system has graceful performance evolution, low decoding latency, and no quantization noise. Numerical results show that under the same bandwidth expansion, the proposed analog system outperforms the digital ones over a wide signal-to-noise (SNR) range.

Compensated Box-Jenkins transfer function for short term load forecast

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

Breipohl, A.; Yu, Z.; Lee, F.N.

In the past years, the Box-Jenkins ARIMA method and the Box-Jenkins transfer function method (BJTF) have been among the most commonly used methods for short term electrical load forecasting. But when there exists a sudden change in the temperature, both methods tend to exhibit larger errors in the forecast. This paper demonstrates that the load forecasting errors resulting from either the BJ ARIMA model or the BJTF model are not simply white noise, but rather well-patterned noise, and the patterns in the noise can be used to improve the forecasts. Thus a compensated Box-Jenkins transfer method (CBJTF) is proposed tomore » improve the accuracy of the load prediction. Some case studies have been made which result in about a 14-33% reduction of the root mean square (RMS) errors of the forecasts, depending on the compensation time period as well as the compensation method used.« less

An Investigation of the Sample Performance of Two Nonnormality Corrections for RMSEA

ERIC Educational Resources Information Center

Brosseau-Liard, Patricia E.; Savalei, Victoria; Li, Libo

2012-01-01

The root mean square error of approximation (RMSEA) is a popular fit index in structural equation modeling (SEM). Typically, RMSEA is computed using the normal theory maximum likelihood (ML) fit function. Under nonnormality, the uncorrected sample estimate of the ML RMSEA tends to be inflated. Two robust corrections to the sample ML RMSEA have…

Choosing the Number of Clusters in K-Means Clustering

ERIC Educational Resources Information Center

Steinley, Douglas; Brusco, Michael J.

2011-01-01

Steinley (2007) provided a lower bound for the sum-of-squares error criterion function used in K-means clustering. In this article, on the basis of the lower bound, the authors propose a method to distinguish between 1 cluster (i.e., a single distribution) versus more than 1 cluster. Additionally, conditional on indicating there are multiple…

Two-body potential model based on cosine series expansion for ionic materials

DOE PAGES

Oda, Takuji; Weber, William J.; Tanigawa, Hisashi

2015-09-23

There is a method to construct a two-body potential model for ionic materials with a Fourier series basis and we examine it. For this method, the coefficients of cosine basis functions are uniquely determined by solving simultaneous linear equations to minimize the sum of weighted mean square errors in energy, force and stress, where first-principles calculation results are used as the reference data. As a validation test of the method, potential models for magnesium oxide are constructed. The mean square errors appropriately converge with respect to the truncation of the cosine series. This result mathematically indicates that the constructed potentialmore » model is sufficiently close to the one that is achieved with the non-truncated Fourier series and demonstrates that this potential virtually provides minimum error from the reference data within the two-body representation. The constructed potential models work appropriately in both molecular statics and dynamics simulations, especially if a two-step correction to revise errors expected in the reference data is performed, and the models clearly outperform two existing Buckingham potential models that were tested. Moreover, the good agreement over a broad range of energies and forces with first-principles calculations should enable the prediction of materials behavior away from equilibrium conditions, such as a system under irradiation.« less

A fast least-squares algorithm for population inference

PubMed Central

2013-01-01

Background Population inference is an important problem in genetics used to remove population stratification in genome-wide association studies and to detect migration patterns or shared ancestry. An individual’s genotype can be modeled as a probabilistic function of ancestral population memberships, Q, and the allele frequencies in those populations, P. The parameters, P and Q, of this binomial likelihood model can be inferred using slow sampling methods such as Markov Chain Monte Carlo methods or faster gradient based approaches such as sequential quadratic programming. This paper proposes a least-squares simplification of the binomial likelihood model motivated by a Euclidean interpretation of the genotype feature space. This results in a faster algorithm that easily incorporates the degree of admixture within the sample of individuals and improves estimates without requiring trial-and-error tuning. Results We show that the expected value of the least-squares solution across all possible genotype datasets is equal to the true solution when part of the problem has been solved, and that the variance of the solution approaches zero as its size increases. The Least-squares algorithm performs nearly as well as Admixture for these theoretical scenarios. We compare least-squares, Admixture, and FRAPPE for a variety of problem sizes and difficulties. For particularly hard problems with a large number of populations, small number of samples, or greater degree of admixture, least-squares performs better than the other methods. On simulated mixtures of real population allele frequencies from the HapMap project, Admixture estimates sparsely mixed individuals better than Least-squares. The least-squares approach, however, performs within 1.5% of the Admixture error. On individual genotypes from the HapMap project, Admixture and least-squares perform qualitatively similarly and within 1.2% of each other. Significantly, the least-squares approach nearly always converges 1.5- to 6-times faster. Conclusions The computational advantage of the least-squares approach along with its good estimation performance warrants further research, especially for very large datasets. As problem sizes increase, the difference in estimation performance between all algorithms decreases. In addition, when prior information is known, the least-squares approach easily incorporates the expected degree of admixture to improve the estimate. PMID:23343408

A fast least-squares algorithm for population inference.

PubMed

Parry, R Mitchell; Wang, May D

2013-01-23

Population inference is an important problem in genetics used to remove population stratification in genome-wide association studies and to detect migration patterns or shared ancestry. An individual's genotype can be modeled as a probabilistic function of ancestral population memberships, Q, and the allele frequencies in those populations, P. The parameters, P and Q, of this binomial likelihood model can be inferred using slow sampling methods such as Markov Chain Monte Carlo methods or faster gradient based approaches such as sequential quadratic programming. This paper proposes a least-squares simplification of the binomial likelihood model motivated by a Euclidean interpretation of the genotype feature space. This results in a faster algorithm that easily incorporates the degree of admixture within the sample of individuals and improves estimates without requiring trial-and-error tuning. We show that the expected value of the least-squares solution across all possible genotype datasets is equal to the true solution when part of the problem has been solved, and that the variance of the solution approaches zero as its size increases. The Least-squares algorithm performs nearly as well as Admixture for these theoretical scenarios. We compare least-squares, Admixture, and FRAPPE for a variety of problem sizes and difficulties. For particularly hard problems with a large number of populations, small number of samples, or greater degree of admixture, least-squares performs better than the other methods. On simulated mixtures of real population allele frequencies from the HapMap project, Admixture estimates sparsely mixed individuals better than Least-squares. The least-squares approach, however, performs within 1.5% of the Admixture error. On individual genotypes from the HapMap project, Admixture and least-squares perform qualitatively similarly and within 1.2% of each other. Significantly, the least-squares approach nearly always converges 1.5- to 6-times faster. The computational advantage of the least-squares approach along with its good estimation performance warrants further research, especially for very large datasets. As problem sizes increase, the difference in estimation performance between all algorithms decreases. In addition, when prior information is known, the least-squares approach easily incorporates the expected degree of admixture to improve the estimate.

Analysis of tractable distortion metrics for EEG compression applications.

PubMed

Bazán-Prieto, Carlos; Blanco-Velasco, Manuel; Cárdenas-Barrera, Julián; Cruz-Roldán, Fernando

2012-07-01

Coding distortion in lossy electroencephalographic (EEG) signal compression methods is evaluated through tractable objective criteria. The percentage root-mean-square difference, which is a global and relative indicator of the quality held by reconstructed waveforms, is the most widely used criterion. However, this parameter does not ensure compliance with clinical standard guidelines that specify limits to allowable noise in EEG recordings. As a result, expert clinicians may have difficulties interpreting the resulting distortion of the EEG for a given value of this parameter. Conversely, the root-mean-square error is an alternative criterion that quantifies distortion in understandable units. In this paper, we demonstrate that the root-mean-square error is better suited to control and to assess the distortion introduced by compression methods. The experiments conducted in this paper show that the use of the root-mean-square error as target parameter in EEG compression allows both clinicians and scientists to infer whether coding error is clinically acceptable or not at no cost for the compression ratio.

Global optimization method based on ray tracing to achieve optimum figure error compensation

NASA Astrophysics Data System (ADS)

Liu, Xiaolin; Guo, Xuejia; Tang, Tianjin

2017-02-01

Figure error would degrade the performance of optical system. When predicting the performance and performing system assembly, compensation by clocking of optical components around the optical axis is a conventional but user-dependent method. Commercial optical software cannot optimize this clocking. Meanwhile existing automatic figure-error balancing methods can introduce approximate calculation error and the build process of optimization model is complex and time-consuming. To overcome these limitations, an accurate and automatic global optimization method of figure error balancing is proposed. This method is based on precise ray tracing to calculate the wavefront error, not approximate calculation, under a given elements' rotation angles combination. The composite wavefront error root-mean-square (RMS) acts as the cost function. Simulated annealing algorithm is used to seek the optimal combination of rotation angles of each optical element. This method can be applied to all rotational symmetric optics. Optimization results show that this method is 49% better than previous approximate analytical method.

Development of an errorable car-following driver model

NASA Astrophysics Data System (ADS)

Yang, H.-H.; Peng, H.

2010-06-01

An errorable car-following driver model is presented in this paper. An errorable driver model is one that emulates human driver's functions and can generate both nominal (error-free), as well as devious (with error) behaviours. This model was developed for evaluation and design of active safety systems. The car-following data used for developing and validating the model were obtained from a large-scale naturalistic driving database. The stochastic car-following behaviour was first analysed and modelled as a random process. Three error-inducing behaviours were then introduced. First, human perceptual limitation was studied and implemented. Distraction due to non-driving tasks was then identified based on the statistical analysis of the driving data. Finally, time delay of human drivers was estimated through a recursive least-square identification process. By including these three error-inducing behaviours, rear-end collisions with the lead vehicle could occur. The simulated crash rate was found to be similar but somewhat higher than that reported in traffic statistics.

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

NASA Astrophysics Data System (ADS)

Becker, Roland; Vexler, Boris

2005-06-01

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

A Survey of Terrain Modeling Technologies and Techniques

DTIC Science & Technology

2007-09-01

Washington , DC 20314-1000 ERDC/TEC TR-08-2 ii Abstract: Test planning, rehearsal, and distributed test events for Future Combat Systems (FCS) require...distance) for all five lines of control points. Blue circles are errors of DSM (original data), red squares are DTM (bare Earth, processed by Intermap...circles are DSM, red squares are DTM ........... 8 5 Distribution of errors for line No. 729. Blue circles are DSM, red squares are DTM

Ocean data assimilation using optimal interpolation with a quasi-geostrophic model

NASA Technical Reports Server (NTRS)

Rienecker, Michele M.; Miller, Robert N.

1991-01-01

A quasi-geostrophic (QG) stream function is analyzed by optimal interpolation (OI) over a 59-day period in a 150-km-square domain off northern California. Hydrographic observations acquired over five surveys were assimilated into a QG open boundary ocean model. Assimilation experiments were conducted separately for individual surveys to investigate the sensitivity of the OI analyses to parameters defining the decorrelation scale of an assumed error covariance function. The analyses were intercompared through dynamical hindcasts between surveys. The best hindcast was obtained using the smooth analyses produced with assumed error decorrelation scales identical to those of the observed stream function. The rms difference between the hindcast stream function and the final analysis was only 23 percent of the observation standard deviation. The two sets of OI analyses were temporally smoother than the fields from statistical objective analysis and in good agreement with the only independent data available for comparison.

Space-Time Joint Interference Cancellation Using Fuzzy-Inference-Based Adaptive Filtering Techniques in Frequency-Selective Multipath Channels

NASA Astrophysics Data System (ADS)

Hu, Chia-Chang; Lin, Hsuan-Yu; Chen, Yu-Fan; Wen, Jyh-Horng

2006-12-01

An adaptive minimum mean-square error (MMSE) array receiver based on the fuzzy-logic recursive least-squares (RLS) algorithm is developed for asynchronous DS-CDMA interference suppression in the presence of frequency-selective multipath fading. This receiver employs a fuzzy-logic control mechanism to perform the nonlinear mapping of the squared error and squared error variation, denoted by ([InlineEquation not available: see fulltext.],[InlineEquation not available: see fulltext.]), into a forgetting factor[InlineEquation not available: see fulltext.]. For the real-time applicability, a computationally efficient version of the proposed receiver is derived based on the least-mean-square (LMS) algorithm using the fuzzy-inference-controlled step-size[InlineEquation not available: see fulltext.]. This receiver is capable of providing both fast convergence/tracking capability as well as small steady-state misadjustment as compared with conventional LMS- and RLS-based MMSE DS-CDMA receivers. Simulations show that the fuzzy-logic LMS and RLS algorithms outperform, respectively, other variable step-size LMS (VSS-LMS) and variable forgetting factor RLS (VFF-RLS) algorithms at least 3 dB and 1.5 dB in bit-error-rate (BER) for multipath fading channels.

Guaranteed estimation of solutions to Helmholtz transmission problems with uncertain data from their indirect noisy observations

NASA Astrophysics Data System (ADS)

Podlipenko, Yu. K.; Shestopalov, Yu. V.

2017-09-01

We investigate the guaranteed estimation problem of linear functionals from solutions to transmission problems for the Helmholtz equation with inexact data. The right-hand sides of equations entering the statements of transmission problems and the statistical characteristics of observation errors are supposed to be unknown and belonging to certain sets. It is shown that the optimal linear mean square estimates of the above mentioned functionals and estimation errors are expressed via solutions to the systems of transmission problems of the special type. The results and techniques can be applied in the analysis and estimation of solution to forward and inverse electromagnetic and acoustic problems with uncertain data that arise in mathematical models of the wave diffraction on transparent bodies.

Travel Time Estimation Using Freeway Point Detector Data Based on Evolving Fuzzy Neural Inference System.

PubMed

Tang, Jinjun; Zou, Yajie; Ash, John; Zhang, Shen; Liu, Fang; Wang, Yinhai

2016-01-01

Travel time is an important measurement used to evaluate the extent of congestion within road networks. This paper presents a new method to estimate the travel time based on an evolving fuzzy neural inference system. The input variables in the system are traffic flow data (volume, occupancy, and speed) collected from loop detectors located at points both upstream and downstream of a given link, and the output variable is the link travel time. A first order Takagi-Sugeno fuzzy rule set is used to complete the inference. For training the evolving fuzzy neural network (EFNN), two learning processes are proposed: (1) a K-means method is employed to partition input samples into different clusters, and a Gaussian fuzzy membership function is designed for each cluster to measure the membership degree of samples to the cluster centers. As the number of input samples increases, the cluster centers are modified and membership functions are also updated; (2) a weighted recursive least squares estimator is used to optimize the parameters of the linear functions in the Takagi-Sugeno type fuzzy rules. Testing datasets consisting of actual and simulated data are used to test the proposed method. Three common criteria including mean absolute error (MAE), root mean square error (RMSE), and mean absolute relative error (MARE) are utilized to evaluate the estimation performance. Estimation results demonstrate the accuracy and effectiveness of the EFNN method through comparison with existing methods including: multiple linear regression (MLR), instantaneous model (IM), linear model (LM), neural network (NN), and cumulative plots (CP).

Travel Time Estimation Using Freeway Point Detector Data Based on Evolving Fuzzy Neural Inference System

PubMed Central

Tang, Jinjun; Zou, Yajie; Ash, John; Zhang, Shen; Liu, Fang; Wang, Yinhai

2016-01-01

Travel time is an important measurement used to evaluate the extent of congestion within road networks. This paper presents a new method to estimate the travel time based on an evolving fuzzy neural inference system. The input variables in the system are traffic flow data (volume, occupancy, and speed) collected from loop detectors located at points both upstream and downstream of a given link, and the output variable is the link travel time. A first order Takagi-Sugeno fuzzy rule set is used to complete the inference. For training the evolving fuzzy neural network (EFNN), two learning processes are proposed: (1) a K-means method is employed to partition input samples into different clusters, and a Gaussian fuzzy membership function is designed for each cluster to measure the membership degree of samples to the cluster centers. As the number of input samples increases, the cluster centers are modified and membership functions are also updated; (2) a weighted recursive least squares estimator is used to optimize the parameters of the linear functions in the Takagi-Sugeno type fuzzy rules. Testing datasets consisting of actual and simulated data are used to test the proposed method. Three common criteria including mean absolute error (MAE), root mean square error (RMSE), and mean absolute relative error (MARE) are utilized to evaluate the estimation performance. Estimation results demonstrate the accuracy and effectiveness of the EFNN method through comparison with existing methods including: multiple linear regression (MLR), instantaneous model (IM), linear model (LM), neural network (NN), and cumulative plots (CP). PMID:26829639

Obstacle Detection in Indoor Environment for Visually Impaired Using Mobile Camera

NASA Astrophysics Data System (ADS)

Rahman, Samiur; Ullah, Sana; Ullah, Sehat

2018-01-01

Obstacle detection can improve the mobility as well as the safety of visually impaired people. In this paper, we present a system using mobile camera for visually impaired people. The proposed algorithm works in indoor environment and it uses a very simple technique of using few pre-stored floor images. In indoor environment all unique floor types are considered and a single image is stored for each unique floor type. These floor images are considered as reference images. The algorithm acquires an input image frame and then a region of interest is selected and is scanned for obstacle using pre-stored floor images. The algorithm compares the present frame and the next frame and compute mean square error of the two frames. If mean square error is less than a threshold value α then it means that there is no obstacle in the next frame. If mean square error is greater than α then there are two possibilities; either there is an obstacle or the floor type is changed. In order to check if the floor is changed, the algorithm computes mean square error of next frame and all stored floor types. If minimum of mean square error is less than a threshold value α then flour is changed otherwise there exist an obstacle. The proposed algorithm works in real-time and 96% accuracy has been achieved.

Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning.

PubMed

Gorban, A N; Mirkes, E M; Zinovyev, A

2016-12-01

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L 1 norm or even sub-linear potentials corresponding to quasinorms L p (0

Least-squares dual characterization for ROI assessment in emission tomography

NASA Astrophysics Data System (ADS)

Ben Bouallègue, F.; Crouzet, J. F.; Dubois, A.; Buvat, I.; Mariano-Goulart, D.

2013-06-01

Our aim is to describe an original method for estimating the statistical properties of regions of interest (ROIs) in emission tomography. Drawn upon the works of Louis on the approximate inverse, we propose a dual formulation of the ROI estimation problem to derive the ROI activity and variance directly from the measured data without any image reconstruction. The method requires the definition of an ROI characteristic function that can be extracted from a co-registered morphological image. This characteristic function can be smoothed to optimize the resolution-variance tradeoff. An iterative procedure is detailed for the solution of the dual problem in the least-squares sense (least-squares dual (LSD) characterization), and a linear extrapolation scheme is described to compensate for sampling partial volume effect and reduce the estimation bias (LSD-ex). LSD and LSD-ex are compared with classical ROI estimation using pixel summation after image reconstruction and with Huesman's method. For this comparison, we used Monte Carlo simulations (GATE simulation tool) of 2D PET data of a Hoffman brain phantom containing three small uniform high-contrast ROIs and a large non-uniform low-contrast ROI. Our results show that the performances of LSD characterization are at least as good as those of the classical methods in terms of root mean square (RMS) error. For the three small tumor regions, LSD-ex allows a reduction in the estimation bias by up to 14%, resulting in a reduction in the RMS error of up to 8.5%, compared with the optimal classical estimation. For the large non-specific region, LSD using appropriate smoothing could intuitively and efficiently handle the resolution-variance tradeoff.

Individualized Cognitive Modeling for Close-Loop Task Mitigation

NASA Technical Reports Server (NTRS)

Zhang, Guangfan; Xu, Roger; Wang, Wei; Li, Jiang; Schnell, Tom; Keller, Mike

2010-01-01

An accurate real-time operator functional state assessment makes it possible to perform task management, minimize risks, and improve mission performance. In this paper, we discuss the development of an individualized operator functional state assessment model that identifies states likely leading to operational errors. To address large individual variations, we use two different approaches to build a model for each individual using its data as well as data from subjects with similar responses. If a subject's response is similar to that of the individual of interest in a specific functional state, all the training data from this subject will be used to build the individual model. The individualization methods have been successfully verified and validated with a driving test data set provided by University of Iowa. With the individualized models, the mean squared error can be significantly decreased (by around 20%).

Forecasting Error Calculation with Mean Absolute Deviation and Mean Absolute Percentage Error

NASA Astrophysics Data System (ADS)

Khair, Ummul; Fahmi, Hasanul; Hakim, Sarudin Al; Rahim, Robbi

2017-12-01

Prediction using a forecasting method is one of the most important things for an organization, the selection of appropriate forecasting methods is also important but the percentage error of a method is more important in order for decision makers to adopt the right culture, the use of the Mean Absolute Deviation and Mean Absolute Percentage Error to calculate the percentage of mistakes in the least square method resulted in a percentage of 9.77% and it was decided that the least square method be worked for time series and trend data.

A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging.

PubMed

Koay, Cheng Guan; Chang, Lin-Ching; Carew, John D; Pierpaoli, Carlo; Basser, Peter J

2006-09-01

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (

Modified locally weighted--partial least squares regression improving clinical predictions from infrared spectra of human serum samples.

PubMed

Perez-Guaita, David; Kuligowski, Julia; Quintás, Guillermo; Garrigues, Salvador; Guardia, Miguel de la

2013-03-30

Locally weighted partial least squares regression (LW-PLSR) has been applied to the determination of four clinical parameters in human serum samples (total protein, triglyceride, glucose and urea contents) by Fourier transform infrared (FTIR) spectroscopy. Classical LW-PLSR models were constructed using different spectral regions. For the selection of parameters by LW-PLSR modeling, a multi-parametric study was carried out employing the minimum root-mean square error of cross validation (RMSCV) as objective function. In order to overcome the effect of strong matrix interferences on the predictive accuracy of LW-PLSR models, this work focuses on sample selection. Accordingly, a novel strategy for the development of local models is proposed. It was based on the use of: (i) principal component analysis (PCA) performed on an analyte specific spectral region for identifying most similar sample spectra and (ii) partial least squares regression (PLSR) constructed using the whole spectrum. Results found by using this strategy were compared to those provided by PLSR using the same spectral intervals as for LW-PLSR. Prediction errors found by both, classical and modified LW-PLSR improved those obtained by PLSR. Hence, both proposed approaches were useful for the determination of analytes present in a complex matrix as in the case of human serum samples. Copyright © 2013 Elsevier B.V. All rights reserved.

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

Zhou, S; Fan, Q; Lei, Y

Purpose: In-Water-Output-Ratio (IWOR) plays a significant role in linac-based radiotherapy treatment planning, linking MUs to delivered radiation dose. For an open rectangular field, IWOR depends on both its width and length, and changes rapidly when one of them becomes small. In this study, a universal functional form is proposed to fit the open field IWOR tables in Varian TrueBeam representative datasets for all photon energies. Methods: A novel Generalized Mean formula is first used to estimate the Equivalent Square (ES) for a rectangular field. The formula’s weighting factor and power index are determined by collapsing all data points as muchmore » as possible onto a single curve in IWOR vs. ES plot. The result is then fitted with a novel universal function IWOR=1+b*Log(ES/10cm)/(ES/10cm)^c via a least-square procedure to determine the optimal values for parameters b and c. The maximum relative residual error in IWOR over the entire two-dimensional measurement table with field sizes between 3cm and 40cm is used to evaluate the quality of fit for the function. Results: The two-step fitting strategy works very well in determining the optimal parameter values for open field IWOR of each photon energies in the Varian data-set. Relative residual error ≤0.71% is achieved for all photon energies (including Flattening-Filter-Free modes) with field sizes between 3cm and 40cm. The optimal parameter values change smoothly with regular photon beam quality. Conclusion: The universal functional form fits the Varian TrueBeam open field IWOR measurement tables accurately with small relative residual errors for all photon energies. Therefore, it can be an excellent choice to represent IWOR in absolute dose and MU calculations. The functional form can also be used as a QA/commissioning tool to verify the measured data quality and consistency by checking the IWOR data behavior against the function for new photon energies with arbitrary beam quality.« less

Estimation of water level and steam temperature using ensemble Kalman filter square root (EnKF-SR)

NASA Astrophysics Data System (ADS)

Herlambang, T.; Mufarrikoh, Z.; Karya, D. F.; Rahmalia, D.

2018-04-01

The equipment unit which has the most vital role in the steam-powered electric power plant is boiler. Steam drum boiler is a tank functioning to separate fluida into has phase and liquid phase. The existence in boiler system has a vital role. The controlled variables in the steam drum boiler are water level and the steam temperature. If the water level is higher than the determined level, then the gas phase resulted will contain steam endangering the following process and making the resulted steam going to turbine get less, and the by causing damages to pipes in the boiler. On the contrary, if less than the height of determined water level, the resulted height will result in dry steam likely to endanger steam drum. Thus an error was observed between the determined. This paper studied the implementation of the Ensemble Kalman Filter Square Root (EnKF-SR) method in nonlinear model of the steam drum boiler equation. The computation to estimate the height of water level and the temperature of steam was by simulation using Matlab software. Thus an error was observed between the determined water level and the steam temperature, and that of estimated water level and steam temperature. The result of simulation by Ensemble Kalman Filter Square Root (EnKF-SR) on the nonlinear model of steam drum boiler showed that the error was less than 2%. The implementation of EnKF-SR on the steam drum boiler r model comprises of three simulations, each of which generates 200, 300 and 400 ensembles. The best simulation exhibited the error between the real condition and the estimated result, by generating 400 ensemble. The simulation in water level in order of 0.00002145 m, whereas in the steam temperature was some 0.00002121 kelvin.

Smoothness of In vivo Spectral Baseline Determined by Mean Squared Error

PubMed Central

Zhang, Yan; Shen, Jun

2013-01-01

Purpose A nonparametric smooth line is usually added to spectral model to account for background signals in vivo magnetic resonance spectroscopy (MRS). The assumed smoothness of the baseline significantly influences quantitative spectral fitting. In this paper, a method is proposed to minimize baseline influences on estimated spectral parameters. Methods In this paper, the non-parametric baseline function with a given smoothness was treated as a function of spectral parameters. Its uncertainty was measured by root-mean-squared error (RMSE). The proposed method was demonstrated with a simulated spectrum and in vivo spectra of both short echo time (TE) and averaged echo times. The estimated in vivo baselines were compared with the metabolite-nulled spectra, and the LCModel-estimated baselines. The accuracies of estimated baseline and metabolite concentrations were further verified by cross-validation. Results An optimal smoothness condition was found that led to the minimal baseline RMSE. In this condition, the best fit was balanced against minimal baseline influences on metabolite concentration estimates. Conclusion Baseline RMSE can be used to indicate estimated baseline uncertainties and serve as the criterion for determining the baseline smoothness of in vivo MRS. PMID:24259436

On the calibration process of film dosimetry: OLS inverse regression versus WLS inverse prediction.

PubMed

Crop, F; Van Rompaye, B; Paelinck, L; Vakaet, L; Thierens, H; De Wagter, C

2008-07-21

The purpose of this study was both putting forward a statistically correct model for film calibration and the optimization of this process. A reliable calibration is needed in order to perform accurate reference dosimetry with radiographic (Gafchromic) film. Sometimes, an ordinary least squares simple linear (in the parameters) regression is applied to the dose-optical-density (OD) curve with the dose as a function of OD (inverse regression) or sometimes OD as a function of dose (inverse prediction). The application of a simple linear regression fit is an invalid method because heteroscedasticity of the data is not taken into account. This could lead to erroneous results originating from the calibration process itself and thus to a lower accuracy. In this work, we compare the ordinary least squares (OLS) inverse regression method with the correct weighted least squares (WLS) inverse prediction method to create calibration curves. We found that the OLS inverse regression method could lead to a prediction bias of up to 7.3 cGy at 300 cGy and total prediction errors of 3% or more for Gafchromic EBT film. Application of the WLS inverse prediction method resulted in a maximum prediction bias of 1.4 cGy and total prediction errors below 2% in a 0-400 cGy range. We developed a Monte-Carlo-based process to optimize calibrations, depending on the needs of the experiment. This type of thorough analysis can lead to a higher accuracy for film dosimetry.

47 CFR 87.145 - Acceptability of transmitters for licensing.

Code of Federal Regulations, 2014 CFR

2014-10-01

... square error which assumes zero error for the received ground earth station signal and includes the AES transmit/receive frequency reference error and the AES automatic frequency control residual errors.) The...

47 CFR 87.145 - Acceptability of transmitters for licensing.

Code of Federal Regulations, 2013 CFR

2013-10-01

... square error which assumes zero error for the received ground earth station signal and includes the AES transmit/receive frequency reference error and the AES automatic frequency control residual errors.) The...

47 CFR 87.145 - Acceptability of transmitters for licensing.

Code of Federal Regulations, 2012 CFR

2012-10-01

... square error which assumes zero error for the received ground earth station signal and includes the AES transmit/receive frequency reference error and the AES automatic frequency control residual errors.) The...

47 CFR 87.145 - Acceptability of transmitters for licensing.

Code of Federal Regulations, 2011 CFR

2011-10-01

... square error which assumes zero error for the received ground earth station signal and includes the AES transmit/receive frequency reference error and the AES automatic frequency control residual errors.) The...

Relationship between cutoff frequency and accuracy in time-interval photon statistics applied to oscillating signals

NASA Astrophysics Data System (ADS)

Rebolledo, M. A.; Martinez-Betorz, J. A.

1989-04-01

In this paper the accuracy in the determination of the period of an oscillating signal, when obtained from the photon statistics time-interval probability, is studied as a function of the precision (the inverse of the cutoff frequency of the photon counting system) with which time intervals are measured. The results are obtained by means of an experiment with a square-wave signal, where the Fourier or square-wave transforms of the time-interval probability are measured. It is found that for values of the frequency of the signal near the cutoff frequency the errors in the period are small.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Recursive least-squares learning algorithms for neural networks

NASA Astrophysics Data System (ADS)

Lewis, Paul S.; Hwang, Jenq N.

1990-11-01

This paper presents the development of a pair of recursive least squares (ItLS) algorithms for online training of multilayer perceptrons which are a class of feedforward artificial neural networks. These algorithms incorporate second order information about the training error surface in order to achieve faster learning rates than are possible using first order gradient descent algorithms such as the generalized delta rule. A least squares formulation is derived from a linearization of the training error function. Individual training pattern errors are linearized about the network parameters that were in effect when the pattern was presented. This permits the recursive solution of the least squares approximation either via conventional RLS recursions or by recursive QR decomposition-based techniques. The computational complexity of the update is 0(N2) where N is the number of network parameters. This is due to the estimation of the N x N inverse Hessian matrix. Less computationally intensive approximations of the ilLS algorithms can be easily derived by using only block diagonal elements of this matrix thereby partitioning the learning into independent sets. A simulation example is presented in which a neural network is trained to approximate a two dimensional Gaussian bump. In this example RLS training required an order of magnitude fewer iterations on average (527) than did training with the generalized delta rule (6 1 BACKGROUND Artificial neural networks (ANNs) offer an interesting and potentially useful paradigm for signal processing and pattern recognition. The majority of ANN applications employ the feed-forward multilayer perceptron (MLP) network architecture in which network parameters are " trained" by a supervised learning algorithm employing the generalized delta rule (GDIt) [1 2]. The GDR algorithm approximates a fixed step steepest descent algorithm using derivatives computed by error backpropagatiori. The GDII algorithm is sometimes referred to as the backpropagation algorithm. However in this paper we will use the term backpropagation to refer only to the process of computing error derivatives. While multilayer perceptrons provide a very powerful nonlinear modeling capability GDR training can be very slow and inefficient. In linear adaptive filtering the analog of the GDR algorithm is the leastmean- squares (LMS) algorithm. Steepest descent-based algorithms such as GDR or LMS are first order because they use only first derivative or gradient information about the training error to be minimized. To speed up the training process second order algorithms may be employed that take advantage of second derivative or Hessian matrix information. Second order information can be incorporated into MLP training in different ways. In many applications especially in the area of pattern recognition the training set is finite. In these cases block learning can be applied using standard nonlinear optimization techniques [3 4 5].

Mitigating Errors in External Respiratory Surrogate-Based Models of Tumor Position

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

Malinowski, Kathleen T.; Fischell Department of Bioengineering, University of Maryland, College Park, MD; McAvoy, Thomas J.

2012-04-01

Purpose: To investigate the effect of tumor site, measurement precision, tumor-surrogate correlation, training data selection, model design, and interpatient and interfraction variations on the accuracy of external marker-based models of tumor position. Methods and Materials: Cyberknife Synchrony system log files comprising synchronously acquired positions of external markers and the tumor from 167 treatment fractions were analyzed. The accuracy of Synchrony, ordinary-least-squares regression, and partial-least-squares regression models for predicting the tumor position from the external markers was evaluated. The quantity and timing of the data used to build the predictive model were varied. The effects of tumor-surrogate correlation and the precisionmore » in both the tumor and the external surrogate position measurements were explored by adding noise to the data. Results: The tumor position prediction errors increased during the duration of a fraction. Increasing the training data quantities did not always lead to more accurate models. Adding uncorrelated noise to the external marker-based inputs degraded the tumor-surrogate correlation models by 16% for partial-least-squares and 57% for ordinary-least-squares. External marker and tumor position measurement errors led to tumor position prediction changes 0.3-3.6 times the magnitude of the measurement errors, varying widely with model algorithm. The tumor position prediction errors were significantly associated with the patient index but not with the fraction index or tumor site. Partial-least-squares was as accurate as Synchrony and more accurate than ordinary-least-squares. Conclusions: The accuracy of surrogate-based inferential models of tumor position was affected by all the investigated factors, except for the tumor site and fraction index.« less

Performance evaluation of spectral vegetation indices using a statistical sensitivity function

USGS Publications Warehouse

Ji, Lei; Peters, Albert J.

2007-01-01

A great number of spectral vegetation indices (VIs) have been developed to estimate biophysical parameters of vegetation. Traditional techniques for evaluating the performance of VIs are regression-based statistics, such as the coefficient of determination and root mean square error. These statistics, however, are not capable of quantifying the detailed relationship between VIs and biophysical parameters because the sensitivity of a VI is usually a function of the biophysical parameter instead of a constant. To better quantify this relationship, we developed a “sensitivity function” for measuring the sensitivity of a VI to biophysical parameters. The sensitivity function is defined as the first derivative of the regression function, divided by the standard error of the dependent variable prediction. The function elucidates the change in sensitivity over the range of the biophysical parameter. The Student's t- or z-statistic can be used to test the significance of VI sensitivity. Additionally, we developed a “relative sensitivity function” that compares the sensitivities of two VIs when the biophysical parameters are unavailable.

Estimation of fast and slow wave properties in cancellous bone using Prony's method and curve fitting.

PubMed

Wear, Keith A

2013-04-01

The presence of two longitudinal waves in poroelastic media is predicted by Biot's theory and has been confirmed experimentally in through-transmission measurements in cancellous bone. Estimation of attenuation coefficients and velocities of the two waves is challenging when the two waves overlap in time. The modified least squares Prony's (MLSP) method in conjuction with curve-fitting (MLSP + CF) is tested using simulations based on published values for fast and slow wave attenuation coefficients and velocities in cancellous bone from several studies in bovine femur, human femur, and human calcaneus. The search algorithm is accelerated by exploiting correlations among search parameters. The performance of the algorithm is evaluated as a function of signal-to-noise ratio (SNR). For a typical experimental SNR (40 dB), the root-mean-square errors (RMSEs) for one example (human femur) with fast and slow waves separated by approximately half of a pulse duration were 1 m/s (slow wave velocity), 4 m/s (fast wave velocity), 0.4 dB/cm MHz (slow wave attenuation slope), and 1.7 dB/cm MHz (fast wave attenuation slope). The MLSP + CF method is fast (requiring less than 2 s at SNR = 40 dB on a consumer-grade notebook computer) and is flexible with respect to the functional form of the parametric model for the transmission coefficient. The MLSP + CF method provides sufficient accuracy and precision for many applications such that experimental error is a greater limiting factor than estimation error.

Three-dimensional holoscopic image coding scheme using high-efficiency video coding with kernel-based minimum mean-square-error estimation

NASA Astrophysics Data System (ADS)

Liu, Deyang; An, Ping; Ma, Ran; Yang, Chao; Shen, Liquan; Li, Kai

2016-07-01

Three-dimensional (3-D) holoscopic imaging, also known as integral imaging, light field imaging, or plenoptic imaging, can provide natural and fatigue-free 3-D visualization. However, a large amount of data is required to represent the 3-D holoscopic content. Therefore, efficient coding schemes for this particular type of image are needed. A 3-D holoscopic image coding scheme with kernel-based minimum mean square error (MMSE) estimation is proposed. In the proposed scheme, the coding block is predicted by an MMSE estimator under statistical modeling. In order to obtain the signal statistical behavior, kernel density estimation (KDE) is utilized to estimate the probability density function of the statistical modeling. As bandwidth estimation (BE) is a key issue in the KDE problem, we also propose a BE method based on kernel trick. The experimental results demonstrate that the proposed scheme can achieve a better rate-distortion performance and a better visual rendering quality.

Radon-222 concentrations in ground water and soil gas on Indian reservations in Wisconsin

USGS Publications Warehouse

DeWild, John F.; Krohelski, James T.

1995-01-01

For sites with wells finished in the sand and gravel aquifer, the coefficient of determination (R2) of the regression of concentration of radon-222 in ground water as a function of well depth is 0.003 and the significance level is 0.32, which indicates that there is not a statistically significant relation between radon-222 concentrations in ground water and well depth. The coefficient of determination of the regression of radon-222 in ground water and soil gas is 0.19 and the root mean square error of the regression line is 271 picocuries per liter. Even though the significance level (0.036) indicates a statistical relation, the root mean square error of the regression is so large that the regression equation would not give reliable predictions. Because of an inadequate number of samples, similar statistical analyses could not be performed for sites with wells finished in the crystalline and sedimentary bedrock aquifers.

Measuring a diffusion coefficient by single-particle tracking: statistical analysis of experimental mean squared displacement curves.

PubMed

Ernst, Dominique; Köhler, Jürgen

2013-01-21

We provide experimental results on the accuracy of diffusion coefficients obtained by a mean squared displacement (MSD) analysis of single-particle trajectories. We have recorded very long trajectories comprising more than 1.5 × 10(5) data points and decomposed these long trajectories into shorter segments providing us with ensembles of trajectories of variable lengths. This enabled a statistical analysis of the resulting MSD curves as a function of the lengths of the segments. We find that the relative error of the diffusion coefficient can be minimized by taking an optimum number of points into account for fitting the MSD curves, and that this optimum does not depend on the segment length. Yet, the magnitude of the relative error for the diffusion coefficient does, and achieving an accuracy in the order of 10% requires the recording of trajectories with about 1000 data points. Finally, we compare our results with theoretical predictions and find very good qualitative and quantitative agreement between experiment and theory.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Spiral tracing on a touchscreen is influenced by age, hand, implement, and friction.

PubMed

Heintz, Brittany D; Keenan, Kevin G

2018-01-01

Dexterity impairments are well documented in older adults, though it is unclear how these influence touchscreen manipulation. This study examined age-related differences while tracing on high- and low-friction touchscreens using the finger or stylus. 26 young and 24 older adults completed an Archimedes spiral tracing task on a touchscreen mounted on a force sensor. Root mean square error was calculated to quantify performance. Root mean square error increased by 29.9% for older vs. young adults using the fingertip, but was similar to young adults when using the stylus. Although other variables (e.g., touchscreen usage, sensation, and reaction time) differed between age groups, these variables were not related to increased error in older adults while using their fingertip. Root mean square error also increased on the low-friction surface for all subjects. These findings suggest that utilizing a stylus and increasing surface friction may improve touchscreen use in older adults.

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

NASA Technical Reports Server (NTRS)

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

2016-01-01

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

Metric for evaluation of filter efficiency in spectral cameras.

PubMed

Nahavandi, Alireza Mahmoudi; Tehran, Mohammad Amani

2016-11-10

Although metric functions that show the performance of a colorimetric imaging device have been investigated, a metric for performance analysis of a set of filters in wideband filter-based spectral cameras has rarely been studied. Based on a generalization of Vora's Measure of Goodness (MOG) and the spanning theorem, a single function metric that estimates the effectiveness of a filter set is introduced. The improved metric, named MMOG, varies between one, for a perfect, and zero, for the worst possible set of filters. Results showed that MMOG exhibits a trend that is more similar to the mean square of spectral reflectance reconstruction errors than does Vora's MOG index, and it is robust to noise in the imaging system. MMOG as a single metric could be exploited for further analysis of manufacturing errors.

Residual depressive symptoms, sleep disturbance and perceived cognitive impairment as determinants of functioning in patients with bipolar disorder.

PubMed

Samalin, Ludovic; Boyer, Laurent; Murru, Andrea; Pacchiarotti, Isabella; Reinares, María; Bonnin, Caterina Mar; Torrent, Carla; Verdolini, Norma; Pancheri, Corinna; de Chazeron, Ingrid; Boucekine, Mohamed; Geoffroy, Pierre-Alexis; Bellivier, Frank; Llorca, Pierre-Michel; Vieta, Eduard

2017-03-01

Many patients with bipolar disorder (BD) experience residual symptoms during their inter-episodic periods. The study aimed to analyse the relationship between residual depressive symptoms, sleep disturbances and self-reported cognitive impairment as determinants of psychosocial functioning in a large sample of euthymic BD patients. This was a cross-sectional study of 468 euthymic BD outpatients. We evaluated the residual depressive symptoms with the Bipolar Depression Rating Scale, the sleep disturbances with the Pittsburgh Sleep Quality Index, the perceived cognitive performance using visual analogic scales and functioning with the Functioning Assessment Short Test. Structural equation modelling (SEM) was used to describe the relationships among the residual depressive symptoms, sleep disturbances, perceived cognitive performance and functioning. SEM showed good fit with normed chi square=2.46, comparative fit index=0.94, root mean square error of approximation=0.05 and standardized root mean square residuals=0.06. This model revealed that residual depressive symptoms (path coefficient =0.37) and perceived cognitive performance (path coefficient=0.27) were the most important features significantly related to psychosocial functioning. Sleep disturbances were indirectly associated with functioning via residual depressive symptoms and perceived cognitive performance (path coefficient=0.23). This study contributes to a better understanding of the determinants of psychosocial functioning during the inter-episodic periods of BD patients. These findings should facilitate decision-making in therapeutics to improve the functional outcomes of BD during this period. Copyright © 2017 Elsevier B.V. All rights reserved.

Optimized System Identification

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Longman, Richard W.

1999-01-01

In system identification, one usually cares most about finding a model whose outputs are as close as possible to the true system outputs when the same input is applied to both. However, most system identification algorithms do not minimize this output error. Often they minimize model equation error instead, as in typical least-squares fits using a finite-difference model, and it is seen here that this distinction is significant. Here, we develop a set of system identification algorithms that minimize output error for multi-input/multi-output and multi-input/single-output systems. This is done with sequential quadratic programming iterations on the nonlinear least-squares problems, with an eigendecomposition to handle indefinite second partials. This optimization minimizes a nonlinear function of many variables, and hence can converge to local minima. To handle this problem, we start the iterations from the OKID (Observer/Kalman Identification) algorithm result. Not only has OKID proved very effective in practice, it minimizes an output error of an observer which has the property that as the data set gets large, it converges to minimizing the criterion of interest here. Hence, it is a particularly good starting point for the nonlinear iterations here. Examples show that the methods developed here eliminate the bias that is often observed using any system identification methods of either over-estimating or under-estimating the damping of vibration modes in lightly damped structures.

Principal components and iterative regression analysis of geophysical series: Application to Sunspot number (1750 2004)

NASA Astrophysics Data System (ADS)

Nordemann, D. J. R.; Rigozo, N. R.; de Souza Echer, M. P.; Echer, E.

2008-11-01

We present here an implementation of a least squares iterative regression method applied to the sine functions embedded in the principal components extracted from geophysical time series. This method seems to represent a useful improvement for the non-stationary time series periodicity quantitative analysis. The principal components determination followed by the least squares iterative regression method was implemented in an algorithm written in the Scilab (2006) language. The main result of the method is to obtain the set of sine functions embedded in the series analyzed in decreasing order of significance, from the most important ones, likely to represent the physical processes involved in the generation of the series, to the less important ones that represent noise components. Taking into account the need of a deeper knowledge of the Sun's past history and its implication to global climate change, the method was applied to the Sunspot Number series (1750-2004). With the threshold and parameter values used here, the application of the method leads to a total of 441 explicit sine functions, among which 65 were considered as being significant and were used for a reconstruction that gave a normalized mean squared error of 0.146.

Oceanographic and meteorological research based on the data products of SEASAT

NASA Technical Reports Server (NTRS)

Pierson, W. J., Jr.

1985-01-01

Reservations were expressed concerning the sum of squares wind recovery algorithm and the power law model function. The SAS sum of squares (SOS) method for recovering winds from backscatter data leads to inconsistent results when V pol and H pol winds are compared. A model function that does not use a power law and that accounts for sea surface temperature is needed and is under study both theoretically and by means of the SASS mode 4 data. Aspects of the determination of winds by means of scatterometry and of the utilization of vector wind data for meteorological forecasts are elaborated. The operational aspect of an intermittent assimilation scheme currently utilized for the specification of the initial value field is considered with focus on quantifying the absolute 12-hour linear displacement error of the movement of low centers.

Hypothesis Testing Using Factor Score Regression

PubMed Central

Devlieger, Ines; Mayer, Axel; Rosseel, Yves

2015-01-01

In this article, an overview is given of four methods to perform factor score regression (FSR), namely regression FSR, Bartlett FSR, the bias avoiding method of Skrondal and Laake, and the bias correcting method of Croon. The bias correcting method is extended to include a reliable standard error. The four methods are compared with each other and with structural equation modeling (SEM) by using analytic calculations and two Monte Carlo simulation studies to examine their finite sample characteristics. Several performance criteria are used, such as the bias using the unstandardized and standardized parameterization, efficiency, mean square error, standard error bias, type I error rate, and power. The results show that the bias correcting method, with the newly developed standard error, is the only suitable alternative for SEM. While it has a higher standard error bias than SEM, it has a comparable bias, efficiency, mean square error, power, and type I error rate. PMID:29795886

Weighted linear regression using D2H and D2 as the independent variables

Treesearch

Hans T. Schreuder; Michael S. Williams

1998-01-01

Several error structures for weighted regression equations used for predicting volume were examined for 2 large data sets of felled and standing loblolly pine trees (Pinus taeda L.). The generally accepted model with variance of error proportional to the value of the covariate squared ( D2H = diameter squared times height or D...

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

ERIC Educational Resources Information Center

Savalei, Victoria

2012-01-01

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

A method of bias correction for maximal reliability with dichotomous measures.

PubMed

Penev, Spiridon; Raykov, Tenko

2010-02-01

This paper is concerned with the reliability of weighted combinations of a given set of dichotomous measures. Maximal reliability for such measures has been discussed in the past, but the pertinent estimator exhibits a considerable bias and mean squared error for moderate sample sizes. We examine this bias, propose a procedure for bias correction, and develop a more accurate asymptotic confidence interval for the resulting estimator. In most empirically relevant cases, the bias correction and mean squared error correction can be performed simultaneously. We propose an approximate (asymptotic) confidence interval for the maximal reliability coefficient, discuss the implementation of this estimator, and investigate the mean squared error of the associated asymptotic approximation. We illustrate the proposed methods using a numerical example.

Synthetic Aperture Sonar Processing with MMSE Estimation of Image Sample Values

DTIC Science & Technology

2016-12-01

UNCLASSIFIED/UNLIMITED 13. SUPPLEMENTARY NOTES 14. ABSTRACT MMSE (minimum mean- square error) target sample estimation using non-orthogonal basis...orthogonal, they can still be used in a minimum mean‐ square  error (MMSE)  estimator that models the object echo as a weighted sum of the multi‐aspect basis...problem.                     3    Introduction      Minimum mean‐ square  error (MMSE) estimation is applied to target imaging with synthetic aperture

Designing an artificial neural network using radial basis function to model exergetic efficiency of nanofluids in mini double pipe heat exchanger

NASA Astrophysics Data System (ADS)

Ghasemi, Nahid; Aghayari, Reza; Maddah, Heydar

2018-06-01

The present study aims at predicting and optimizing exergetic efficiency of TiO2-Al2O3/water nanofluid at different Reynolds numbers, volume fractions and twisted ratios using Artificial Neural Networks (ANN) and experimental data. Central Composite Design (CCD) and cascade Radial Basis Function (RBF) were used to display the significant levels of the analyzed factors on the exergetic efficiency. The size of TiO2-Al2O3/water nanocomposite was 20-70 nm. The parameters of ANN model were adapted by a training algorithm of radial basis function (RBF) with a wide range of experimental data set. Total mean square error and correlation coefficient were used to evaluate the results which the best result was obtained from double layer perceptron neural network with 30 neurons in which total Mean Square Error(MSE) and correlation coefficient (R2) were equal to 0.002 and 0.999, respectively. This indicated successful prediction of the network. Moreover, the proposed equation for predicting exergetic efficiency was extremely successful. According to the optimal curves, the optimum designing parameters of double pipe heat exchanger with inner twisted tape and nanofluid under the constrains of exergetic efficiency 0.937 are found to be Reynolds number 2500, twisted ratio 2.5 and volume fraction( v/v%) 0.05.

An experimental study of interstitial lung tissue classification in HRCT images using ANN and role of cost functions

NASA Astrophysics Data System (ADS)

Dash, Jatindra K.; Kale, Mandar; Mukhopadhyay, Sudipta; Khandelwal, Niranjan; Prabhakar, Nidhi; Garg, Mandeep; Kalra, Naveen

2017-03-01

In this paper, we investigate the effect of the error criteria used during a training phase of the artificial neural network (ANN) on the accuracy of the classifier for classification of lung tissues affected with Interstitial Lung Diseases (ILD). Mean square error (MSE) and the cross-entropy (CE) criteria are chosen being most popular choice in state-of-the-art implementations. The classification experiment performed on the six interstitial lung disease (ILD) patterns viz. Consolidation, Emphysema, Ground Glass Opacity, Micronodules, Fibrosis and Healthy from MedGIFT database. The texture features from an arbitrary region of interest (AROI) are extracted using Gabor filter. Two different neural networks are trained with the scaled conjugate gradient back propagation algorithm with MSE and CE error criteria function respectively for weight updation. Performance is evaluated in terms of average accuracy of these classifiers using 4 fold cross-validation. Each network is trained for five times for each fold with randomly initialized weight vectors and accuracies are computed. Significant improvement in classification accuracy is observed when ANN is trained by using CE (67.27%) as error function compared to MSE (63.60%). Moreover, standard deviation of the classification accuracy for the network trained with CE (6.69) error criteria is found less as compared to network trained with MSE (10.32) criteria.

On the appropriateness of applying chi-square distribution based confidence intervals to spectral estimates of helicopter flyover data

NASA Technical Reports Server (NTRS)

Rutledge, Charles K.

1988-01-01

The validity of applying chi-square based confidence intervals to far-field acoustic flyover spectral estimates was investigated. Simulated data, using a Kendall series and experimental acoustic data from the NASA/McDonnell Douglas 500E acoustics test, were analyzed. Statistical significance tests to determine the equality of distributions of the simulated and experimental data relative to theoretical chi-square distributions were performed. Bias and uncertainty errors associated with the spectral estimates were easily identified from the data sets. A model relating the uncertainty and bias errors to the estimates resulted, which aided in determining the appropriateness of the chi-square distribution based confidence intervals. Such confidence intervals were appropriate for nontonally associated frequencies of the experimental data but were inappropriate for tonally associated estimate distributions. The appropriateness at the tonally associated frequencies was indicated by the presence of bias error and noncomformity of the distributions to the theoretical chi-square distribution. A technique for determining appropriate confidence intervals at the tonally associated frequencies was suggested.

Regional application of multi-layer artificial neural networks in 3-D ionosphere tomography

NASA Astrophysics Data System (ADS)

Ghaffari Razin, Mir Reza; Voosoghi, Behzad

2016-08-01

Tomography is a very cost-effective method to study physical properties of the ionosphere. In this paper, residual minimization training neural network (RMTNN) is used in voxel-based tomography to reconstruct of 3-D ionosphere electron density with high spatial resolution. For numerical experiments, observations collected at 37 GPS stations from Iranian permanent GPS network (IPGN) are used. A smoothed TEC approach was used for absolute STEC recovery. To improve the vertical resolution, empirical orthogonal functions (EOFs) obtained from international reference ionosphere 2012 (IRI-2012) used as object function in training neural network. Ionosonde observations is used for validate reliability of the proposed method. Minimum relative error for RMTNN is 1.64% and maximum relative error is 15.61%. Also root mean square error (RMSE) of 0.17 × 1011 (electrons/m3) is computed for RMTNN which is less than RMSE of IRI2012. The results show that RMTNN has higher accuracy and compiles speed than other ionosphere reconstruction methods.

Performance analysis of adaptive equalization for coherent acoustic communications in the time-varying ocean environment.

PubMed

Preisig, James C

2005-07-01

Equations are derived for analyzing the performance of channel estimate based equalizers. The performance is characterized in terms of the mean squared soft decision error (sigma2(s)) of each equalizer. This error is decomposed into two components. These are the minimum achievable error (sigma2(0)) and the excess error (sigma2(e)). The former is the soft decision error that would be realized by the equalizer if the filter coefficient calculation were based upon perfect knowledge of the channel impulse response and statistics of the interfering noise field. The latter is the additional soft decision error that is realized due to errors in the estimates of these channel parameters. These expressions accurately predict the equalizer errors observed in the processing of experimental data by a channel estimate based decision feedback equalizer (DFE) and a passive time-reversal equalizer. Further expressions are presented that allow equalizer performance to be predicted given the scattering function of the acoustic channel. The analysis using these expressions yields insights into the features of surface scattering that most significantly impact equalizer performance in shallow water environments and motivates the implementation of a DFE that is robust with respect to channel estimation errors.

Eta Squared, Partial Eta Squared, and Misreporting of Effect Size in Communication Research.

ERIC Educational Resources Information Center

Levine, Timothy R.; Hullett, Craig R.

2002-01-01

Alerts communication researchers to potential errors stemming from the use of SPSS (Statistical Package for the Social Sciences) to obtain estimates of eta squared in analysis of variance (ANOVA). Strives to clarify issues concerning the development and appropriate use of eta squared and partial eta squared in ANOVA. Discusses the reporting of…

Error analysis of stochastic gradient descent ranking.

PubMed

Chen, Hong; Tang, Yi; Li, Luoqing; Yuan, Yuan; Li, Xuelong; Tang, Yuanyan

2013-06-01

Ranking is always an important task in machine learning and information retrieval, e.g., collaborative filtering, recommender systems, drug discovery, etc. A kernel-based stochastic gradient descent algorithm with the least squares loss is proposed for ranking in this paper. The implementation of this algorithm is simple, and an expression of the solution is derived via a sampling operator and an integral operator. An explicit convergence rate for leaning a ranking function is given in terms of the suitable choices of the step size and the regularization parameter. The analysis technique used here is capacity independent and is novel in error analysis of ranking learning. Experimental results on real-world data have shown the effectiveness of the proposed algorithm in ranking tasks, which verifies the theoretical analysis in ranking error.

Multi-muscle FES force control of the human arm for arbitrary goals.

PubMed

Schearer, Eric M; Liao, Yu-Wei; Perreault, Eric J; Tresch, Matthew C; Memberg, William D; Kirsch, Robert F; Lynch, Kevin M

2014-05-01

We present a method for controlling a neuroprosthesis for a paralyzed human arm using functional electrical stimulation (FES) and characterize the errors of the controller. The subject has surgically implanted electrodes for stimulating muscles in her shoulder and arm. Using input/output data, a model mapping muscle stimulations to isometric endpoint forces measured at the subject's hand was identified. We inverted the model of this redundant and coupled multiple-input multiple-output system by minimizing muscle activations and used this inverse for feedforward control. The magnitude of the total root mean square error over a grid in the volume of achievable isometric endpoint force targets was 11% of the total range of achievable forces. Major sources of error were random error due to trial-to-trial variability and model bias due to nonstationary system properties. Because the muscles working collectively are the actuators of the skeletal system, the quantification of errors in force control guides designs of motion controllers for multi-joint, multi-muscle FES systems that can achieve arbitrary goals.

POOLMS: A computer program for fitting and model selection for two level factorial replication-free experiments

NASA Technical Reports Server (NTRS)

Amling, G. E.; Holms, A. G.

1973-01-01

A computer program is described that performs a statistical multiple-decision procedure called chain pooling. It uses a number of mean squares assigned to error variance that is conditioned on the relative magnitudes of the mean squares. The model selection is done according to user-specified levels of type 1 or type 2 error probabilities.

Validating Clusters with the Lower Bound for Sum-of-Squares Error

ERIC Educational Resources Information Center

Steinley, Douglas

2007-01-01

Given that a minor condition holds (e.g., the number of variables is greater than the number of clusters), a nontrivial lower bound for the sum-of-squares error criterion in K-means clustering is derived. By calculating the lower bound for several different situations, a method is developed to determine the adequacy of cluster solution based on…

Assessing the performance of the generalized propensity score for estimating the effect of quantitative or continuous exposures on binary outcomes

PubMed Central

2018-01-01

Propensity score methods are increasingly being used to estimate the effects of treatments and exposures when using observational data. The propensity score was initially developed for use with binary exposures. The generalized propensity score (GPS) is an extension of the propensity score for use with quantitative or continuous exposures (eg, dose or quantity of medication, income, or years of education). We used Monte Carlo simulations to examine the performance of different methods of using the GPS to estimate the effect of continuous exposures on binary outcomes. We examined covariate adjustment using the GPS and weighting using weights based on the inverse of the GPS. We examined both the use of ordinary least squares to estimate the propensity function and the use of the covariate balancing propensity score algorithm. The use of methods based on the GPS was compared with the use of G‐computation. All methods resulted in essentially unbiased estimation of the population dose‐response function. However, GPS‐based weighting tended to result in estimates that displayed greater variability and had higher mean squared error when the magnitude of confounding was strong. Of the methods based on the GPS, covariate adjustment using the GPS tended to result in estimates with lower variability and mean squared error when the magnitude of confounding was strong. We illustrate the application of these methods by estimating the effect of average neighborhood income on the probability of death within 1 year of hospitalization for an acute myocardial infarction. PMID:29508424

Assessing the performance of the generalized propensity score for estimating the effect of quantitative or continuous exposures on binary outcomes.

PubMed

Austin, Peter C

2018-05-20

Propensity score methods are increasingly being used to estimate the effects of treatments and exposures when using observational data. The propensity score was initially developed for use with binary exposures. The generalized propensity score (GPS) is an extension of the propensity score for use with quantitative or continuous exposures (eg, dose or quantity of medication, income, or years of education). We used Monte Carlo simulations to examine the performance of different methods of using the GPS to estimate the effect of continuous exposures on binary outcomes. We examined covariate adjustment using the GPS and weighting using weights based on the inverse of the GPS. We examined both the use of ordinary least squares to estimate the propensity function and the use of the covariate balancing propensity score algorithm. The use of methods based on the GPS was compared with the use of G-computation. All methods resulted in essentially unbiased estimation of the population dose-response function. However, GPS-based weighting tended to result in estimates that displayed greater variability and had higher mean squared error when the magnitude of confounding was strong. Of the methods based on the GPS, covariate adjustment using the GPS tended to result in estimates with lower variability and mean squared error when the magnitude of confounding was strong. We illustrate the application of these methods by estimating the effect of average neighborhood income on the probability of death within 1 year of hospitalization for an acute myocardial infarction. © 2018 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Parameterisation of rainfall-runoff models for forecasting low and average flows, I: Conceptual modelling

NASA Astrophysics Data System (ADS)

Castiglioni, S.; Toth, E.

2009-04-01

In the calibration procedure of continuously-simulating models, the hydrologist has to choose which part of the observed hydrograph is most important to fit, either implicitly, through the visual agreement in manual calibration, or explicitly, through the choice of the objective function(s). Changing the objective functions it is in fact possible to emphasise different kind of errors, giving them more weight in the calibration phase. The objective functions used for calibrating hydrological models are generally of the quadratic type (mean squared error, correlation coefficient, coefficient of determination, etc) and are therefore oversensitive to high and extreme error values, that typically correspond to high and extreme streamflow values. This is appropriate when, like in the majority of streamflow forecasting applications, the focus is on the ability to reproduce potentially dangerous flood events; on the contrary, if the aim of the modelling is the reproduction of low and average flows, as it is the case in water resource management problems, this may result in a deterioration of the forecasting performance. This contribution presents the results of a series of automatic calibration experiments of a continuously-simulating rainfall-runoff model applied over several real-world case-studies, where the objective function is chosen so to highlight the fit of average and low flows. In this work a simple conceptual model will be used, of the lumped type, with a relatively low number of parameters to be calibrated. The experiments will be carried out for a set of case-study watersheds in Central Italy, covering an extremely wide range of geo-morphologic conditions and for whom at least five years of contemporary daily series of streamflow, precipitation and evapotranspiration estimates are available. Different objective functions will be tested in calibration and the results will be compared, over validation data, against those obtained with traditional squared functions. A companion work presents the results, over the same case-study watersheds and observation periods, of a system-theoretic model, again calibrated for reproducing average and low streamflows.

[Formula: see text]-regularized recursive total least squares based sparse system identification for the error-in-variables.

PubMed

Lim, Jun-Seok; Pang, Hee-Suk

2016-01-01

In this paper an [Formula: see text]-regularized recursive total least squares (RTLS) algorithm is considered for the sparse system identification. Although recursive least squares (RLS) has been successfully applied in sparse system identification, the estimation performance in RLS based algorithms becomes worse, when both input and output are contaminated by noise (the error-in-variables problem). We proposed an algorithm to handle the error-in-variables problem. The proposed [Formula: see text]-RTLS algorithm is an RLS like iteration using the [Formula: see text] regularization. The proposed algorithm not only gives excellent performance but also reduces the required complexity through the effective inversion matrix handling. Simulations demonstrate the superiority of the proposed [Formula: see text]-regularized RTLS for the sparse system identification setting.

An algorithm for propagating the square-root covariance matrix in triangular form

NASA Technical Reports Server (NTRS)

Tapley, B. D.; Choe, C. Y.

1976-01-01

A method for propagating the square root of the state error covariance matrix in lower triangular form is described. The algorithm can be combined with any triangular square-root measurement update algorithm to obtain a triangular square-root sequential estimation algorithm. The triangular square-root algorithm compares favorably with the conventional sequential estimation algorithm with regard to computation time.

Criterion for estimation of stress-deformed state of SD-materials

NASA Astrophysics Data System (ADS)

Orekhov, Andrey V.

2018-05-01

A criterion is proposed that determines the moment when the growth pattern of the monotonic numerical sequence varies from the linear to the parabolic one. The criterion is based on the comparison of squares of errors for the linear and the incomplete quadratic approximation. The approximating functions are constructed locally, only at those points that are located near a possible change in nature of the increase in the sequence.

Quality assessment of gasoline using comprehensive two-dimensional gas chromatography combined with unfolded partial least squares: A reliable approach for the detection of gasoline adulteration.

PubMed

Parastar, Hadi; Mostafapour, Sara; Azimi, Gholamhasan

2016-01-01

Comprehensive two-dimensional gas chromatography and flame ionization detection combined with unfolded-partial least squares is proposed as a simple, fast and reliable method to assess the quality of gasoline and to detect its potential adulterants. The data for the calibration set are first baseline corrected using a two-dimensional asymmetric least squares algorithm. The number of significant partial least squares components to build the model is determined using the minimum value of root-mean square error of leave-one out cross validation, which was 4. In this regard, blends of gasoline with kerosene, white spirit and paint thinner as frequently used adulterants are used to make calibration samples. Appropriate statistical parameters of regression coefficient of 0.996-0.998, root-mean square error of prediction of 0.005-0.010 and relative error of prediction of 1.54-3.82% for the calibration set show the reliability of the developed method. In addition, the developed method is externally validated with three samples in validation set (with a relative error of prediction below 10.0%). Finally, to test the applicability of the proposed strategy for the analysis of real samples, five real gasoline samples collected from gas stations are used for this purpose and the gasoline proportions were in range of 70-85%. Also, the relative standard deviations were below 8.5% for different samples in the prediction set. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

{lambda} elements for one-dimensional singular problems with known strength of singularity

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

Wong, K.K.; Surana, K.S.

1996-10-01

This paper presents a new and general procedure for designing special elements called {lambda} elements for one dimensional singular problems where the strength of the singularity is know. The {lambda} elements presented here are of type C{sup 0}. These elements also provide inter-element C{sup 0} continuity with p-version elements. The {lambda} elements do not require a precise knowledge of the extent of singular zone, i.e., their use may be extended beyond the singular zone. When {lambda} elements are used at the singularity, a singular problem behaves like a smooth problem thereby eliminating the need for h, p-adaptive processes all together.more » One dimensional steady state radial flow of an upper convected Maxwell fluid is considered as a sample problem. Least squares approach (or least squares finite element formulation: LSFEF) is used to construct the integral form (error functional I) from the differential equations. Numerical results presented for radially inward flow with inner radius r{sub i} = 0.1, 0.01, 0.001, 0.0001, 0.00001, and Deborah number of 2 (De = 2) demonstrate the accuracy, faster convergence of the iterative solution procedure, faster convergence rate of the error functional and mesh independent characteristics of the {lambda} elements regardless of the severity of the singularity.« less

Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays.

PubMed

Rakkiyappan, R; Sakthivel, N; Cao, Jinde

2015-06-01

This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-data controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen's inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen's inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-data controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods. Copyright © 2015 Elsevier Ltd. All rights reserved.

Nonlinear dynamic systems identification using recurrent interval type-2 TSK fuzzy neural network - A novel structure.

PubMed

El-Nagar, Ahmad M

2018-01-01

In this study, a novel structure of a recurrent interval type-2 Takagi-Sugeno-Kang (TSK) fuzzy neural network (FNN) is introduced for nonlinear dynamic and time-varying systems identification. It combines the type-2 fuzzy sets (T2FSs) and a recurrent FNN to avoid the data uncertainties. The fuzzy firing strengths in the proposed structure are returned to the network input as internal variables. The interval type-2 fuzzy sets (IT2FSs) is used to describe the antecedent part for each rule while the consequent part is a TSK-type, which is a linear function of the internal variables and the external inputs with interval weights. All the type-2 fuzzy rules for the proposed RIT2TSKFNN are learned on-line based on structure and parameter learning, which are performed using the type-2 fuzzy clustering. The antecedent and consequent parameters of the proposed RIT2TSKFNN are updated based on the Lyapunov function to achieve network stability. The obtained results indicate that our proposed network has a small root mean square error (RMSE) and a small integral of square error (ISE) with a small number of rules and a small computation time compared with other type-2 FNNs. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

SU-G-BRB-03: Assessing the Sensitivity and False Positive Rate of the Integrated Quality Monitor (IQM) Large Area Ion Chamber to MLC Positioning Errors

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

Boehnke, E McKenzie; DeMarco, J; Steers, J

2016-06-15

Purpose: To examine both the IQM’s sensitivity and false positive rate to varying MLC errors. By balancing these two characteristics, an optimal tolerance value can be derived. Methods: An un-modified SBRT Liver IMRT plan containing 7 fields was randomly selected as a representative clinical case. The active MLC positions for all fields were perturbed randomly from a square distribution of varying width (±1mm to ±5mm). These unmodified and modified plans were measured multiple times each by the IQM (a large area ion chamber mounted to a TrueBeam linac head). Measurements were analyzed relative to the initial, unmodified measurement. IQM readingsmore » are analyzed as a function of control points. In order to examine sensitivity to errors along a field’s delivery, each measured field was divided into 5 groups of control points, and the maximum error in each group was recorded. Since the plans have known errors, we compared how well the IQM is able to differentiate between unmodified and error plans. ROC curves and logistic regression were used to analyze this, independent of thresholds. Results: A likelihood-ratio Chi-square test showed that the IQM could significantly predict whether a plan had MLC errors, with the exception of the beginning and ending control points. Upon further examination, we determined there was ramp-up occurring at the beginning of delivery. Once the linac AFC was tuned, the subsequent measurements (relative to a new baseline) showed significant (p <0.005) abilities to predict MLC errors. Using the area under the curve, we show the IQM’s ability to detect errors increases with increasing MLC error (Spearman’s Rho=0.8056, p<0.0001). The optimal IQM count thresholds from the ROC curves are ±3%, ±2%, and ±7% for the beginning, middle 3, and end segments, respectively. Conclusion: The IQM has proven to be able to detect not only MLC errors, but also differences in beam tuning (ramp-up). Partially supported by the Susan Scott Foundation.« less

Estimation of correlation functions by stochastic approximation.

NASA Technical Reports Server (NTRS)

Habibi, A.; Wintz, P. A.

1972-01-01

Consideration of the autocorrelation function of a zero-mean stationary random process. The techniques are applicable to processes with nonzero mean provided the mean is estimated first and subtracted. Two recursive techniques are proposed, both of which are based on the method of stochastic approximation and assume a functional form for the correlation function that depends on a number of parameters that are recursively estimated from successive records. One technique uses a standard point estimator of the correlation function to provide estimates of the parameters that minimize the mean-square error between the point estimates and the parametric function. The other technique provides estimates of the parameters that maximize a likelihood function relating the parameters of the function to the random process. Examples are presented.

Least-squares model-based halftoning

NASA Astrophysics Data System (ADS)

Pappas, Thrasyvoulos N.; Neuhoff, David L.

1992-08-01

A least-squares model-based approach to digital halftoning is proposed. It exploits both a printer model and a model for visual perception. It attempts to produce an 'optimal' halftoned reproduction, by minimizing the squared error between the response of the cascade of the printer and visual models to the binary image and the response of the visual model to the original gray-scale image. Conventional methods, such as clustered ordered dither, use the properties of the eye only implicitly, and resist printer distortions at the expense of spatial and gray-scale resolution. In previous work we showed that our printer model can be used to modify error diffusion to account for printer distortions. The modified error diffusion algorithm has better spatial and gray-scale resolution than conventional techniques, but produces some well known artifacts and asymmetries because it does not make use of an explicit eye model. Least-squares model-based halftoning uses explicit eye models and relies on printer models that predict distortions and exploit them to increase, rather than decrease, both spatial and gray-scale resolution. We have shown that the one-dimensional least-squares problem, in which each row or column of the image is halftoned independently, can be implemented with the Viterbi's algorithm. Unfortunately, no closed form solution can be found in two dimensions. The two-dimensional least squares solution is obtained by iterative techniques. Experiments show that least-squares model-based halftoning produces more gray levels and better spatial resolution than conventional techniques. We also show that the least- squares approach eliminates the problems associated with error diffusion. Model-based halftoning can be especially useful in transmission of high quality documents using high fidelity gray-scale image encoders. As we have shown, in such cases halftoning can be performed at the receiver, just before printing. Apart from coding efficiency, this approach permits the halftoner to be tuned to the individual printer, whose characteristics may vary considerably from those of other printers, for example, write-black vs. write-white laser printers.

Does the sensorimotor system minimize prediction error or select the most likely prediction during object lifting?

PubMed Central

McGregor, Heather R.; Pun, Henry C. H.; Buckingham, Gavin; Gribble, Paul L.

2016-01-01

The human sensorimotor system is routinely capable of making accurate predictions about an object's weight, which allows for energetically efficient lifts and prevents objects from being dropped. Often, however, poor predictions arise when the weight of an object can vary and sensory cues about object weight are sparse (e.g., picking up an opaque water bottle). The question arises, what strategies does the sensorimotor system use to make weight predictions when one is dealing with an object whose weight may vary? For example, does the sensorimotor system use a strategy that minimizes prediction error (minimal squared error) or one that selects the weight that is most likely to be correct (maximum a posteriori)? In this study we dissociated the predictions of these two strategies by having participants lift an object whose weight varied according to a skewed probability distribution. We found, using a small range of weight uncertainty, that four indexes of sensorimotor prediction (grip force rate, grip force, load force rate, and load force) were consistent with a feedforward strategy that minimizes the square of prediction errors. These findings match research in the visuomotor system, suggesting parallels in underlying processes. We interpret our findings within a Bayesian framework and discuss the potential benefits of using a minimal squared error strategy. NEW & NOTEWORTHY Using a novel experimental model of object lifting, we tested whether the sensorimotor system models the weight of objects by minimizing lifting errors or by selecting the statistically most likely weight. We found that the sensorimotor system minimizes the square of prediction errors for object lifting. This parallels the results of studies that investigated visually guided reaching, suggesting an overlap in the underlying mechanisms between tasks that involve different sensory systems. PMID:27760821

The influence of the uplink noise on the performance of satellite data transmission systems

NASA Astrophysics Data System (ADS)

Dewal, Vrinda P.

The problem of transmission of binary phase shift keying (BPSK) modulated digital data through a bandlimited nonlinear satellite channel in the presence of uplink, downlink Gaussian noise and intersymbol interface is examined. The satellite transponder is represented by a zero memory bandpass nonlinearity, with AM/AM conversion. The proposed optimum linear receiver structure consists of tapped-delay lines followed by a decision device. The linear receiver is designed to minimize the mean square error that is a function of the intersymbol interface, the uplink and the downlink noise. The minimum mean square error equalizer (MMSE) is derived using the Wiener-Kolmogorov theory. In this receiver, the decision about the transmitted signal is made by taking into account the received sequence of present sample, and the interfering past and future samples, which represent the intersymbol interference (ISI). Illustrative examples of the receiver structures are considered for the nonlinear channels with a symmetrical and asymmetrical frequency responses of the transmitter filter. The transponder nonlinearity is simulated by a polynomial using only the first and the third orders terms. A computer simulation determines the tap gain coefficients of the MMSE equalizer that adapt to the various uplink and downlink noise levels. The performance of the MMSE equalizer is evaluated in terms of an estimate of the average probability of error.

Prediction of pH of cola beverage using Vis/NIR spectroscopy and least squares-support vector machine

NASA Astrophysics Data System (ADS)

Liu, Fei; He, Yong

2008-02-01

Visible and near infrared (Vis/NIR) transmission spectroscopy and chemometric methods were utilized to predict the pH values of cola beverages. Five varieties of cola were prepared and 225 samples (45 samples for each variety) were selected for the calibration set, while 75 samples (15 samples for each variety) for the validation set. The smoothing way of Savitzky-Golay and standard normal variate (SNV) followed by first-derivative were used as the pre-processing methods. Partial least squares (PLS) analysis was employed to extract the principal components (PCs) which were used as the inputs of least squares-support vector machine (LS-SVM) model according to their accumulative reliabilities. Then LS-SVM with radial basis function (RBF) kernel function and a two-step grid search technique were applied to build the regression model with a comparison of PLS regression. The correlation coefficient (r), root mean square error of prediction (RMSEP) and bias were 0.961, 0.040 and 0.012 for PLS, while 0.975, 0.031 and 4.697x10 -3 for LS-SVM, respectively. Both methods obtained a satisfying precision. The results indicated that Vis/NIR spectroscopy combined with chemometric methods could be applied as an alternative way for the prediction of pH of cola beverages.

Variable forgetting factor mechanisms for diffusion recursive least squares algorithm in sensor networks

NASA Astrophysics Data System (ADS)

Zhang, Ling; Cai, Yunlong; Li, Chunguang; de Lamare, Rodrigo C.

2017-12-01

In this work, we present low-complexity variable forgetting factor (VFF) techniques for diffusion recursive least squares (DRLS) algorithms. Particularly, we propose low-complexity VFF-DRLS algorithms for distributed parameter and spectrum estimation in sensor networks. For the proposed algorithms, they can adjust the forgetting factor automatically according to the posteriori error signal. We develop detailed analyses in terms of mean and mean square performance for the proposed algorithms and derive mathematical expressions for the mean square deviation (MSD) and the excess mean square error (EMSE). The simulation results show that the proposed low-complexity VFF-DRLS algorithms achieve superior performance to the existing DRLS algorithm with fixed forgetting factor when applied to scenarios of distributed parameter and spectrum estimation. Besides, the simulation results also demonstrate a good match for our proposed analytical expressions.

Doppler-shift estimation of flat underwater channel using data-aided least-square approach

NASA Astrophysics Data System (ADS)

Pan, Weiqiang; Liu, Ping; Chen, Fangjiong; Ji, Fei; Feng, Jing

2015-06-01

In this paper we proposed a dada-aided Doppler estimation method for underwater acoustic communication. The training sequence is non-dedicate, hence it can be designed for Doppler estimation as well as channel equalization. We assume the channel has been equalized and consider only flat-fading channel. First, based on the training symbols the theoretical received sequence is composed. Next the least square principle is applied to build the objective function, which minimizes the error between the composed and the actual received signal. Then an iterative approach is applied to solve the least square problem. The proposed approach involves an outer loop and inner loop, which resolve the channel gain and Doppler coefficient, respectively. The theoretical performance bound, i.e. the Cramer-Rao Lower Bound (CRLB) of estimation is also derived. Computer simulations results show that the proposed algorithm achieves the CRLB in medium to high SNR cases.

Multivariable frequency domain identification via 2-norm minimization

NASA Technical Reports Server (NTRS)

Bayard, David S.

1992-01-01

The author develops a computational approach to multivariable frequency domain identification, based on 2-norm minimization. In particular, a Gauss-Newton (GN) iteration is developed to minimize the 2-norm of the error between frequency domain data and a matrix fraction transfer function estimate. To improve the global performance of the optimization algorithm, the GN iteration is initialized using the solution to a particular sequentially reweighted least squares problem, denoted as the SK iteration. The least squares problems which arise from both the SK and GN iterations are shown to involve sparse matrices with identical block structure. A sparse matrix QR factorization method is developed to exploit the special block structure, and to efficiently compute the least squares solution. A numerical example involving the identification of a multiple-input multiple-output (MIMO) plant having 286 unknown parameters is given to illustrate the effectiveness of the algorithm.

Enhancing Least-Squares Finite Element Methods Through a Quantity-of-Interest

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

Chaudhry, Jehanzeb Hameed; Cyr, Eric C.; Liu, Kuo

2014-12-18

Here, we introduce an approach that augments least-squares finite element formulations with user-specified quantities-of-interest. The method incorporates the quantity-of-interest into the least-squares functional and inherits the global approximation properties of the standard formulation as well as increased resolution of the quantity-of-interest. We establish theoretical properties such as optimality and enhanced convergence under a set of general assumptions. Central to the approach is that it offers an element-level estimate of the error in the quantity-of-interest. As a result, we introduce an adaptive approach that yields efficient, adaptively refined approximations. Several numerical experiments for a range of situations are presented to supportmore » the theory and highlight the effectiveness of our methodology. Notably, the results show that the new approach is effective at improving the accuracy per total computational cost.« less

Costas loop lock detection in the advanced receiver

NASA Technical Reports Server (NTRS)

Mileant, A.; Hinedi, S.

1989-01-01

The advanced receiver currently being developed uses a Costas digital loop to demodulate the subcarrier. Previous analyses of lock detector algorithms for Costas loops have ignored the effects of the inherent correlation between the samples of the phase-error process. Accounting for this correlation is necessary to achieve the desired lock-detection probability for a given false-alarm rate. Both analysis and simulations are used to quantify the effects of phase correlation on lock detection for the square-law and the absolute-value type detectors. Results are obtained which depict the lock-detection probability as a function of loop signal-to-noise ratio for a given false-alarm rate. The mathematical model and computer simulation show that the square-law detector experiences less degradation due to phase jitter than the absolute-value detector and that the degradation in detector signal-to-noise ratio is more pronounced for square-wave than for sine-wave signals.

Predicting cognitive function from clinical measures of physical function and health status in older adults.

PubMed

Bolandzadeh, Niousha; Kording, Konrad; Salowitz, Nicole; Davis, Jennifer C; Hsu, Liang; Chan, Alison; Sharma, Devika; Blohm, Gunnar; Liu-Ambrose, Teresa

2015-01-01

Current research suggests that the neuropathology of dementia-including brain changes leading to memory impairment and cognitive decline-is evident years before the onset of this disease. Older adults with cognitive decline have reduced functional independence and quality of life, and are at greater risk for developing dementia. Therefore, identifying biomarkers that can be easily assessed within the clinical setting and predict cognitive decline is important. Early recognition of cognitive decline could promote timely implementation of preventive strategies. We included 89 community-dwelling adults aged 70 years and older in our study, and collected 32 measures of physical function, health status and cognitive function at baseline. We utilized an L1-L2 regularized regression model (elastic net) to identify which of the 32 baseline measures were strongly predictive of cognitive function after one year. We built three linear regression models: 1) based on baseline cognitive function, 2) based on variables consistently selected in every cross-validation loop, and 3) a full model based on all the 32 variables. Each of these models was carefully tested with nested cross-validation. Our model with the six variables consistently selected in every cross-validation loop had a mean squared prediction error of 7.47. This number was smaller than that of the full model (115.33) and the model with baseline cognitive function (7.98). Our model explained 47% of the variance in cognitive function after one year. We built a parsimonious model based on a selected set of six physical function and health status measures strongly predictive of cognitive function after one year. In addition to reducing the complexity of the model without changing the model significantly, our model with the top variables improved the mean prediction error and R-squared. These six physical function and health status measures can be easily implemented in a clinical setting.

Application of Rapid Visco Analyser (RVA) viscograms and chemometrics for maize hardness characterisation.

PubMed

Guelpa, Anina; Bevilacqua, Marta; Marini, Federico; O'Kennedy, Kim; Geladi, Paul; Manley, Marena

2015-04-15

It has been established in this study that the Rapid Visco Analyser (RVA) can describe maize hardness, irrespective of the RVA profile, when used in association with appropriate multivariate data analysis techniques. Therefore, the RVA can complement or replace current and/or conventional methods as a hardness descriptor. Hardness modelling based on RVA viscograms was carried out using seven conventional hardness methods (hectoliter mass (HLM), hundred kernel mass (HKM), particle size index (PSI), percentage vitreous endosperm (%VE), protein content, percentage chop (%chop) and near infrared (NIR) spectroscopy) as references and three different RVA profiles (hard, soft and standard) as predictors. An approach using locally weighted partial least squares (LW-PLS) was followed to build the regression models. The resulted prediction errors (root mean square error of cross-validation (RMSECV) and root mean square error of prediction (RMSEP)) for the quantification of hardness values were always lower or in the same order of the laboratory error of the reference method. Copyright © 2014 Elsevier Ltd. All rights reserved.

The Relationship between Mean Square Differences and Standard Error of Measurement: Comment on Barchard (2012)

ERIC Educational Resources Information Center

Pan, Tianshu; Yin, Yue

2012-01-01

In the discussion of mean square difference (MSD) and standard error of measurement (SEM), Barchard (2012) concluded that the MSD between 2 sets of test scores is greater than 2(SEM)[superscript 2] and SEM underestimates the score difference between 2 tests when the 2 tests are not parallel. This conclusion has limitations for 2 reasons. First,…

Quantified Choice of Root-Mean-Square Errors of Approximation for Evaluation and Power Analysis of Small Differences between Structural Equation Models

ERIC Educational Resources Information Center

Li, Libo; Bentler, Peter M.

2011-01-01

MacCallum, Browne, and Cai (2006) proposed a new framework for evaluation and power analysis of small differences between nested structural equation models (SEMs). In their framework, the null and alternative hypotheses for testing a small difference in fit and its related power analyses were defined by some chosen root-mean-square error of…

Analysis of surface-water data network in Kansas for effectiveness in providing regional streamflow information; with a section on theory and application of generalized least squares

USGS Publications Warehouse

Medina, K.D.; Tasker, Gary D.

1987-01-01

This report documents the results of an analysis of the surface-water data network in Kansas for its effectiveness in providing regional streamflow information. The network was analyzed using generalized least squares regression. The correlation and time-sampling error of the streamflow characteristic are considered in the generalized least squares method. Unregulated medium-, low-, and high-flow characteristics were selected to be representative of the regional information that can be obtained from streamflow-gaging-station records for use in evaluating the effectiveness of continuing the present network stations, discontinuing some stations, and (or) adding new stations. The analysis used streamflow records for all currently operated stations that were not affected by regulation and for discontinued stations for which unregulated flow characteristics, as well as physical and climatic characteristics, were available. The State was divided into three network areas, western, northeastern, and southeastern Kansas, and analysis was made for the three streamflow characteristics in each area, using three planning horizons. The analysis showed that the maximum reduction of sampling mean-square error for each cost level could be obtained by adding new stations and discontinuing some current network stations. Large reductions in sampling mean-square error for low-flow information could be achieved in all three network areas, the reduction in western Kansas being the most dramatic. The addition of new stations would be most beneficial for mean-flow information in western Kansas. The reduction of sampling mean-square error for high-flow information would benefit most from the addition of new stations in western Kansas. Southeastern Kansas showed the smallest error reduction in high-flow information. A comparison among all three network areas indicated that funding resources could be most effectively used by discontinuing more stations in northeastern and southeastern Kansas and establishing more new stations in western Kansas.

An Application of Interactive Computer Graphics to the Study of Inferential Statistics and the General Linear Model

DTIC Science & Technology

1991-09-01

matrix, the Regression Sum of Squares (SSR) and Error Sum of Squares (SSE) are also displayed as a percentage of the Total Sum of Squares ( SSTO ...vector when the student compares the SSR to the SSE. In addition to the plot, the actual values of SSR, SSE, and SSTO are also provided. Figure 3 gives the...Es ainSpace = E 3 Error- Eor Space =n t! L . Pro~cio q Yonto Pro~rct on of Y onto the simaton, pac ror Space SSR SSEL0.20 IV = 14,1 +IErrorI 2 SSTO

An improved algorithm for the determination of the system paramters of a visual binary by least squares

NASA Astrophysics Data System (ADS)

Xu, Yu-Lin

The problem of computing the orbit of a visual binary from a set of observed positions is reconsidered. It is a least squares adjustment problem, if the observational errors follow a bias-free multivariate Gaussian distribution and the covariance matrix of the observations is assumed to be known. The condition equations are constructed to satisfy both the conic section equation and the area theorem, which are nonlinear in both the observations and the adjustment parameters. The traditional least squares algorithm, which employs condition equations that are solved with respect to the uncorrelated observations and either linear in the adjustment parameters or linearized by developing them in Taylor series by first-order approximation, is inadequate in our orbit problem. D.C. Brown proposed an algorithm solving a more general least squares adjustment problem in which the scalar residual function, however, is still constructed by first-order approximation. Not long ago, a completely general solution was published by W.H Jefferys, who proposed a rigorous adjustment algorithm for models in which the observations appear nonlinearly in the condition equations and may be correlated, and in which construction of the normal equations and the residual function involves no approximation. This method was successfully applied in our problem. The normal equations were first solved by Newton's scheme. Practical examples show that this converges fast if the observational errors are sufficiently small and the initial approximate solution is sufficiently accurate, and that it fails otherwise. Newton's method was modified to yield a definitive solution in the case the normal approach fails, by combination with the method of steepest descent and other sophisticated algorithms. Practical examples show that the modified Newton scheme can always lead to a final solution. The weighting of observations, the orthogonal parameters and the efficiency of a set of adjustment parameters are also considered. The definition of efficiency is revised.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Effect of Numerical Error on Gravity Field Estimation for GRACE and Future Gravity Missions

NASA Astrophysics Data System (ADS)

McCullough, Christopher; Bettadpur, Srinivas

2015-04-01

In recent decades, gravity field determination from low Earth orbiting satellites, such as the Gravity Recovery and Climate Experiment (GRACE), has become increasingly more effective due to the incorporation of high accuracy measurement devices. Since instrumentation quality will only increase in the near future and the gravity field determination process is computationally and numerically intensive, numerical error from the use of double precision arithmetic will eventually become a prominent error source. While using double-extended or quadruple precision arithmetic will reduce these errors, the numerical limitations of current orbit determination algorithms and processes must be accurately identified and quantified in order to adequately inform the science data processing techniques of future gravity missions. The most obvious numerical limitation in the orbit determination process is evident in the comparison of measured observables with computed values, derived from mathematical models relating the satellites' numerically integrated state to the observable. Significant error in the computed trajectory will corrupt this comparison and induce error in the least squares solution of the gravitational field. In addition, errors in the numerically computed trajectory propagate into the evaluation of the mathematical measurement model's partial derivatives. These errors amalgamate in turn with numerical error from the computation of the state transition matrix, computed using the variational equations of motion, in the least squares mapping matrix. Finally, the solution of the linearized least squares system, computed using a QR factorization, is also susceptible to numerical error. Certain interesting combinations of each of these numerical errors are examined in the framework of GRACE gravity field determination to analyze and quantify their effects on gravity field recovery.

Accurate phase extraction algorithm based on Gram–Schmidt orthonormalization and least square ellipse fitting method

NASA Astrophysics Data System (ADS)

Lei, Hebing; Yao, Yong; Liu, Haopeng; Tian, Yiting; Yang, Yanfu; Gu, Yinglong

2018-06-01

An accurate algorithm by combing Gram-Schmidt orthonormalization and least square ellipse fitting technology is proposed, which could be used for phase extraction from two or three interferograms. The DC term of background intensity is suppressed by subtraction operation on three interferograms or by high-pass filter on two interferograms. Performing Gram-Schmidt orthonormalization on pre-processing interferograms, the phase shift error is corrected and a general ellipse form is derived. Then the background intensity error and the corrected error could be compensated by least square ellipse fitting method. Finally, the phase could be extracted rapidly. The algorithm could cope with the two or three interferograms with environmental disturbance, low fringe number or small phase shifts. The accuracy and effectiveness of the proposed algorithm are verified by both of the numerical simulations and experiments.

Geomagnetic matching navigation algorithm based on robust estimation

NASA Astrophysics Data System (ADS)

Xie, Weinan; Huang, Liping; Qu, Zhenshen; Wang, Zhenhuan

2017-08-01

The outliers in the geomagnetic survey data seriously affect the precision of the geomagnetic matching navigation and badly disrupt its reliability. A novel algorithm which can eliminate the outliers influence is investigated in this paper. First, the weight function is designed and its principle of the robust estimation is introduced. By combining the relation equation between the matching trajectory and the reference trajectory with the Taylor series expansion for geomagnetic information, a mathematical expression of the longitude, latitude and heading errors is acquired. The robust target function is obtained by the weight function and the mathematical expression. Then the geomagnetic matching problem is converted to the solutions of nonlinear equations. Finally, Newton iteration is applied to implement the novel algorithm. Simulation results show that the matching error of the novel algorithm is decreased to 7.75% compared to the conventional mean square difference (MSD) algorithm, and is decreased to 18.39% to the conventional iterative contour matching algorithm when the outlier is 40nT. Meanwhile, the position error of the novel algorithm is 0.017° while the other two algorithms fail to match when the outlier is 400nT.

Parameter Estimation for Thurstone Choice Models

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

Vojnovic, Milan; Yun, Seyoung

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

Resistive sensitivity functions for van der Pauw astroid and rounded crosses and cloverleafs

NASA Astrophysics Data System (ADS)

Koon, Daniel; Hansen, Ole

2014-03-01

We have calculated the sensitivity of van der Pauw resistances to local resistive variations for circular, square and astroid discs of infinitesimal thickness, as well as for the families of rounded crosses and cloverleafs, as a function of specimen parameters, using the direct formulas of our recent paper (Koon et al. 2013 J. Appl. Phys.114 163710) applied to ``reciprocally dual geometries'' (swapped Dirichlet and Neumann boundary conditions) described by Mareš et al.(2012 Meas. Sci. Technol. 23 045004). These results show that (a) the product of any such sensitivity function times differential area, and thus (b) the ratio of any two sensitivities, is invariant under conformal mapping, allowing for the pointwise determination of the conformal mapping function. The family of rounded crosses, which is bounded in parameter space by the square, the astroid and an ``infinitesimally thin'' cross, seems to represent the best geometry for focusing transport measurements on the center of the specimen while minimizing errors due to edge- or contact-effects. Made possible by an SLU Faculty research grant.

A new art code for tomographic interferometry

NASA Technical Reports Server (NTRS)

Tan, H.; Modarress, D.

1987-01-01

A new algebraic reconstruction technique (ART) code based on the iterative refinement method of least squares solution for tomographic reconstruction is presented. Accuracy and the convergence of the technique is evaluated through the application of numerically generated interferometric data. It was found that, in general, the accuracy of the results was superior to other reported techniques. The iterative method unconditionally converged to a solution for which the residual was minimum. The effects of increased data were studied. The inversion error was found to be a function of the input data error only. The convergence rate, on the other hand, was affected by all three parameters. Finally, the technique was applied to experimental data, and the results are reported.

Optimal design of minimum mean-square error noise reduction algorithms using the simulated annealing technique.

PubMed

Bai, Mingsian R; Hsieh, Ping-Ju; Hur, Kur-Nan

2009-02-01

The performance of the minimum mean-square error noise reduction (MMSE-NR) algorithm in conjunction with time-recursive averaging (TRA) for noise estimation is found to be very sensitive to the choice of two recursion parameters. To address this problem in a more systematic manner, this paper proposes an optimization method to efficiently search the optimal parameters of the MMSE-TRA-NR algorithms. The objective function is based on a regression model, whereas the optimization process is carried out with the simulated annealing algorithm that is well suited for problems with many local optima. Another NR algorithm proposed in the paper employs linear prediction coding as a preprocessor for extracting the correlated portion of human speech. Objective and subjective tests were undertaken to compare the optimized MMSE-TRA-NR algorithm with several conventional NR algorithms. The results of subjective tests were processed by using analysis of variance to justify the statistic significance. A post hoc test, Tukey's Honestly Significant Difference, was conducted to further assess the pairwise difference between the NR algorithms.

Three-dimensional relationship between high-order root-mean-square wavefront error, pupil diameter, and aging

PubMed Central

Applegate, Raymond A.; Donnelly, William J.; Marsack, Jason D.; Koenig, Darren E.; Pesudovs, Konrad

2007-01-01

We report root-mean-square (RMS) wavefront error (WFE) for individual aberrations and cumulative high-order (HO) RMS WFE for the normal human eye as a function of age by decade and pupil diameter in 1 mm steps from 3 to 7 mm and determine the relationship among HO RMS WFE, mean age for each decade of life, and luminance for physiologic pupil diameters. Subjects included 146 healthy individuals from 20 to 80 years of age. Ocular aberration was measured on the preferred eye of each subject (for a total of 146 eyes through dilated pupils; computed for 3, 4, 5, 6, and 7 mm pupils; and described with a tenth-radial-order normalized Zernike expansion. We found that HO RMS WFE increases faster with increasing pupil diameter for any given age and pupil diameter than it does with increasing age alone. A planar function accounts for 99% of the variance in the 3-D space defined by mean log HO RMS WFE, mean age for each decade of life, and pupil diameter. When physiologic pupil diameters are used to estimate HO RMS WFE as a function of luminance and age, at low luminance (9 cd/m2) HO RMS WFE decreases with increasing age. This normative data set details (1) the 3-D relationship between HO RMS WFE and age for fixed pupil diameters and (2) the 3-D relationship among HO RMS WFE, age, and luminance for physiologic pupil diameters. PMID:17301847

A Nonlinear Least Squares Approach to Time of Death Estimation Via Body Cooling.

PubMed

Rodrigo, Marianito R

2016-01-01

The problem of time of death (TOD) estimation by body cooling is revisited by proposing a nonlinear least squares approach that takes as input a series of temperature readings only. Using a reformulation of the Marshall-Hoare double exponential formula and a technique for reducing the dimension of the state space, an error function that depends on the two cooling rates is constructed, with the aim of minimizing this function. Standard nonlinear optimization methods that are used to minimize the bivariate error function require an initial guess for these unknown rates. Hence, a systematic procedure based on the given temperature data is also proposed to determine an initial estimate for the rates. Then, an explicit formula for the TOD is given. Results of numerical simulations using both theoretical and experimental data are presented, both yielding reasonable estimates. The proposed procedure does not require knowledge of the temperature at death nor the body mass. In fact, the method allows the estimation of the temperature at death once the cooling rates and the TOD have been calculated. The procedure requires at least three temperature readings, although more measured readings could improve the estimates. With the aid of computerized recording and thermocouple detectors, temperature readings spaced 10-15 min apart, for example, can be taken. The formulas can be straightforwardly programmed and installed on a hand-held device for field use. © 2015 American Academy of Forensic Sciences.

Some Integrated Squared Error Procedures for Multivariate Normal Data,

DTIC Science & Technology

1986-01-01

a lnear regresmion or experimental design model). Our procedures have &lSO been usned wcelyOn non -linear models but we do not addres nan-lnear...of fit, outliers, influence functions, experimental design , cluster analysis, robustness 24L A =TO ACT (VCefme - pvre alli of magsy MW identif by...structured data such as multivariate experimental designs . Several illustrations are provided. * 0 %41 %-. 4.’. * " , -.--, ,. -,, ., -, ’v ’ , " ,,- ,, . -,-. . ., * . - tAma- t

Global Methods for Image Motion Analysis

DTIC Science & Technology

1992-10-01

a variant of the same error function as in Adiv [2]. Another related approach was presented by Maybank [46,45]. Nearly all researchers in motion...with an application to stereo vision. In Proc. 7th Intern. Joint Conference on AI, pages 674{679, Vancouver, 1981. [45] S. J. Maybank . Algorithm for...analysing optical ow based on the least-squares method. Image and Vision Computing, 4:38{42, 1986. [46] S. J. Maybank . A Theoretical Study of Optical

Intrinsic Raman spectroscopy for quantitative biological spectroscopy Part II

PubMed Central

Bechtel, Kate L.; Shih, Wei-Chuan; Feld, Michael S.

2009-01-01

We demonstrate the effectiveness of intrinsic Raman spectroscopy (IRS) at reducing errors caused by absorption and scattering. Physical tissue models, solutions of varying absorption and scattering coefficients with known concentrations of Raman scatterers, are studied. We show significant improvement in prediction error by implementing IRS to predict concentrations of Raman scatterers using both ordinary least squares regression (OLS) and partial least squares regression (PLS). In particular, we show that IRS provides a robust calibration model that does not increase in error when applied to samples with optical properties outside the range of calibration. PMID:18711512

mBEEF-vdW: Robust fitting of error estimation density functionals

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

Lundgaard, Keld T.; Wellendorff, Jess; Voss, Johannes

Here, we propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator overmore » the training datasets. Using this estimator, we show that the robust loss function leads to a 10% improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.« less

mBEEF-vdW: Robust fitting of error estimation density functionals

DOE PAGES

Lundgaard, Keld T.; Wellendorff, Jess; Voss, Johannes; ...

2016-06-15

Here, we propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator overmore » the training datasets. Using this estimator, we show that the robust loss function leads to a 10% improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.« less

A component prediction method for flue gas of natural gas combustion based on nonlinear partial least squares method.

PubMed

Cao, Hui; Yan, Xingyu; Li, Yaojiang; Wang, Yanxia; Zhou, Yan; Yang, Sanchun

2014-01-01

Quantitative analysis for the flue gas of natural gas-fired generator is significant for energy conservation and emission reduction. The traditional partial least squares method may not deal with the nonlinear problems effectively. In the paper, a nonlinear partial least squares method with extended input based on radial basis function neural network (RBFNN) is used for components prediction of flue gas. For the proposed method, the original independent input matrix is the input of RBFNN and the outputs of hidden layer nodes of RBFNN are the extension term of the original independent input matrix. Then, the partial least squares regression is performed on the extended input matrix and the output matrix to establish the components prediction model of flue gas. A near-infrared spectral dataset of flue gas of natural gas combustion is used for estimating the effectiveness of the proposed method compared with PLS. The experiments results show that the root-mean-square errors of prediction values of the proposed method for methane, carbon monoxide, and carbon dioxide are, respectively, reduced by 4.74%, 21.76%, and 5.32% compared to those of PLS. Hence, the proposed method has higher predictive capabilities and better robustness.

Applicability of AgMERRA Forcing Dataset to Fill Gaps in Historical in-situ Meteorological Data

NASA Astrophysics Data System (ADS)

Bannayan, M.; Lashkari, A.; Zare, H.; Asadi, S.; Salehnia, N.

2015-12-01

Integrated assessment studies of food production systems use crop models to simulate the effects of climate and socio-economic changes on food security. Climate forcing data is one of those key inputs of crop models. This study evaluated the performance of AgMERRA climate forcing dataset to fill gaps in historical in-situ meteorological data for different climatic regions of Iran. AgMERRA dataset intercompared with in- situ observational dataset for daily maximum and minimum temperature and precipitation during 1980-2010 periods via Root Mean Square error (RMSE), Mean Absolute Error (MAE) and Mean Bias Error (MBE) for 17 stations in four climatic regions included humid and moderate, cold, dry and arid, hot and humid. Moreover, probability distribution function and cumulative distribution function compared between model and observed data. The results of measures of agreement between AgMERRA data and observed data demonstrated that there are small errors in model data for all stations. Except for stations which are located in cold regions, model data in the other stations illustrated under-prediction for daily maximum temperature and precipitation. However, it was not significant. In addition, probability distribution function and cumulative distribution function showed the same trend for all stations between model and observed data. Therefore, the reliability of AgMERRA dataset is high to fill gaps in historical observations in different climatic regions of Iran as well as it could be applied as a basis for future climate scenarios.

Error Analyses of the North Alabama Lightning Mapping Array (LMA)

NASA Technical Reports Server (NTRS)

Koshak, W. J.; Solokiewicz, R. J.; Blakeslee, R. J.; Goodman, S. J.; Christian, H. J.; Hall, J. M.; Bailey, J. C.; Krider, E. P.; Bateman, M. G.; Boccippio, D. J.

2003-01-01

Two approaches are used to characterize how accurately the North Alabama Lightning Mapping Array (LMA) is able to locate lightning VHF sources in space and in time. The first method uses a Monte Carlo computer simulation to estimate source retrieval errors. The simulation applies a VHF source retrieval algorithm that was recently developed at the NASA-MSFC and that is similar, but not identical to, the standard New Mexico Tech retrieval algorithm. The second method uses a purely theoretical technique (i.e., chi-squared Curvature Matrix theory) to estimate retrieval errors. Both methods assume that the LMA system has an overall rms timing error of 50ns, but all other possible errors (e.g., multiple sources per retrieval attempt) are neglected. The detailed spatial distributions of retrieval errors are provided. Given that the two methods are completely independent of one another, it is shown that they provide remarkably similar results, except that the chi-squared theory produces larger altitude error estimates than the (more realistic) Monte Carlo simulation.

Estimating riparian understory vegetation cover with beta regression and copula models

USGS Publications Warehouse

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

2011-01-01

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

Development of a transformation model to derive general population-based utility: Mapping the pruritus-visual analog scale (VAS) to the EQ-5D utility.

PubMed

Park, Sun-Young; Park, Eun-Ja; Suh, Hae Sun; Ha, Dongmun; Lee, Eui-Kyung

2017-08-01

Although nonpreference-based disease-specific measures are widely used in clinical studies, they cannot generate utilities for economic evaluation. A solution to this problem is to estimate utilities from disease-specific instruments using the mapping function. This study aimed to develop a transformation model for mapping the pruritus-visual analog scale (VAS) to the EuroQol 5-Dimension 3-Level (EQ-5D-3L) utility index in pruritus. A cross-sectional survey was conducted with a sample (n = 268) drawn from the general population of South Korea. Data were randomly divided into 2 groups, one for estimating and the other for validating mapping models. To select the best model, we developed and compared 3 separate models using demographic information and the pruritus-VAS as independent variables. The predictive performance was assessed using the mean absolute deviation and root mean square error in a separate dataset. Among the 3 models, model 2 using age, age squared, sex, and the pruritus-VAS as independent variables had the best performance based on the goodness of fit and model simplicity, with a log likelihood of 187.13. The 3 models had similar precision errors based on mean absolute deviation and root mean square error in the validation dataset. No statistically significant difference was observed between the mean observed and predicted values in all models. In conclusion, model 2 was chosen as the preferred mapping model. Outcomes measured as the pruritus-VAS can be transformed into the EQ-5D-3L utility index using this mapping model, which makes an economic evaluation possible when only pruritus-VAS data are available. © 2017 John Wiley & Sons, Ltd.

Robust Nonrigid Multimodal Image Registration using Local Frequency Maps*

PubMed Central

Jian, Bing; Vemuri, Baba C.; Marroquin, José L.

2008-01-01

Automatic multi-modal image registration is central to numerous tasks in medical imaging today and has a vast range of applications e.g., image guidance, atlas construction, etc. In this paper, we present a novel multi-modal 3D non-rigid registration algorithm where in 3D images to be registered are represented by their corresponding local frequency maps efficiently computed using the Riesz transform as opposed to the popularly used Gabor filters. The non-rigid registration between these local frequency maps is formulated in a statistically robust framework involving the minimization of the integral squared error a.k.a. L2E (L2 error). This error is expressed as the squared difference between the true density of the residual (which is the squared difference between the non-rigidly transformed reference and the target local frequency representations) and a Gaussian or mixture of Gaussians density approximation of the same. The non-rigid transformation is expressed in a B-spline basis to achieve the desired smoothness in the transformation as well as computational efficiency. The key contributions of this work are (i) the use of Riesz transform to achieve better efficiency in computing the local frequency representation in comparison to Gabor filter-based approaches, (ii) new mathematical model for local-frequency based non-rigid registration, (iii) analytic computation of the gradient of the robust non-rigid registration cost function to achieve efficient and accurate registration. The proposed non-rigid L2E-based registration is a significant extension of research reported in literature to date. We present experimental results for registering several real data sets with synthetic and real non-rigid misalignments. PMID:17354721

Robust signal recovery using the prolate spherical wave functions and maximum correntropy criterion

NASA Astrophysics Data System (ADS)

Zou, Cuiming; Kou, Kit Ian

2018-05-01

Signal recovery is one of the most important problem in signal processing. This paper proposes a novel signal recovery method based on prolate spherical wave functions (PSWFs). PSWFs are a kind of special functions, which have been proved having good performance in signal recovery. However, the existing PSWFs based recovery methods used the mean square error (MSE) criterion, which depends on the Gaussianity assumption of the noise distributions. For the non-Gaussian noises, such as impulsive noise or outliers, the MSE criterion is sensitive, which may lead to large reconstruction error. Unlike the existing PSWFs based recovery methods, our proposed PSWFs based recovery method employs the maximum correntropy criterion (MCC), which is independent of the noise distribution. The proposed method can reduce the impact of the large and non-Gaussian noises. The experimental results on synthetic signals with various types of noises show that the proposed MCC based signal recovery method has better robust property against various noises compared to other existing methods.

Error Estimation of An Ensemble Statistical Seasonal Precipitation Prediction Model

NASA Technical Reports Server (NTRS)

Shen, Samuel S. P.; Lau, William K. M.; Kim, Kyu-Myong; Li, Gui-Long

2001-01-01

This NASA Technical Memorandum describes an optimal ensemble canonical correlation forecasting model for seasonal precipitation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. Since new CCA scheme is derived for continuous fields of predictor and predictand, an area-factor is automatically included. Thus our model is an improvement of the spectral CCA scheme of Barnett and Preisendorfer. The improvements include (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States (US) precipitation field. The predictor is the sea surface temperature (SST). The US Climate Prediction Center's reconstructed SST is used as the predictor's historical data. The US National Center for Environmental Prediction's optimally interpolated precipitation (1951-2000) is used as the predictand's historical data. Our forecast experiments show that the new ensemble canonical correlation scheme renders a reasonable forecasting skill. For example, when using September-October-November SST to predict the next season December-January-February precipitation, the spatial pattern correlation between the observed and predicted are positive in 46 years among the 50 years of experiments. The positive correlations are close to or greater than 0.4 in 29 years, which indicates excellent performance of the forecasting model. The forecasting skill can be further enhanced when several predictors are used.

Improved modification for the density-functional theory calculation of thermodynamic properties for C-H-O composite compounds.

PubMed

Liu, Min Hsien; Chen, Cheng; Hong, Yaw Shun

2005-02-08

A three-parametric modification equation and the least-squares approach are adopted to calibrating hybrid density-functional theory energies of C(1)-C(10) straight-chain aldehydes, alcohols, and alkoxides to accurate enthalpies of formation DeltaH(f) and Gibbs free energies of formation DeltaG(f), respectively. All calculated energies of the C-H-O composite compounds were obtained based on B3LYP6-311++G(3df,2pd) single-point energies and the related thermal corrections of B3LYP6-31G(d,p) optimized geometries. This investigation revealed that all compounds had 0.05% average absolute relative error (ARE) for the atomization energies, with mean value of absolute error (MAE) of just 2.1 kJ/mol (0.5 kcal/mol) for the DeltaH(f) and 2.4 kJ/mol (0.6 kcal/mol) for the DeltaG(f) of formation.

Optical phase-locked loop (OPLL) for free-space laser communications with heterodyne detection

NASA Technical Reports Server (NTRS)

Win, Moe Z.; Chen, Chien-Chung; Scholtz, Robert A.

1991-01-01

Several advantages of coherent free-space optical communications are outlined. Theoretical analysis is formulated for an OPLL disturbed by shot noise, modulation noise, and frequency noise consisting of a white component, a 1/f component, and a 1/f-squared component. Each of the noise components is characterized by its associated power spectral density. It is shown that the effect of modulation depends only on the ratio of loop bandwidth and data rate, and is negligible for an OPLL with loop bandwidth smaller than one fourth the data rate. Total phase error variance as a function of loop bandwidth is displayed for several values of carrier signal to noise ratio. Optimal loop bandwidth is also calculated as a function of carrier signal to noise ratio. An OPLL experiment is performed, where it is shown that the measured phase error variance closely matches the theoretical predictions.

Numerical Analysis of Modeling Based on Improved Elman Neural Network

PubMed Central

Jie, Shao

2014-01-01

A modeling based on the improved Elman neural network (IENN) is proposed to analyze the nonlinear circuits with the memory effect. The hidden layer neurons are activated by a group of Chebyshev orthogonal basis functions instead of sigmoid functions in this model. The error curves of the sum of squared error (SSE) varying with the number of hidden neurons and the iteration step are studied to determine the number of the hidden layer neurons. Simulation results of the half-bridge class-D power amplifier (CDPA) with two-tone signal and broadband signals as input have shown that the proposed behavioral modeling can reconstruct the system of CDPAs accurately and depict the memory effect of CDPAs well. Compared with Volterra-Laguerre (VL) model, Chebyshev neural network (CNN) model, and basic Elman neural network (BENN) model, the proposed model has better performance. PMID:25054172

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

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

Mu, Lin; Wang, Junping; Ye, Xiu

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-08-17

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Error analysis for reducing noisy wide-gap concentric cylinder rheometric data for nonlinear fluids - Theory and applications

NASA Technical Reports Server (NTRS)

Borgia, Andrea; Spera, Frank J.

1990-01-01

This work discusses the propagation of errors for the recovery of the shear rate from wide-gap concentric cylinder viscometric measurements of non-Newtonian fluids. A least-square regression of stress on angular velocity data to a system of arbitrary functions is used to propagate the errors for the series solution to the viscometric flow developed by Krieger and Elrod (1953) and Pawlowski (1953) ('power-law' approximation) and for the first term of the series developed by Krieger (1968). A numerical experiment shows that, for measurements affected by significant errors, the first term of the Krieger-Elrod-Pawlowski series ('infinite radius' approximation) and the power-law approximation may recover the shear rate with equal accuracy as the full Krieger-Elrod-Pawlowski solution. An experiment on a clay slurry indicates that the clay has a larger yield stress at rest than during shearing, and that, for the range of shear rates investigated, a four-parameter constitutive equation approximates reasonably well its rheology. The error analysis presented is useful for studying the rheology of fluids such as particle suspensions, slurries, foams, and magma.

Reconstruction of regional mean temperature for East Asia since 1900s and its uncertainties

NASA Astrophysics Data System (ADS)

Hua, W.

2017-12-01

Regional average surface air temperature (SAT) is one of the key variables often used to investigate climate change. Unfortunately, because of the limited observations over East Asia, there were also some gaps in the observation data sampling for regional mean SAT analysis, which was important to estimate past climate change. In this study, the regional average temperature of East Asia since 1900s is calculated by the Empirical Orthogonal Function (EOF)-based optimal interpolation (OA) method with considering the data errors. The results show that our estimate is more precise and robust than the results from simple average, which provides a better way for past climate reconstruction. In addition to the reconstructed regional average SAT anomaly time series, we also estimated uncertainties of reconstruction. The root mean square error (RMSE) results show that the the error decreases with respect to time, and are not sufficiently large to alter the conclusions on the persist warming in East Asia during twenty-first century. Moreover, the test of influence of data error on reconstruction clearly shows the sensitivity of reconstruction to the size of the data error.

DFT-based method for more accurate adsorption energies: An adaptive sum of energies from RPBE and vdW density functionals

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

Hensley, Alyssa J. R.; Ghale, Kushal; Rieg, Carolin

In recent years, the popularity of density functional theory with periodic boundary conditions (DFT) has surged for the design and optimization of functional materials. However, no single DFT exchange–correlation functional currently available gives accurate adsorption energies on transition metals both when bonding to the surface is dominated by strong covalent or ionic bonding and when it has strong contributions from van der Waals interactions (i.e., dispersion forces). Here we present a new, simple method for accurately predicting adsorption energies on transition-metal surfaces based on DFT calculations, using an adaptively weighted sum of energies from RPBE and optB86b-vdW (or optB88-vdW) densitymore » functionals. This method has been benchmarked against a set of 39 reliable experimental energies for adsorption reactions. Our results show that this method has a mean absolute error and root mean squared error relative to experiments of 13.4 and 19.3 kJ/mol, respectively, compared to 20.4 and 26.4 kJ/mol for the BEEF-vdW functional. For systems with large van der Waals contributions, this method decreases these errors to 11.6 and 17.5 kJ/mol. Furthermore, this method provides predictions of adsorption energies both for processes dominated by strong covalent or ionic bonding and for those dominated by dispersion forces that are more accurate than those of any current standard DFT functional alone.« less

DFT-based method for more accurate adsorption energies: An adaptive sum of energies from RPBE and vdW density functionals

DOE PAGES

Hensley, Alyssa J. R.; Ghale, Kushal; Rieg, Carolin; ...

2017-01-26

In recent years, the popularity of density functional theory with periodic boundary conditions (DFT) has surged for the design and optimization of functional materials. However, no single DFT exchange–correlation functional currently available gives accurate adsorption energies on transition metals both when bonding to the surface is dominated by strong covalent or ionic bonding and when it has strong contributions from van der Waals interactions (i.e., dispersion forces). Here we present a new, simple method for accurately predicting adsorption energies on transition-metal surfaces based on DFT calculations, using an adaptively weighted sum of energies from RPBE and optB86b-vdW (or optB88-vdW) densitymore » functionals. This method has been benchmarked against a set of 39 reliable experimental energies for adsorption reactions. Our results show that this method has a mean absolute error and root mean squared error relative to experiments of 13.4 and 19.3 kJ/mol, respectively, compared to 20.4 and 26.4 kJ/mol for the BEEF-vdW functional. For systems with large van der Waals contributions, this method decreases these errors to 11.6 and 17.5 kJ/mol. Furthermore, this method provides predictions of adsorption energies both for processes dominated by strong covalent or ionic bonding and for those dominated by dispersion forces that are more accurate than those of any current standard DFT functional alone.« less

The determination of gravity anomalies from geoid heights using the inverse Stokes' formula, Fourier transforms, and least squares collocation

NASA Technical Reports Server (NTRS)

Rummel, R.; Sjoeberg, L.; Rapp, R. H.

1978-01-01

A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.

Transfer-function-parameter estimation from frequency response data: A FORTRAN program

NASA Technical Reports Server (NTRS)

Seidel, R. C.

1975-01-01

A FORTRAN computer program designed to fit a linear transfer function model to given frequency response magnitude and phase data is presented. A conjugate gradient search is used that minimizes the integral of the absolute value of the error squared between the model and the data. The search is constrained to insure model stability. A scaling of the model parameters by their own magnitude aids search convergence. Efficient computer algorithms result in a small and fast program suitable for a minicomputer. A sample problem with different model structures and parameter estimates is reported.

Analysis of Point Based Image Registration Errors With Applications in Single Molecule Microscopy

PubMed Central

Cohen, E. A. K.; Ober, R. J.

2014-01-01

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data. PMID:24634573

Tourism forecasting using modified empirical mode decomposition and group method of data handling

NASA Astrophysics Data System (ADS)

Yahya, N. A.; Samsudin, R.; Shabri, A.

2017-09-01

In this study, a hybrid model using modified Empirical Mode Decomposition (EMD) and Group Method of Data Handling (GMDH) model is proposed for tourism forecasting. This approach reconstructs intrinsic mode functions (IMFs) produced by EMD using trial and error method. The new component and the remaining IMFs is then predicted respectively using GMDH model. Finally, the forecasted results for each component are aggregated to construct an ensemble forecast. The data used in this experiment are monthly time series data of tourist arrivals from China, Thailand and India to Malaysia from year 2000 to 2016. The performance of the model is evaluated using Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) where conventional GMDH model and EMD-GMDH model are used as benchmark models. Empirical results proved that the proposed model performed better forecasts than the benchmarked models.

A two dimensional interface element for coupling of independently modeled three dimensional finite element meshes and extensions to dynamic and non-linear regimes

NASA Technical Reports Server (NTRS)

Aminpour, Mohammad

1995-01-01

The work reported here pertains only to the first year of research for a three year proposal period. As a prelude to this two dimensional interface element, the one dimensional element was tested and errors were discovered in the code for built-up structures and curved interfaces. These errors were corrected and the benchmark Boeing composite crown panel was analyzed successfully. A study of various splines led to the conclusion that cubic B-splines best suit this interface element application. A least squares approach combined with cubic B-splines was constructed to make a smooth function from the noisy data obtained with random error in the coordinate data points of the Boeing crown panel analysis. Preliminary investigations for the formulation of discontinuous 2-D shell and 3-D solid elements were conducted.

Predicting the random drift of MEMS gyroscope based on K-means clustering and OLS RBF Neural Network

NASA Astrophysics Data System (ADS)

Wang, Zhen-yu; Zhang, Li-jie

2017-10-01

Measure error of the sensor can be effectively compensated with prediction. Aiming at large random drift error of MEMS(Micro Electro Mechanical System))gyroscope, an improved learning algorithm of Radial Basis Function(RBF) Neural Network(NN) based on K-means clustering and Orthogonal Least-Squares (OLS) is proposed in this paper. The algorithm selects the typical samples as the initial cluster centers of RBF NN firstly, candidates centers with K-means algorithm secondly, and optimizes the candidate centers with OLS algorithm thirdly, which makes the network structure simpler and makes the prediction performance better. Experimental results show that the proposed K-means clustering OLS learning algorithm can predict the random drift of MEMS gyroscope effectively, the prediction error of which is 9.8019e-007°/s and the prediction time of which is 2.4169e-006s

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

PubMed

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

2015-12-18

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

Energy Performance Measurement and Simulation Modeling of Tactical Soft-Wall Shelters

DTIC Science & Technology

2015-07-01

was too low to measure was on the order of 5 hours. Because the research team did not have access to the site between 1700 and 0500 hours the...Basic for Applications ( VBA ). The objective function was the root mean square (RMS) errors between modeled and measured heating load and the modeled...References Phase Change Energy Solutions. (2013). BioPCM web page, http://phasechange.com/index.php/en/about/our-material. Accessed 16 September

Training the Recurrent neural network by the Fuzzy Min-Max algorithm for fault prediction

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

Zemouri, Ryad; Racoceanu, Daniel; Zerhouni, Noureddine

2009-03-05

In this paper, we present a training technique of a Recurrent Radial Basis Function neural network for fault prediction. We use the Fuzzy Min-Max technique to initialize the k-center of the RRBF neural network. The k-means algorithm is then applied to calculate the centers that minimize the mean square error of the prediction task. The performances of the k-means algorithm are then boosted by the Fuzzy Min-Max technique.

A novel method for improving the accuracy of coordinate transformation in multiple measurement systems

NASA Astrophysics Data System (ADS)

Liu, W. L.; Li, Y. W.

2017-09-01

Large-scale dimensional metrology usually requires a combination of multiple measurement systems, such as laser tracking, total station, laser scanning, coordinate measuring arm and video photogrammetry, etc. Often, the results from different measurement systems must be combined to provide useful results. The coordinate transformation is used to unify coordinate frames in combination; however, coordinate transformation uncertainties directly affect the accuracy of the final measurement results. In this paper, a novel method is proposed for improving the accuracy of coordinate transformation, combining the advantages of the best-fit least-square and radial basis function (RBF) neural networks. First of all, the configuration of coordinate transformation is introduced and a transformation matrix containing seven variables is obtained. Second, the 3D uncertainty of the transformation model and the residual error variable vector are established based on the best-fit least-square. Finally, in order to optimize the uncertainty of the developed seven-variable transformation model, we used the RBF neural network to identify the uncertainty of the dynamic, and unstructured, owing to its great ability to approximate any nonlinear function to the designed accuracy. Intensive experimental studies were conducted to check the validity of the theoretical results. The results show that the mean error of coordinate transformation decreased from 0.078 mm to 0.054 mm after using this method in contrast with the GUM method.

Fundamental Flux Equations for Fracture-Matrix Interactions with Linear Diffusion

NASA Astrophysics Data System (ADS)

Oldenburg, C. M.; Zhou, Q.; Rutqvist, J.; Birkholzer, J. T.

2017-12-01

The conventional dual-continuum models are only applicable for late-time behavior of pressure propagation in fractured rock, while discrete-fracture-network models may explicitly deal with matrix blocks at high computational expense. To address these issues, we developed a unified-form diffusive flux equation for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular matrix blocks (squares, cubes, rectangles, and rectangular parallelepipeds) by partitioning the entire dimensionless-time domain (Zhou et al., 2017a, b). For each matrix block, this flux equation consists of the early-time solution up until a switch-over time after which the late-time solution is applied to create continuity from early to late time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the coefficients dependent on dimensionless area-to-volume ratio and aspect ratios for rectangular blocks. For the late-time solutions, one exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic blocks. The time-partitioning method was also used for calculating pressure/concentration/temperature distribution within a matrix block. The approximate solution contains an error-function solution for early times and an exponential solution for late times, with relative errors less than 0.003. These solutions form the kernel of multirate and multidimensional hydraulic, solute and thermal diffusion in fractured reservoirs.

Power of tests for comparing trend curves with application to national immunization survey (NIS).

PubMed

Zhao, Zhen

2011-02-28

To develop statistical tests for comparing trend curves of study outcomes between two socio-demographic strata across consecutive time points, and compare statistical power of the proposed tests under different trend curves data, three statistical tests were proposed. For large sample size with independent normal assumption among strata and across consecutive time points, the Z and Chi-square test statistics were developed, which are functions of outcome estimates and the standard errors at each of the study time points for the two strata. For small sample size with independent normal assumption, the F-test statistic was generated, which is a function of sample size of the two strata and estimated parameters across study period. If two trend curves are approximately parallel, the power of Z-test is consistently higher than that of both Chi-square and F-test. If two trend curves cross at low interaction, the power of Z-test is higher than or equal to the power of both Chi-square and F-test; however, at high interaction, the powers of Chi-square and F-test are higher than that of Z-test. The measurement of interaction of two trend curves was defined. These tests were applied to the comparison of trend curves of vaccination coverage estimates of standard vaccine series with National Immunization Survey (NIS) 2000-2007 data. Copyright © 2011 John Wiley & Sons, Ltd.

Benchmark fragment-based 1H, 13C, 15N and 17O chemical shift predictions in molecular crystals†

PubMed Central

Hartman, Joshua D.; Kudla, Ryan A.; Day, Graeme M.; Mueller, Leonard J.; Beran, Gregory J. O.

2016-01-01

The performance of fragment-based ab initio 1H, 13C, 15N and 17O chemical shift predictions is assessed against experimental NMR chemical shift data in four benchmark sets of molecular crystals. Employing a variety of commonly used density functionals (PBE0, B3LYP, TPSSh, OPBE, PBE, TPSS), we explore the relative performance of cluster, two-body fragment, and combined cluster/fragment models. The hybrid density functionals (PBE0, B3LYP and TPSSh) generally out-perform their generalized gradient approximation (GGA)-based counterparts. 1H, 13C, 15N, and 17O isotropic chemical shifts can be predicted with root-mean-square errors of 0.3, 1.5, 4.2, and 9.8 ppm, respectively, using a computationally inexpensive electrostatically embedded two-body PBE0 fragment model. Oxygen chemical shieldings prove particularly sensitive to local many-body effects, and using a combined cluster/fragment model instead of the simple two-body fragment model decreases the root-mean-square errors to 7.6 ppm. These fragment-based model errors compare favorably with GIPAW PBE ones of 0.4, 2.2, 5.4, and 7.2 ppm for the same 1H, 13C, 15N, and 17O test sets. Using these benchmark calculations, a set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided and their robustness assessed using statistical cross-validation. We demonstrate the utility of these approaches and the reported scaling parameters on applications to 9-tertbutyl anthracene, several histidine co-crystals, benzoic acid and the C-nitrosoarene SnCl2(CH3)2(NODMA)2. PMID:27431490

Benchmark fragment-based (1)H, (13)C, (15)N and (17)O chemical shift predictions in molecular crystals.

PubMed

Hartman, Joshua D; Kudla, Ryan A; Day, Graeme M; Mueller, Leonard J; Beran, Gregory J O

2016-08-21

The performance of fragment-based ab initio(1)H, (13)C, (15)N and (17)O chemical shift predictions is assessed against experimental NMR chemical shift data in four benchmark sets of molecular crystals. Employing a variety of commonly used density functionals (PBE0, B3LYP, TPSSh, OPBE, PBE, TPSS), we explore the relative performance of cluster, two-body fragment, and combined cluster/fragment models. The hybrid density functionals (PBE0, B3LYP and TPSSh) generally out-perform their generalized gradient approximation (GGA)-based counterparts. (1)H, (13)C, (15)N, and (17)O isotropic chemical shifts can be predicted with root-mean-square errors of 0.3, 1.5, 4.2, and 9.8 ppm, respectively, using a computationally inexpensive electrostatically embedded two-body PBE0 fragment model. Oxygen chemical shieldings prove particularly sensitive to local many-body effects, and using a combined cluster/fragment model instead of the simple two-body fragment model decreases the root-mean-square errors to 7.6 ppm. These fragment-based model errors compare favorably with GIPAW PBE ones of 0.4, 2.2, 5.4, and 7.2 ppm for the same (1)H, (13)C, (15)N, and (17)O test sets. Using these benchmark calculations, a set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided and their robustness assessed using statistical cross-validation. We demonstrate the utility of these approaches and the reported scaling parameters on applications to 9-tert-butyl anthracene, several histidine co-crystals, benzoic acid and the C-nitrosoarene SnCl2(CH3)2(NODMA)2.

Most suitable mother wavelet for the analysis of fractal properties of stride interval time series via the average wavelet coefficient

PubMed Central

Zhang, Zhenwei; VanSwearingen, Jessie; Brach, Jennifer S.; Perera, Subashan

2016-01-01

Human gait is a complex interaction of many nonlinear systems and stride intervals exhibit self-similarity over long time scales that can be modeled as a fractal process. The scaling exponent represents the fractal degree and can be interpreted as a biomarker of relative diseases. The previous study showed that the average wavelet method provides the most accurate results to estimate this scaling exponent when applied to stride interval time series. The purpose of this paper is to determine the most suitable mother wavelet for the average wavelet method. This paper presents a comparative numerical analysis of sixteen mother wavelets using simulated and real fractal signals. Simulated fractal signals were generated under varying signal lengths and scaling exponents that indicate a range of physiologically conceivable fractal signals. The five candidates were chosen due to their good performance on the mean square error test for both short and long signals. Next, we comparatively analyzed these five mother wavelets for physiologically relevant stride time series lengths. Our analysis showed that the symlet 2 mother wavelet provides a low mean square error and low variance for long time intervals and relatively low errors for short signal lengths. It can be considered as the most suitable mother function without the burden of considering the signal length. PMID:27960102

Using Redundancy To Reduce Errors in Magnetometer Readings

NASA Technical Reports Server (NTRS)

Kulikov, Igor; Zak, Michail

2004-01-01

A method of reducing errors in noisy magnetic-field measurements involves exploitation of redundancy in the readings of multiple magnetometers in a cluster. By "redundancy"is meant that the readings are not entirely independent of each other because the relationships among the magnetic-field components that one seeks to measure are governed by the fundamental laws of electromagnetism as expressed by Maxwell's equations. Assuming that the magnetometers are located outside a magnetic material, that the magnetic field is steady or quasi-steady, and that there are no electric currents flowing in or near the magnetometers, the applicable Maxwell 's equations are delta x B = 0 and delta(raised dot) B = 0, where B is the magnetic-flux-density vector. By suitable algebraic manipulation, these equations can be shown to impose three independent constraints on the values of the components of B at the various magnetometer positions. In general, the problem of reducing the errors in noisy measurements is one of finding a set of corrected values that minimize an error function. In the present method, the error function is formulated as (1) the sum of squares of the differences between the corrected and noisy measurement values plus (2) a sum of three terms, each comprising the product of a Lagrange multiplier and one of the three constraints. The partial derivatives of the error function with respect to the corrected magnetic-field component values and the Lagrange multipliers are set equal to zero, leading to a set of equations that can be put into matrix.vector form. The matrix can be inverted to solve for a vector that comprises the corrected magnetic-field component values and the Lagrange multipliers.

Calibration of a texture-based model of a ground-water flow system, western San Joaquin Valley, California

USGS Publications Warehouse

Phillips, Steven P.; Belitz, Kenneth

1991-01-01

The occurrence of selenium in agricultural drain water from the western San Joaquin Valley, California, has focused concern on the semiconfined ground-water flow system, which is underlain by the Corcoran Clay Member of the Tulare Formation. A two-step procedure is used to calibrate a preliminary model of the system for the purpose of determining the steady-state hydraulic properties. Horizontal and vertical hydraulic conductivities are modeled as functions of the percentage of coarse sediment, hydraulic conductivities of coarse-textured (Kcoarse) and fine-textured (Kfine) end members, and averaging methods used to calculate equivalent hydraulic conductivities. The vertical conductivity of the Corcoran (Kcorc) is an additional parameter to be evaluated. In the first step of the calibration procedure, the model is run by systematically varying the following variables: (1) Kcoarse/Kfine, (2) Kcoarse/Kcorc, and (3) choice of averaging methods in the horizontal and vertical directions. Root mean square error and bias values calculated from the model results are functions of these variables. These measures of error provide a means for evaluating model sensitivity and for selecting values of Kcoarse, Kfine, and Kcorc for use in the second step of the calibration procedure. In the second step, recharge rates are evaluated as functions of Kcoarse, Kcorc, and a combination of averaging methods. The associated Kfine values are selected so that the root mean square error is minimized on the basis of the results from the first step. The results of the two-step procedure indicate that the spatial distribution of hydraulic conductivity that best produces the measured hydraulic head distribution is created through the use of arithmetic averaging in the horizontal direction and either geometric or harmonic averaging in the vertical direction. The equivalent hydraulic conductivities resulting from either combination of averaging methods compare favorably to field- and laboratory-based values.

Credit Risk Evaluation Using a C-Variable Least Squares Support Vector Classification Model

NASA Astrophysics Data System (ADS)

Yu, Lean; Wang, Shouyang; Lai, K. K.

Credit risk evaluation is one of the most important issues in financial risk management. In this paper, a C-variable least squares support vector classification (C-VLSSVC) model is proposed for credit risk analysis. The main idea of this model is based on the prior knowledge that different classes may have different importance for modeling and more weights should be given to those classes with more importance. The C-VLSSVC model can be constructed by a simple modification of the regularization parameter in LSSVC, whereby more weights are given to the lease squares classification errors with important classes than the lease squares classification errors with unimportant classes while keeping the regularized terms in its original form. For illustration purpose, a real-world credit dataset is used to test the effectiveness of the C-VLSSVC model.

Error analysis on squareness of multi-sensor integrated CMM for the multistep registration method

NASA Astrophysics Data System (ADS)

Zhao, Yan; Wang, Yiwen; Ye, Xiuling; Wang, Zhong; Fu, Luhua

2018-01-01

The multistep registration(MSR) method in [1] is to register two different classes of sensors deployed on z-arm of CMM(coordinate measuring machine): a video camera and a tactile probe sensor. In general, it is difficult to obtain a very precise registration result with a single common standard, instead, this method is achieved by measuring two different standards with a constant distance between them two which are fixed on a steel plate. Although many factors have been considered such as the measuring ability of sensors, the uncertainty of the machine and the number of data pairs, there is no exact analysis on the squareness between the x-axis and the y-axis on the xy plane. For this sake, error analysis on the squareness of multi-sensor integrated CMM for the multistep registration method will be made to examine the validation of the MSR method. Synthetic experiments on the squareness on the xy plane for the simplified MSR with an inclination rotation are simulated, which will lead to a regular result. Experiments have been carried out with the multi-standard device designed also in [1], meanwhile, inspections with the help of a laser interferometer on the xy plane have been carried out. The final results are conformed to the simulations, and the squareness errors of the MSR method are also similar to the results of interferometer. In other word, the MSR can also adopted/utilized to verify the squareness of a CMM.

Random errors in interferometry with the least-squares method

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

Wang Qi

2011-01-20

This investigation analyzes random errors in interferometric surface profilers using the least-squares method when random noises are present. Two types of random noise are considered here: intensity noise and position noise. Two formulas have been derived for estimating the standard deviations of the surface height measurements: one is for estimating the standard deviation when only intensity noise is present, and the other is for estimating the standard deviation when only position noise is present. Measurements on simulated noisy interferometric data have been performed, and standard deviations of the simulated measurements have been compared with those theoretically derived. The relationships havemore » also been discussed between random error and the wavelength of the light source and between random error and the amplitude of the interference fringe.« less

Attenuation of the Squared Canonical Correlation Coefficient under Varying Estimates of Score Reliability

ERIC Educational Resources Information Center

Wilson, Celia M.

2010-01-01

Research pertaining to the distortion of the squared canonical correlation coefficient has traditionally been limited to the effects of sampling error and associated correction formulas. The purpose of this study was to compare the degree of attenuation of the squared canonical correlation coefficient under varying conditions of score reliability.…

Rotation Matrix Method Based on Ambiguity Function for GNSS Attitude Determination.

PubMed

Yang, Yingdong; Mao, Xuchu; Tian, Weifeng

2016-06-08

Global navigation satellite systems (GNSS) are well suited for attitude determination. In this study, we use the rotation matrix method to resolve the attitude angle. This method achieves better performance in reducing computational complexity and selecting satellites. The condition of the baseline length is combined with the ambiguity function method (AFM) to search for integer ambiguity, and it is validated in reducing the span of candidates. The noise error is always the key factor to the success rate. It is closely related to the satellite geometry model. In contrast to the AFM, the LAMBDA (Least-squares AMBiguity Decorrelation Adjustment) method gets better results in solving the relationship of the geometric model and the noise error. Although the AFM is more flexible, it is lack of analysis on this aspect. In this study, the influence of the satellite geometry model on the success rate is analyzed in detail. The computation error and the noise error are effectively treated. Not only is the flexibility of the AFM inherited, but the success rate is also increased. An experiment is conducted in a selected campus, and the performance is proved to be effective. Our results are based on simulated and real-time GNSS data and are applied on single-frequency processing, which is known as one of the challenging case of GNSS attitude determination.

Heuristic-driven graph wavelet modeling of complex terrain

NASA Astrophysics Data System (ADS)

Cioacǎ, Teodor; Dumitrescu, Bogdan; Stupariu, Mihai-Sorin; Pǎtru-Stupariu, Ileana; Nǎpǎrus, Magdalena; Stoicescu, Ioana; Peringer, Alexander; Buttler, Alexandre; Golay, François

2015-03-01

We present a novel method for building a multi-resolution representation of large digital surface models. The surface points coincide with the nodes of a planar graph which can be processed using a critically sampled, invertible lifting scheme. To drive the lazy wavelet node partitioning, we employ an attribute aware cost function based on the generalized quadric error metric. The resulting algorithm can be applied to multivariate data by storing additional attributes at the graph's nodes. We discuss how the cost computation mechanism can be coupled with the lifting scheme and examine the results by evaluating the root mean square error. The algorithm is experimentally tested using two multivariate LiDAR sets representing terrain surface and vegetation structure with different sampling densities.

Generalized regression neural network (GRNN)-based approach for colored dissolved organic matter (CDOM) retrieval: case study of Connecticut River at Middle Haddam Station, USA.

PubMed

Heddam, Salim

2014-11-01

The prediction of colored dissolved organic matter (CDOM) using artificial neural network approaches has received little attention in the past few decades. In this study, colored dissolved organic matter (CDOM) was modeled using generalized regression neural network (GRNN) and multiple linear regression (MLR) models as a function of Water temperature (TE), pH, specific conductance (SC), and turbidity (TU). Evaluation of the prediction accuracy of the models is based on the root mean square error (RMSE), mean absolute error (MAE), coefficient of correlation (CC), and Willmott's index of agreement (d). The results indicated that GRNN can be applied successfully for prediction of colored dissolved organic matter (CDOM).

Accuracy of measurement of star images on a pixel array

NASA Technical Reports Server (NTRS)

King, I. R.

1983-01-01

Algorithms are developed for predicting the accuracy with which the brightness of a star can be determined from its image on a digital detector array, as a function of the brightness of the background. The assumption is made that a known profile is being fitted by least squares. The two profiles used correspond to ST images and to ground-based observations. The first result is an approximate rule of thumb for equivalent noise area. More rigorous results are then given in tabular form. The size of the pixels, relative to the image size, is taken into account. Astronometric accuracy is also discussed briefly; the error, relative to image size, is very similar to the photometric error relative to brightness.

An adaptive learning control system for large flexible structures

NASA Technical Reports Server (NTRS)

Thau, F. E.

1985-01-01

The objective of the research has been to study the design of adaptive/learning control systems for the control of large flexible structures. In the first activity an adaptive/learning control methodology for flexible space structures was investigated. The approach was based on using a modal model of the flexible structure dynamics and an output-error identification scheme to identify modal parameters. In the second activity, a least-squares identification scheme was proposed for estimating both modal parameters and modal-to-actuator and modal-to-sensor shape functions. The technique was applied to experimental data obtained from the NASA Langley beam experiment. In the third activity, a separable nonlinear least-squares approach was developed for estimating the number of excited modes, shape functions, modal parameters, and modal amplitude and velocity time functions for a flexible structure. In the final research activity, a dual-adaptive control strategy was developed for regulating the modal dynamics and identifying modal parameters of a flexible structure. A min-max approach was used for finding an input to provide modal parameter identification while not exceeding reasonable bounds on modal displacement.

Modular design and implementation of field-programmable-gate-array-based Gaussian noise generator

NASA Astrophysics Data System (ADS)

Li, Yuan-Ping; Lee, Ta-Sung; Hwang, Jeng-Kuang

2016-05-01

The modular design of a Gaussian noise generator (GNG) based on field-programmable gate array (FPGA) technology was studied. A new range reduction architecture was included in a series of elementary function evaluation modules and was integrated into the GNG system. The approximation and quantisation errors for the square root module with a first polynomial approximation were high; therefore, we used the central limit theorem (CLT) to improve the noise quality. This resulted in an output rate of one sample per clock cycle. We subsequently applied Newton's method for the square root module, thus eliminating the need for the use of the CLT because applying the CLT resulted in an output rate of two samples per clock cycle (>200 million samples per second). Two statistical tests confirmed that our GNG is of high quality. Furthermore, the range reduction, which is used to solve a limited interval of the function approximation algorithms of the System Generator platform using Xilinx FPGAs, appeared to have a higher numerical accuracy, was operated at >350 MHz, and can be suitably applied for any function evaluation.

Analysis of surface-water data network in Kansas for effectiveness in providing regional streamflow information

USGS Publications Warehouse

Medina, K.D.; Tasker, Gary D.

1985-01-01

The surface water data network in Kansas was analyzed using generalized least squares regression for its effectiveness in providing regional streamflow information. The correlation and time-sampling error of the streamflow characteristic are considered in the generalized least squares method. Unregulated medium-flow, low-flow and high-flow characteristics were selected to be representative of the regional information that can be obtained from streamflow gaging station records for use in evaluating the effectiveness of continuing the present network stations, discontinuing some stations; and/or adding new stations. The analysis used streamflow records for all currently operated stations that were not affected by regulation and discontinued stations for which unregulated flow characteristics , as well as physical and climatic characteristics, were available. The state was divided into three network areas, western, northeastern, and southeastern Kansas, and analysis was made for three streamflow characteristics in each area, using three planning horizons. The analysis showed that the maximum reduction of sampling mean square error for each cost level could be obtained by adding new stations and discontinuing some of the present network stations. Large reductions in sampling mean square error for low-flow information could be accomplished in all three network areas, with western Kansas having the most dramatic reduction. The addition of new stations would be most beneficial for man- flow information in western Kansas, and to lesser degrees in the other two areas. The reduction of sampling mean square error for high-flow information would benefit most from the addition of new stations in western Kansas, and the effect diminishes to lesser degrees in the other two areas. Southeastern Kansas showed the smallest error reduction in high-flow information. A comparison among all three network areas indicated that funding resources could be most effectively used by discontinuing more stations in northeastern and southeastern Kansas and establishing more new stations in western Kansas. (Author 's abstract)

Analytical study of the effects of soft tissue artefacts on functional techniques to define axes of rotation.

PubMed

De Rosario, Helios; Page, Álvaro; Besa, Antonio

2017-09-06

The accurate location of the main axes of rotation (AoR) is a crucial step in many applications of human movement analysis. There are different formal methods to determine the direction and position of the AoR, whose performance varies across studies, depending on the pose and the source of errors. Most methods are based on minimizing squared differences between observed and modelled marker positions or rigid motion parameters, implicitly assuming independent and uncorrelated errors, but the largest error usually results from soft tissue artefacts (STA), which do not have such statistical properties and are not effectively cancelled out by such methods. However, with adequate methods it is possible to assume that STA only account for a small fraction of the observed motion and to obtain explicit formulas through differential analysis that relate STA components to the resulting errors in AoR parameters. In this paper such formulas are derived for three different functional calibration techniques (Geometric Fitting, mean Finite Helical Axis, and SARA), to explain why each technique behaves differently from the others, and to propose strategies to compensate for those errors. These techniques were tested with published data from a sit-to-stand activity, where the true axis was defined using bi-planar fluoroscopy. All the methods were able to estimate the direction of the AoR with an error of less than 5°, whereas there were errors in the location of the axis of 30-40mm. Such location errors could be reduced to less than 17mm by the methods based on equations that use rigid motion parameters (mean Finite Helical Axis, SARA) when the translation component was calculated using the three markers nearest to the axis. Copyright © 2017 Elsevier Ltd. All rights reserved.

mBEEF-vdW: Robust fitting of error estimation density functionals

NASA Astrophysics Data System (ADS)

Lundgaard, Keld T.; Wellendorff, Jess; Voss, Johannes; Jacobsen, Karsten W.; Bligaard, Thomas

2016-06-01

We propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework [J. Wellendorff et al., Phys. Rev. B 85, 235149 (2012), 10.1103/PhysRevB.85.235149; J. Wellendorff et al., J. Chem. Phys. 140, 144107 (2014), 10.1063/1.4870397]. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator over the training datasets. Using this estimator, we show that the robust loss function leads to a 10 % improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.

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

Morley, Steven

The PyForecastTools package provides Python routines for calculating metrics for model validation, forecast verification and model comparison. For continuous predictands the package provides functions for calculating bias (mean error, mean percentage error, median log accuracy, symmetric signed bias), and for calculating accuracy (mean squared error, mean absolute error, mean absolute scaled error, normalized RMSE, median symmetric accuracy). Convenience routines to calculate the component parts (e.g. forecast error, scaled error) of each metric are also provided. To compare models the package provides: generic skill score; percent better. Robust measures of scale including median absolute deviation, robust standard deviation, robust coefficient ofmore » variation and the Sn estimator are all provided by the package. Finally, the package implements Python classes for NxN contingency tables. In the case of a multi-class prediction, accuracy and skill metrics such as proportion correct and the Heidke and Peirce skill scores are provided as object methods. The special case of a 2x2 contingency table inherits from the NxN class and provides many additional metrics for binary classification: probability of detection, probability of false detection, false alarm ration, threat score, equitable threat score, bias. Confidence intervals for many of these quantities can be calculated using either the Wald method or Agresti-Coull intervals.« less

Experimental power spectral density analysis for mid- to high-spatial frequency surface error control.

PubMed

Hoyo, Javier Del; Choi, Heejoo; Burge, James H; Kim, Geon-Hee; Kim, Dae Wook

2017-06-20

The control of surface errors as a function of spatial frequency is critical during the fabrication of modern optical systems. A large-scale surface figure error is controlled by a guided removal process, such as computer-controlled optical surfacing. Smaller-scale surface errors are controlled by polishing process parameters. Surface errors of only a few millimeters may degrade the performance of an optical system, causing background noise from scattered light and reducing imaging contrast for large optical systems. Conventionally, the microsurface roughness is often given by the root mean square at a high spatial frequency range, with errors within a 0.5×0.5  mm local surface map with 500×500 pixels. This surface specification is not adequate to fully describe the characteristics for advanced optical systems. The process for controlling and minimizing mid- to high-spatial frequency surface errors with periods of up to ∼2-3  mm was investigated for many optical fabrication conditions using the measured surface power spectral density (PSD) of a finished Zerodur optical surface. Then, the surface PSD was systematically related to various fabrication process parameters, such as the grinding methods, polishing interface materials, and polishing compounds. The retraceable experimental polishing conditions and processes used to produce an optimal optical surface PSD are presented.

Systemic inflammatory markers and sources of social support among older adults in the Memory Research Unit cohort.

PubMed

McHugh Power, Joanna; Carney, Sile; Hannigan, Caoimhe; Brennan, Sabina; Wolfe, Hannah; Lynch, Marina; Kee, Frank; Lawlor, Brian

2016-11-01

Potential associations between systemic inflammation and social support received by a sample of 120 older adults were examined here. Inflammatory markers, cognitive function, social support and psychosocial wellbeing were evaluated. A structural equation modelling approach was used to analyse the data. The model was a good fit [Formula: see text], p < 0.001; comparative fit index = 0.973; Tucker-Lewis Index = 0.962; root mean square error of approximation = 0.021; standardised root mean-square residual = 0.074). Chemokine levels were associated with increased age ( β = 0.276), receipt of less social support from friends ( β = -0.256) and body mass index ( β = -0.256). Results are discussed in relation to social signal transduction theory.

Fourier transform infrared reflectance spectra of latent fingerprints: a biometric gauge for the age of an individual.

PubMed

Hemmila, April; McGill, Jim; Ritter, David

2008-03-01

To determine if changes in fingerprint infrared spectra linear with age can be found, partial least squares (PLS1) regression of 155 fingerprint infrared spectra against the person's age was constructed. The regression produced a linear model of age as a function of spectrum with a root mean square error of calibration of less than 4 years, showing an inflection at about 25 years of age. The spectral ranges emphasized by the regression do not correspond to the highest concentration constituents of the fingerprints. Separate linear regression models for old and young people can be constructed with even more statistical rigor. The success of the regression demonstrates that a combination of constituents can be found that changes linearly with age, with a significant shift around puberty.

Over length quantification of the multiaxial mechanical properties of the ascending, descending and abdominal aorta using Digital Image Correlation.

PubMed

Peña, Juan A; Corral, Victoria; Martínez, Miguel A; Peña, Estefanía

2018-01-01

In this paper, we hypothesize that the biaxial mechanical properties of the aorta may be dependent on arterial location. To demonstrate any possible position-related difference, our study analyzed and compared the biaxial mechanical properties of the ascending thoracic aorta, descending thoracic aorta and infrarenal abdominal aorta stemming from the same porcine subjects, and reported values of constitutive parameters for well-known strain energy functions, showing how these mechanical properties are affected by location along the aorta. When comparing ascending thoracic aorta, descending thoracic aorta and infrarenal abdominal aorta, abdominal tissues were found to be stiffer and highly anisotropic. We found that the aorta changed from a more isotropic to a more anisotropic tissue and became progressively less compliant and stiffer with the distance to the heart. We observed substantial differences in the anisotropy parameter between aortic samples where abdominal samples were more anisotropic and nonlinear than the thoracic samples. The phenomenological model was not able to capture the passive biaxial properties of each specific porcine aorta over a wide range of biaxial deformations, showing the best prediction root mean square error ε=0.2621 for ascending thoracic samples and, especially, the worst for the infrarenal abdominal samples ε=0.3780. The micro-structured model with Bingham orientation density function was able to better predict biaxial deformations (ε=0.1372 for ascending thoracic aorta samples). The root mean square error of the micro-structural model and the micro-structured model with von Mises orientation density function were similar for all positions. Copyright © 2017 Elsevier Ltd. All rights reserved.

Simple Forest Canopy Thermal Exitance Model

NASA Technical Reports Server (NTRS)

Smith J. A.; Goltz, S. M.

1999-01-01

We describe a model to calculate brightness temperature and surface energy balance for a forest canopy system. The model is an extension of an earlier vegetation only model by inclusion of a simple soil layer. The root mean square error in brightness temperature for a dense forest canopy was 2.5 C. Surface energy balance predictions were also in good agreement. The corresponding root mean square errors for net radiation, latent, and sensible heat were 38.9, 30.7, and 41.4 W/sq m respectively.

Using absolute gravimeter data to determine vertical gravity gradients

USGS Publications Warehouse

Robertson, D.S.

2001-01-01

The position versus time data from a free-fall absolute gravimeter can be used to estimate the vertical gravity gradient in addition to the gravity value itself. Hipkin has reported success in estimating the vertical gradient value using a data set of unusually good quality. This paper explores techniques that may be applicable to a broader class of data that may be contaminated with "system response" errors of larger magnitude than were evident in the data used by Hipkin. This system response function is usually modelled as a sum of exponentially decaying sinusoidal components. The technique employed here involves combining the x0, v0 and g parameters from all the drops made during a site occupation into a single least-squares solution, and including the value of the vertical gradient and the coefficients of system response function in the same solution. The resulting non-linear equations must be solved iteratively and convergence presents some difficulties. Sparse matrix techniques are used to make the least-squares problem computationally tractable.

The augmented Lagrangian method for parameter estimation in elliptic systems

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Kunisch, Karl

1990-01-01

In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented Lagrangian formulation, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined Lagrangian functional. To obtain this coercivity estimate a seminorm regularization technique is used.

Mean-Square Error Due to Gradiometer Field Measuring Devices

DTIC Science & Technology

1991-06-01

convolving the gradiometer data with the inverse transform of I /T(a, 13), applying an ap- Hence (2) may be expressed in the transform domain as propriate... inverse transform of I / T(ot, 1) will not be possible quency measurements," Superconductor Applications: SQUID’s and because its inverse does not exist...and because it is a high- Machines, B. B. Schwartz and S. Foner, Eds. New York: Plenum pass function its use in an inverse transform technique Press

Measuring Dispersion Effects of Factors in Factorial Experiments.

DTIC Science & Technology

1988-01-01

error is MSE =i=l j=1 i n r (SSE/(N-p)), the sum of squares of pure error is SSPE = Z E Y i=1 j=1 and the mean square of pure error is MSPE - ( SSPE /n...the level of the factor in the ith run is 0. 3.1. First Measure We have n r n r SSPE = 1 Is it -yi) 2 + E r (1-8 )(yjj li-l j=l (iYjj +i= j=l l - i...The first component in SSPE corresponds to level I of the factor and has n degrees of freedom ( E 6i)(r-I). The second component corresponds to i=l n

Smooth empirical Bayes estimation of observation error variances in linear systems

NASA Technical Reports Server (NTRS)

Martz, H. F., Jr.; Lian, M. W.

1972-01-01

A smooth empirical Bayes estimator was developed for estimating the unknown random scale component of each of a set of observation error variances. It is shown that the estimator possesses a smaller average squared error loss than other estimators for a discrete time linear system.

Inelastic scattering with Chebyshev polynomials and preconditioned conjugate gradient minimization.

PubMed

Temel, Burcin; Mills, Greg; Metiu, Horia

2008-03-27

We describe and test an implementation, using a basis set of Chebyshev polynomials, of a variational method for solving scattering problems in quantum mechanics. This minimum error method (MEM) determines the wave function Psi by minimizing the least-squares error in the function (H Psi - E Psi), where E is the desired scattering energy. We compare the MEM to an alternative, the Kohn variational principle (KVP), by solving the Secrest-Johnson model of two-dimensional inelastic scattering, which has been studied previously using the KVP and for which other numerical solutions are available. We use a conjugate gradient (CG) method to minimize the error, and by preconditioning the CG search, we are able to greatly reduce the number of iterations necessary; the method is thus faster and more stable than a matrix inversion, as is required in the KVP. Also, we avoid errors due to scattering off of the boundaries, which presents substantial problems for other methods, by matching the wave function in the interaction region to the correct asymptotic states at the specified energy; the use of Chebyshev polynomials allows this boundary condition to be implemented accurately. The use of Chebyshev polynomials allows for a rapid and accurate evaluation of the kinetic energy. This basis set is as efficient as plane waves but does not impose an artificial periodicity on the system. There are problems in surface science and molecular electronics which cannot be solved if periodicity is imposed, and the Chebyshev basis set is a good alternative in such situations.

Modeling Multiplicative Error Variance: An Example Predicting Tree Diameter from Stump Dimensions in Baldcypress

Treesearch

Bernard R. Parresol

1993-01-01

In the context of forest modeling, it is often reasonable to assume a multiplicative heteroscedastic error structure to the data. Under such circumstances ordinary least squares no longer provides minimum variance estimates of the model parameters. Through study of the error structure, a suitable error variance model can be specified and its parameters estimated. This...

Temperature variation effects on stochastic characteristics for low-cost MEMS-based inertial sensor error

NASA Astrophysics Data System (ADS)

El-Diasty, M.; El-Rabbany, A.; Pagiatakis, S.

2007-11-01

We examine the effect of varying the temperature points on MEMS inertial sensors' noise models using Allan variance and least-squares spectral analysis (LSSA). Allan variance is a method of representing root-mean-square random drift error as a function of averaging times. LSSA is an alternative to the classical Fourier methods and has been applied successfully by a number of researchers in the study of the noise characteristics of experimental series. Static data sets are collected at different temperature points using two MEMS-based IMUs, namely MotionPakII and Crossbow AHRS300CC. The performance of the two MEMS inertial sensors is predicted from the Allan variance estimation results at different temperature points and the LSSA is used to study the noise characteristics and define the sensors' stochastic model parameters. It is shown that the stochastic characteristics of MEMS-based inertial sensors can be identified using Allan variance estimation and LSSA and the sensors' stochastic model parameters are temperature dependent. Also, the Kaiser window FIR low-pass filter is used to investigate the effect of de-noising stage on the stochastic model. It is shown that the stochastic model is also dependent on the chosen cut-off frequency.

Parameter identification of JONSWAP spectrum acquired by airborne LIDAR

NASA Astrophysics Data System (ADS)

Yu, Yang; Pei, Hailong; Xu, Chengzhong

2017-12-01

In this study, we developed the first linear Joint North Sea Wave Project (JONSWAP) spectrum (JS), which involves a transformation from the JS solution to the natural logarithmic scale. This transformation is convenient for defining the least squares function in terms of the scale and shape parameters. We identified these two wind-dependent parameters to better understand the wind effect on surface waves. Due to its efficiency and high-resolution, we employed the airborne Light Detection and Ranging (LIDAR) system for our measurements. Due to the lack of actual data, we simulated ocean waves in the MATLAB environment, which can be easily translated into industrial programming language. We utilized the Longuet-Higgin (LH) random-phase method to generate the time series of wave records and used the fast Fourier transform (FFT) technique to compute the power spectra density. After validating these procedures, we identified the JS parameters by minimizing the mean-square error of the target spectrum to that of the estimated spectrum obtained by FFT. We determined that the estimation error is relative to the amount of available wave record data. Finally, we found the inverse computation of wind factors (wind speed and wind fetch length) to be robust and sufficiently precise for wave forecasting.

Quantifying creatinine and urea in human urine through Raman spectroscopy aiming at diagnosis of kidney disease

NASA Astrophysics Data System (ADS)

Saatkamp, Cassiano Junior; de Almeida, Maurício Liberal; Bispo, Jeyse Aliana Martins; Pinheiro, Antonio Luiz Barbosa; Fernandes, Adriana Barrinha; Silveira, Landulfo, Jr.

2016-03-01

Due to their importance in the regulation of metabolites, the kidneys need continuous monitoring to check for correct functioning, mainly by urea and creatinine urinalysis. This study aimed to develop a model to estimate the concentrations of urea and creatinine in urine by means of Raman spectroscopy (RS) that could be used to diagnose kidney disease. Midstream urine samples were obtained from 54 volunteers with no kidney complaints. Samples were subjected to a standard colorimetric assay of urea and creatinine and submitted to spectroscopic analysis by means of a dispersive Raman spectrometer (830 nm, 350 mW, 30 s). The Raman spectra of urine showed peaks related mainly to urea and creatinine. Partial least squares models were developed using selected Raman bands related to urea and creatinine and the biochemical concentrations in urine measured by the colorimetric method, resulting in r=0.90 and 0.91 for urea and creatinine, respectively, with root mean square error of cross-validation (RMSEcv) of 312 and 25.2 mg/dL, respectively. RS may become a technique for rapid urinalysis, with concentration errors suitable for population screening aimed at the prevention of renal diseases.

Comparison of estimators of standard deviation for hydrologic time series

USGS Publications Warehouse

Tasker, Gary D.; Gilroy, Edward J.

1982-01-01

Unbiasing factors as a function of serial correlation, ρ, and sample size, n for the sample standard deviation of a lag one autoregressive model were generated by random number simulation. Monte Carlo experiments were used to compare the performance of several alternative methods for estimating the standard deviation σ of a lag one autoregressive model in terms of bias, root mean square error, probability of underestimation, and expected opportunity design loss. Three methods provided estimates of σ which were much less biased but had greater mean square errors than the usual estimate of σ: s = (1/(n - 1) ∑ (xi −x¯)2)½. The three methods may be briefly characterized as (1) a method using a maximum likelihood estimate of the unbiasing factor, (2) a method using an empirical Bayes estimate of the unbiasing factor, and (3) a robust nonparametric estimate of σ suggested by Quenouille. Because s tends to underestimate σ, its use as an estimate of a model parameter results in a tendency to underdesign. If underdesign losses are considered more serious than overdesign losses, then the choice of one of the less biased methods may be wise.

A partial least squares based spectrum normalization method for uncertainty reduction for laser-induced breakdown spectroscopy measurements

NASA Astrophysics Data System (ADS)

Li, Xiongwei; Wang, Zhe; Lui, Siu-Lung; Fu, Yangting; Li, Zheng; Liu, Jianming; Ni, Weidou

2013-10-01

A bottleneck of the wide commercial application of laser-induced breakdown spectroscopy (LIBS) technology is its relatively high measurement uncertainty. A partial least squares (PLS) based normalization method was proposed to improve pulse-to-pulse measurement precision for LIBS based on our previous spectrum standardization method. The proposed model utilized multi-line spectral information of the measured element and characterized the signal fluctuations due to the variation of plasma characteristic parameters (plasma temperature, electron number density, and total number density) for signal uncertainty reduction. The model was validated by the application of copper concentration prediction in 29 brass alloy samples. The results demonstrated an improvement on both measurement precision and accuracy over the generally applied normalization as well as our previously proposed simplified spectrum standardization method. The average relative standard deviation (RSD), average of the standard error (error bar), the coefficient of determination (R2), the root-mean-square error of prediction (RMSEP), and average value of the maximum relative error (MRE) were 1.80%, 0.23%, 0.992, 1.30%, and 5.23%, respectively, while those for the generally applied spectral area normalization were 3.72%, 0.71%, 0.973, 1.98%, and 14.92%, respectively.

Super-linear Precision in Simple Neural Population Codes

NASA Astrophysics Data System (ADS)

Schwab, David; Fiete, Ila

2015-03-01

A widely used tool for quantifying the precision with which a population of noisy sensory neurons encodes the value of an external stimulus is the Fisher Information (FI). Maximizing the FI is also a commonly used objective for constructing optimal neural codes. The primary utility and importance of the FI arises because it gives, through the Cramer-Rao bound, the smallest mean-squared error achievable by any unbiased stimulus estimator. However, it is well-known that when neural firing is sparse, optimizing the FI can result in codes that perform very poorly when considering the resulting mean-squared error, a measure with direct biological relevance. Here we construct optimal population codes by minimizing mean-squared error directly and study the scaling properties of the resulting network, focusing on the optimal tuning curve width. We then extend our results to continuous attractor networks that maintain short-term memory of external stimuli in their dynamics. Here we find similar scaling properties in the structure of the interactions that minimize diffusive information loss.

Geospatial distribution modeling and determining suitability of groundwater quality for irrigation purpose using geospatial methods and water quality index (WQI) in Northern Ethiopia

NASA Astrophysics Data System (ADS)

Gidey, Amanuel

2018-06-01

Determining suitability and vulnerability of groundwater quality for irrigation use is a key alarm and first aid for careful management of groundwater resources to diminish the impacts on irrigation. This study was conducted to determine the overall suitability of groundwater quality for irrigation use and to generate their spatial distribution maps in Elala catchment, Northern Ethiopia. Thirty-nine groundwater samples were collected to analyze and map the water quality variables. Atomic absorption spectrophotometer, ultraviolet spectrophotometer, titration and calculation methods were used for laboratory groundwater quality analysis. Arc GIS, geospatial analysis tools, semivariogram model types and interpolation methods were used to generate geospatial distribution maps. Twelve and eight water quality variables were used to produce weighted overlay and irrigation water quality index models, respectively. Root-mean-square error, mean square error, absolute square error, mean error, root-mean-square standardized error, measured values versus predicted values were used for cross-validation. The overall weighted overlay model result showed that 146 km2 areas are highly suitable, 135 km2 moderately suitable and 60 km2 area unsuitable for irrigation use. The result of irrigation water quality index confirms 10.26% with no restriction, 23.08% with low restriction, 20.51% with moderate restriction, 15.38% with high restriction and 30.76% with the severe restriction for irrigation use. GIS and irrigation water quality index are better methods for irrigation water resources management to achieve a full yield irrigation production to improve food security and to sustain it for a long period, to avoid the possibility of increasing environmental problems for the future generation.

Methods for estimating the magnitude and frequency of peak streamflows at ungaged sites in and near the Oklahoma Panhandle

USGS Publications Warehouse

Smith, S. Jerrod; Lewis, Jason M.; Graves, Grant M.

2015-09-28

Generalized-least-squares multiple-linear regression analysis was used to formulate regression relations between peak-streamflow frequency statistics and basin characteristics. Contributing drainage area was the only basin characteristic determined to be statistically significant for all percentage of annual exceedance probabilities and was the only basin characteristic used in regional regression equations for estimating peak-streamflow frequency statistics on unregulated streams in and near the Oklahoma Panhandle. The regression model pseudo-coefficient of determination, converted to percent, for the Oklahoma Panhandle regional regression equations ranged from about 38 to 63 percent. The standard errors of prediction and the standard model errors for the Oklahoma Panhandle regional regression equations ranged from about 84 to 148 percent and from about 76 to 138 percent, respectively. These errors were comparable to those reported for regional peak-streamflow frequency regression equations for the High Plains areas of Texas and Colorado. The root mean square errors for the Oklahoma Panhandle regional regression equations (ranging from 3,170 to 92,000 cubic feet per second) were less than the root mean square errors for the Oklahoma statewide regression equations (ranging from 18,900 to 412,000 cubic feet per second); therefore, the Oklahoma Panhandle regional regression equations produce more accurate peak-streamflow statistic estimates for the irrigated period of record in the Oklahoma Panhandle than do the Oklahoma statewide regression equations. The regression equations developed in this report are applicable to streams that are not substantially affected by regulation, impoundment, or surface-water withdrawals. These regression equations are intended for use for stream sites with contributing drainage areas less than or equal to about 2,060 square miles, the maximum value for the independent variable used in the regression analysis.

Analysis of the variability in ground-motion synthesis and inversion

USGS Publications Warehouse

Spudich, Paul A.; Cirella, Antonella; Scognamiglio, Laura; Tinti, Elisa

2017-12-07

In almost all past inversions of large-earthquake ground motions for rupture behavior, the goal of the inversion is to find the “best fitting” rupture model that predicts ground motions which optimize some function of the difference between predicted and observed ground motions. This type of inversion was pioneered in the linear-inverse sense by Olson and Apsel (1982), who minimized the square of the difference between observed and simulated motions (“least squares”) while simultaneously minimizing the rupture-model norm (by setting the null-space component of the rupture model to zero), and has been extended in many ways, one of which is the use of nonlinear inversion schemes such as simulated annealing algorithms that optimize some other misfit function. For example, the simulated annealing algorithm of Piatanesi and others (2007) finds the rupture model that minimizes a “cost” function which combines a least-squares and a waveform-correlation measure of misfit.All such inversions that look for a unique “best” model have at least three problems. (1) They have removed the null-space component of the rupture model—that is, an infinite family of rupture models that all fit the data equally well have been narrowed down to a single model. Some property of interest in the rupture model might have been discarded in this winnowing process. (2) Smoothing constraints are commonly used to yield a unique “best” model, in which case spatially rough rupture models will have been discarded, even if they provide a good fit to the data. (3) No estimate of confidence in the resulting rupture models can be given because the effects of unknown errors in the Green’s functions (“theory errors”) have not been assessed. In inversion for rupture behavior, these theory errors are generally larger than the data errors caused by ground noise and instrumental limitations, and so overfitting of the data is probably ubiquitous for such inversions.Recently, attention has turned to the inclusion of theory errors in the inversion process. Yagi and Fukahata (2011) made an important contribution by presenting a method to estimate the uncertainties in predicted large-earthquake ground motions due to uncertainties in the Green’s functions. Here we derive their result and compare it with the results of other recent studies that look at theory errors in a Bayesian inversion context particularly those by Bodin and others (2012), Duputel and others (2012), Dettmer and others (2014), and Minson and others (2014).Notably, in all these studies, the estimates of theory error were obtained from theoretical considerations alone; none of the investigators actually measured Green’s function errors. Large earthquakes typically have aftershocks, which, if their rupture surfaces are physically small enough, can be considered point evaluations of the real Green’s functions of the Earth. Here we simulate smallaftershock ground motions with (erroneous) theoretical Green’s functions. Taking differences between aftershock ground motions and simulated motions to be the “theory error,” we derive a statistical model of the sources of discrepancies between the theoretical and real Green’s functions. We use this model with an extended frequency-domain version of the time-domain theory of Yagi and Fukahata (2011) to determine the expected variance 2 τ caused by Green’s function error in ground motions from a larger (nonpoint) earthquake that we seek to model.We also differ from the above-mentioned Bayesian inversions in our handling of the nonuniqueness problem of seismic inversion. We follow the philosophy of Segall and Du (1993), who, instead of looking for a best-fitting model, looked for slip models that answered specific questions about the earthquakes they studied. In their Bayesian inversions, they inductively derived a posterior probability-density function (PDF) for every model parameter. We instead seek to find two extremal rupture models whose ground motions fit the data within the error bounds given by 2 τ , as quantified by using a chi-squared test described below. So, we can ask questions such as, “What are the rupture models with the highest and lowest average rupture speed consistent with the theory errors?” Having found those models, we can then say with confidence that the true rupture speed is somewhere between those values. Although the Bayesian approach gives a complete solution to the inverse problem, it is computationally demanding: Minson and others (2014) needed 1010 forward kinematic simulations to derive their posterior probability distribution. In our approach, only about107 simulations are needed. Moreover, in practical application, only a small set of rupture models may be needed to answer the relevant questions—for example, determining the maximum likelihood solution (achievable through standard inversion techniques) and the two rupture models bounding some property of interest.The specific property that we wish to investigate is the correlation between various rupturemodel parameters, such as peak slip velocity and rupture velocity, in models of real earthquakes. In some simulations of ground motions for hypothetical large earthquakes, such as those by Aagaard and others (2010) and the Southern California Earthquake Center Broadband Simulation Platform (Graves and Pitarka, 2015), rupture speed is assumed to correlate locally with peak slip, although there is evidence that rupture speed should correlate better with peak slip speed, owing to its dependence on local stress drop. We may be able to determine ways to modify Piatanesi and others’s (2007) inversion’s “cost” function to find rupture models with either high or low degrees of correlation between pairs of rupture parameters. We propose a cost function designed to find these two extremal models.

Phase and Pupil Amplitude Recovery for JWST Space-Optics Control

NASA Technical Reports Server (NTRS)

Dean, B. H.; Zielinski, T. P.; Smith, J. S.; Bolcar, M. R.; Aronstein, D. L.; Fienup, J. R.

2010-01-01

This slide presentation reviews the phase and pupil amplitude recovery for the James Webb Space Telescope (JWST) Near Infrared Camera (NIRCam). It includes views of the Integrated Science Instrument Module (ISIM), the NIRCam, examples of Phase Retrieval Data, Ghost Irradiance, Pupil Amplitude Estimation, Amplitude Retrieval, Initial Plate Scale Estimation using the Modulation Transfer Function (MTF), Pupil Amplitude Estimation vs lambda, Pupil Amplitude Estimation vs. number of Images, Pupil Amplitude Estimation vs Rotation (clocking), and Typical Phase Retrieval Results Also included is information about the phase retrieval approach, Non-Linear Optimization (NLO) Optimized Diversity Functions, and Least Square Error vs. Starting Pupil Amplitude.

[NIR Assignment of Magnolol by 2D-COS Technology and Model Application Huoxiangzhengqi Oral Liduid].

PubMed

Pei, Yan-ling; Wu, Zhi-sheng; Shi, Xin-yuan; Pan, Xiao-ning; Peng, Yan-fang; Qiao, Yan-jiang

2015-08-01

Near infrared (NIR) spectroscopy assignment of Magnolol was performed using deuterated chloroform solvent and two-dimensional correlation spectroscopy (2D-COS) technology. According to the synchronous spectra of deuterated chloroform solvent and Magnolol, 1365~1455, 1600~1720, 2000~2181 and 2275~2465 nm were the characteristic absorption of Magnolol. Connected with the structure of Magnolol, 1440 nm was the stretching vibration of phenolic group O-H, 1679 nm was the stretching vibration of aryl and methyl which connected with aryl, 2117, 2304, 2339 and 2370 nm were the combination of the stretching vibration, bending vibration and deformation vibration for aryl C-H, 2445 nm were the bending vibration of methyl which linked with aryl group, these bands attribut to the characteristics of Magnolol. Huoxiangzhengqi Oral Liduid was adopted to study the Magnolol, the characteristic band by spectral assignment and the band by interval Partial Least Squares (iPLS) and Synergy interval Partial Least Squares (SiPLS) were used to establish Partial Least Squares (PLS) quantitative model, the coefficient of determination Rcal(2) and Rpre(2) were greater than 0.99, the Root Mean of Square Error of Calibration (RM-SEC), Root Mean of Square Error of Cross Validation (RMSECV) and Root Mean of Square Error of Prediction (RMSEP) were very small. It indicated that the characteristic band by spectral assignment has the same results with the Chemometrics in PLS model. It provided a reference for NIR spectral assignment of chemical compositions in Chinese Materia Medica, and the band filters of NIR were interpreted.

A new open-loop fiber optic gyro error compensation method based on angular velocity error modeling.

PubMed

Zhang, Yanshun; Guo, Yajing; Li, Chunyu; Wang, Yixin; Wang, Zhanqing

2015-02-27

With the open-loop fiber optic gyro (OFOG) model, output voltage and angular velocity can effectively compensate OFOG errors. However, the model cannot reflect the characteristics of OFOG errors well when it comes to pretty large dynamic angular velocities. This paper puts forward a modeling scheme with OFOG output voltage u and temperature T as the input variables and angular velocity error Δω as the output variable. Firstly, the angular velocity error Δω is extracted from OFOG output signals, and then the output voltage u, temperature T and angular velocity error Δω are used as the learning samples to train a Radial-Basis-Function (RBF) neural network model. Then the nonlinear mapping model over T, u and Δω is established and thus Δω can be calculated automatically to compensate OFOG errors according to T and u. The results of the experiments show that the established model can be used to compensate the nonlinear OFOG errors. The maximum, the minimum and the mean square error of OFOG angular velocity are decreased by 97.0%, 97.1% and 96.5% relative to their initial values, respectively. Compared with the direct modeling of gyro angular velocity, which we researched before, the experimental results of the compensating method proposed in this paper are further reduced by 1.6%, 1.4% and 1.42%, respectively, so the performance of this method is better than that of the direct modeling for gyro angular velocity.

A New Open-Loop Fiber Optic Gyro Error Compensation Method Based on Angular Velocity Error Modeling

PubMed Central

Zhang, Yanshun; Guo, Yajing; Li, Chunyu; Wang, Yixin; Wang, Zhanqing

2015-01-01

With the open-loop fiber optic gyro (OFOG) model, output voltage and angular velocity can effectively compensate OFOG errors. However, the model cannot reflect the characteristics of OFOG errors well when it comes to pretty large dynamic angular velocities. This paper puts forward a modeling scheme with OFOG output voltage u and temperature T as the input variables and angular velocity error Δω as the output variable. Firstly, the angular velocity error Δω is extracted from OFOG output signals, and then the output voltage u, temperature T and angular velocity error Δω are used as the learning samples to train a Radial-Basis-Function (RBF) neural network model. Then the nonlinear mapping model over T, u and Δω is established and thus Δω can be calculated automatically to compensate OFOG errors according to T and u. The results of the experiments show that the established model can be used to compensate the nonlinear OFOG errors. The maximum, the minimum and the mean square error of OFOG angular velocity are decreased by 97.0%, 97.1% and 96.5% relative to their initial values, respectively. Compared with the direct modeling of gyro angular velocity, which we researched before, the experimental results of the compensating method proposed in this paper are further reduced by 1.6%, 1.4% and 1.2%, respectively, so the performance of this method is better than that of the direct modeling for gyro angular velocity. PMID:25734642

Improved volumetric measurement of brain structure with a distortion correction procedure using an ADNI phantom.

PubMed

Maikusa, Norihide; Yamashita, Fumio; Tanaka, Kenichiro; Abe, Osamu; Kawaguchi, Atsushi; Kabasawa, Hiroyuki; Chiba, Shoma; Kasahara, Akihiro; Kobayashi, Nobuhisa; Yuasa, Tetsuya; Sato, Noriko; Matsuda, Hiroshi; Iwatsubo, Takeshi

2013-06-01

Serial magnetic resonance imaging (MRI) images acquired from multisite and multivendor MRI scanners are widely used in measuring longitudinal structural changes in the brain. Precise and accurate measurements are important in understanding the natural progression of neurodegenerative disorders such as Alzheimer's disease. However, geometric distortions in MRI images decrease the accuracy and precision of volumetric or morphometric measurements. To solve this problem, the authors suggest a commercially available phantom-based distortion correction method that accommodates the variation in geometric distortion within MRI images obtained with multivendor MRI scanners. The authors' method is based on image warping using a polynomial function. The method detects fiducial points within a phantom image using phantom analysis software developed by the Mayo Clinic and calculates warping functions for distortion correction. To quantify the effectiveness of the authors' method, the authors corrected phantom images obtained from multivendor MRI scanners and calculated the root-mean-square (RMS) of fiducial errors and the circularity ratio as evaluation values. The authors also compared the performance of the authors' method with that of a distortion correction method based on a spherical harmonics description of the generic gradient design parameters. Moreover, the authors evaluated whether this correction improves the test-retest reproducibility of voxel-based morphometry in human studies. A Wilcoxon signed-rank test with uncorrected and corrected images was performed. The root-mean-square errors and circularity ratios for all slices significantly improved (p < 0.0001) after the authors' distortion correction. Additionally, the authors' method was significantly better than a distortion correction method based on a description of spherical harmonics in improving the distortion of root-mean-square errors (p < 0.001 and 0.0337, respectively). Moreover, the authors' method reduced the RMS error arising from gradient nonlinearity more than gradwarp methods. In human studies, the coefficient of variation of voxel-based morphometry analysis of the whole brain improved significantly from 3.46% to 2.70% after distortion correction of the whole gray matter using the authors' method (Wilcoxon signed-rank test, p < 0.05). The authors proposed a phantom-based distortion correction method to improve reproducibility in longitudinal structural brain analysis using multivendor MRI. The authors evaluated the authors' method for phantom images in terms of two geometrical values and for human images in terms of test-retest reproducibility. The results showed that distortion was corrected significantly using the authors' method. In human studies, the reproducibility of voxel-based morphometry analysis for the whole gray matter significantly improved after distortion correction using the authors' method.

Using weighted power mean for equivalent square estimation.

PubMed

Zhou, Sumin; Wu, Qiuwen; Li, Xiaobo; Ma, Rongtao; Zheng, Dandan; Wang, Shuo; Zhang, Mutian; Li, Sicong; Lei, Yu; Fan, Qiyong; Hyun, Megan; Diener, Tyler; Enke, Charles

2017-11-01

Equivalent Square (ES) enables the calculation of many radiation quantities for rectangular treatment fields, based only on measurements from square fields. While it is widely applied in radiotherapy, its accuracy, especially for extremely elongated fields, still leaves room for improvement. In this study, we introduce a novel explicit ES formula based on Weighted Power Mean (WPM) function and compare its performance with the Sterling formula and Vadash/Bjärngard's formula. The proposed WPM formula is ESWPMa,b=waα+1-wbα1/α for a rectangular photon field with sides a and b. The formula performance was evaluated by three methods: standard deviation of model fitting residual error, maximum relative model prediction error, and model's Akaike Information Criterion (AIC). Testing datasets included the ES table from British Journal of Radiology (BJR), photon output factors (S cp ) from the Varian TrueBeam Representative Beam Data (Med Phys. 2012;39:6981-7018), and published S cp data for Varian TrueBeam Edge (J Appl Clin Med Phys. 2015;16:125-148). For the BJR dataset, the best-fit parameter value α = -1.25 achieved a 20% reduction in standard deviation in ES estimation residual error compared with the two established formulae. For the two Varian datasets, employing WPM reduced the maximum relative error from 3.5% (Sterling) or 2% (Vadash/Bjärngard) to 0.7% for open field sizes ranging from 3 cm to 40 cm, and the reduction was even more prominent for 1 cm field sizes on Edge (J Appl Clin Med Phys. 2015;16:125-148). The AIC value of the WPM formula was consistently lower than its counterparts from the traditional formulae on photon output factors, most prominent on very elongated small fields. The WPM formula outperformed the traditional formulae on three testing datasets. With increasing utilization of very elongated, small rectangular fields in modern radiotherapy, improved photon output factor estimation is expected by adopting the WPM formula in treatment planning and secondary MU check. © 2017 The Authors. Journal of Applied Clinical Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine.

Intelligent Ensemble Forecasting System of Stock Market Fluctuations Based on Symetric and Asymetric Wavelet Functions

NASA Astrophysics Data System (ADS)

Lahmiri, Salim; Boukadoum, Mounir

2015-08-01

We present a new ensemble system for stock market returns prediction where continuous wavelet transform (CWT) is used to analyze return series and backpropagation neural networks (BPNNs) for processing CWT-based coefficients, determining the optimal ensemble weights, and providing final forecasts. Particle swarm optimization (PSO) is used for finding optimal weights and biases for each BPNN. To capture symmetry/asymmetry in the underlying data, three wavelet functions with different shapes are adopted. The proposed ensemble system was tested on three Asian stock markets: The Hang Seng, KOSPI, and Taiwan stock market data. Three statistical metrics were used to evaluate the forecasting accuracy; including, mean of absolute errors (MAE), root mean of squared errors (RMSE), and mean of absolute deviations (MADs). Experimental results showed that our proposed ensemble system outperformed the individual CWT-ANN models each with different wavelet function. In addition, the proposed ensemble system outperformed the conventional autoregressive moving average process. As a result, the proposed ensemble system is suitable to capture symmetry/asymmetry in financial data fluctuations for better prediction accuracy.

Accurate B-spline-based 3-D interpolation scheme for digital volume correlation

NASA Astrophysics Data System (ADS)

Ren, Maodong; Liang, Jin; Wei, Bin

2016-12-01

An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.

An Autonomous Satellite Time Synchronization System Using Remotely Disciplined VC-OCXOs.

PubMed

Gu, Xiaobo; Chang, Qing; Glennon, Eamonn P; Xu, Baoda; Dempseter, Andrew G; Wang, Dun; Wu, Jiapeng

2015-07-23

An autonomous remote clock control system is proposed to provide time synchronization and frequency syntonization for satellite to satellite or ground to satellite time transfer, with the system comprising on-board voltage controlled oven controlled crystal oscillators (VC-OCXOs) that are disciplined to a remote master atomic clock or oscillator. The synchronization loop aims to provide autonomous operation over extended periods, be widely applicable to a variety of scenarios and robust. A new architecture comprising the use of frequency division duplex (FDD), synchronous time division (STDD) duplex and code division multiple access (CDMA) with a centralized topology is employed. This new design utilizes dual one-way ranging methods to precisely measure the clock error, adopts least square (LS) methods to predict the clock error and employs a third-order phase lock loop (PLL) to generate the voltage control signal. A general functional model for this system is proposed and the error sources and delays that affect the time synchronization are discussed. Related algorithms for estimating and correcting these errors are also proposed. The performance of the proposed system is simulated and guidance for selecting the clock is provided.

Point of optimal kinematic error: improvement of the instantaneous helical pivot method for locating centers of rotation.

PubMed

De Rosario, Helios; Page, Alvaro; Mata, Vicente

2014-05-07

This paper proposes a variation of the instantaneous helical pivot technique for locating centers of rotation. The point of optimal kinematic error (POKE), which minimizes the velocity at the center of rotation, may be obtained by just adding a weighting factor equal to the square of angular velocity in Woltring׳s equation of the pivot of instantaneous helical axes (PIHA). Calculations are simplified with respect to the original method, since it is not necessary to make explicit calculations of the helical axis, and the effect of accidental errors is reduced. The improved performance of this method was validated by simulations based on a functional calibration task for the gleno-humeral joint center. Noisy data caused a systematic dislocation of the calculated center of rotation towards the center of the arm marker cluster. This error in PIHA could even exceed the effect of soft tissue artifacts associated to small and medium deformations, but it was successfully reduced by the POKE estimation. Copyright © 2014 Elsevier Ltd. All rights reserved.

Robust scoring functions for protein-ligand interactions with quantum chemical charge models.

PubMed

Wang, Jui-Chih; Lin, Jung-Hsin; Chen, Chung-Ming; Perryman, Alex L; Olson, Arthur J

2011-10-24

Ordinary least-squares (OLS) regression has been used widely for constructing the scoring functions for protein-ligand interactions. However, OLS is very sensitive to the existence of outliers, and models constructed using it are easily affected by the outliers or even the choice of the data set. On the other hand, determination of atomic charges is regarded as of central importance, because the electrostatic interaction is known to be a key contributing factor for biomolecular association. In the development of the AutoDock4 scoring function, only OLS was conducted, and the simple Gasteiger method was adopted. It is therefore of considerable interest to see whether more rigorous charge models could improve the statistical performance of the AutoDock4 scoring function. In this study, we have employed two well-established quantum chemical approaches, namely the restrained electrostatic potential (RESP) and the Austin-model 1-bond charge correction (AM1-BCC) methods, to obtain atomic partial charges, and we have compared how different charge models affect the performance of AutoDock4 scoring functions. In combination with robust regression analysis and outlier exclusion, our new protein-ligand free energy regression model with AM1-BCC charges for ligands and Amber99SB charges for proteins achieve lowest root-mean-squared error of 1.637 kcal/mol for the training set of 147 complexes and 2.176 kcal/mol for the external test set of 1427 complexes. The assessment for binding pose prediction with the 100 external decoy sets indicates very high success rate of 87% with the criteria of predicted root-mean-squared deviation of less than 2 Å. The success rates and statistical performance of our robust scoring functions are only weakly class-dependent (hydrophobic, hydrophilic, or mixed).

An empirical model for estimating solar radiation in the Algerian Sahara

NASA Astrophysics Data System (ADS)

Benatiallah, Djelloul; Benatiallah, Ali; Bouchouicha, Kada; Hamouda, Messaoud; Nasri, Bahous

2018-05-01

The present work aims to determine the empirical model R.sun that will allow us to evaluate the solar radiation flues on a horizontal plane and in clear-sky on the located Adrar city (27°18 N and 0°11 W) of Algeria and compare with the results measured at the localized site. The expected results of this comparison are of importance for the investment study of solar systems (solar power plants for electricity production, CSP) and also for the design and performance analysis of any system using the solar energy. Statistical indicators used to evaluate the accuracy of the model where the mean bias error (MBE), root mean square error (RMSE) and coefficient of determination. The results show that for global radiation, the daily correlation coefficient is 0.9984. The mean absolute percentage error is 9.44 %. The daily mean bias error is -7.94 %. The daily root mean square error is 12.31 %.

Effective Algorithm for Detection and Correction of the Wave Reconstruction Errors Caused by the Tilt of Reference Wave in Phase-shifting Interferometry

NASA Astrophysics Data System (ADS)

Xu, Xianfeng; Cai, Luzhong; Li, Dailin; Mao, Jieying

2010-04-01

In phase-shifting interferometry (PSI) the reference wave is usually supposed to be an on-axis plane wave. But in practice a slight tilt of reference wave often occurs, and this tilt will introduce unexpected errors of the reconstructed object wave-front. Usually the least-square method with iterations, which is time consuming, is employed to analyze the phase errors caused by the tilt of reference wave. Here a simple effective algorithm is suggested to detect and then correct this kind of errors. In this method, only some simple mathematic operation is used, avoiding using least-square equations as needed in most methods reported before. It can be used for generalized phase-shifting interferometry with two or more frames for both smooth and diffusing objects, and the excellent performance has been verified by computer simulations. The numerical simulations show that the wave reconstruction errors can be reduced by 2 orders of magnitude.

Validation of Core Temperature Estimation Algorithm

DTIC Science & Technology

2016-01-29

plot of observed versus estimated core temperature with the line of identity (dashed) and the least squares regression line (solid) and line equation...estimated PSI with the line of identity (dashed) and the least squares regression line (solid) and line equation in the top left corner. (b) Bland...for comparison. The root mean squared error (RMSE) was also computed, as given by Equation 2.

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.

Systematic Error Modeling and Bias Estimation

PubMed Central

Zhang, Feihu; Knoll, Alois

2016-01-01

This paper analyzes the statistic properties of the systematic error in terms of range and bearing during the transformation process. Furthermore, we rely on a weighted nonlinear least square method to calculate the biases based on the proposed models. The results show the high performance of the proposed approach for error modeling and bias estimation. PMID:27213386

Including sheath effects in the interpretation of planar retarding potential analyzer's low-energy ion data

NASA Astrophysics Data System (ADS)

Fisher, L. E.; Lynch, K. A.; Fernandes, P. A.; Bekkeng, T. A.; Moen, J.; Zettergren, M.; Miceli, R. J.; Powell, S.; Lessard, M. R.; Horak, P.

2016-04-01

The interpretation of planar retarding potential analyzers (RPA) during ionospheric sounding rocket missions requires modeling the thick 3D plasma sheath. This paper overviews the theory of RPAs with an emphasis placed on the impact of the sheath on current-voltage (I-V) curves. It then describes the Petite Ion Probe (PIP) which has been designed to function in this difficult regime. The data analysis procedure for this instrument is discussed in detail. Data analysis begins by modeling the sheath with the Spacecraft Plasma Interaction System (SPIS), a particle-in-cell code. Test particles are traced through the sheath and detector to determine the detector's response. A training set is constructed from these simulated curves for a support vector regression analysis which relates the properties of the I-V curve to the properties of the plasma. The first in situ use of the PIPs occurred during the MICA sounding rocket mission which launched from Poker Flat, Alaska in February of 2012. These data are presented as a case study, providing valuable cross-instrument comparisons. A heritage top-hat thermal ion electrostatic analyzer, called the HT, and a multi-needle Langmuir probe have been used to validate both the PIPs and the data analysis method. Compared to the HT, the PIP ion temperature measurements agree with a root-mean-square error of 0.023 eV. These two instruments agree on the parallel-to-B plasma flow velocity with a root-mean-square error of 130 m/s. The PIP with its field of view aligned perpendicular-to-B provided a density measurement with an 11% error compared to the multi-needle Langmuir Probe. Higher error in the other PIP's density measurement is likely due to simplifications in the SPIS model geometry.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

Publisher Correction: Imaging the square of the correlated two-electron wave function of a hydrogen molecule.

PubMed

Waitz, M; Bello, R Y; Metz, D; Lower, J; Trinter, F; Schober, C; Keiling, M; Lenz, U; Pitzer, M; Mertens, K; Martins, M; Viefhaus, J; Klumpp, S; Weber, T; Schmidt, L Ph H; Williams, J B; Schöffler, M S; Serov, V V; Kheifets, A S; Argenti, L; Palacios, A; Martín, F; Jahnke, T; Dörner, R

2018-06-05

The original version of this Article contained an error in the fifth sentence of the first paragraph of the 'Application on H 2 ' section of the Results, which incorrectly read 'The role of electron correlation is quite apparent in this presentation: Fig. 1a is empty for the uncorrelated Hartree-Fock wave function, since projection of the latter wave function onto the 2pσ u orbital is exactly zero, while this is not the case for the fully correlated wave function (Fig. 1d); also, Fig. 1b, c for the uncorrelated description are identical, while Fig. 1e, f for the correlated case are significantly different.' The correct version replaces 'Fig. 1e, f' with 'Fig. 2e and f'.

Jig-Shape Optimization of a Low-Boom Supersonic Aircraft

NASA Technical Reports Server (NTRS)

Pak, Chan-Gi

2018-01-01

A simple approach for optimizing the jig-shape is proposed in this study. This simple approach is based on an unconstrained optimization problem and applied to a low-boom supersonic aircraft. In this study, the jig-shape optimization is performed using the two-step approach. First, starting design variables are computed using the least-squares surface fitting technique. Next, the jig-shape is further tuned using a numerical optimization procedure based on an in-house object-oriented optimization tool. During the numerical optimization procedure, a design jig-shape is determined by the baseline jig-shape and basis functions. A total of 12 symmetric mode shapes of the cruise-weight configuration, rigid pitch shape, rigid left and right stabilator rotation shapes, and a residual shape are selected as sixteen basis functions. After three optimization runs, the trim shape error distribution is improved, and the maximum trim shape error of 0.9844 inches of the starting configuration becomes 0.00367 inch by the end of the third optimization run.

The growth pattern and fuel life cycle analysis of the electricity consumption of Hong Kong.

PubMed

To, W M; Lai, T M; Lo, W C; Lam, K H; Chung, W L

2012-06-01

As the consumption of electricity increases, air pollutants from power generation increase. In metropolitans such as Hong Kong and other Asian cities, the surge of electricity consumption has been phenomenal over the past decades. This paper presents a historical review about electricity consumption, population, and change in economic structure in Hong Kong. It is hypothesized that the growth of electricity consumption and change in gross domestic product can be modeled by 4-parameter logistic functions. The accuracy of the functions was assessed by Pearson's correlation coefficient, mean absolute percent error, and root mean squared percent error. The paper also applies the life cycle approach to determine carbon dioxide, methane, nitrous oxide, sulfur dioxide, and nitrogen oxide emissions for the electricity consumption of Hong Kong. Monte Carlo simulations were applied to determine the confidence intervals of pollutant emissions. The implications of importing more nuclear power are discussed. Copyright © 2012 Elsevier Ltd. All rights reserved.

Cursor Control Device Test Battery

NASA Technical Reports Server (NTRS)

Holden, Kritina; Sandor, Aniko; Pace, John; Thompson, Shelby

2013-01-01

The test battery was developed to provide a standard procedure for cursor control device evaluation. The software was built in Visual Basic and consists of nine tasks and a main menu that integrates the set-up of the tasks. The tasks can be used individually, or in a series defined in the main menu. Task 1, the Unidirectional Pointing Task, tests the speed and accuracy of clicking on targets. Two rectangles with an adjustable width and adjustable center- to-center distance are presented. The task is to click back and forth between the two rectangles. Clicks outside of the rectangles are recorded as errors. Task 2, Multidirectional Pointing Task, measures speed and accuracy of clicking on targets approached from different angles. Twenty-five numbered squares of adjustable width are arranged around an adjustable diameter circle. The task is to point and click on the numbered squares (placed on opposite sides of the circle) in consecutive order. Clicks outside of the squares are recorded as errors. Task 3, Unidirectional (horizontal) Dragging Task, is similar to dragging a file into a folder on a computer desktop. Task 3 requires dragging a square of adjustable width from one rectangle and dropping it into another. The width of each rectangle is adjustable, as well as the distance between the two rectangles. Dropping the square outside of the rectangles is recorded as an error. Task 4, Unidirectional Path Following, is similar to Task 3. The task is to drag a square through a tunnel consisting of two lines. The size of the square and the width of the tunnel are adjustable. If the square touches any of the lines, it is counted as an error and the task is restarted. Task 5, Text Selection, involves clicking on a Start button, and then moving directly to the underlined portion of the displayed text and highlighting it. The pointing distance to the text is adjustable, as well as the to-be-selected font size and the underlined character length. If the selection does not include all of the underlined characters, or includes non-underlined characters, it is recorded as an error. Task 6, Multi-size and Multi-distance Pointing, presents the participant with 24 consecutively numbered buttons of different sizes (63 to 163 pixels), and at different distances (60 to 80 pixels) from the Start button. The task is to click on the Start button, and then move directly to, and click on, each numbered target button in consecutive order. Clicks outside of the target area are errors. Task 7, Standard Interface Elements Task, involves interacting with standard interface elements as instructed in written procedures, including: drop-down menus, sliders, text boxes, radio buttons, and check boxes. Task completion time is recorded. In Task 8, a circular track is presented with a disc in it at the top. Track width and disc size are adjustable. The task is to move the disc with circular motion within the path without touching the boundaries of the track. Time and errors are recorded. Task 9 is a discrete task that allows evaluation of discrete cursor control devices that tab from target to target, such as a castle switch. The task is to follow a predefined path and to click on the yellow targets along the path.

Insights into the Earth System mass variability from CSR-RL05 GRACE gravity fields

NASA Astrophysics Data System (ADS)

Bettadpur, S.

2012-04-01

The next-generation Release-05 GRACE gravity field data products are the result of extensive effort applied to the improvements to the GRACE Level-1 (tracking) data products, and to improvements in the background gravity models and processing methodology. As a result, the squared-error upper-bound in RL05 fields is half or less than the squared-error upper-bound in RL04 fields. The CSR-RL05 field release consists of unconstrained gravity fields as well as a regularized gravity field time-series that can be used for several applications without any post-processing error reduction. This paper will describe the background and the nature of these improvements in the data products, and provide an error characterization. We will describe the insights these new series offer in measuring the mass flux due to diverse Hydrologic, Oceanographic and Cryospheric processes.

Retrieval of the aerosol optical thickness from UV global irradiance measurements

NASA Astrophysics Data System (ADS)

Costa, M. J.; Salgueiro, V.; Bortoli, D.; Obregón, M. A.; Antón, M.; Silva, A. M.

2015-12-01

The UV irradiance is measured at Évora since several years, where a CIMEL sunphotometer integrated in AERONET is also installed. In the present work, measurements of UVA (315 - 400 nm) irradiances taken with Kipp&Zonen radiometers, as well as satellite data of ozone total column values, are used in combination with radiative transfer calculations, to estimate the aerosol optical thickness (AOT) in the UV. The retrieved UV AOT in Évora is compared with AERONET AOT (at 340 and 380 nm) and a fairly good agreement is found with a root mean square error of 0.05 (normalized root mean square error of 8.3%) and a mean absolute error of 0.04 (mean percentage error of 2.9%). The methodology is then used to estimate the UV AOT in Sines, an industrialized site on the Atlantic western coast, where the UV irradiance is monitored since 2013 but no aerosol information is available.

Uncertainty based pressure reconstruction from velocity measurement with generalized least squares

NASA Astrophysics Data System (ADS)

Zhang, Jiacheng; Scalo, Carlo; Vlachos, Pavlos

2017-11-01

A method using generalized least squares reconstruction of instantaneous pressure field from velocity measurement and velocity uncertainty is introduced and applied to both planar and volumetric flow data. Pressure gradients are computed on a staggered grid from flow acceleration. The variance-covariance matrix of the pressure gradients is evaluated from the velocity uncertainty by approximating the pressure gradient error to a linear combination of velocity errors. An overdetermined system of linear equations which relates the pressure and the computed pressure gradients is formulated and then solved using generalized least squares with the variance-covariance matrix of the pressure gradients. By comparing the reconstructed pressure field against other methods such as solving the pressure Poisson equation, the omni-directional integration, and the ordinary least squares reconstruction, generalized least squares method is found to be more robust to the noise in velocity measurement. The improvement on pressure result becomes more remarkable when the velocity measurement becomes less accurate and more heteroscedastic. The uncertainty of the reconstructed pressure field is also quantified and compared across the different methods.

Hybrid robust model based on an improved functional link neural network integrating with partial least square (IFLNN-PLS) and its application to predicting key process variables.

PubMed

He, Yan-Lin; Xu, Yuan; Geng, Zhi-Qiang; Zhu, Qun-Xiong

2016-03-01

In this paper, a hybrid robust model based on an improved functional link neural network integrating with partial least square (IFLNN-PLS) is proposed. Firstly, an improved functional link neural network with small norm of expanded weights and high input-output correlation (SNEWHIOC-FLNN) was proposed for enhancing the generalization performance of FLNN. Unlike the traditional FLNN, the expanded variables of the original inputs are not directly used as the inputs in the proposed SNEWHIOC-FLNN model. The original inputs are attached to some small norm of expanded weights. As a result, the correlation coefficient between some of the expanded variables and the outputs is enhanced. The larger the correlation coefficient is, the more relevant the expanded variables tend to be. In the end, the expanded variables with larger correlation coefficient are selected as the inputs to improve the performance of the traditional FLNN. In order to test the proposed SNEWHIOC-FLNN model, three UCI (University of California, Irvine) regression datasets named Housing, Concrete Compressive Strength (CCS), and Yacht Hydro Dynamics (YHD) are selected. Then a hybrid model based on the improved FLNN integrating with partial least square (IFLNN-PLS) was built. In IFLNN-PLS model, the connection weights are calculated using the partial least square method but not the error back propagation algorithm. Lastly, IFLNN-PLS was developed as an intelligent measurement model for accurately predicting the key variables in the Purified Terephthalic Acid (PTA) process and the High Density Polyethylene (HDPE) process. Simulation results illustrated that the IFLNN-PLS could significant improve the prediction performance. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Designing Artificial Neural Networks Using Particle Swarm Optimization Algorithms

PubMed Central

Vázquez, Roberto A.

2015-01-01

Artificial Neural Network (ANN) design is a complex task because its performance depends on the architecture, the selected transfer function, and the learning algorithm used to train the set of synaptic weights. In this paper we present a methodology that automatically designs an ANN using particle swarm optimization algorithms such as Basic Particle Swarm Optimization (PSO), Second Generation of Particle Swarm Optimization (SGPSO), and a New Model of PSO called NMPSO. The aim of these algorithms is to evolve, at the same time, the three principal components of an ANN: the set of synaptic weights, the connections or architecture, and the transfer functions for each neuron. Eight different fitness functions were proposed to evaluate the fitness of each solution and find the best design. These functions are based on the mean square error (MSE) and the classification error (CER) and implement a strategy to avoid overtraining and to reduce the number of connections in the ANN. In addition, the ANN designed with the proposed methodology is compared with those designed manually using the well-known Back-Propagation and Levenberg-Marquardt Learning Algorithms. Finally, the accuracy of the method is tested with different nonlinear pattern classification problems. PMID:26221132

The DES Science Verification Weak Lensing Shear Catalogs

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

Jarvis, M.

We present weak lensing shear catalogs for 139 square degrees of data taken during the Science Verification (SV) time for the new Dark Energy Camera (DECam) being used for the Dark Energy Survey (DES). We describe our object selection, point spread function estimation and shear measurement procedures using two independent shear pipelines, IM3SHAPE and NGMIX, which produce catalogs of 2.12 million and 3.44 million galaxies respectively. We also detail a set of null tests for the shear measurements and find that they pass the requirements for systematic errors at the level necessary for weak lensing science applications using the SVmore » data. Furthermore, we discuss some of the planned algorithmic improvements that will be necessary to produce sufficiently accurate shear catalogs for the full 5-year DES, which is expected to cover 5000 square degrees.« less

The DES Science Verification Weak Lensing Shear Catalogs

DOE PAGES

Jarvis, M.

2016-05-01

We present weak lensing shear catalogs for 139 square degrees of data taken during the Science Verification (SV) time for the new Dark Energy Camera (DECam) being used for the Dark Energy Survey (DES). We describe our object selection, point spread function estimation and shear measurement procedures using two independent shear pipelines, IM3SHAPE and NGMIX, which produce catalogs of 2.12 million and 3.44 million galaxies respectively. We also detail a set of null tests for the shear measurements and find that they pass the requirements for systematic errors at the level necessary for weak lensing science applications using the SVmore » data. Furthermore, we discuss some of the planned algorithmic improvements that will be necessary to produce sufficiently accurate shear catalogs for the full 5-year DES, which is expected to cover 5000 square degrees.« less

An Empirical State Error Covariance Matrix for Batch State Estimation

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2011-01-01

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. Consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. It then follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully account for the error in the state estimate. By way of a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm, it is possible to arrive at an appropriate, and formally correct, empirical state error covariance matrix. The first specific step of the method is to use the average form of the weighted measurement residual variance performance index rather than its usual total weighted residual form. Next it is helpful to interpret the solution to the normal equations as the average of a collection of sample vectors drawn from a hypothetical parent population. From here, using a standard statistical analysis approach, it directly follows as to how to determine the standard empirical state error covariance matrix. This matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty. Also, in its most straight forward form, the technique only requires supplemental calculations to be added to existing batch algorithms. The generation of this direct, empirical form of the state error covariance matrix is independent of the dimensionality of the observations. Mixed degrees of freedom for an observation set are allowed. As is the case with any simple, empirical sample variance problems, the presented approach offers an opportunity (at least in the case of weighted least squares) to investigate confidence interval estimates for the error covariance matrix elements. The diagonal or variance terms of the error covariance matrix have a particularly simple form to associate with either a multiple degree of freedom chi-square distribution (more approximate) or with a gamma distribution (less approximate). The off diagonal or covariance terms of the matrix are less clear in their statistical behavior. However, the off diagonal covariance matrix elements still lend themselves to standard confidence interval error analysis. The distributional forms associated with the off diagonal terms are more varied and, perhaps, more approximate than those associated with the diagonal terms. Using a simple weighted least squares sample problem, results obtained through use of the proposed technique are presented. The example consists of a simple, two observer, triangulation problem with range only measurements. Variations of this problem reflect an ideal case (perfect knowledge of the range errors) and a mismodeled case (incorrect knowledge of the range errors).

Proposing a new iterative learning control algorithm based on a non-linear least square formulation - Minimising draw-in errors

NASA Astrophysics Data System (ADS)

Endelt, B.

2017-09-01

Forming operation are subject to external disturbances and changing operating conditions e.g. new material batch, increasing tool temperature due to plastic work, material properties and lubrication is sensitive to tool temperature. It is generally accepted that forming operations are not stable over time and it is not uncommon to adjust the process parameters during the first half hour production, indicating that process instability is gradually developing over time. Thus, in-process feedback control scheme might not-be necessary to stabilize the process and an alternative approach is to apply an iterative learning algorithm, which can learn from previously produced parts i.e. a self learning system which gradually reduces error based on historical process information. What is proposed in the paper is a simple algorithm which can be applied to a wide range of sheet-metal forming processes. The input to the algorithm is the final flange edge geometry and the basic idea is to reduce the least-square error between the current flange geometry and a reference geometry using a non-linear least square algorithm. The ILC scheme is applied to a square deep-drawing and the Numisheet’08 S-rail benchmark problem, the numerical tests shows that the proposed control scheme is able control and stabilise both processes.

Online measurement of urea concentration in spent dialysate during hemodialysis.

PubMed

Olesberg, Jonathon T; Arnold, Mark A; Flanigan, Michael J

2004-01-01

We describe online optical measurements of urea in the effluent dialysate line during regular hemodialysis treatment of several patients. Monitoring urea removal can provide valuable information about dialysis efficiency. Spectral measurements were performed with a Fourier-transform infrared spectrometer equipped with a flow-through cell. Spectra were recorded across the 5000-4000 cm(-1) (2.0-2.5 microm) wavelength range at 1-min intervals. Savitzky-Golay filtering was used to remove baseline variations attributable to the temperature dependence of the water absorption spectrum. Urea concentrations were extracted from the filtered spectra by use of partial least-squares regression and the net analyte signal of urea. Urea concentrations predicted by partial least-squares regression matched concentrations obtained from standard chemical assays with a root mean square error of 0.30 mmol/L (0.84 mg/dL urea nitrogen) over an observed concentration range of 0-11 mmol/L. The root mean square error obtained with the net analyte signal of urea was 0.43 mmol/L with a calibration based only on a set of pure-component spectra. The error decreased to 0.23 mmol/L when a slope and offset correction were used. Urea concentrations can be continuously monitored during hemodialysis by near-infrared spectroscopy. Calibrations based on the net analyte signal of urea are particularly appealing because they do not require a training step, as do statistical multivariate calibration procedures such as partial least-squares regression.

Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction.

PubMed

Huang, Ling; Zhang, Hongping; Xu, Peiliang; Geng, Jianghui; Wang, Cheng; Liu, Jingnan

2017-02-27

Ionospheric delay effect is a critical issue that limits the accuracy of precise Global Navigation Satellite System (GNSS) positioning and navigation for single-frequency users, especially in mid- and low-latitude regions where variations in the ionosphere are larger. Kriging spatial interpolation techniques have been recently introduced to model the spatial correlation and variability of ionosphere, which intrinsically assume that the ionosphere field is stochastically stationary but does not take the random observational errors into account. In this paper, by treating the spatial statistical information on ionosphere as prior knowledge and based on Total Electron Content (TEC) semivariogram analysis, we use Kriging techniques to spatially interpolate TEC values. By assuming that the stochastic models of both the ionospheric signals and measurement errors are only known up to some unknown factors, we propose a new Kriging spatial interpolation method with unknown variance components for both the signals of ionosphere and TEC measurements. Variance component estimation has been integrated with Kriging to reconstruct regional ionospheric delays. The method has been applied to data from the Crustal Movement Observation Network of China (CMONOC) and compared with the ordinary Kriging and polynomial interpolations with spherical cap harmonic functions, polynomial functions and low-degree spherical harmonic functions. The statistics of results indicate that the daily ionospheric variations during the experimental period characterized by the proposed approach have good agreement with the other methods, ranging from 10 to 80 TEC Unit (TECU, 1 TECU = 1 × 10 16 electrons/m²) with an overall mean of 28.2 TECU. The proposed method can produce more appropriate estimations whose general TEC level is as smooth as the ordinary Kriging but with a smaller standard deviation around 3 TECU than others. The residual results show that the interpolation precision of the new proposed method is better than the ordinary Kriging and polynomial interpolation by about 1.2 TECU and 0.7 TECU, respectively. The root mean squared error of the proposed new Kriging with variance components is within 1.5 TECU and is smaller than those from other methods under comparison by about 1 TECU. When compared with ionospheric grid points, the mean squared error of the proposed method is within 6 TECU and smaller than Kriging, indicating that the proposed method can produce more accurate ionospheric delays and better estimation accuracy over China regional area.

Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction

PubMed Central

Huang, Ling; Zhang, Hongping; Xu, Peiliang; Geng, Jianghui; Wang, Cheng; Liu, Jingnan

2017-01-01

Ionospheric delay effect is a critical issue that limits the accuracy of precise Global Navigation Satellite System (GNSS) positioning and navigation for single-frequency users, especially in mid- and low-latitude regions where variations in the ionosphere are larger. Kriging spatial interpolation techniques have been recently introduced to model the spatial correlation and variability of ionosphere, which intrinsically assume that the ionosphere field is stochastically stationary but does not take the random observational errors into account. In this paper, by treating the spatial statistical information on ionosphere as prior knowledge and based on Total Electron Content (TEC) semivariogram analysis, we use Kriging techniques to spatially interpolate TEC values. By assuming that the stochastic models of both the ionospheric signals and measurement errors are only known up to some unknown factors, we propose a new Kriging spatial interpolation method with unknown variance components for both the signals of ionosphere and TEC measurements. Variance component estimation has been integrated with Kriging to reconstruct regional ionospheric delays. The method has been applied to data from the Crustal Movement Observation Network of China (CMONOC) and compared with the ordinary Kriging and polynomial interpolations with spherical cap harmonic functions, polynomial functions and low-degree spherical harmonic functions. The statistics of results indicate that the daily ionospheric variations during the experimental period characterized by the proposed approach have good agreement with the other methods, ranging from 10 to 80 TEC Unit (TECU, 1 TECU = 1 × 1016 electrons/m2) with an overall mean of 28.2 TECU. The proposed method can produce more appropriate estimations whose general TEC level is as smooth as the ordinary Kriging but with a smaller standard deviation around 3 TECU than others. The residual results show that the interpolation precision of the new proposed method is better than the ordinary Kriging and polynomial interpolation by about 1.2 TECU and 0.7 TECU, respectively. The root mean squared error of the proposed new Kriging with variance components is within 1.5 TECU and is smaller than those from other methods under comparison by about 1 TECU. When compared with ionospheric grid points, the mean squared error of the proposed method is within 6 TECU and smaller than Kriging, indicating that the proposed method can produce more accurate ionospheric delays and better estimation accuracy over China regional area. PMID:28264424

Effect of the image resolution on the statistical descriptors of heterogeneous media.

PubMed

Ledesma-Alonso, René; Barbosa, Romeli; Ortegón, Jaime

2018-02-01

The characterization and reconstruction of heterogeneous materials, such as porous media and electrode materials, involve the application of image processing methods to data acquired by scanning electron microscopy or other microscopy techniques. Among them, binarization and decimation are critical in order to compute the correlation functions that characterize the microstructure of the above-mentioned materials. In this study, we present a theoretical analysis of the effects of the image-size reduction, due to the progressive and sequential decimation of the original image. Three different decimation procedures (random, bilinear, and bicubic) were implemented and their consequences on the discrete correlation functions (two-point, line-path, and pore-size distribution) and the coarseness (derived from the local volume fraction) are reported and analyzed. The chosen statistical descriptors (correlation functions and coarseness) are typically employed to characterize and reconstruct heterogeneous materials. A normalization for each of the correlation functions has been performed. When the loss of statistical information has not been significant for a decimated image, its normalized correlation function is forecast by the trend of the original image (reference function). In contrast, when the decimated image does not hold statistical evidence of the original one, the normalized correlation function diverts from the reference function. Moreover, the equally weighted sum of the average of the squared difference, between the discrete correlation functions of the decimated images and the reference functions, leads to a definition of an overall error. During the first stages of the gradual decimation, the error remains relatively small and independent of the decimation procedure. Above a threshold defined by the correlation length of the reference function, the error becomes a function of the number of decimation steps. At this stage, some statistical information is lost and the error becomes dependent on the decimation procedure. These results may help us to restrict the amount of information that one can afford to lose during a decimation process, in order to reduce the computational and memory cost, when one aims to diminish the time consumed by a characterization or reconstruction technique, yet maintaining the statistical quality of the digitized sample.

Effect of the image resolution on the statistical descriptors of heterogeneous media

NASA Astrophysics Data System (ADS)

Ledesma-Alonso, René; Barbosa, Romeli; Ortegón, Jaime

2018-02-01

The characterization and reconstruction of heterogeneous materials, such as porous media and electrode materials, involve the application of image processing methods to data acquired by scanning electron microscopy or other microscopy techniques. Among them, binarization and decimation are critical in order to compute the correlation functions that characterize the microstructure of the above-mentioned materials. In this study, we present a theoretical analysis of the effects of the image-size reduction, due to the progressive and sequential decimation of the original image. Three different decimation procedures (random, bilinear, and bicubic) were implemented and their consequences on the discrete correlation functions (two-point, line-path, and pore-size distribution) and the coarseness (derived from the local volume fraction) are reported and analyzed. The chosen statistical descriptors (correlation functions and coarseness) are typically employed to characterize and reconstruct heterogeneous materials. A normalization for each of the correlation functions has been performed. When the loss of statistical information has not been significant for a decimated image, its normalized correlation function is forecast by the trend of the original image (reference function). In contrast, when the decimated image does not hold statistical evidence of the original one, the normalized correlation function diverts from the reference function. Moreover, the equally weighted sum of the average of the squared difference, between the discrete correlation functions of the decimated images and the reference functions, leads to a definition of an overall error. During the first stages of the gradual decimation, the error remains relatively small and independent of the decimation procedure. Above a threshold defined by the correlation length of the reference function, the error becomes a function of the number of decimation steps. At this stage, some statistical information is lost and the error becomes dependent on the decimation procedure. These results may help us to restrict the amount of information that one can afford to lose during a decimation process, in order to reduce the computational and memory cost, when one aims to diminish the time consumed by a characterization or reconstruction technique, yet maintaining the statistical quality of the digitized sample.

An information-theoretic approach to motor action decoding with a reconfigurable parallel architecture.

PubMed

Craciun, Stefan; Brockmeier, Austin J; George, Alan D; Lam, Herman; Príncipe, José C

2011-01-01

Methods for decoding movements from neural spike counts using adaptive filters often rely on minimizing the mean-squared error. However, for non-Gaussian distribution of errors, this approach is not optimal for performance. Therefore, rather than using probabilistic modeling, we propose an alternate non-parametric approach. In order to extract more structure from the input signal (neuronal spike counts) we propose using minimum error entropy (MEE), an information-theoretic approach that minimizes the error entropy as part of an iterative cost function. However, the disadvantage of using MEE as the cost function for adaptive filters is the increase in computational complexity. In this paper we present a comparison between the decoding performance of the analytic Wiener filter and a linear filter trained with MEE, which is then mapped to a parallel architecture in reconfigurable hardware tailored to the computational needs of the MEE filter. We observe considerable speedup from the hardware design. The adaptation of filter weights for the multiple-input, multiple-output linear filters, necessary in motor decoding, is a highly parallelizable algorithm. It can be decomposed into many independent computational blocks with a parallel architecture readily mapped to a field-programmable gate array (FPGA) and scales to large numbers of neurons. By pipelining and parallelizing independent computations in the algorithm, the proposed parallel architecture has sublinear increases in execution time with respect to both window size and filter order.

Computer routines for probability distributions, random numbers, and related functions

USGS Publications Warehouse

Kirby, W.

1983-01-01

Use of previously coded and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main progress. The probability distributions provided include the beta, chi-square, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F. Other mathematical functions include the Bessel function, I sub o, gamma and log-gamma functions, error functions, and exponential integral. Auxiliary services include sorting and printer-plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)

Criterion Predictability: Identifying Differences Between [r-squares

ERIC Educational Resources Information Center

Malgady, Robert G.

1976-01-01

An analysis of variance procedure for testing differences in r-squared, the coefficient of determination, across independent samples is proposed and briefly discussed. The principal advantage of the procedure is to minimize Type I error for follow-up tests of pairwise differences. (Author/JKS)

Computational Thermochemistry: Scale Factor Databases and Scale Factors for Vibrational Frequencies Obtained from Electronic Model Chemistries.

PubMed

Alecu, I M; Zheng, Jingjing; Zhao, Yan; Truhlar, Donald G

2010-09-14

Optimized scale factors for calculating vibrational harmonic and fundamental frequencies and zero-point energies have been determined for 145 electronic model chemistries, including 119 based on approximate functionals depending on occupied orbitals, 19 based on single-level wave function theory, three based on the neglect-of-diatomic-differential-overlap, two based on doubly hybrid density functional theory, and two based on multicoefficient correlation methods. Forty of the scale factors are obtained from large databases, which are also used to derive two universal scale factor ratios that can be used to interconvert between scale factors optimized for various properties, enabling the derivation of three key scale factors at the effort of optimizing only one of them. A reduced scale factor optimization model is formulated in order to further reduce the cost of optimizing scale factors, and the reduced model is illustrated by using it to obtain 105 additional scale factors. Using root-mean-square errors from the values in the large databases, we find that scaling reduces errors in zero-point energies by a factor of 2.3 and errors in fundamental vibrational frequencies by a factor of 3.0, but it reduces errors in harmonic vibrational frequencies by only a factor of 1.3. It is shown that, upon scaling, the balanced multicoefficient correlation method based on coupled cluster theory with single and double excitations (BMC-CCSD) can lead to very accurate predictions of vibrational frequencies. With a polarized, minimally augmented basis set, the density functionals with zero-point energy scale factors closest to unity are MPWLYP1M (1.009), τHCTHhyb (0.989), BB95 (1.012), BLYP (1.013), BP86 (1.014), B3LYP (0.986), MPW3LYP (0.986), and VSXC (0.986).

Estimation of time averages from irregularly spaced observations - With application to coastal zone color scanner estimates of chlorophyll concentration

NASA Technical Reports Server (NTRS)

Chelton, Dudley B.; Schlax, Michael G.

1991-01-01

The sampling error of an arbitrary linear estimate of a time-averaged quantity constructed from a time series of irregularly spaced observations at a fixed located is quantified through a formalism. The method is applied to satellite observations of chlorophyll from the coastal zone color scanner. The two specific linear estimates under consideration are the composite average formed from the simple average of all observations within the averaging period and the optimal estimate formed by minimizing the mean squared error of the temporal average based on all the observations in the time series. The resulting suboptimal estimates are shown to be more accurate than composite averages. Suboptimal estimates are also found to be nearly as accurate as optimal estimates using the correct signal and measurement error variances and correlation functions for realistic ranges of these parameters, which makes it a viable practical alternative to the composite average method generally employed at present.

Prediction of thermal conductivity of polyvinylpyrrolidone (PVP) electrospun nanocomposite fibers using artificial neural network and prey-predator algorithm.

PubMed

Khan, Waseem S; Hamadneh, Nawaf N; Khan, Waqar A

2017-01-01

In this study, multilayer perception neural network (MLPNN) was employed to predict thermal conductivity of PVP electrospun nanocomposite fibers with multiwalled carbon nanotubes (MWCNTs) and Nickel Zinc ferrites [(Ni0.6Zn0.4) Fe2O4]. This is the second attempt on the application of MLPNN with prey predator algorithm for the prediction of thermal conductivity of PVP electrospun nanocomposite fibers. The prey predator algorithm was used to train the neural networks to find the best models. The best models have the minimal of sum squared error between the experimental testing data and the corresponding models results. The minimal error was found to be 0.0028 for MWCNTs model and 0.00199 for Ni-Zn ferrites model. The predicted artificial neural networks (ANNs) responses were analyzed statistically using z-test, correlation coefficient, and the error functions for both inclusions. The predicted ANN responses for PVP electrospun nanocomposite fibers were compared with the experimental data and were found in good agreement.

Performance of the Generalized S-X[squared] Item Fit Index for the Graded Response Model

ERIC Educational Resources Information Center

Kang, Taehoon; Chen, Troy T.

2011-01-01

The utility of Orlando and Thissen's ("2000", "2003") S-X[squared] fit index was extended to the model-fit analysis of the graded response model (GRM). The performance of a modified S-X[squared] in assessing item-fit of the GRM was investigated in light of empirical Type I error rates and power with a simulation study having…

Chemometrics resolution and quantification power evaluation: Application on pharmaceutical quaternary mixture of Paracetamol, Guaifenesin, Phenylephrine and p-aminophenol

NASA Astrophysics Data System (ADS)

Yehia, Ali M.; Mohamed, Heba M.

2016-01-01

Three advanced chemmometric-assisted spectrophotometric methods namely; Concentration Residuals Augmented Classical Least Squares (CRACLS), Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) and Principal Component Analysis-Artificial Neural Networks (PCA-ANN) were developed, validated and benchmarked to PLS calibration; to resolve the severely overlapped spectra and simultaneously determine; Paracetamol (PAR), Guaifenesin (GUA) and Phenylephrine (PHE) in their ternary mixture and in presence of p-aminophenol (AP) the main degradation product and synthesis impurity of Paracetamol. The analytical performance of the proposed methods was described by percentage recoveries, root mean square error of calibration and standard error of prediction. The four multivariate calibration methods could be directly used without any preliminary separation step and successfully applied for pharmaceutical formulation analysis, showing no excipients' interference.

An Interactive Computer Package for Use with Simulation Models Which Performs Multidimensional Sensitivity Analysis by Employing the Techniques of Response Surface Methodology.

DTIC Science & Technology

1984-12-01

total sum of squares at the center points minus the correction factor for the mean at the center points ( SSpe =Y’Y-nlY), where n1 is the number of...SSlac=SSres- SSpe ). The sum of squares due to pure error estimates 0" and the sum of squares due to lack-of-fit estimates 0’" plus a bias term if...Response Surface Methodology Source d.f. SS MS Regression n b’X1 Y b’XVY/n Residual rn-n Y’Y-b’X’ *Y (Y’Y-b’X’Y)/(n-n) Pure Error ni-i Y’Y-nl1Y SSpe / (ni

RM2: rms error comparisons

NASA Technical Reports Server (NTRS)

Rice, R. F.

1976-01-01

The root-mean-square error performance measure is used to compare the relative performance of several widely known source coding algorithms with the RM2 image data compression system. The results demonstrate that RM2 has a uniformly significant performance advantage.

Cervicocephalic kinesthetic sensibility in young and middle-aged adults with or without a history of mild neck pain.

PubMed

Teng, C-C; Chai, H; Lai, D-M; Wang, S-F

2007-02-01

Previous research has shown that there is no significant relationship between the degree of structural degeneration of the cervical spine and neck pain. We therefore sought to investigate the potential role of sensory dysfunction in chronic neck pain. Cervicocephalic kinesthetic sensibility, expressed by how accurately an individual can reposition the head, was studied in three groups of individuals, a control group of 20 asymptomatic young adults and two groups of middle-aged adults (20 subjects in each group) with or without a history of mild neck pain. An ultrasound-based three-dimensional coordinate measuring system was used to measure the position of the head and to test the accuracy of repositioning. Constant error (indicating that the subject overshot or undershot the intended position) and root mean square errors (representing total errors of accuracy and variability) were measured during repositioning of the head to the neutral head position (Head-to-NHP) and repositioning of the head to the target (Head-to-Target) in three cardinal planes (sagittal, transverse, and frontal). Analysis of covariance (ANCOVA) was used to test the group effect, with age used as a covariate. The constant errors during repositioning from a flexed position and from an extended position to the NHP were significantly greater in the middle-aged subjects than in the control group (beta=0.30 and beta=0.60, respectively; P<0.05 for both). In addition, the root mean square errors during repositioning from a flexed or extended position to the NHP were greater in the middle-aged subjects than in the control group (beta=0.27 and beta=0.49, respectively; P<0.05 for both). The root mean square errors also increased during Head-to-Target in left rotation (beta=0.24;P<0.05), but there was no difference in the constant errors or root mean square errors during Head-to-NHP repositioning from other target positions (P>0.05). The results indicate that, after controlling for age as a covariate, there was no group effect. Thus, age appears to have a profound effect on an individual's ability to accurately reposition the head toward the neutral position in the sagittal plane and repositioning the head toward left rotation. A history of mild chronic neck pain alone had no significant effect on cervicocephalic kinesthetic sensibility.

Monte Carlo point process estimation of electromyographic envelopes from motor cortical spikes for brain-machine interfaces

NASA Astrophysics Data System (ADS)

Liao, Yuxi; She, Xiwei; Wang, Yiwen; Zhang, Shaomin; Zhang, Qiaosheng; Zheng, Xiaoxiang; Principe, Jose C.

2015-12-01

Objective. Representation of movement in the motor cortex (M1) has been widely studied in brain-machine interfaces (BMIs). The electromyogram (EMG) has greater bandwidth than the conventional kinematic variables (such as position, velocity), and is functionally related to the discharge of cortical neurons. As the stochastic information of EMG is derived from the explicit spike time structure, point process (PP) methods will be a good solution for decoding EMG directly from neural spike trains. Previous studies usually assume linear or exponential tuning curves between neural firing and EMG, which may not be true. Approach. In our analysis, we estimate the tuning curves in a data-driven way and find both the traditional functional-excitatory and functional-inhibitory neurons, which are widely found across a rat’s motor cortex. To accurately decode EMG envelopes from M1 neural spike trains, the Monte Carlo point process (MCPP) method is implemented based on such nonlinear tuning properties. Main results. Better reconstruction of EMG signals is shown on baseline and extreme high peaks, as our method can better preserve the nonlinearity of the neural tuning during decoding. The MCPP improves the prediction accuracy (the normalized mean squared error) 57% and 66% on average compared with the adaptive point process filter using linear and exponential tuning curves respectively, for all 112 data segments across six rats. Compared to a Wiener filter using spike rates with an optimal window size of 50 ms, MCPP decoding EMG from a point process improves the normalized mean square error (NMSE) by 59% on average. Significance. These results suggest that neural tuning is constantly changing during task execution and therefore, the use of spike timing methodologies and estimation of appropriate tuning curves needs to be undertaken for better EMG decoding in motor BMIs.

What Are Error Rates for Classifying Teacher and School Performance Using Value-Added Models?

ERIC Educational Resources Information Center

Schochet, Peter Z.; Chiang, Hanley S.

2013-01-01

This article addresses likely error rates for measuring teacher and school performance in the upper elementary grades using value-added models applied to student test score gain data. Using a realistic performance measurement system scheme based on hypothesis testing, the authors develop error rate formulas based on ordinary least squares and…

Quantitative Modelling of Trace Elements in Hard Coal.

PubMed

Smoliński, Adam; Howaniec, Natalia

2016-01-01

The significance of coal in the world economy remains unquestionable for decades. It is also expected to be the dominant fossil fuel in the foreseeable future. The increased awareness of sustainable development reflected in the relevant regulations implies, however, the need for the development and implementation of clean coal technologies on the one hand, and adequate analytical tools on the other. The paper presents the application of the quantitative Partial Least Squares method in modeling the concentrations of trace elements (As, Ba, Cd, Co, Cr, Cu, Mn, Ni, Pb, Rb, Sr, V and Zn) in hard coal based on the physical and chemical parameters of coal, and coal ash components. The study was focused on trace elements potentially hazardous to the environment when emitted from coal processing systems. The studied data included 24 parameters determined for 132 coal samples provided by 17 coal mines of the Upper Silesian Coal Basin, Poland. Since the data set contained outliers, the construction of robust Partial Least Squares models for contaminated data set and the correct identification of outlying objects based on the robust scales were required. These enabled the development of the correct Partial Least Squares models, characterized by good fit and prediction abilities. The root mean square error was below 10% for all except for one the final Partial Least Squares models constructed, and the prediction error (root mean square error of cross-validation) exceeded 10% only for three models constructed. The study is of both cognitive and applicative importance. It presents the unique application of the chemometric methods of data exploration in modeling the content of trace elements in coal. In this way it contributes to the development of useful tools of coal quality assessment.

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

NASA Astrophysics Data System (ADS)

Schaffrin, Burkhard; Felus, Yaron A.

2008-06-01

The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model ( Y- E Y = ( X- E X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E Y and E X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler-Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335-342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.

Quantitative Modelling of Trace Elements in Hard Coal

PubMed Central

Smoliński, Adam; Howaniec, Natalia

2016-01-01

The significance of coal in the world economy remains unquestionable for decades. It is also expected to be the dominant fossil fuel in the foreseeable future. The increased awareness of sustainable development reflected in the relevant regulations implies, however, the need for the development and implementation of clean coal technologies on the one hand, and adequate analytical tools on the other. The paper presents the application of the quantitative Partial Least Squares method in modeling the concentrations of trace elements (As, Ba, Cd, Co, Cr, Cu, Mn, Ni, Pb, Rb, Sr, V and Zn) in hard coal based on the physical and chemical parameters of coal, and coal ash components. The study was focused on trace elements potentially hazardous to the environment when emitted from coal processing systems. The studied data included 24 parameters determined for 132 coal samples provided by 17 coal mines of the Upper Silesian Coal Basin, Poland. Since the data set contained outliers, the construction of robust Partial Least Squares models for contaminated data set and the correct identification of outlying objects based on the robust scales were required. These enabled the development of the correct Partial Least Squares models, characterized by good fit and prediction abilities. The root mean square error was below 10% for all except for one the final Partial Least Squares models constructed, and the prediction error (root mean square error of cross–validation) exceeded 10% only for three models constructed. The study is of both cognitive and applicative importance. It presents the unique application of the chemometric methods of data exploration in modeling the content of trace elements in coal. In this way it contributes to the development of useful tools of coal quality assessment. PMID:27438794

Psychometric characteristics of the Functional Assessment of Cancer Therapy-General when applied to Brazilian cancer patients: a cross-cultural adaptation and validation.

PubMed

Campos, Juliana Alvares Duarte Bonini; Spexoto, Maria Cláudia Bernardes; Serrano, Sergio Vicente; Maroco, João

2016-01-13

The psychometric properties of an instrument should be evaluated routinely when using different samples. This study evaluated the psychometric properties of the Functional Assessment of Cancer Therapy-General (FACT-G) when applied to a sample of Brazilian cancer patients. The face, content, and construct (factorial, convergent, and discriminant) validities of the FACT-G were estimated. Confirmatory factor analysis (CFA) was conducted the ratio chi-square by degrees of freedom (χ (2)/df), the comparative fit index (CFI), the Tucker-Lewis index (TLI), and the root mean square error of approximation (RMSEA) as indices. The invariance of the best model was assessed with multi-group analysis using the difference of chi-squares method (Δχ(2)). Convergent validity was assessed using Average Variance Extracted (AVE) and discriminant validity was determined via correlational analysis. Internal consistency was assessed using the Cronbach's alpha (α) coefficient, and the Composite Reliability (CR) was estimated. A total of 975 cancer patients participated in the study, with a mean age of 53.3 (SD = 13.0) years. Of these participants, 61.5 % were women. In CFA, five correlations between errors were included to fit the FACT-G to the sample (χ (2)/df = 8.611, CFI = .913, TLI = .902, RMSEA = .088). The model did not indicate invariant independent samples (Δχ(2): μ: p < .001, i: p < .958, Cov: p < .001, Res: p < .001). While there was adequate convergent validity for the physical well-being (AVE = .54) and social and family Well-being factors (AVE = .55), there was low convergent validity for the other factors. Reliability was adequate (CR = .76-.89 and α = .71-.82). Functional well-being, emotional well-being, and physical well-being were the factors that demonstrated a strong contribution to patients' health-related quality of life (β = -.99, .88, and .64, respectively). The FACT-G was found to be a valid and reliable assessment of health-related quality of life in a Brazilian sample of patients with cancer.

A GPU-based symmetric non-rigid image registration method in human lung.

PubMed

Haghighi, Babak; D Ellingwood, Nathan; Yin, Youbing; Hoffman, Eric A; Lin, Ching-Long

2018-03-01

Quantitative computed tomography (QCT) of the lungs plays an increasing role in identifying sub-phenotypes of pathologies previously lumped into broad categories such as chronic obstructive pulmonary disease and asthma. Methods for image matching and linking multiple lung volumes have proven useful in linking structure to function and in the identification of regional longitudinal changes. Here, we seek to improve the accuracy of image matching via the use of a symmetric multi-level non-rigid registration employing an inverse consistent (IC) transformation whereby images are registered both in the forward and reverse directions. To develop the symmetric method, two similarity measures, the sum of squared intensity difference (SSD) and the sum of squared tissue volume difference (SSTVD), were used. The method is based on a novel generic mathematical framework to include forward and backward transformations, simultaneously, eliminating the need to compute the inverse transformation. Two implementations were used to assess the proposed method: a two-dimensional (2-D) implementation using synthetic examples with SSD, and a multi-core CPU and graphics processing unit (GPU) implementation with SSTVD for three-dimensional (3-D) human lung datasets (six normal adults studied at total lung capacity (TLC) and functional residual capacity (FRC)). Success was evaluated in terms of the IC transformation consistency serving to link TLC to FRC. 2-D registration on synthetic images, using both symmetric and non-symmetric SSD methods, and comparison of displacement fields showed that the symmetric method gave a symmetrical grid shape and reduced IC errors, with the mean values of IC errors decreased by 37%. Results for both symmetric and non-symmetric transformations of human datasets showed that the symmetric method gave better results for IC errors in all cases, with mean values of IC errors for the symmetric method lower than the non-symmetric methods using both SSD and SSTVD. The GPU version demonstrated an average of 43 times speedup and ~5.2 times speedup over the single-threaded and 12-threaded CPU versions, respectively. Run times with the GPU were as fast as 2 min. The symmetric method improved the inverse consistency, aiding the use of image registration in the QCT-based evaluation of the lung.

Phase-Based Adaptive Estimation of Magnitude-Squared Coherence Between Turbofan Internal Sensors and Far-Field Microphone Signals

NASA Technical Reports Server (NTRS)

Miles, Jeffrey Hilton

2015-01-01

A cross-power spectrum phase based adaptive technique is discussed which iteratively determines the time delay between two digitized signals that are coherent. The adaptive delay algorithm belongs to a class of algorithms that identifies a minimum of a pattern matching function. The algorithm uses a gradient technique to find the value of the adaptive delay that minimizes a cost function based in part on the slope of a linear function that fits the measured cross power spectrum phase and in part on the standard error of the curve fit. This procedure is applied to data from a Honeywell TECH977 static-engine test. Data was obtained using a combustor probe, two turbine exit probes, and far-field microphones. Signals from this instrumentation are used estimate the post-combustion residence time in the combustor. Comparison with previous studies of the post-combustion residence time validates this approach. In addition, the procedure removes the bias due to misalignment of signals in the calculation of coherence which is a first step in applying array processing methods to the magnitude squared coherence data. The procedure also provides an estimate of the cross-spectrum phase-offset.

Validation of the Malay version of the Inventory of Functional Status after Childbirth questionnaire.

PubMed

Noor, Norhayati Mohd; Aziz, Aniza Abd; Mostapa, Mohd Rosmizaki; Awang, Zainudin

2015-01-01

This study was designed to examine the psychometric properties of Malay version of the Inventory of Functional Status after Childbirth (IFSAC). A cross-sectional study. A total of 108 postpartum mothers attending Obstetrics and Gynaecology Clinic, in a tertiary teaching hospital in Malaysia, were involved. Construct validity and internal consistency were performed after the translation, content validity, and face validity process. The data were analyzed using Analysis of Moment Structure version 18 and Statistical Packages for the Social Sciences version 20. The final model consists of four constructs, namely, infant care, personal care, household activities, and social and community activities, with 18 items demonstrating acceptable factor loadings, domain to domain correlation, and best fit (Chi-squared/degree of freedom = 1.678; Tucker-Lewis index = 0.923; comparative fit index = 0.936; and root mean square error of approximation = 0.080). Composite reliability and average variance extracted of the domains ranged from 0.659 to 0.921 and from 0.499 to 0.628, respectively. The study suggested that the four-factor model with 18 items of the Malay version of IFSAC was acceptable to be used to measure functional status after childbirth because it is valid, reliable, and simple.

Electrocardiogram signal denoising based on a new improved wavelet thresholding

NASA Astrophysics Data System (ADS)

Han, Guoqiang; Xu, Zhijun

2016-08-01

Good quality electrocardiogram (ECG) is utilized by physicians for the interpretation and identification of physiological and pathological phenomena. In general, ECG signals may mix various noises such as baseline wander, power line interference, and electromagnetic interference in gathering and recording process. As ECG signals are non-stationary physiological signals, wavelet transform is investigated to be an effective tool to discard noises from corrupted signals. A new compromising threshold function called sigmoid function-based thresholding scheme is adopted in processing ECG signals. Compared with other methods such as hard/soft thresholding or other existing thresholding functions, the new algorithm has many advantages in the noise reduction of ECG signals. It perfectly overcomes the discontinuity at ±T of hard thresholding and reduces the fixed deviation of soft thresholding. The improved wavelet thresholding denoising can be proved to be more efficient than existing algorithms in ECG signal denoising. The signal to noise ratio, mean square error, and percent root mean square difference are calculated to verify the denoising performance as quantitative tools. The experimental results reveal that the waves including P, Q, R, and S waves of ECG signals after denoising coincide with the original ECG signals by employing the new proposed method.

Postural control model interpretation of stabilogram diffusion analysis

NASA Technical Reports Server (NTRS)

Peterka, R. J.

2000-01-01

Collins and De Luca [Collins JJ. De Luca CJ (1993) Exp Brain Res 95: 308-318] introduced a new method known as stabilogram diffusion analysis that provides a quantitative statistical measure of the apparently random variations of center-of-pressure (COP) trajectories recorded during quiet upright stance in humans. This analysis generates a stabilogram diffusion function (SDF) that summarizes the mean square COP displacement as a function of the time interval between COP comparisons. SDFs have a characteristic two-part form that suggests the presence of two different control regimes: a short-term open-loop control behavior and a longer-term closed-loop behavior. This paper demonstrates that a very simple closed-loop control model of upright stance can generate realistic SDFs. The model consists of an inverted pendulum body with torque applied at the ankle joint. This torque includes a random disturbance torque and a control torque. The control torque is a function of the deviation (error signal) between the desired upright body position and the actual body position, and is generated in proportion to the error signal, the derivative of the error signal, and the integral of the error signal [i.e. a proportional, integral and derivative (PID) neural controller]. The control torque is applied with a time delay representing conduction, processing, and muscle activation delays. Variations in the PID parameters and the time delay generate variations in SDFs that mimic real experimental SDFs. This model analysis allows one to interpret experimentally observed changes in SDFs in terms of variations in neural controller and time delay parameters rather than in terms of open-loop versus closed-loop behavior.

Determining particle size and water content by near-infrared spectroscopy in the granulation of naproxen sodium.

PubMed

Bär, David; Debus, Heiko; Brzenczek, Sina; Fischer, Wolfgang; Imming, Peter

2018-03-20

Near-infrared spectroscopy is frequently used by the pharmaceutical industry to monitor and optimize several production processes. In combination with chemometrics, a mathematical-statistical technique, the following advantages of near-infrared spectroscopy can be applied: It is a fast, non-destructive, non-invasive, and economical analytical method. One of the most advanced and popular chemometric technique is the partial least square algorithm with its best applicability in routine and its results. The required reference analytic enables the analysis of various parameters of interest, for example, moisture content, particle size, and many others. Parameters like the correlation coefficient, root mean square error of prediction, root mean square error of calibration, and root mean square error of validation have been used for evaluating the applicability and robustness of these analytical methods developed. This study deals with investigating a Naproxen Sodium granulation process using near-infrared spectroscopy and the development of water content and particle-size methods. For the water content method, one should consider a maximum water content of about 21% in the granulation process, which must be confirmed by the loss on drying. Further influences to be considered are the constantly changing product temperature, rising to about 54 °C, the creation of hydrated states of Naproxen Sodium when using a maximum of about 21% water content, and the large quantity of about 87% Naproxen Sodium in the formulation. It was considered to use a combination of these influences in developing the near-infrared spectroscopy method for the water content of Naproxen Sodium granules. The "Root Mean Square Error" was 0.25% for calibration dataset and 0.30% for the validation dataset, which was obtained after different stages of optimization by multiplicative scatter correction and the first derivative. Using laser diffraction, the granules have been analyzed for particle sizes and obtaining the summary sieve sizes of >63 μm and >100 μm. The following influences should be considered for application in routine production: constant changes in water content up to 21% and a product temperature up to 54 °C. The different stages of optimization result in a "Root Mean Square Error" of 2.54% for the calibration data set and 3.53% for the validation set by using the Kubelka-Munk conversion and first derivative for the near-infrared spectroscopy method for a particle size >63 μm. For the near-infrared spectroscopy method using a particle size >100 μm, the "Root Mean Square Error" was 3.47% for the calibration data set and 4.51% for the validation set, while using the same pre-treatments. - The robustness and suitability of this methodology has already been demonstrated by its recent successful implementation in a routine granulate production process. Copyright © 2018 Elsevier B.V. All rights reserved.

The Influence of Dimensionality on Estimation in the Partial Credit Model.

ERIC Educational Resources Information Center

De Ayala, R. J.

1995-01-01

The effect of multidimensionality on partial credit model parameter estimation was studied with noncompensatory and compensatory data. Analysis results, consisting of root mean square error bias, Pearson product-moment corrections, standardized root mean squared differences, standardized differences between means, and descriptive statistics…

Silicon photonic integrated circuit for fast and precise dual-comb distance metrology.

PubMed

Weimann, C; Lauermann, M; Hoeller, F; Freude, W; Koos, C

2017-11-27

We demonstrate an optical distance sensor integrated on a silicon photonic chip with a footprint of well below 1 mm 2 . The integrated system comprises a heterodyne receiver structure with tunable power splitting ratio and on-chip photodetectors. The functionality of the device is demonstrated in a synthetic-wavelength interferometry experiment using frequency combs as optical sources. We obtain accurate and fast distance measurements with an unambiguity range of 3.75 mm, a root-mean-square error of 3.4 µm and acquisition times of 14 µs.

A unified development of several techniques for the representation of random vectors and data sets

NASA Technical Reports Server (NTRS)

Bundick, W. T.

1973-01-01

Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.

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

USGS Publications Warehouse

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

2008-01-01

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

Computational logic with square rings of nanomagnets

NASA Astrophysics Data System (ADS)

Arava, Hanu; Derlet, Peter M.; Vijayakumar, Jaianth; Cui, Jizhai; Bingham, Nicholas S.; Kleibert, Armin; Heyderman, Laura J.

2018-06-01

Nanomagnets are a promising low-power alternative to traditional computing. However, the successful implementation of nanomagnets in logic gates has been hindered so far by a lack of reliability. Here, we present a novel design with dipolar-coupled nanomagnets arranged on a square lattice to (i) support transfer of information and (ii) perform logic operations. We introduce a thermal protocol, using thermally active nanomagnets as a means to perform computation. Within this scheme, the nanomagnets are initialized by a global magnetic field and thermally relax on raising the temperature with a resistive heater. We demonstrate error-free transfer of information in chains of up to 19 square rings and we show a high level of reliability with successful gate operations of ∼94% across more than 2000 logic gates. Finally, we present a functionally complete prototype NAND/NOR logic gate that could be implemented for advanced logic operations. Here we support our experiments with simulations of the thermally averaged output and determine the optimal gate parameters. Our approach provides a new pathway to a long standing problem concerning reliability in the use of nanomagnets for computation.

Static shape control for flexible structures

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Scheid, R. E., Jr.

1986-01-01

An integrated methodology is described for defining static shape control laws for large flexible structures. The techniques include modeling, identifying and estimating the control laws of distributed systems characterized in terms of infinite dimensional state and parameter spaces. The models are expressed as interconnected elliptic partial differential equations governing a range of static loads, with the capability of analyzing electromagnetic fields around antenna systems. A second-order analysis is carried out for statistical errors, and model parameters are determined by maximizing an appropriate defined likelihood functional which adjusts the model to observational data. The parameter estimates are derived from the conditional mean of the observational data, resulting in a least squares superposition of shape functions obtained from the structural model.

Predicting ambient aerosol Thermal Optical Reflectance (TOR) measurements from infrared spectra: organic carbon

NASA Astrophysics Data System (ADS)

Dillner, A. M.; Takahama, S.

2014-11-01

Organic carbon (OC) can constitute 50% or more of the mass of atmospheric particulate matter. Typically, the organic carbon concentration is measured using thermal methods such as Thermal-Optical Reflectance (TOR) from quartz fiber filters. Here, methods are presented whereby Fourier Transform Infrared (FT-IR) absorbance spectra from polytetrafluoroethylene (PTFE or Teflon) filters are used to accurately predict TOR OC. Transmittance FT-IR analysis is rapid, inexpensive, and non-destructive to the PTFE filters. To develop and test the method, FT-IR absorbance spectra are obtained from 794 samples from seven Interagency Monitoring of PROtected Visual Environment (IMPROVE) sites sampled during 2011. Partial least squares regression is used to calibrate sample FT-IR absorbance spectra to artifact-corrected TOR OC. The FTIR spectra are divided into calibration and test sets by sampling site and date which leads to precise and accurate OC predictions by FT-IR as indicated by high coefficient of determination (R2; 0.96), low bias (0.02 μg m-3, all μg m-3 values based on the nominal IMPROVE sample volume of 32.8 m-3), low error (0.08 μg m-3) and low normalized error (11%). These performance metrics can be achieved with various degrees of spectral pretreatment (e.g., including or excluding substrate contributions to the absorbances) and are comparable in precision and accuracy to collocated TOR measurements. FT-IR spectra are also divided into calibration and test sets by OC mass and by OM / OC which reflects the organic composition of the particulate matter and is obtained from organic functional group composition; this division also leads to precise and accurate OC predictions. Low OC concentrations have higher bias and normalized error due to TOR analytical errors and artifact correction errors, not due to the range of OC mass of the samples in the calibration set. However, samples with low OC mass can be used to predict samples with high OC mass indicating that the calibration is linear. Using samples in the calibration set that have a different OM / OC or ammonium / OC distributions than the test set leads to only a modest increase in bias and normalized error in the predicted samples. We conclude that FT-IR analysis with partial least squares regression is a robust method for accurately predicting TOR OC in IMPROVE network samples; providing complementary information to the organic functional group composition and organic aerosol mass estimated previously from the same set of sample spectra (Ruthenburg et al., 2014).

Superresolution Interferometric Imaging with Sparse Modeling Using Total Squared Variation: Application to Imaging the Black Hole Shadow

NASA Astrophysics Data System (ADS)

Kuramochi, Kazuki; Akiyama, Kazunori; Ikeda, Shiro; Tazaki, Fumie; Fish, Vincent L.; Pu, Hung-Yi; Asada, Keiichi; Honma, Mareki

2018-05-01

We propose a new imaging technique for interferometry using sparse modeling, utilizing two regularization terms: the ℓ 1-norm and a new function named total squared variation (TSV) of the brightness distribution. First, we demonstrate that our technique may achieve a superresolution of ∼30% compared with the traditional CLEAN beam size using synthetic observations of two point sources. Second, we present simulated observations of three physically motivated static models of Sgr A* with the Event Horizon Telescope (EHT) to show the performance of proposed techniques in greater detail. Remarkably, in both the image and gradient domains, the optimal beam size minimizing root-mean-squared errors is ≲10% of the traditional CLEAN beam size for ℓ 1+TSV regularization, and non-convolved reconstructed images have smaller errors than beam-convolved reconstructed images. This indicates that TSV is well matched to the expected physical properties of the astronomical images and the traditional post-processing technique of Gaussian convolution in interferometric imaging may not be required. We also propose a feature-extraction method to detect circular features from the image of a black hole shadow and use it to evaluate the performance of the image reconstruction. With this method and reconstructed images, the EHT can constrain the radius of the black hole shadow with an accuracy of ∼10%–20% in present simulations for Sgr A*, suggesting that the EHT would be able to provide useful independent measurements of the mass of the supermassive black holes in Sgr A* and also another primary target, M87.

Navy Fuel Composition and Screening Tool (FCAST) v2.8

DTIC Science & Technology

2016-05-10

allowed us to develop partial least squares (PLS) models based on gas chromatography–mass spectrometry (GC-MS) data that predict fuel properties. The...Chemometric property modeling Partial least squares PLS Compositional profiler Naval Air Systems Command Air-4.4.5 Patuxent River Naval Air Station Patuxent...Cumulative predicted residual error sum of squares DiEGME Diethylene glycol monomethyl ether FCAST Fuel Composition and Screening Tool FFP Fit for

Robust Mean and Covariance Structure Analysis through Iteratively Reweighted Least Squares.

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Bentler, Peter M.

2000-01-01

Adapts robust schemes to mean and covariance structures, providing an iteratively reweighted least squares approach to robust structural equation modeling. Each case is weighted according to its distance, based on first and second order moments. Test statistics and standard error estimators are given. (SLD)

Latin-square three-dimensional gage master

DOEpatents

Jones, L.

1981-05-12

A gage master for coordinate measuring machines has an nxn array of objects distributed in the Z coordinate utilizing the concept of a Latin square experimental design. Using analysis of variance techniques, the invention may be used to identify sources of error in machine geometry and quantify machine accuracy.

Latin square three dimensional gage master

DOEpatents

Jones, Lynn L.

1982-01-01

A gage master for coordinate measuring machines has an nxn array of objects distributed in the Z coordinate utilizing the concept of a Latin square experimental design. Using analysis of variance techniques, the invention may be used to identify sources of error in machine geometry and quantify machine accuracy.

Effect of nonideal square-law detection on static calibration in noise-injection radiometers

NASA Technical Reports Server (NTRS)

Hearn, C. P.

1984-01-01

The effect of nonideal square-law detection on the static calibration for a class of Dicke radiometers is examined. It is shown that fourth-order curvature in the detection characteristic adds a nonlinear term to the linear calibration relationship normally ascribed to noise-injection, balanced Dicke radiometers. The minimum error, based on an optimum straight-line fit to the calibration curve, is derived in terms of the power series coefficients describing the input-output characteristics of the detector. These coefficients can be determined by simple measurements, and detection nonlinearity is, therefore, quantitatively related to radiometric measurement error.

VizieR Online Data Catalog: delta Cep VEGA/CHARA observing log (Nardetto+, 2016)

NASA Astrophysics Data System (ADS)

Nardetto, N.; Merand, A.; Mourard, D.; Storm, J.; Gieren, W.; Fouque, P.; Gallenne, A.; Graczyk, D.; Kervella, P.; Neilson, H.; Pietrzynski, G.; Pilecki, B.; Breitfelder, J.; Berio, P.; Challouf, M.; Clausse, J.-M.; Ligi, R.; Mathias, P.; Meilland, A.; Perraut, K.; Poretti, E.; Rainer, M.; Spang, A.; Stee, P.; Tallon-Bosc, I.; Ten Brummelaar, T.

2016-07-01

The columns give, respectively, the date, the RJD, the hour angle (HA), the minimum and maximum wavelengths over which the squared visibility is calculated, the projected baseline length Bp and its orientation PA, the signal-to-noise ratio on the fringe peak; the last column provides the calibrated squared visibility V2 together with the statistic error on V2, and the systematic error on V2 (see text for details). The data are available on the Jean-Marie Mariotti Center OiDB service (Available at http://oidb.jmmc.fr). (1 data file).

A network application for modeling a centrifugal compressor performance map

NASA Astrophysics Data System (ADS)

Nikiforov, A.; Popova, D.; Soldatova, K.

2017-08-01

The approximation of aerodynamic performance of a centrifugal compressor stage and vaneless diffuser by neural networks is presented. Advantages, difficulties and specific features of the method are described. An example of a neural network and its structure is shown. The performances in terms of efficiency, pressure ratio and work coefficient of 39 model stages within the range of flow coefficient from 0.01 to 0.08 were modeled with mean squared error 1.5 %. In addition, the loss and friction coefficients of vaneless diffusers of relative widths 0.014-0.10 are modeled with mean squared error 2.45 %.

Predicting preference-based SF-6D index scores from the SF-8 health survey.

PubMed

Wang, P; Fu, A Z; Wee, H L; Lee, J; Tai, E S; Thumboo, J; Luo, N

2013-09-01

To develop and test functions for predicting the preference-based SF-6D index scores from the SF-8 health survey. This study was a secondary analysis of data collected in a population health survey in which respondents (n = 7,529) completed both the SF-36 and the SF-8 questionnaires. We examined seven ordinary least-square estimators for their performance in predicting SF-6D scores from the SF-8 at both the individual and the group levels. In general, all functions performed similarly well in predicting SF-6D scores, and the predictions at the group level were better than predictions at the individual level. At the individual level, 42.5-51.5% of prediction errors were smaller than the minimally important difference (MID) of the SF-6D scores, depending on the function specifications, while almost all prediction errors of the tested functions were smaller than the MID of SF-6D at the group level. At both individual and group levels, the tested functions predicted lower than actual scores at the higher end of the SF-6D scale. Our study developed functions to generate preference-based SF-6D index scores from the SF-8 health survey, the first of its kind. Further research is needed to evaluate the performance and validity of the prediction functions.

Tissue resistivity estimation in the presence of positional and geometrical uncertainties.

PubMed

Baysal, U; Eyüboğlu, B M

2000-08-01

Geometrical uncertainties (organ boundary variation and electrode position uncertainties) are the biggest sources of error in estimating electrical resistivity of tissues from body surface measurements. In this study, in order to decrease estimation errors, the statistically constrained minimum mean squared error estimation algorithm (MiMSEE) is constrained with a priori knowledge of the geometrical uncertainties in addition to the constraints based on geometry, resistivity range, linearization and instrumentation errors. The MiMSEE calculates an optimum inverse matrix, which maps the surface measurements to the unknown resistivity distribution. The required data are obtained from four-electrode impedance measurements, similar to injected-current electrical impedance tomography (EIT). In this study, the surface measurements are simulated by using a numerical thorax model. The data are perturbed with additive instrumentation noise. Simulated surface measurements are then used to estimate the tissue resistivities by using the proposed algorithm. The results are compared with the results of conventional least squares error estimator (LSEE). Depending on the region, the MiMSEE yields an estimation error between 0.42% and 31.3% compared with 7.12% to 2010% for the LSEE. It is shown that the MiMSEE is quite robust even in the case of geometrical uncertainties.

A nonlinear model of gold production in Malaysia

NASA Astrophysics Data System (ADS)

Ramli, Norashikin; Muda, Nora; Umor, Mohd Rozi

2014-06-01

Malaysia is a country which is rich in natural resources and one of it is a gold. Gold has already become an important national commodity. This study is conducted to determine a model that can be well fitted with the gold production in Malaysia from the year 1995-2010. Five nonlinear models are presented in this study which are Logistic model, Gompertz, Richard, Weibull and Chapman-Richard model. These model are used to fit the cumulative gold production in Malaysia. The best model is then selected based on the model performance. The performance of the fitted model is measured by sum squares error, root mean squares error, coefficient of determination, mean relative error, mean absolute error and mean absolute percentage error. This study has found that a Weibull model is shown to have significantly outperform compare to the other models. To confirm that Weibull is the best model, the latest data are fitted to the model. Once again, Weibull model gives the lowest readings at all types of measurement error. We can concluded that the future gold production in Malaysia can be predicted according to the Weibull model and this could be important findings for Malaysia to plan their economic activities.

Comparison of structural and least-squares lines for estimating geologic relations

USGS Publications Warehouse

Williams, G.P.; Troutman, B.M.

1990-01-01

Two different goals in fitting straight lines to data are to estimate a "true" linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating "true" straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal-predicting the dependent variable-OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples. ?? 1990 International Association for Mathematical Geology.

A Generic Nonlinear Aerodynamic Model for Aircraft

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2014-01-01

A generic model of the aerodynamic coefficients was developed using wind tunnel databases for eight different aircraft and multivariate orthogonal functions. For each database and each coefficient, models were determined using polynomials expanded about the state and control variables, and an othgonalization procedure. A predicted squared-error criterion was used to automatically select the model terms. Modeling terms picked in at least half of the analyses, which totalled 45 terms, were retained to form the generic nonlinear aerodynamic (GNA) model. Least squares was then used to estimate the model parameters and associated uncertainty that best fit the GNA model to each database. Nonlinear flight simulations were used to demonstrate that the GNA model produces accurate trim solutions, local behavior (modal frequencies and damping ratios), and global dynamic behavior (91% accurate state histories and 80% accurate aerodynamic coefficient histories) under large-amplitude excitation. This compact aerodynamics model can be used to decrease on-board memory storage requirements, quickly change conceptual aircraft models, provide smooth analytical functions for control and optimization applications, and facilitate real-time parametric system identification.

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

NASA Astrophysics Data System (ADS)

Parmar, Kulwinder Singh; Bhardwaj, Rashmi

2014-12-01

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

Evaluation of the CEAS model for barley yields in North Dakota and Minnesota

NASA Technical Reports Server (NTRS)

Barnett, T. L. (Principal Investigator)

1981-01-01

The CEAS yield model is based upon multiple regression analysis at the CRD and state levels. For the historical time series, yield is regressed on a set of variables derived from monthly mean temperature and monthly precipitation. Technological trend is represented by piecewise linear and/or quadriatic functions of year. Indicators of yield reliability obtained from a ten-year bootstrap test (1970-79) demonstrated that biases are small and performance as indicated by the root mean square errors are acceptable for intended application, however, model response for individual years particularly unusual years, is not very reliable and shows some large errors. The model is objective, adequate, timely, simple and not costly. It considers scientific knowledge on a broad scale but not in detail, and does not provide a good current measure of modeled yield reliability.

Measurement accuracies in band-limited extrapolation

NASA Technical Reports Server (NTRS)

Kritikos, H. N.

1982-01-01

The problem of numerical instability associated with extrapolation algorithms is addressed. An attempt is made to estimate the bounds for the acceptable errors and to place a ceiling on the measurement accuracy and computational accuracy needed for the extrapolation. It is shown that in band limited (or visible angle limited) extrapolation the larger effective aperture L' that can be realized from a finite aperture L by over sampling is a function of the accuracy of measurements. It is shown that for sampling in the interval L/b absolute value of xL, b1 the signal must be known within an error e sub N given by e sub N squared approximately = 1/4(2kL') cubed (e/8b L/L')(2kL') where L is the physical aperture, L' is the extrapolated aperture, and k = 2pi lambda.

Prediction of pKa Values for Neutral and Basic Drugs based on Hybrid Artificial Intelligence Methods.

PubMed

Li, Mengshan; Zhang, Huaijing; Chen, Bingsheng; Wu, Yan; Guan, Lixin

2018-03-05

The pKa value of drugs is an important parameter in drug design and pharmacology. In this paper, an improved particle swarm optimization (PSO) algorithm was proposed based on the population entropy diversity. In the improved algorithm, when the population entropy was higher than the set maximum threshold, the convergence strategy was adopted; when the population entropy was lower than the set minimum threshold the divergence strategy was adopted; when the population entropy was between the maximum and minimum threshold, the self-adaptive adjustment strategy was maintained. The improved PSO algorithm was applied in the training of radial basis function artificial neural network (RBF ANN) model and the selection of molecular descriptors. A quantitative structure-activity relationship model based on RBF ANN trained by the improved PSO algorithm was proposed to predict the pKa values of 74 kinds of neutral and basic drugs and then validated by another database containing 20 molecules. The validation results showed that the model had a good prediction performance. The absolute average relative error, root mean square error, and squared correlation coefficient were 0.3105, 0.0411, and 0.9685, respectively. The model can be used as a reference for exploring other quantitative structure-activity relationships.

Estimating the concentration of urea and creatinine in the human serum of normal and dialysis patients through Raman spectroscopy.

PubMed

de Almeida, Maurício Liberal; Saatkamp, Cassiano Junior; Fernandes, Adriana Barrinha; Pinheiro, Antonio Luiz Barbosa; Silveira, Landulfo

2016-09-01

Urea and creatinine are commonly used as biomarkers of renal function. Abnormal concentrations of these biomarkers are indicative of pathological processes such as renal failure. This study aimed to develop a model based on Raman spectroscopy to estimate the concentration values of urea and creatinine in human serum. Blood sera from 55 clinically normal subjects and 47 patients with chronic kidney disease undergoing dialysis were collected, and concentrations of urea and creatinine were determined by spectrophotometric methods. A Raman spectrum was obtained with a high-resolution dispersive Raman spectrometer (830 nm). A spectral model was developed based on partial least squares (PLS), where the concentrations of urea and creatinine were correlated with the Raman features. Principal components analysis (PCA) was used to discriminate dialysis patients from normal subjects. The PLS model showed r = 0.97 and r = 0.93 for urea and creatinine, respectively. The root mean square errors of cross-validation (RMSECV) for the model were 17.6 and 1.94 mg/dL, respectively. PCA showed high discrimination between dialysis and normality (95 % accuracy). The Raman technique was able to determine the concentrations with low error and to discriminate dialysis from normal subjects, consistent with a rapid and low-cost test.

Mortality risk score prediction in an elderly population using machine learning.

PubMed

Rose, Sherri

2013-03-01

Standard practice for prediction often relies on parametric regression methods. Interesting new methods from the machine learning literature have been introduced in epidemiologic studies, such as random forest and neural networks. However, a priori, an investigator will not know which algorithm to select and may wish to try several. Here I apply the super learner, an ensembling machine learning approach that combines multiple algorithms into a single algorithm and returns a prediction function with the best cross-validated mean squared error. Super learning is a generalization of stacking methods. I used super learning in the Study of Physical Performance and Age-Related Changes in Sonomans (SPPARCS) to predict death among 2,066 residents of Sonoma, California, aged 54 years or more during the period 1993-1999. The super learner for predicting death (risk score) improved upon all single algorithms in the collection of algorithms, although its performance was similar to that of several algorithms. Super learner outperformed the worst algorithm (neural networks) by 44% with respect to estimated cross-validated mean squared error and had an R2 value of 0.201. The improvement of super learner over random forest with respect to R2 was approximately 2-fold. Alternatives for risk score prediction include the super learner, which can provide improved performance.

Acoustic-articulatory mapping in vowels by locally weighted regression

PubMed Central

McGowan, Richard S.; Berger, Michael A.

2009-01-01

A method for mapping between simultaneously measured articulatory and acoustic data is proposed. The method uses principal components analysis on the articulatory and acoustic variables, and mapping between the domains by locally weighted linear regression, or loess [Cleveland, W. S. (1979). J. Am. Stat. Assoc. 74, 829–836]. The latter method permits local variation in the slopes of the linear regression, assuming that the function being approximated is smooth. The methodology is applied to vowels of four speakers in the Wisconsin X-ray Microbeam Speech Production Database, with formant analysis. Results are examined in terms of (1) examples of forward (articulation-to-acoustics) mappings and inverse mappings, (2) distributions of local slopes and constants, (3) examples of correlations among slopes and constants, (4) root-mean-square error, and (5) sensitivity of formant frequencies to articulatory change. It is shown that the results are qualitatively correct and that loess performs better than global regression. The forward mappings show different root-mean-square error properties than the inverse mappings indicating that this method is better suited for the forward mappings than the inverse mappings, at least for the data chosen for the current study. Some preliminary results on sensitivity of the first two formant frequencies to the two most important articulatory principal components are presented. PMID:19813812

A comparative study of kinetic and connectionist modeling for shelf-life prediction of Basundi mix.

PubMed

Ruhil, A P; Singh, R R B; Jain, D K; Patel, A A; Patil, G R

2011-04-01

A ready-to-reconstitute formulation of Basundi, a popular Indian dairy dessert was subjected to storage at various temperatures (10, 25 and 40 °C) and deteriorative changes in the Basundi mix were monitored using quality indices like pH, hydroxyl methyl furfural (HMF), bulk density (BD) and insolubility index (II). The multiple regression equations and the Arrhenius functions that describe the parameters' dependence on temperature for the four physico-chemical parameters were integrated to develop mathematical models for predicting sensory quality of Basundi mix. Connectionist model using multilayer feed forward neural network with back propagation algorithm was also developed for predicting the storage life of the product employing artificial neural network (ANN) tool box of MATLAB software. The quality indices served as the input parameters whereas the output parameters were the sensorily evaluated flavour and total sensory score. A total of 140 observations were used and the prediction performance was judged on the basis of per cent root mean square error. The results obtained from the two approaches were compared. Relatively lower magnitudes of percent root mean square error for both the sensory parameters indicated that the connectionist models were better fitted than kinetic models for predicting storage life.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Methods of automatic nucleotide-sequence analysis. Multicomponent spectrophotometric analysis of mixtures of nucleic acid components by a least-squares procedure

PubMed Central

Lee, Sheila; McMullen, D.; Brown, G. L.; Stokes, A. R.

1965-01-01

1. A theoretical analysis of the errors in multicomponent spectrophotometric analysis of nucleoside mixtures, by a least-squares procedure, has been made to obtain an expression for the error coefficient, relating the error in calculated concentration to the error in extinction measurements. 2. The error coefficients, which depend only on the `library' of spectra used to fit the experimental curves, have been computed for a number of `libraries' containing the following nucleosides found in s-RNA: adenosine, guanosine, cytidine, uridine, 5-ribosyluracil, 7-methylguanosine, 6-dimethylaminopurine riboside, 6-methylaminopurine riboside and thymine riboside. 3. The error coefficients have been used to determine the best conditions for maximum accuracy in the determination of the compositions of nucleoside mixtures. 4. Experimental determinations of the compositions of nucleoside mixtures have been made and the errors found to be consistent with those predicted by the theoretical analysis. 5. It has been demonstrated that, with certain precautions, the multicomponent spectrophotometric method described is suitable as a basis for automatic nucleotide-composition analysis of oligonucleotides containing nine nucleotides. Used in conjunction with continuous chromatography and flow chemical techniques, this method can be applied to the study of the sequence of s-RNA. PMID:14346087

From least squares to multilevel modeling: A graphical introduction to Bayesian inference

NASA Astrophysics Data System (ADS)

Loredo, Thomas J.

2016-01-01

This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.

Chemometrics resolution and quantification power evaluation: Application on pharmaceutical quaternary mixture of Paracetamol, Guaifenesin, Phenylephrine and p-aminophenol.

PubMed

Yehia, Ali M; Mohamed, Heba M

2016-01-05

Three advanced chemmometric-assisted spectrophotometric methods namely; Concentration Residuals Augmented Classical Least Squares (CRACLS), Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) and Principal Component Analysis-Artificial Neural Networks (PCA-ANN) were developed, validated and benchmarked to PLS calibration; to resolve the severely overlapped spectra and simultaneously determine; Paracetamol (PAR), Guaifenesin (GUA) and Phenylephrine (PHE) in their ternary mixture and in presence of p-aminophenol (AP) the main degradation product and synthesis impurity of Paracetamol. The analytical performance of the proposed methods was described by percentage recoveries, root mean square error of calibration and standard error of prediction. The four multivariate calibration methods could be directly used without any preliminary separation step and successfully applied for pharmaceutical formulation analysis, showing no excipients' interference. Copyright © 2015 Elsevier B.V. All rights reserved.

CARS Spectral Fitting with Multiple Resonant Species using Sparse Libraries

NASA Technical Reports Server (NTRS)

Cutler, Andrew D.; Magnotti, Gaetano

2010-01-01

The dual pump CARS technique is often used in the study of turbulent flames. Fast and accurate algorithms are needed for fitting dual-pump CARS spectra for temperature and multiple chemical species. This paper describes the development of such an algorithm. The algorithm employs sparse libraries, whose size grows much more slowly with number of species than a conventional library. The method was demonstrated by fitting synthetic "experimental" spectra containing 4 resonant species (N2, O2, H2 and CO2), both with noise and without it, and by fitting experimental spectra from a H2-air flame produced by a Hencken burner. In both studies, weighted least squares fitting of signal, as opposed to least squares fitting signal or square-root signal, was shown to produce the least random error and minimize bias error in the fitted parameters.

Nondestructive quantification of the soluble-solids content and the available acidity of apples by Fourier-transform near-infrared spectroscopy

NASA Astrophysics Data System (ADS)

Ying, Yibin; Liu, Yande; Tao, Yang

2005-09-01

This research evaluated the feasibility of using Fourier-transform near-infrared (FT-NIR) spectroscopy to quantify the soluble-solids content (SSC) and the available acidity (VA) in intact apples. Partial least-squares calibration models, obtained from several preprocessing techniques (smoothing, derivative, etc.) in several wave-number ranges were compared. The best models were obtained with the high coefficient determination (r) 0.940 for the SSC and a moderate r of 0.801 for the VA, root-mean-square errors of prediction of 0.272% and 0.053%, and root-mean-square errors of calibration of 0.261% and 0.046%, respectively. The results indicate that the FT-NIR spectroscopy yields good predictions of the SSC and also showed the feasibility of using it to predict the VA of apples.

Rovibrational spectra of ammonia. I. Unprecedented accuracy of a potential energy surface used with nonadiabatic corrections.

PubMed

Huang, Xinchuan; Schwenke, David W; Lee, Timothy J

2011-01-28

In this work, we build upon our previous work on the theoretical spectroscopy of ammonia, NH(3). Compared to our 2008 study, we include more physics in our rovibrational calculations and more experimental data in the refinement procedure, and these enable us to produce a potential energy surface (PES) of unprecedented accuracy. We call this the HSL-2 PES. The additional physics we include is a second-order correction for the breakdown of the Born-Oppenheimer approximation, and we find it to be critical for improved results. By including experimental data for higher rotational levels in the refinement procedure, we were able to greatly reduce our systematic errors for the rotational dependence of our predictions. These additions together lead to a significantly improved total angular momentum (J) dependence in our computed rovibrational energies. The root-mean-square error between our predictions using the HSL-2 PES and the reliable energy levels from the HITRAN database for J = 0-6 and J = 7∕8 for (14)NH(3) is only 0.015 cm(-1) and 0.020∕0.023 cm(-1), respectively. The root-mean-square errors for the characteristic inversion splittings are approximately 1∕3 smaller than those for energy levels. The root-mean-square error for the 6002 J = 0-8 transition energies is 0.020 cm(-1). Overall, for J = 0-8, the spectroscopic data computed with HSL-2 is roughly an order of magnitude more accurate relative to our previous best ammonia PES (denoted HSL-1). These impressive numbers are eclipsed only by the root-mean-square error between our predictions for purely rotational transition energies of (15)NH(3) and the highly accurate Cologne database (CDMS): 0.00034 cm(-1) (10 MHz), in other words, 2 orders of magnitude smaller. In addition, we identify a deficiency in the (15)NH(3) energy levels determined from a model of the experimental data.

Simultaneous estimation of cross-validation errors in least squares collocation applied for statistical testing and evaluation of the noise variance components

NASA Astrophysics Data System (ADS)

Behnabian, Behzad; Mashhadi Hossainali, Masoud; Malekzadeh, Ahad

2018-02-01

The cross-validation technique is a popular method to assess and improve the quality of prediction by least squares collocation (LSC). We present a formula for direct estimation of the vector of cross-validation errors (CVEs) in LSC which is much faster than element-wise CVE computation. We show that a quadratic form of CVEs follows Chi-squared distribution. Furthermore, a posteriori noise variance factor is derived by the quadratic form of CVEs. In order to detect blunders in the observations, estimated standardized CVE is proposed as the test statistic which can be applied when noise variances are known or unknown. We use LSC together with the methods proposed in this research for interpolation of crustal subsidence in the northern coast of the Gulf of Mexico. The results show that after detection and removing outliers, the root mean square (RMS) of CVEs and estimated noise standard deviation are reduced about 51 and 59%, respectively. In addition, RMS of LSC prediction error at data points and RMS of estimated noise of observations are decreased by 39 and 67%, respectively. However, RMS of LSC prediction error on a regular grid of interpolation points covering the area is only reduced about 4% which is a consequence of sparse distribution of data points for this case study. The influence of gross errors on LSC prediction results is also investigated by lower cutoff CVEs. It is indicated that after elimination of outliers, RMS of this type of errors is also reduced by 19.5% for a 5 km radius of vicinity. We propose a method using standardized CVEs for classification of dataset into three groups with presumed different noise variances. The noise variance components for each of the groups are estimated using restricted maximum-likelihood method via Fisher scoring technique. Finally, LSC assessment measures were computed for the estimated heterogeneous noise variance model and compared with those of the homogeneous model. The advantage of the proposed method is the reduction in estimated noise levels for those groups with the fewer number of noisy data points.

Prediction of gas chromatographic retention indices by the use of radial basis function neural networks.

PubMed

Yao, Xiaojun; Zhang, Xiaoyun; Zhang, Ruisheng; Liu, Mancang; Hu, Zhide; Fan, Botao

2002-05-16

A new method for the prediction of retention indices for a diverse set of compounds from their physicochemical parameters has been proposed. The two used input parameters for representing molecular properties are boiling point and molar volume. Models relating relationships between physicochemical parameters and retention indices of compounds are constructed by means of radial basis function neural networks. To get the best prediction results, some strategies are also employed to optimize the topology and learning parameters of the RBFNNs. For the test set, a predictive correlation coefficient R=0.9910 and root mean squared error of 14.1 are obtained. Results show that radial basis function networks can give satisfactory prediction ability and its optimization is less-time consuming and easy to implement.

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

DOE PAGES

Huang, Lei; Xue, Junpeng; Gao, Bo; ...

2016-12-21

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

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

Huang, Lei; Xue, Junpeng; Gao, Bo

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

Measures of precision for dissimilarity-based multivariate analysis of ecological communities

PubMed Central

Anderson, Marti J; Santana-Garcon, Julia

2015-01-01

Ecological studies require key decisions regarding the appropriate size and number of sampling units. No methods currently exist to measure precision for multivariate assemblage data when dissimilarity-based analyses are intended to follow. Here, we propose a pseudo multivariate dissimilarity-based standard error (MultSE) as a useful quantity for assessing sample-size adequacy in studies of ecological communities. Based on sums of squared dissimilarities, MultSE measures variability in the position of the centroid in the space of a chosen dissimilarity measure under repeated sampling for a given sample size. We describe a novel double resampling method to quantify uncertainty in MultSE values with increasing sample size. For more complex designs, values of MultSE can be calculated from the pseudo residual mean square of a permanova model, with the double resampling done within appropriate cells in the design. R code functions for implementing these techniques, along with ecological examples, are provided. PMID:25438826

Pursuit gain and saccadic intrusions in first-degree relatives of probands with schizophrenia.

PubMed

Clementz, B A; Sweeney, J A; Hirt, M; Haas, G

1990-11-01

Oculomotor functioning of 26 probands with schizophrenia, 12 spectrum and 46 nonspectrum first-degree relatives, and 38 nonpsychiatric control subjects was evaluated. Spectrum relatives had more anticipatory saccades (ASs) and lower pursuit gain than nonspectrum relatives, who had more ASs and lower pursuit gain than control subjects. Probands also had lower pursuit gain than nonspectrum relatives and control subjects but did not differ from other groups on AS frequency. Control subjects had more globally accurate pursuit tracking (root mean square [RMS] error deviation) than both relative groups, whereas probands had the poorest RMS scores. Square wave jerk frequency did not differentiate the groups. Attention enhancement affected the frequency of ASs but did not affect either the other intrusive saccadic event or RMS scores. These results offer evidence that eye-movement dysfunction may serve as a biological marker for schizophrenia.

Small convolution kernels for high-fidelity image restoration

NASA Technical Reports Server (NTRS)

Reichenbach, Stephen E.; Park, Stephen K.

1991-01-01

An algorithm is developed for computing the mean-square-optimal values for small, image-restoration kernels. The algorithm is based on a comprehensive, end-to-end imaging system model that accounts for the important components of the imaging process: the statistics of the scene, the point-spread function of the image-gathering device, sampling effects, noise, and display reconstruction. Subject to constraints on the spatial support of the kernel, the algorithm generates the kernel values that restore the image with maximum fidelity, that is, the kernel minimizes the expected mean-square restoration error. The algorithm is consistent with the derivation of the spatially unconstrained Wiener filter, but leads to a small, spatially constrained kernel that, unlike the unconstrained filter, can be efficiently implemented by convolution. Simulation experiments demonstrate that for a wide range of imaging systems these small kernels can restore images with fidelity comparable to images restored with the unconstrained Wiener filter.

Simultaneous determination of three herbicides by differential pulse voltammetry and chemometrics.

PubMed

Ni, Yongnian; Wang, Lin; Kokot, Serge

2011-01-01

A novel differential pulse voltammetry method (DPV) was researched and developed for the simultaneous determination of Pendimethalin, Dinoseb and sodium 5-nitroguaiacolate (5NG) with the aid of chemometrics. The voltammograms of these three compounds overlapped significantly, and to facilitate the simultaneous determination of the three analytes, chemometrics methods were applied. These included classical least squares (CLS), principal component regression (PCR), partial least squares (PLS) and radial basis function-artificial neural networks (RBF-ANN). A separately prepared verification data set was used to confirm the calibrations, which were built from the original and first derivative data matrices of the voltammograms. On the basis relative prediction errors and recoveries of the analytes, the RBF-ANN and the DPLS (D - first derivative spectra) models performed best and are particularly recommended for application. The DPLS calibration model was applied satisfactorily for the prediction of the three analytes from market vegetables and lake water samples.

Red Wine Age Estimation by the Alteration of Its Color Parameters: Fourier Transform Infrared Spectroscopy as a Tool to Monitor Wine Maturation Time

PubMed Central

Basalekou, M.; Pappas, C.; Kotseridis, Y.; Tarantilis, P. A.; Kontaxakis, E.

2017-01-01

Color, phenolic content, and chemical age values of red wines made from Cretan grape varieties (Kotsifali, Mandilari) were evaluated over nine months of maturation in different containers for two vintages. The wines differed greatly on their anthocyanin profiles. Mid-IR spectra were also recorded with the use of a Fourier Transform Infrared Spectrophotometer in ZnSe disk mode. Analysis of Variance was used to explore the parameter's dependency on time. Determination models were developed for the chemical age indexes using Partial Least Squares (PLS) (TQ Analyst software) considering the spectral region 1830–1500 cm−1. The correlation coefficients (r) for chemical age index i were 0.86 for Kotsifali (Root Mean Square Error of Calibration (RMSEC) = 0.067, Root Mean Square Error of Prediction (RMSEP) = 0,115, and Root Mean Square Error of Validation (RMSECV) = 0.164) and 0.90 for Mandilari (RMSEC = 0.050, RMSEP = 0.040, and RMSECV = 0.089). For chemical age index ii the correlation coefficients (r) were 0.86 and 0.97 for Kotsifali (RMSEC 0.044, RMSEP = 0.087, and RMSECV = 0.214) and Mandilari (RMSEC = 0.024, RMSEP = 0.033, and RMSECV = 0.078), respectively. The proposed method is simpler, less time consuming, and more economical and does not require chemical reagents. PMID:29225994

Application of near-infrared spectroscopy for the rapid quality assessment of Radix Paeoniae Rubra

NASA Astrophysics Data System (ADS)

Zhan, Hao; Fang, Jing; Tang, Liying; Yang, Hongjun; Li, Hua; Wang, Zhuju; Yang, Bin; Wu, Hongwei; Fu, Meihong

2017-08-01

Near-infrared (NIR) spectroscopy with multivariate analysis was used to quantify gallic acid, catechin, albiflorin, and paeoniflorin in Radix Paeoniae Rubra, and the feasibility to classify the samples originating from different areas was investigated. A new high-performance liquid chromatography method was developed and validated to analyze gallic acid, catechin, albiflorin, and paeoniflorin in Radix Paeoniae Rubra as the reference. Partial least squares (PLS), principal component regression (PCR), and stepwise multivariate linear regression (SMLR) were performed to calibrate the regression model. Different data pretreatments such as derivatives (1st and 2nd), multiplicative scatter correction, standard normal variate, Savitzky-Golay filter, and Norris derivative filter were applied to remove the systematic errors. The performance of the model was evaluated according to the root mean square of calibration (RMSEC), root mean square error of prediction (RMSEP), root mean square error of cross-validation (RMSECV), and correlation coefficient (r). The results show that compared to PCR and SMLR, PLS had a lower RMSEC, RMSECV, and RMSEP and higher r for all the four analytes. PLS coupled with proper pretreatments showed good performance in both the fitting and predicting results. Furthermore, the original areas of Radix Paeoniae Rubra samples were partly distinguished by principal component analysis. This study shows that NIR with PLS is a reliable, inexpensive, and rapid tool for the quality assessment of Radix Paeoniae Rubra.

Quick method (FT-NIR) for the determination of oil and major fatty acids content in whole achenes of milk thistle (Silybum marianum (L.) Gaertn.).

PubMed

Koláčková, Pavla; Růžičková, Gabriela; Gregor, Tomáš; Šišperová, Eliška

2015-08-30

Calibration models for the Fourier transform-near infrared (FT-NIR) instrument were developed for quick and non-destructive determination of oil and fatty acids in whole achenes of milk thistle. Samples with a range of oil and fatty acid levels were collected and their transmittance spectra were obtained by the FT-NIR instrument. Based on these spectra and data gained by the means of the reference method - Soxhlet extraction and gas chromatography (GC) - calibration models were created by means of partial least square (PLS) regression analysis. Precision and accuracy of the calibration models was verified via the cross-validation of validation samples whose spectra were not part of the calibration model and also according to the root mean square error of prediction (RMSEP), root mean square error of calibration (RMSEC), root mean square error of cross-validation (RMSECV) and the validation coefficient of determination (R(2) ). R(2) for whole seeds were 0.96, 0.96, 0.83 and 0.67 and the RMSEP values were 0.76, 1.68, 1.24, 0.54 for oil, linoleic (C18:2), oleic (C18:1) and palmitic (C16:0) acids, respectively. The calibration models are appropriate for the non-destructive determination of oil and fatty acids levels in whole seeds of milk thistle. © 2014 Society of Chemical Industry.

Green method by diffuse reflectance infrared spectroscopy and spectral region selection for the quantification of sulphamethoxazole and trimethoprim in pharmaceutical formulations.

PubMed

da Silva, Fabiana E B; Flores, Érico M M; Parisotto, Graciele; Müller, Edson I; Ferrão, Marco F

2016-03-01

An alternative method for the quantification of sulphametoxazole (SMZ) and trimethoprim (TMP) using diffuse reflectance infrared Fourier-transform spectroscopy (DRIFTS) and partial least square regression (PLS) was developed. Interval Partial Least Square (iPLS) and Synergy Partial Least Square (siPLS) were applied to select a spectral range that provided the lowest prediction error in comparison to the full-spectrum model. Fifteen commercial tablet formulations and forty-nine synthetic samples were used. The ranges of concentration considered were 400 to 900 mg g-1SMZ and 80 to 240 mg g-1 TMP. Spectral data were recorded between 600 and 4000 cm-1 with a 4 cm-1 resolution by Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS). The proposed procedure was compared to high performance liquid chromatography (HPLC). The results obtained from the root mean square error of prediction (RMSEP), during the validation of the models for samples of sulphamethoxazole (SMZ) and trimethoprim (TMP) using siPLS, demonstrate that this approach is a valid technique for use in quantitative analysis of pharmaceutical formulations. The selected interval algorithm allowed building regression models with minor errors when compared to the full spectrum PLS model. A RMSEP of 13.03 mg g-1for SMZ and 4.88 mg g-1 for TMP was obtained after the selection the best spectral regions by siPLS.

Detection of Glutamic Acid in Oilseed Rape Leaves Using Near Infrared Spectroscopy and the Least Squares-Support Vector Machine

PubMed Central

Bao, Yidan; Kong, Wenwen; Liu, Fei; Qiu, Zhengjun; He, Yong

2012-01-01

Amino acids are quite important indices to indicate the growth status of oilseed rape under herbicide stress. Near infrared (NIR) spectroscopy combined with chemometrics was applied for fast determination of glutamic acid in oilseed rape leaves. The optimal spectral preprocessing method was obtained after comparing Savitzky-Golay smoothing, standard normal variate, multiplicative scatter correction, first and second derivatives, detrending and direct orthogonal signal correction. Linear and nonlinear calibration methods were developed, including partial least squares (PLS) and least squares-support vector machine (LS-SVM). The most effective wavelengths (EWs) were determined by the successive projections algorithm (SPA), and these wavelengths were used as the inputs of PLS and LS-SVM model. The best prediction results were achieved by SPA-LS-SVM (Raw) model with correlation coefficient r = 0.9943 and root mean squares error of prediction (RMSEP) = 0.0569 for prediction set. These results indicated that NIR spectroscopy combined with SPA-LS-SVM was feasible for the fast and effective detection of glutamic acid in oilseed rape leaves. The selected EWs could be used to develop spectral sensors, and the important and basic amino acid data were helpful to study the function mechanism of herbicide. PMID:23203052

New method for propagating the square root covariance matrix in triangular form. [using Kalman-Bucy filter

NASA Technical Reports Server (NTRS)

Choe, C. Y.; Tapley, B. D.

1975-01-01

A method proposed by Potter of applying the Kalman-Bucy filter to the problem of estimating the state of a dynamic system is described, in which the square root of the state error covariance matrix is used to process the observations. A new technique which propagates the covariance square root matrix in lower triangular form is given for the discrete observation case. The technique is faster than previously proposed algorithms and is well-adapted for use with the Carlson square root measurement algorithm.

A Comparison of Normal and Elliptical Estimation Methods in Structural Equation Models.

ERIC Educational Resources Information Center

Schumacker, Randall E.; Cheevatanarak, Suchittra

Monte Carlo simulation compared chi-square statistics, parameter estimates, and root mean square error of approximation values using normal and elliptical estimation methods. Three research conditions were imposed on the simulated data: sample size, population contamination percent, and kurtosis. A Bentler-Weeks structural model established the…

Phase modulation for reduced vibration sensitivity in laser-cooled clocks in space

NASA Technical Reports Server (NTRS)

Klipstein, W.; Dick, G.; Jefferts, S.; Walls, F.

2001-01-01

The standard interrogation technique in atomic beam clocks is square-wave frequency modulation (SWFM), which suffers a first order sensitivity to vibrations as changes in the transit time of the atoms translates to perceived frequency errors. Square-wave phase modulation (SWPM) interrogation eliminates sensitivity to this noise.

An Examination of Statistical Power in Multigroup Dynamic Structural Equation Models

ERIC Educational Resources Information Center

Prindle, John J.; McArdle, John J.

2012-01-01

This study used statistical simulation to calculate differential statistical power in dynamic structural equation models with groups (as in McArdle & Prindle, 2008). Patterns of between-group differences were simulated to provide insight into how model parameters influence power approximations. Chi-square and root mean square error of…

Parameter estimation of Monod model by the Least-Squares method for microalgae Botryococcus Braunii sp

NASA Astrophysics Data System (ADS)

See, J. J.; Jamaian, S. S.; Salleh, R. M.; Nor, M. E.; Aman, F.

2018-04-01

This research aims to estimate the parameters of Monod model of microalgae Botryococcus Braunii sp growth by the Least-Squares method. Monod equation is a non-linear equation which can be transformed into a linear equation form and it is solved by implementing the Least-Squares linear regression method. Meanwhile, Gauss-Newton method is an alternative method to solve the non-linear Least-Squares problem with the aim to obtain the parameters value of Monod model by minimizing the sum of square error ( SSE). As the result, the parameters of the Monod model for microalgae Botryococcus Braunii sp can be estimated by the Least-Squares method. However, the estimated parameters value obtained by the non-linear Least-Squares method are more accurate compared to the linear Least-Squares method since the SSE of the non-linear Least-Squares method is less than the linear Least-Squares method.

Light Scattered from Polished Optical Surfaces: Wings of the Point Spread Function

NASA Technical Reports Server (NTRS)

Kenknight, C. E.

1984-01-01

Random figure errors from the polishing process plus particles on the main mirrors in a telescope cause an extended point spread function (PSF) declining approximately as the inverse square of the sine of the angle from a star from about 100 micro-rad to a right angle. The decline in at least one case, and probably in general, proceeds as the inverse cube at smaller angles where the usual focal plane aperture radius is chosen. The photometric error due to misalignment by one Airy ring spacing with an aperture of n rings depends on the net variance in the figure. It is approximately 60/(n+1)(3) when using the data of Kormendy (1973). A typical value is 6 x 10 to the -5th power per ring of misalignment with n = 100 rings. The encircled power may be modulated on a time scale of hours by parts per thousand in a wavelength dependent manner due to relative humidity effects on mirror dust. The scattering according to an inverse power law is due to a random walk in aberration height caused by a multitude of facets and slope errors left by the polishing process. A deviation from such a law at grazing emergence may permit monitoring the dust effects.

Ventilator-associated pneumonia: the influence of bacterial resistance, prescription errors, and de-escalation of antimicrobial therapy on mortality rates.

PubMed

Souza-Oliveira, Ana Carolina; Cunha, Thúlio Marquez; Passos, Liliane Barbosa da Silva; Lopes, Gustavo Camargo; Gomes, Fabiola Alves; Röder, Denise Von Dolinger de Brito

2016-01-01

Ventilator-associated pneumonia is the most prevalent nosocomial infection in intensive care units and is associated with high mortality rates (14-70%). This study evaluated factors influencing mortality of patients with Ventilator-associated pneumonia (VAP), including bacterial resistance, prescription errors, and de-escalation of antibiotic therapy. This retrospective study included 120 cases of Ventilator-associated pneumonia admitted to the adult adult intensive care unit of the Federal University of Uberlândia. The chi-square test was used to compare qualitative variables. Student's t-test was used for quantitative variables and multiple logistic regression analysis to identify independent predictors of mortality. De-escalation of antibiotic therapy and resistant bacteria did not influence mortality. Mortality was 4 times and 3 times higher, respectively, in patients who received an inappropriate antibiotic loading dose and in patients whose antibiotic dose was not adjusted for renal function. Multiple logistic regression analysis revealed the incorrect adjustment for renal function was the only independent factor associated with increased mortality. Prescription errors influenced mortality of patients with Ventilator-associated pneumonia, underscoring the challenge of proper Ventilator-associated pneumonia treatment, which requires continuous reevaluation to ensure that clinical response to therapy meets expectations. Copyright © 2016. Published by Elsevier Editora Ltda.

Testing for clustering at many ranges inflates family-wise error rate (FWE).

PubMed

Loop, Matthew Shane; McClure, Leslie A

2015-01-15

Testing for clustering at multiple ranges within a single dataset is a common practice in spatial epidemiology. It is not documented whether this approach has an impact on the type 1 error rate. We estimated the family-wise error rate (FWE) for the difference in Ripley's K functions test, when testing at an increasing number of ranges at an alpha-level of 0.05. Case and control locations were generated from a Cox process on a square area the size of the continental US (≈3,000,000 mi2). Two thousand Monte Carlo replicates were used to estimate the FWE with 95% confidence intervals when testing for clustering at one range, as well as 10, 50, and 100 equidistant ranges. The estimated FWE and 95% confidence intervals when testing 10, 50, and 100 ranges were 0.22 (0.20 - 0.24), 0.34 (0.31 - 0.36), and 0.36 (0.34 - 0.38), respectively. Testing for clustering at multiple ranges within a single dataset inflated the FWE above the nominal level of 0.05. Investigators should construct simultaneous critical envelopes (available in spatstat package in R), or use a test statistic that integrates the test statistics from each range, as suggested by the creators of the difference in Ripley's K functions test.

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.

Optimal estimation for discrete time jump processes

NASA Technical Reports Server (NTRS)

Vaca, M. V.; Tretter, S. A.

1977-01-01

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are obtained. The approach is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. A general representation for optimum estimates and recursive equations for minimum mean squared error (MMSE) estimates are obtained. MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a probability density function of the form cx super K (l-x) super m and show that the MMSE estimates are linear in this case. This class of density functions explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

Optimal estimation for discrete time jump processes

NASA Technical Reports Server (NTRS)

Vaca, M. V.; Tretter, S. A.

1978-01-01

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are derived. The approach used is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. Thus a general representation is obtained for optimum estimates, and recursive equations are derived for minimum mean-squared error (MMSE) estimates. In general, MMSE estimates are nonlinear functions of the observations. The problem is considered of estimating the rate of a DTJP when the rate is a random variable with a beta probability density function and the jump amplitudes are binomially distributed. It is shown that the MMSE estimates are linear. The class of beta density functions is rather rich and explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

Satisfiability of logic programming based on radial basis function neural networks

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

Hamadneh, Nawaf; Sathasivam, Saratha; Tilahun, Surafel Luleseged

2014-07-10

In this paper, we propose a new technique to test the Satisfiability of propositional logic programming and quantified Boolean formula problem in radial basis function neural networks. For this purpose, we built radial basis function neural networks to represent the proportional logic which has exactly three variables in each clause. We used the Prey-predator algorithm to calculate the output weights of the neural networks, while the K-means clustering algorithm is used to determine the hidden parameters (the centers and the widths). Mean of the sum squared error function is used to measure the activity of the two algorithms. We appliedmore » the developed technique with the recurrent radial basis function neural networks to represent the quantified Boolean formulas. The new technique can be applied to solve many applications such as electronic circuits and NP-complete problems.« less

Universal Approximation by Using the Correntropy Objective Function.

PubMed

Nayyeri, Mojtaba; Sadoghi Yazdi, Hadi; Maskooki, Alaleh; Rouhani, Modjtaba

2017-10-16

Several objective functions have been proposed in the literature to adjust the input parameters of a node in constructive networks. Furthermore, many researchers have focused on the universal approximation capability of the network based on the existing objective functions. In this brief, we use a correntropy measure based on the sigmoid kernel in the objective function to adjust the input parameters of a newly added node in a cascade network. The proposed network is shown to be capable of approximating any continuous nonlinear mapping with probability one in a compact input sample space. Thus, the convergence is guaranteed. The performance of our method was compared with that of eight different objective functions, as well as with an existing one hidden layer feedforward network on several real regression data sets with and without impulsive noise. The experimental results indicate the benefits of using a correntropy measure in reducing the root mean square error and increasing the robustness to noise.

Novel transform for image description and compression with implementation by neural architectures

NASA Astrophysics Data System (ADS)

Ben-Arie, Jezekiel; Rao, Raghunath K.

1991-10-01

A general method for signal representation using nonorthogonal basis functions that are composed of Gaussians are described. The Gaussians can be combined into groups with predetermined configuration that can approximate any desired basis function. The same configuration at different scales forms a set of self-similar wavelets. The general scheme is demonstrated by representing a natural signal employing an arbitrary basis function. The basic methodology is demonstrated by two novel schemes for efficient representation of 1-D and 2- D signals using Gaussian basis functions (BFs). Special methods are required here since the Gaussian functions are nonorthogonal. The first method employs a paradigm of maximum energy reduction interlaced with the A* heuristic search. The second method uses an adaptive lattice system to find the minimum-squared error of the BFs onto the signal, and a lateral-vertical suppression network to select the most efficient representation in terms of data compression.

Weighted finite impulse response filter for chromatic dispersion equalization in coherent optical fiber communication systems

NASA Astrophysics Data System (ADS)

Zeng, Ziyi; Yang, Aiying; Guo, Peng; Feng, Lihui

2018-01-01

Time-domain CD equalization using finite impulse response (FIR) filter is now a common approach for coherent optical fiber communication systems. The complex weights of FIR taps are calculated from a truncated impulse response of the CD transfer function, and the modulus of the complex weights is constant. In our work, we take the limited bandwidth of a single channel signal into account and propose weighted FIRs to improve the performance of CD equalization. The key in weighted FIR filters is the selection and optimization of weighted functions. In order to present the performance of different types of weighted FIR filters, a square-root raised cosine FIR (SRRC-FIR) and a Gaussian FIR (GS-FIR) are investigated. The optimization of square-root raised cosine FIR and Gaussian FIR are made in term of the bit rate error (BER) of QPSK and 16QAM coherent detection signal. The results demonstrate that the optimized parameters of the weighted filters are independent of the modulation format, symbol rate and the length of transmission fiber. With the optimized weighted FIRs, the BER of CD equalization signal is decreased significantly. Although this paper has investigated two types of weighted FIR filters, i.e. SRRC-FIR filter and GS-FIR filter, the principle of weighted FIR can also be extended to other symmetric functions super Gaussian function, hyperbolic secant function and etc.

Flood loss model transfer: on the value of additional data

NASA Astrophysics Data System (ADS)

Schröter, Kai; Lüdtke, Stefan; Vogel, Kristin; Kreibich, Heidi; Thieken, Annegret; Merz, Bruno

2017-04-01

The transfer of models across geographical regions and flood events is a key challenge in flood loss estimation. Variations in local characteristics and continuous system changes require regional adjustments and continuous updating with current evidence. However, acquiring data on damage influencing factors is expensive and therefore assessing the value of additional data in terms of model reliability and performance improvement is of high relevance. The present study utilizes empirical flood loss data on direct damage to residential buildings available from computer aided telephone interviews that were carried out after the floods in 2002, 2005, 2006, 2010, 2011 and 2013 mainly in the Elbe and Danube catchments in Germany. Flood loss model performance is assessed for incrementally increased numbers of loss data which are differentiated according to region and flood event. Two flood loss modeling approaches are considered: (i) a multi-variable flood loss model approach using Random Forests and (ii) a uni-variable stage damage function. Both model approaches are embedded in a bootstrapping process which allows evaluating the uncertainty of model predictions. Predictive performance of both models is evaluated with regard to mean bias, mean absolute and mean squared errors, as well as hit rate and sharpness. Mean bias and mean absolute error give information about the accuracy of model predictions; mean squared error and sharpness about precision and hit rate is an indicator for model reliability. The results of incremental, regional and temporal updating demonstrate the usefulness of additional data to improve model predictive performance and increase model reliability, particularly in a spatial-temporal transfer setting.

Understanding Scaling Relations in Fracture and Mechanical Deformation of Single Crystal and Polycrystalline Silicon by Performing Atomistic Simulations at Mesoscale

DTIC Science & Technology

2009-07-16

0.25 0.26 -0.85 1 SSR SSE R SSTO SSTO = = − 2 2 ˆ( ) : Regression sum of square, ˆwhere : mean value, : value from the fitted line ˆ...Error sum of square : Total sum of square i i i i SSR Y Y Y Y SSE Y Y SSTO SSE SSR = − = − = + ∑ ∑ Statistical analysis: Coefficient of correlation

Synthesis of hover autopilots for rotary-wing VTOL aircraft

NASA Technical Reports Server (NTRS)

Hall, W. E.; Bryson, A. E., Jr.

1972-01-01

The practical situation is considered where imperfect information on only a few rotor and fuselage state variables is available. Filters are designed to estimate all the state variables from noisy measurements of fuselage pitch/roll angles and from noisy measurements of both fuselage and rotor pitch/roll angles. The mean square response of the vehicle to a very gusty, random wind is computed using various filter/controllers and is found to be quite satisfactory although, of course, not so good as when one has perfect information (idealized case). The second part of the report considers precision hover over a point on the ground. A vehicle model without rotor dynamics is used and feedback signals in position and integral of position error are added. The mean square response of the vehicle to a very gusty, random wind is computed, assuming perfect information feedback, and is found to be excellent. The integral error feedback gives zero position error for a steady wind, and smaller position error for a random wind.

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

NASA Astrophysics Data System (ADS)

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

2005-10-01

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

An Autonomous Satellite Time Synchronization System Using Remotely Disciplined VC-OCXOs

PubMed Central

Gu, Xiaobo; Chang, Qing; Glennon, Eamonn P.; Xu, Baoda; Dempseter, Andrew G.; Wang, Dun; Wu, Jiapeng

2015-01-01

An autonomous remote clock control system is proposed to provide time synchronization and frequency syntonization for satellite to satellite or ground to satellite time transfer, with the system comprising on-board voltage controlled oven controlled crystal oscillators (VC-OCXOs) that are disciplined to a remote master atomic clock or oscillator. The synchronization loop aims to provide autonomous operation over extended periods, be widely applicable to a variety of scenarios and robust. A new architecture comprising the use of frequency division duplex (FDD), synchronous time division (STDD) duplex and code division multiple access (CDMA) with a centralized topology is employed. This new design utilizes dual one-way ranging methods to precisely measure the clock error, adopts least square (LS) methods to predict the clock error and employs a third-order phase lock loop (PLL) to generate the voltage control signal. A general functional model for this system is proposed and the error sources and delays that affect the time synchronization are discussed. Related algorithms for estimating and correcting these errors are also proposed. The performance of the proposed system is simulated and guidance for selecting the clock is provided. PMID:26213929

An efficient computational method for characterizing the effects of random surface errors on the average power pattern of reflectors

NASA Technical Reports Server (NTRS)

Rahmat-Samii, Y.

1983-01-01

Based on the works of Ruze (1966) and Vu (1969), a novel mathematical model has been developed to determine efficiently the average power pattern degradations caused by random surface errors. In this model, both nonuniform root mean square (rms) surface errors and nonuniform illumination functions are employed. In addition, the model incorporates the dependence on F/D in the construction of the solution. The mathematical foundation of the model rests on the assumption that in each prescribed annular region of the antenna, the geometrical rms surface value is known. It is shown that closed-form expressions can then be derived, which result in a very efficient computational method for the average power pattern. Detailed parametric studies are performed with these expressions to determine the effects of different random errors and illumination tapers on parameters such as gain loss and sidelobe levels. The results clearly demonstrate that as sidelobe levels decrease, their dependence on the surface rms/wavelength becomes much stronger and, for a specified tolerance level, a considerably smaller rms/wavelength is required to maintain the low sidelobes within the required bounds.

Analysis of S-box in Image Encryption Using Root Mean Square Error Method

NASA Astrophysics Data System (ADS)

Hussain, Iqtadar; Shah, Tariq; Gondal, Muhammad Asif; Mahmood, Hasan

2012-07-01

The use of substitution boxes (S-boxes) in encryption applications has proven to be an effective nonlinear component in creating confusion and randomness. The S-box is evolving and many variants appear in literature, which include advanced encryption standard (AES) S-box, affine power affine (APA) S-box, Skipjack S-box, Gray S-box, Lui J S-box, residue prime number S-box, Xyi S-box, and S8 S-box. These S-boxes have algebraic and statistical properties which distinguish them from each other in terms of encryption strength. In some circumstances, the parameters from algebraic and statistical analysis yield results which do not provide clear evidence in distinguishing an S-box for an application to a particular set of data. In image encryption applications, the use of S-boxes needs special care because the visual analysis and perception of a viewer can sometimes identify artifacts embedded in the image. In addition to existing algebraic and statistical analysis already used for image encryption applications, we propose an application of root mean square error technique, which further elaborates the results and enables the analyst to vividly distinguish between the performances of various S-boxes. While the use of the root mean square error analysis in statistics has proven to be effective in determining the difference in original data and the processed data, its use in image encryption has shown promising results in estimating the strength of the encryption method. In this paper, we show the application of the root mean square error analysis to S-box image encryption. The parameters from this analysis are used in determining the strength of S-boxes

Development of the Computer-Adaptive Version of the Late-Life Function and Disability Instrument

PubMed Central

Tian, Feng; Kopits, Ilona M.; Moed, Richard; Pardasaney, Poonam K.; Jette, Alan M.

2012-01-01

Background. Having psychometrically strong disability measures that minimize response burden is important in assessing of older adults. Methods. Using the original 48 items from the Late-Life Function and Disability Instrument and newly developed items, a 158-item Activity Limitation and a 62-item Participation Restriction item pool were developed. The item pools were administered to a convenience sample of 520 community-dwelling adults 60 years or older. Confirmatory factor analysis and item response theory were employed to identify content structure, calibrate items, and build the computer-adaptive testings (CATs). We evaluated real-data simulations of 10-item CAT subscales. We collected data from 102 older adults to validate the 10-item CATs against the Veteran’s Short Form-36 and assessed test–retest reliability in a subsample of 57 subjects. Results. Confirmatory factor analysis revealed a bifactor structure, and multi-dimensional item response theory was used to calibrate an overall Activity Limitation Scale (141 items) and an overall Participation Restriction Scale (55 items). Fit statistics were acceptable (Activity Limitation: comparative fit index = 0.95, Tucker Lewis Index = 0.95, root mean square error approximation = 0.03; Participation Restriction: comparative fit index = 0.95, Tucker Lewis Index = 0.95, root mean square error approximation = 0.05). Correlation of 10-item CATs with full item banks were substantial (Activity Limitation: r = .90; Participation Restriction: r = .95). Test–retest reliability estimates were high (Activity Limitation: r = .85; Participation Restriction r = .80). Strength and pattern of correlations with Veteran’s Short Form-36 subscales were as hypothesized. Each CAT, on average, took 3.56 minutes to administer. Conclusions. The Late-Life Function and Disability Instrument CATs demonstrated strong reliability, validity, accuracy, and precision. The Late-Life Function and Disability Instrument CAT can achieve psychometrically sound disability assessment in older persons while reducing respondent burden. Further research is needed to assess their ability to measure change in older adults. PMID:22546960

An Error-Entropy Minimization Algorithm for Tracking Control of Nonlinear Stochastic Systems with Non-Gaussian Variables

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

Liu, Yunlong; Wang, Aiping; Guo, Lei

This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic system. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization criterion is compared with the mean-square-error minimization in the simulation results.

Error-Based Design Space Windowing

NASA Technical Reports Server (NTRS)

Papila, Melih; Papila, Nilay U.; Shyy, Wei; Haftka, Raphael T.; Fitz-Coy, Norman

2002-01-01

Windowing of design space is considered in order to reduce the bias errors due to low-order polynomial response surfaces (RS). Standard design space windowing (DSW) uses a region of interest by setting a requirement on response level and checks it by a global RS predictions over the design space. This approach, however, is vulnerable since RS modeling errors may lead to the wrong region to zoom on. The approach is modified by introducing an eigenvalue error measure based on point-to-point mean squared error criterion. Two examples are presented to demonstrate the benefit of the error-based DSW.

Error in telemetry studies: Effects of animal movement on triangulation

USGS Publications Warehouse

Schmutz, Joel A.; White, Gary C.

1990-01-01

We used Monte Carlo simulations to investigate the effects of animal movement on error of estimated animal locations derived from radio-telemetry triangulation of sequentially obtained bearings. Simulated movements of 0-534 m resulted in up to 10-fold increases in average location error but <10% decreases in location precision when observer-to-animal distances were <1,000 m. Location error and precision were minimally affected by censorship of poor locations with Chi-square goodness-of-fit tests. Location error caused by animal movement can only be eliminated by taking simultaneous bearings.

Correcting bias in the rational polynomial coefficients of satellite imagery using thin-plate smoothing splines

NASA Astrophysics Data System (ADS)

Shen, Xiang; Liu, Bin; Li, Qing-Quan

2017-03-01

The Rational Function Model (RFM) has proven to be a viable alternative to the rigorous sensor models used for geo-processing of high-resolution satellite imagery. Because of various errors in the satellite ephemeris and instrument calibration, the Rational Polynomial Coefficients (RPCs) supplied by image vendors are often not sufficiently accurate, and there is therefore a clear need to correct the systematic biases in order to meet the requirements of high-precision topographic mapping. In this paper, we propose a new RPC bias-correction method using the thin-plate spline modeling technique. Benefiting from its excellent performance and high flexibility in data fitting, the thin-plate spline model has the potential to remove complex distortions in vendor-provided RPCs, such as the errors caused by short-period orbital perturbations. The performance of the new method was evaluated by using Ziyuan-3 satellite images and was compared against the recently developed least-squares collocation approach, as well as the classical affine-transformation and quadratic-polynomial based methods. The results show that the accuracies of the thin-plate spline and the least-squares collocation approaches were better than the other two methods, which indicates that strong non-rigid deformations exist in the test data because they cannot be adequately modeled by simple polynomial-based methods. The performance of the thin-plate spline method was close to that of the least-squares collocation approach when only a few Ground Control Points (GCPs) were used, and it improved more rapidly with an increase in the number of redundant observations. In the test scenario using 21 GCPs (some of them located at the four corners of the scene), the correction residuals of the thin-plate spline method were about 36%, 37%, and 19% smaller than those of the affine transformation method, the quadratic polynomial method, and the least-squares collocation algorithm, respectively, which demonstrates that the new method can be more effective at removing systematic biases in vendor-supplied RPCs.

Quantification of breast density with spectral mammography based on a scanned multi-slit photon-counting detector: a feasibility study.

PubMed

Ding, Huanjun; Molloi, Sabee

2012-08-07

A simple and accurate measurement of breast density is crucial for the understanding of its impact in breast cancer risk models. The feasibility to quantify volumetric breast density with a photon-counting spectral mammography system has been investigated using both computer simulations and physical phantom studies. A computer simulation model involved polyenergetic spectra from a tungsten anode x-ray tube and a Si-based photon-counting detector has been evaluated for breast density quantification. The figure-of-merit (FOM), which was defined as the signal-to-noise ratio of the dual energy image with respect to the square root of mean glandular dose, was chosen to optimize the imaging protocols, in terms of tube voltage and splitting energy. A scanning multi-slit photon-counting spectral mammography system has been employed in the experimental study to quantitatively measure breast density using dual energy decomposition with glandular and adipose equivalent phantoms of uniform thickness. Four different phantom studies were designed to evaluate the accuracy of the technique, each of which addressed one specific variable in the phantom configurations, including thickness, density, area and shape. In addition to the standard calibration fitting function used for dual energy decomposition, a modified fitting function has been proposed, which brought the tube voltages used in the imaging tasks as the third variable in dual energy decomposition. For an average sized 4.5 cm thick breast, the FOM was maximized with a tube voltage of 46 kVp and a splitting energy of 24 keV. To be consistent with the tube voltage used in current clinical screening exam (∼32 kVp), the optimal splitting energy was proposed to be 22 keV, which offered a FOM greater than 90% of the optimal value. In the experimental investigation, the root-mean-square (RMS) error in breast density quantification for all four phantom studies was estimated to be approximately 1.54% using standard calibration function. The results from the modified fitting function, which integrated the tube voltage as a variable in the calibration, indicated a RMS error of approximately 1.35% for all four studies. The results of the current study suggest that photon-counting spectral mammography systems may potentially be implemented for an accurate quantification of volumetric breast density, with an RMS error of less than 2%, using the proposed dual energy imaging technique.

Fundamental Analysis of the Linear Multiple Regression Technique for Quantification of Water Quality Parameters from Remote Sensing Data. Ph.D. Thesis - Old Dominion Univ.

NASA Technical Reports Server (NTRS)

Whitlock, C. H., III

1977-01-01

Constituents with linear radiance gradients with concentration may be quantified from signals which contain nonlinear atmospheric and surface reflection effects for both homogeneous and non-homogeneous water bodies provided accurate data can be obtained and nonlinearities are constant with wavelength. Statistical parameters must be used which give an indication of bias as well as total squared error to insure that an equation with an optimum combination of bands is selected. It is concluded that the effect of error in upwelled radiance measurements is to reduce the accuracy of the least square fitting process and to increase the number of points required to obtain a satisfactory fit. The problem of obtaining a multiple regression equation that is extremely sensitive to error is discussed.

Diffuse-flow conceptualization and simulation of the Edwards aquifer, San Antonio region, Texas

USGS Publications Warehouse

Lindgren, R.J.

2006-01-01

A numerical ground-water-flow model (hereinafter, the conduit-flow Edwards aquifer model) of the karstic Edwards aquifer in south-central Texas was developed for a previous study on the basis of a conceptualization emphasizing conduit development and conduit flow, and included simulating conduits as one-cell-wide, continuously connected features. Uncertainties regarding the degree to which conduits pervade the Edwards aquifer and influence ground-water flow, as well as other uncertainties inherent in simulating conduits, raised the question of whether a model based on the conduit-flow conceptualization was the optimum model for the Edwards aquifer. Accordingly, a model with an alternative hydraulic conductivity distribution without conduits was developed in a study conducted during 2004-05 by the U.S. Geological Survey, in cooperation with the San Antonio Water System. The hydraulic conductivity distribution for the modified Edwards aquifer model (hereinafter, the diffuse-flow Edwards aquifer model), based primarily on a conceptualization in which flow in the aquifer predominantly is through a network of numerous small fractures and openings, includes 38 zones, with hydraulic conductivities ranging from 3 to 50,000 feet per day. Revision of model input data for the diffuse-flow Edwards aquifer model was limited to changes in the simulated hydraulic conductivity distribution. The root-mean-square error for 144 target wells for the calibrated steady-state simulation for the diffuse-flow Edwards aquifer model is 20.9 feet. This error represents about 3 percent of the total head difference across the model area. The simulated springflows for Comal and San Marcos Springs for the calibrated steady-state simulation were within 2.4 and 15 percent of the median springflows for the two springs, respectively. The transient calibration period for the diffuse-flow Edwards aquifer model was 1947-2000, with 648 monthly stress periods, the same as for the conduit-flow Edwards aquifer model. The root-mean-square error for a period of drought (May-November 1956) for the calibrated transient simulation for 171 target wells is 33.4 feet, which represents about 5 percent of the total head difference across the model area. The root-mean-square error for a period of above-normal rainfall (November 1974-July 1975) for the calibrated transient simulation for 169 target wells is 25.8 feet, which represents about 4 percent of the total head difference across the model area. The root-mean-square error ranged from 6.3 to 30.4 feet in 12 target wells with long-term water-level measurements for varying periods during 1947-2000 for the calibrated transient simulation for the diffuse-flow Edwards aquifer model, and these errors represent 5.0 to 31.3 percent of the range in water-level fluctuations of each of those wells. The root-mean-square errors for the five major springs in the San Antonio segment of the aquifer for the calibrated transient simulation, as a percentage of the range of discharge fluctuations measured at the springs, varied from 7.2 percent for San Marcos Springs and 8.1 percent for Comal Springs to 28.8 percent for Leona Springs. The root-mean-square errors for hydraulic heads for the conduit-flow Edwards aquifer model are 27, 76, and 30 percent greater than those for the diffuse-flow Edwards aquifer model for the steady-state, drought, and above-normal rainfall synoptic time periods, respectively. The goodness-of-fit between measured and simulated springflows is similar for Comal, San Marcos, and Leona Springs for the diffuse-flow Edwards aquifer model and the conduit-flow Edwards aquifer model. The root-mean-square errors for Comal and Leona Springs were 15.6 and 21.3 percent less, respectively, whereas the root-mean-square error for San Marcos Springs was 3.3 percent greater for the diffuse-flow Edwards aquifer model compared to the conduit-flow Edwards aquifer model. The root-mean-square errors for San Antonio and San Pedro Springs were appreciably greater, 80.2 and 51.0 percent, respectively, for the diffuse-flow Edwards aquifer model. The simulated water budgets for the diffuse-flow Edwards aquifer model are similar to those for the conduit-flow Edwards aquifer model. Differences in percentage of total sources or discharges for a budget component are 2.0 percent or less for all budget components for the steady-state and transient simulations. The largest difference in terms of the magnitude of water budget components for the transient simulation for 1956 was a decrease of about 10,730 acre-feet per year (about 2 per-cent) in springflow for the diffuse-flow Edwards aquifer model compared to the conduit-flow Edwards aquifer model. This decrease in springflow (a water budget discharge) was largely offset by the decreased net loss of water from storage (a water budget source) of about 10,500 acre-feet per year.

Analysis of the Magnitude and Frequency of Peak Discharge and Maximum Observed Peak Discharge in New Mexico and Surrounding Areas

USGS Publications Warehouse

Waltemeyer, Scott D.

2008-01-01

Estimates of the magnitude and frequency of peak discharges are necessary for the reliable design of bridges, culverts, and open-channel hydraulic analysis, and for flood-hazard mapping in New Mexico and surrounding areas. The U.S. Geological Survey, in cooperation with the New Mexico Department of Transportation, updated estimates of peak-discharge magnitude for gaging stations in the region and updated regional equations for estimation of peak discharge and frequency at ungaged sites. Equations were developed for estimating the magnitude of peak discharges for recurrence intervals of 2, 5, 10, 25, 50, 100, and 500 years at ungaged sites by use of data collected through 2004 for 293 gaging stations on unregulated streams that have 10 or more years of record. Peak discharges for selected recurrence intervals were determined at gaging stations by fitting observed data to a log-Pearson Type III distribution with adjustments for a low-discharge threshold and a zero skew coefficient. A low-discharge threshold was applied to frequency analysis of 140 of the 293 gaging stations. This application provides an improved fit of the log-Pearson Type III frequency distribution. Use of the low-discharge threshold generally eliminated the peak discharge by having a recurrence interval of less than 1.4 years in the probability-density function. Within each of the nine regions, logarithms of the maximum peak discharges for selected recurrence intervals were related to logarithms of basin and climatic characteristics by using stepwise ordinary least-squares regression techniques for exploratory data analysis. Generalized least-squares regression techniques, an improved regression procedure that accounts for time and spatial sampling errors, then were applied to the same data used in the ordinary least-squares regression analyses. The average standard error of prediction, which includes average sampling error and average standard error of regression, ranged from 38 to 93 percent (mean value is 62, and median value is 59) for the 100-year flood. The 1996 investigation standard error of prediction for the flood regions ranged from 41 to 96 percent (mean value is 67, and median value is 68) for the 100-year flood that was analyzed by using generalized least-squares regression analysis. Overall, the equations based on generalized least-squares regression techniques are more reliable than those in the 1996 report because of the increased length of record and improved geographic information system (GIS) method to determine basin and climatic characteristics. Flood-frequency estimates can be made for ungaged sites upstream or downstream from gaging stations by using a method that transfers flood-frequency data at the gaging station to the ungaged site by using a drainage-area ratio adjustment equation. The peak discharge for a given recurrence interval at the gaging station, drainage-area ratio, and the drainage-area exponent from the regional regression equation of the respective region is used to transfer the peak discharge for the recurrence interval to the ungaged site. Maximum observed peak discharge as related to drainage area was determined for New Mexico. Extreme events are commonly used in the design and appraisal of bridge crossings and other structures. Bridge-scour evaluations are commonly made by using the 500-year peak discharge for these appraisals. Peak-discharge data collected at 293 gaging stations and 367 miscellaneous sites were used to develop a maximum peak-discharge relation as an alternative method of estimating peak discharge of an extreme event such as a maximum probable flood.

Investigation of adaptive filtering and MDL mitigation based on space-time block-coding for spatial division multiplexed coherent receivers

NASA Astrophysics Data System (ADS)

Weng, Yi; He, Xuan; Yao, Wang; Pacheco, Michelle C.; Wang, Junyi; Pan, Zhongqi

2017-07-01

In this paper, we explored the performance of space-time block-coding (STBC) assisted multiple-input multiple-output (MIMO) scheme for modal dispersion and mode-dependent loss (MDL) mitigation in spatial-division multiplexed optical communication systems, whereas the weight matrices of frequency-domain equalization (FDE) were updated heuristically using decision-directed recursive least squares (RLS) algorithm for convergence and channel estimation. The proposed STBC-RLS algorithm can achieve 43.6% enhancement on convergence rate over conventional least mean squares (LMS) for quadrature phase-shift keying (QPSK) signals with merely 16.2% increase in hardware complexity. The overall optical signal to noise ratio (OSNR) tolerance can be improved via STBC by approximately 3.1, 4.9, 7.8 dB for QPSK, 16-quadrature amplitude modulation (QAM) and 64-QAM with respective bit-error-rates (BER) and minimum-mean-square-error (MMSE).

Quantitative determination of additive Chlorantraniliprole in Abamectin preparation: Investigation of bootstrapping soft shrinkage approach by mid-infrared spectroscopy

NASA Astrophysics Data System (ADS)

Yan, Hong; Song, Xiangzhong; Tian, Kuangda; Chen, Yilin; Xiong, Yanmei; Min, Shungeng

2018-02-01

A novel method, mid-infrared (MIR) spectroscopy, which enables the determination of Chlorantraniliprole in Abamectin within minutes, is proposed. We further evaluate the prediction ability of four wavelength selection methods, including bootstrapping soft shrinkage approach (BOSS), Monte Carlo uninformative variable elimination (MCUVE), genetic algorithm partial least squares (GA-PLS) and competitive adaptive reweighted sampling (CARS) respectively. The results showed that BOSS method obtained the lowest root mean squared error of cross validation (RMSECV) (0.0245) and root mean squared error of prediction (RMSEP) (0.0271), as well as the highest coefficient of determination of cross-validation (Qcv2) (0.9998) and the coefficient of determination of test set (Q2test) (0.9989), which demonstrated that the mid infrared spectroscopy can be used to detect Chlorantraniliprole in Abamectin conveniently. Meanwhile, a suitable wavelength selection method (BOSS) is essential to conducting a component spectral analysis.

RLS Channel Estimation with Adaptive Forgetting Factor for DS-CDMA Frequency-Domain Equalization

NASA Astrophysics Data System (ADS)

Kojima, Yohei; Tomeba, Hiromichi; Takeda, Kazuaki; Adachi, Fumiyuki

Frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can increase the downlink bit error rate (BER) performance of DS-CDMA beyond that possible with conventional rake combining in a frequency-selective fading channel. FDE requires accurate channel estimation. Recently, we proposed a pilot-assisted channel estimation (CE) based on the MMSE criterion. Using MMSE-CE, the channel estimation accuracy is almost insensitive to the pilot chip sequence, and a good BER performance is achieved. In this paper, we propose a channel estimation scheme using one-tap recursive least square (RLS) algorithm, where the forgetting factor is adapted to the changing channel condition by the least mean square (LMS)algorithm, for DS-CDMA with FDE. We evaluate the BER performance using RLS-CE with adaptive forgetting factor in a frequency-selective fast Rayleigh fading channel by computer simulation.

Accuracy of least-squares methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bochev, Pavel B.; Gunzburger, Max D.

1993-01-01

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

Nondestructive quantification of the soluble-solids content and the available acidity of apples by Fourier-transform near-infrared spectroscopy

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

Ying Yibin; Liu Yande; Tao Yang

2005-09-01

This research evaluated the feasibility of using Fourier-transform near-infrared (FT-NIR) spectroscopy to quantify the soluble-solids content (SSC) and the available acidity (VA) in intact apples. Partial least-squares calibration models, obtained from several preprocessing techniques (smoothing, derivative, etc.) in several wave-number ranges were compared. The best models were obtained with the high coefficient determination (r{sup 2}) 0.940 for the SSC and a moderate r{sup 2} of 0.801 for the VA, root-mean-square errors of prediction of 0.272% and 0.053%, and root-mean-square errors of calibration of 0.261% and 0.046%, respectively. The results indicate that the FT-NIR spectroscopy yields good predictions of the SSCmore » and also showed the feasibility of using it to predict the VA of apples.« less

Aerodynamic coefficient identification package dynamic data accuracy determinations: Lessons learned

NASA Technical Reports Server (NTRS)

Heck, M. L.; Findlay, J. T.; Compton, H. R.

1983-01-01

The errors in the dynamic data output from the Aerodynamic Coefficient Identification Packages (ACIP) flown on Shuttle flights 1, 3, 4, and 5 were determined using the output from the Inertial Measurement Units (IMU). A weighted least-squares batch algorithm was empolyed. Using an averaging technique, signal detection was enhanced; this allowed improved calibration solutions. Global errors as large as 0.04 deg/sec for the ACIP gyros, 30 mg for linear accelerometers, and 0.5 deg/sec squared in the angular accelerometer channels were detected and removed with a combination is bias, scale factor, misalignment, and g-sensitive calibration constants. No attempt was made to minimize local ACIP dynamic data deviations representing sensed high-frequency vibration or instrument noise. Resulting 1sigma calibrated ACIP global accuracies were within 0.003 eg/sec, 1.0 mg, and 0.05 deg/sec squared for the gyros, linear accelerometers, and angular accelerometers, respectively.

Robust THP Transceiver Designs for Multiuser MIMO Downlink with Imperfect CSIT

NASA Astrophysics Data System (ADS)

Ubaidulla, P.; Chockalingam, A.

2009-12-01

We present robust joint nonlinear transceiver designs for multiuser multiple-input multiple-output (MIMO) downlink in the presence of imperfections in the channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas, and each user terminal is equipped with one or more receive antennas. The BS employs Tomlinson-Harashima precoding (THP) for interuser interference precancellation at the transmitter. We consider robust transceiver designs that jointly optimize the transmit THP filters and receive filter for two models of CSIT errors. The first model is a stochastic error (SE) model, where the CSIT error is Gaussian-distributed. This model is applicable when the CSIT error is dominated by channel estimation error. In this case, the proposed robust transceiver design seeks to minimize a stochastic function of the sum mean square error (SMSE) under a constraint on the total BS transmit power. We propose an iterative algorithm to solve this problem. The other model we consider is a norm-bounded error (NBE) model, where the CSIT error can be specified by an uncertainty set. This model is applicable when the CSIT error is dominated by quantization errors. In this case, we consider a worst-case design. For this model, we consider robust (i) minimum SMSE, (ii) MSE-constrained, and (iii) MSE-balancing transceiver designs. We propose iterative algorithms to solve these problems, wherein each iteration involves a pair of semidefinite programs (SDPs). Further, we consider an extension of the proposed algorithm to the case with per-antenna power constraints. We evaluate the robustness of the proposed algorithms to imperfections in CSIT through simulation, and show that the proposed robust designs outperform nonrobust designs as well as robust linear transceiver designs reported in the recent literature.

Combating speckle in SAR images - Vector filtering and sequential classification based on a multiplicative noise model

NASA Technical Reports Server (NTRS)

Lin, Qian; Allebach, Jan P.

1990-01-01

An adaptive vector linear minimum mean-squared error (LMMSE) filter for multichannel images with multiplicative noise is presented. It is shown theoretically that the mean-squared error in the filter output is reduced by making use of the correlation between image bands. The vector and conventional scalar LMMSE filters are applied to a three-band SIR-B SAR, and their performance is compared. Based on a mutliplicative noise model, the per-pel maximum likelihood classifier was derived. The authors extend this to the design of sequential and robust classifiers. These classifiers are also applied to the three-band SIR-B SAR image.

Reliable and accurate extraction of Hamaker constants from surface force measurements.

PubMed

Miklavcic, S J

2018-08-15

A simple and accurate closed-form expression for the Hamaker constant that best represents experimental surface force data is presented. Numerical comparisons are made with the current standard least squares approach, which falsely assumes error-free separation measurements, and a nonlinear version assuming independent measurements of force and separation are subject to error. The comparisons demonstrate that not only is the proposed formula easily implemented it is also considerably more accurate. This option is appropriate for any value of Hamaker constant, high or low, and certainly for any interacting system exhibiting an inverse square distance dependent van der Waals force. Copyright © 2018 Elsevier Inc. All rights reserved.

[Gaussian process regression and its application in near-infrared spectroscopy analysis].

PubMed

Feng, Ai-Ming; Fang, Li-Min; Lin, Min

2011-06-01

Gaussian process (GP) is applied in the present paper as a chemometric method to explore the complicated relationship between the near infrared (NIR) spectra and ingredients. After the outliers were detected by Monte Carlo cross validation (MCCV) method and removed from dataset, different preprocessing methods, such as multiplicative scatter correction (MSC), smoothing and derivate, were tried for the best performance of the models. Furthermore, uninformative variable elimination (UVE) was introduced as a variable selection technique and the characteristic wavelengths obtained were further employed as input for modeling. A public dataset with 80 NIR spectra of corn was introduced as an example for evaluating the new algorithm. The optimal models for oil, starch and protein were obtained by the GP regression method. The performance of the final models were evaluated according to the root mean square error of calibration (RMSEC), root mean square error of cross-validation (RMSECV), root mean square error of prediction (RMSEP) and correlation coefficient (r). The models give good calibration ability with r values above 0.99 and the prediction ability is also satisfactory with r values higher than 0.96. The overall results demonstrate that GP algorithm is an effective chemometric method and is promising for the NIR analysis.

Optimal least-squares finite element method for elliptic problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

Performance of the S - [chi][squared] Statistic for Full-Information Bifactor Models

ERIC Educational Resources Information Center

Li, Ying; Rupp, Andre A.

2011-01-01

This study investigated the Type I error rate and power of the multivariate extension of the S - [chi][squared] statistic using unidimensional and multidimensional item response theory (UIRT and MIRT, respectively) models as well as full-information bifactor (FI-bifactor) models through simulation. Manipulated factors included test length, sample…

F-Test Alternatives to Fisher's Exact Test and to the Chi-Square Test of Homogeneity in 2x2 Tables.

ERIC Educational Resources Information Center

Overall, John E.; Starbuck, Robert R.

1983-01-01

An alternative to Fisher's exact test and the chi-square test for homogeneity in two-by-two tables is developed. The method provides for Type I error rates which are closer to the stated alpha level than either of the alternatives. (JKS)

Multilevel Modeling and Ordinary Least Squares Regression: How Comparable Are They?

ERIC Educational Resources Information Center

Huang, Francis L.

2018-01-01

Studies analyzing clustered data sets using both multilevel models (MLMs) and ordinary least squares (OLS) regression have generally concluded that resulting point estimates, but not the standard errors, are comparable with each other. However, the accuracy of the estimates of OLS models is important to consider, as several alternative techniques…

Nondestructive evaluation of soluble solid content in strawberry by near infrared spectroscopy

NASA Astrophysics Data System (ADS)

Guo, Zhiming; Huang, Wenqian; Chen, Liping; Wang, Xiu; Peng, Yankun

This paper indicates the feasibility to use near infrared (NIR) spectroscopy combined with synergy interval partial least squares (siPLS) algorithms as a rapid nondestructive method to estimate the soluble solid content (SSC) in strawberry. Spectral preprocessing methods were optimized selected by cross-validation in the model calibration. Partial least squares (PLS) algorithm was conducted on the calibration of regression model. The performance of the final model was back-evaluated according to root mean square error of calibration (RMSEC) and correlation coefficient (R2 c) in calibration set, and tested by mean square error of prediction (RMSEP) and correlation coefficient (R2 p) in prediction set. The optimal siPLS model was obtained with after first derivation spectra preprocessing. The measurement results of best model were achieved as follow: RMSEC = 0.2259, R2 c = 0.9590 in the calibration set; and RMSEP = 0.2892, R2 p = 0.9390 in the prediction set. This work demonstrated that NIR spectroscopy and siPLS with efficient spectral preprocessing is a useful tool for nondestructively evaluation SSC in strawberry.

An analytical model for regular respiratory signals derived from the probability density function of Rayleigh distribution.

PubMed

Li, Xin; Li, Ye

2015-01-01

Regular respiratory signals (RRSs) acquired with physiological sensing systems (e.g., the life-detection radar system) can be used to locate survivors trapped in debris in disaster rescue, or predict the breathing motion to allow beam delivery under free breathing conditions in external beam radiotherapy. Among the existing analytical models for RRSs, the harmonic-based random model (HRM) is shown to be the most accurate, which, however, is found to be subject to considerable error if the RRS has a slowly descending end-of-exhale (EOE) phase. The defect of the HRM motivates us to construct a more accurate analytical model for the RRS. In this paper, we derive a new analytical RRS model from the probability density function of Rayleigh distribution. We evaluate the derived RRS model by using it to fit a real-life RRS in the sense of least squares, and the evaluation result shows that, our presented model exhibits lower error and fits the slowly descending EOE phases of the real-life RRS better than the HRM.

Ion beam figuring of high-slope surfaces based on figure error compensation algorithm.

PubMed

Dai, Yifan; Liao, Wenlin; Zhou, Lin; Chen, Shanyong; Xie, Xuhui

2010-12-01

In a deterministic figuring process, it is critical to guarantee high stability of the removal function as well as the accuracy of the dwell time solution, which directly influence the convergence of the figuring process. Hence, when figuring steep optics, the ion beam is required to keep a perpendicular incidence, and a five-axis figuring machine is typically utilized. In this paper, however, a method for high-precision figuring of high-slope optics is proposed with a linear three-axis machine, allowing for inclined beam incidence. First, the changing rule of the removal function and the normal removal rate with the incidence angle is analyzed according to the removal characteristics of ion beam figuring (IBF). Then, we propose to reduce the influence of varying removal function and projection distortion on the dwell time solution by means of figure error compensation. Consequently, the incident ion beam is allowed to keep parallel to the optical axis. Simulations and experiments are given to verify the removal analysis. Finally, a figuring experiment is conducted on a linear three-axis IBF machine, which proves the validity of the method for high-slope surfaces. It takes two iterations and about 9 min to successfully figure a fused silica sample, whose aperture is 21.3 mm and radius of curvature is 16 mm. The root-mean-square figure error of the convex surface is reduced from 13.13 to 5.86 nm.

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

PubMed

Baranwal, Vipul K; Pandey, Ram K; Singh, Om P

2014-01-01

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

Computation of forces from deformed visco-elastic biological tissues

NASA Astrophysics Data System (ADS)

Muñoz, José J.; Amat, David; Conte, Vito

2018-04-01

We present a least-squares based inverse analysis of visco-elastic biological tissues. The proposed method computes the set of contractile forces (dipoles) at the cell boundaries that induce the observed and quantified deformations. We show that the computation of these forces requires the regularisation of the problem functional for some load configurations that we study here. The functional measures the error of the dynamic problem being discretised in time with a second-order implicit time-stepping and in space with standard finite elements. We analyse the uniqueness of the inverse problem and estimate the regularisation parameter by means of an L-curved criterion. We apply the methodology to a simple toy problem and to an in vivo set of morphogenetic deformations of the Drosophila embryo.

Smooth conditional distribution function and quantiles under random censorship.

PubMed

Leconte, Eve; Poiraud-Casanova, Sandrine; Thomas-Agnan, Christine

2002-09-01

We consider a nonparametric random design regression model in which the response variable is possibly right censored. The aim of this paper is to estimate the conditional distribution function and the conditional alpha-quantile of the response variable. We restrict attention to the case where the response variable as well as the explanatory variable are unidimensional and continuous. We propose and discuss two classes of estimators which are smooth with respect to the response variable as well as to the covariate. Some simulations demonstrate that the new methods have better mean square error performances than the generalized Kaplan-Meier estimator introduced by Beran (1981) and considered in the literature by Dabrowska (1989, 1992) and Gonzalez-Manteiga and Cadarso-Suarez (1994).

Efficient estimation of Pareto model: Some modified percentile estimators.

PubMed

Bhatti, Sajjad Haider; Hussain, Shahzad; Ahmad, Tanvir; Aslam, Muhammad; Aftab, Muhammad; Raza, Muhammad Ali

2018-01-01

The article proposes three modified percentile estimators for parameter estimation of the Pareto distribution. These modifications are based on median, geometric mean and expectation of empirical cumulative distribution function of first-order statistic. The proposed modified estimators are compared with traditional percentile estimators through a Monte Carlo simulation for different parameter combinations with varying sample sizes. Performance of different estimators is assessed in terms of total mean square error and total relative deviation. It is determined that modified percentile estimator based on expectation of empirical cumulative distribution function of first-order statistic provides efficient and precise parameter estimates compared to other estimators considered. The simulation results were further confirmed using two real life examples where maximum likelihood and moment estimators were also considered.

Hypoglycemia early alarm systems based on recursive autoregressive partial least squares models.

PubMed

Bayrak, Elif Seyma; Turksoy, Kamuran; Cinar, Ali; Quinn, Lauretta; Littlejohn, Elizabeth; Rollins, Derrick

2013-01-01

Hypoglycemia caused by intensive insulin therapy is a major challenge for artificial pancreas systems. Early detection and prevention of potential hypoglycemia are essential for the acceptance of fully automated artificial pancreas systems. Many of the proposed alarm systems are based on interpretation of recent values or trends in glucose values. In the present study, subject-specific linear models are introduced to capture glucose variations and predict future blood glucose concentrations. These models can be used in early alarm systems of potential hypoglycemia. A recursive autoregressive partial least squares (RARPLS) algorithm is used to model the continuous glucose monitoring sensor data and predict future glucose concentrations for use in hypoglycemia alarm systems. The partial least squares models constructed are updated recursively at each sampling step with a moving window. An early hypoglycemia alarm algorithm using these models is proposed and evaluated. Glucose prediction models based on real-time filtered data has a root mean squared error of 7.79 and a sum of squares of glucose prediction error of 7.35% for six-step-ahead (30 min) glucose predictions. The early alarm systems based on RARPLS shows good performance. A sensitivity of 86% and a false alarm rate of 0.42 false positive/day are obtained for the early alarm system based on six-step-ahead predicted glucose values with an average early detection time of 25.25 min. The RARPLS models developed provide satisfactory glucose prediction with relatively smaller error than other proposed algorithms and are good candidates to forecast and warn about potential hypoglycemia unless preventive action is taken far in advance. © 2012 Diabetes Technology Society.

Hypoglycemia Early Alarm Systems Based on Recursive Autoregressive Partial Least Squares Models

PubMed Central

Bayrak, Elif Seyma; Turksoy, Kamuran; Cinar, Ali; Quinn, Lauretta; Littlejohn, Elizabeth; Rollins, Derrick

2013-01-01

Background Hypoglycemia caused by intensive insulin therapy is a major challenge for artificial pancreas systems. Early detection and prevention of potential hypoglycemia are essential for the acceptance of fully automated artificial pancreas systems. Many of the proposed alarm systems are based on interpretation of recent values or trends in glucose values. In the present study, subject-specific linear models are introduced to capture glucose variations and predict future blood glucose concentrations. These models can be used in early alarm systems of potential hypoglycemia. Methods A recursive autoregressive partial least squares (RARPLS) algorithm is used to model the continuous glucose monitoring sensor data and predict future glucose concentrations for use in hypoglycemia alarm systems. The partial least squares models constructed are updated recursively at each sampling step with a moving window. An early hypoglycemia alarm algorithm using these models is proposed and evaluated. Results Glucose prediction models based on real-time filtered data has a root mean squared error of 7.79 and a sum of squares of glucose prediction error of 7.35% for six-step-ahead (30 min) glucose predictions. The early alarm systems based on RARPLS shows good performance. A sensitivity of 86% and a false alarm rate of 0.42 false positive/day are obtained for the early alarm system based on six-step-ahead predicted glucose values with an average early detection time of 25.25 min. Conclusions The RARPLS models developed provide satisfactory glucose prediction with relatively smaller error than other proposed algorithms and are good candidates to forecast and warn about potential hypoglycemia unless preventive action is taken far in advance. PMID:23439179

Aerodynamic influence coefficient method using singularity splines.

NASA Technical Reports Server (NTRS)

Mercer, J. E.; Weber, J. A.; Lesferd, E. P.

1973-01-01

A new numerical formulation with computed results, is presented. This formulation combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of the loading function methods. The formulation employs a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfies all of the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise (termed 'spline'). Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral.

Predictive Behavior of a Computational Foot/Ankle Model through Artificial Neural Networks.

PubMed

Chande, Ruchi D; Hargraves, Rosalyn Hobson; Ortiz-Robinson, Norma; Wayne, Jennifer S

2017-01-01

Computational models are useful tools to study the biomechanics of human joints. Their predictive performance is heavily dependent on bony anatomy and soft tissue properties. Imaging data provides anatomical requirements while approximate tissue properties are implemented from literature data, when available. We sought to improve the predictive capability of a computational foot/ankle model by optimizing its ligament stiffness inputs using feedforward and radial basis function neural networks. While the former demonstrated better performance than the latter per mean square error, both networks provided reasonable stiffness predictions for implementation into the computational model.

Toward autonomous spacecraft

NASA Technical Reports Server (NTRS)

Fogel, L. J.; Calabrese, P. G.; Walsh, M. J.; Owens, A. J.

1982-01-01

Ways in which autonomous behavior of spacecraft can be extended to treat situations wherein a closed loop control by a human may not be appropriate or even possible are explored. Predictive models that minimize mean least squared error and arbitrary cost functions are discussed. A methodology for extracting cyclic components for an arbitrary environment with respect to usual and arbitrary criteria is developed. An approach to prediction and control based on evolutionary programming is outlined. A computer program capable of predicting time series is presented. A design of a control system for a robotic dense with partially unknown physical properties is presented.

Ultrasonic measurements of the reflection coefficient at a water/polyurethane foam interface.

PubMed

Sagers, Jason D; Haberman, Michael R; Wilson, Preston S

2013-09-01

Measured ultrasonic reflection coefficients as a function of normal incidence angle are reported for several samples of polyurethane foam submerged in a water bath. Three reflection coefficient models are employed as needed in this analysis to approximate the measured data: (1) an infinite plane wave impinging on an elastic halfspace, (2) an infinite plane wave impinging on a single fluid layer overlying a fluid halfspace, and (3) a finite acoustic beam impinging on an elastic halfspace. The compressional wave speed in each sample is calculated by minimizing the sum of squared error (SSE) between the measured and modeled data.

Processing TES Level-2 Data

NASA Technical Reports Server (NTRS)

Poosti, Sassaneh; Akopyan, Sirvard; Sakurai, Regina; Yun, Hyejung; Saha, Pranjit; Strickland, Irina; Croft, Kevin; Smith, Weldon; Hoffman, Rodney; Koffend, John;

Finite-time synchronization of stochastic coupled neural networks subject to Markovian switching and input saturation.

PubMed

Selvaraj, P; Sakthivel, R; Kwon, O M

2018-06-07

This paper addresses the problem of finite-time synchronization of stochastic coupled neural networks (SCNNs) subject to Markovian switching, mixed time delay, and actuator saturation. In addition, coupling strengths of the SCNNs are characterized by mutually independent random variables. By utilizing a simple linear transformation, the problem of stochastic finite-time synchronization of SCNNs is converted into a mean-square finite-time stabilization problem of an error system. By choosing a suitable mode dependent switched Lyapunov-Krasovskii functional, a new set of sufficient conditions is derived to guarantee the finite-time stability of the error system. Subsequently, with the help of anti-windup control scheme, the actuator saturation risks could be mitigated. Moreover, the derived conditions help to optimize estimation of the domain of attraction by enlarging the contractively invariant set. Furthermore, simulations are conducted to exhibit the efficiency of proposed control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

Robust pupil center detection using a curvature algorithm

NASA Technical Reports Server (NTRS)

Zhu, D.; Moore, S. T.; Raphan, T.; Wall, C. C. (Principal Investigator)

1999-01-01

Determining the pupil center is fundamental for calculating eye orientation in video-based systems. Existing techniques are error prone and not robust because eyelids, eyelashes, corneal reflections or shadows in many instances occlude the pupil. We have developed a new algorithm which utilizes curvature characteristics of the pupil boundary to eliminate these artifacts. Pupil center is computed based solely on points related to the pupil boundary. For each boundary point, a curvature value is computed. Occlusion of the boundary induces characteristic peaks in the curvature function. Curvature values for normal pupil sizes were determined and a threshold was found which together with heuristics discriminated normal from abnormal curvature. Remaining boundary points were fit with an ellipse using a least squares error criterion. The center of the ellipse is an estimate of the pupil center. This technique is robust and accurately estimates pupil center with less than 40% of the pupil boundary points visible.

Scattering of clusters of spherical particles—Modeling and inverse problem solution in the Rayleigh-Gans approximation

NASA Astrophysics Data System (ADS)

Eliçabe, Guillermo E.

2013-09-01

In this work, an exact scattering model for a system of clusters of spherical particles, based on the Rayleigh-Gans approximation, has been parameterized in such a way that it can be solved in inverse form using Thikhonov Regularization to obtain the morphological parameters of the clusters. That is to say, the average number of particles per cluster, the size of the primary spherical units that form the cluster, and the Discrete Distance Distribution Function from which the z-average square radius of gyration of the system of clusters is obtained. The methodology is validated through a series of simulated and experimental examples of x-ray and light scattering that show that the proposed methodology works satisfactorily in unideal situations such as: presence of error in the measurements, presence of error in the model, and several types of unideallities present in the experimental cases.

Supplemental optical specifications for imaging systems: parameters of phase gradient

NASA Astrophysics Data System (ADS)

Xuan, Bin; Li, Jun-Feng; Wang, Peng; Chen, Xiao-Ping; Song, Shu-Mei; Xie, Jing-Jiang

2009-12-01

Specifications of phase error, peak to valley (PV), and root mean square (rms) are not able to represent the properties of a wavefront reasonably because of their irresponsibility for spatial frequencies. Power spectral density is a parameter that is especially effective to indicate the frequency regime. However, it seems not convenient for opticians to implement. Parameters of phase gradient, PV gradient, and rms gradient are most correlated with a point-spread function of an imaging system, and they can provide clear instruction of manufacture. The algorithms of gradient parameters have been modified in order to represent the image quality better. In order to demonstrate the analyses, an experimental spherical mirror has been worked out. It is clear that imaging performances can be maintained while manufacture difficulties are decreased when a reasonable trade-off between specifications of phase error and phase gradient is made.

Autonomous Navigation Improvements for High-Earth Orbiters Using GPS

NASA Technical Reports Server (NTRS)

Long, Anne; Kelbel, David; Lee, Taesul; Garrison, James; Carpenter, J. Russell; Bauer, F. (Technical Monitor)

2000-01-01

The Goddard Space Flight Center is currently developing autonomous navigation systems for satellites in high-Earth orbits where acquisition of the GPS signals is severely limited This paper discusses autonomous navigation improvements for high-Earth orbiters and assesses projected navigation performance for these satellites using Global Positioning System (GPS) Standard Positioning Service (SPS) measurements. Navigation performance is evaluated as a function of signal acquisition threshold, measurement errors, and dynamic modeling errors using realistic GPS signal strength and user antenna models. These analyses indicate that an autonomous navigation position accuracy of better than 30 meters root-mean-square (RMS) can be achieved for high-Earth orbiting satellites using a GPS receiver with a very stable oscillator. This accuracy improves to better than 15 meters RMS if the GPS receiver's signal acquisition threshold can be reduced by 5 dB-Hertz to track weaker signals.

Survival analysis for the missing censoring indicator model using kernel density estimation techniques

PubMed Central

Subramanian, Sundarraman

2008-01-01

This article concerns asymptotic theory for a new estimator of a survival function in the missing censoring indicator model of random censorship. Specifically, the large sample results for an inverse probability-of-non-missingness weighted estimator of the cumulative hazard function, so far not available, are derived, including an almost sure representation with rate for a remainder term, and uniform strong consistency with rate of convergence. The estimator is based on a kernel estimate for the conditional probability of non-missingness of the censoring indicator. Expressions for its bias and variance, in turn leading to an expression for the mean squared error as a function of the bandwidth, are also obtained. The corresponding estimator of the survival function, whose weak convergence is derived, is asymptotically efficient. A numerical study, comparing the performances of the proposed and two other currently existing efficient estimators, is presented. PMID:18953423

Survival analysis for the missing censoring indicator model using kernel density estimation techniques.

PubMed

Subramanian, Sundarraman

2006-01-01

This article concerns asymptotic theory for a new estimator of a survival function in the missing censoring indicator model of random censorship. Specifically, the large sample results for an inverse probability-of-non-missingness weighted estimator of the cumulative hazard function, so far not available, are derived, including an almost sure representation with rate for a remainder term, and uniform strong consistency with rate of convergence. The estimator is based on a kernel estimate for the conditional probability of non-missingness of the censoring indicator. Expressions for its bias and variance, in turn leading to an expression for the mean squared error as a function of the bandwidth, are also obtained. The corresponding estimator of the survival function, whose weak convergence is derived, is asymptotically efficient. A numerical study, comparing the performances of the proposed and two other currently existing efficient estimators, is presented.

Application of RBFN network and GM (1, 1) for groundwater level simulation

NASA Astrophysics Data System (ADS)

Li, Zijun; Yang, Qingchun; Wang, Luchen; Martín, Jordi Delgado

2017-10-01

Groundwater is a prominent resource of drinking and domestic water in the world. In this context, a feasible water resources management plan necessitates acceptable predictions of groundwater table depth fluctuations, which can help ensure the sustainable use of a watershed's aquifers for urban and rural water supply. Due to the difficulties of identifying non-linear model structure and estimating the associated parameters, in this study radial basis function neural network (RBFNN) and GM (1, 1) models are used for the prediction of monthly groundwater level fluctuations in the city of Longyan, Fujian Province (South China). The monthly groundwater level data monitored from January 2003 to December 2011 are used in both models. The error criteria are estimated using the coefficient of determination ( R 2), mean absolute error (E) and root mean squared error (RMSE). The results show that both the models can forecast the groundwater level with fairly high accuracy, but the RBFN network model can be a promising tool to simulate and forecast groundwater level since it has a relatively smaller RMSE and MAE.

Comparative study of four time series methods in forecasting typhoid fever incidence in China.

PubMed

Zhang, Xingyu; Liu, Yuanyuan; Yang, Min; Zhang, Tao; Young, Alistair A; Li, Xiaosong

2013-01-01

Accurate incidence forecasting of infectious disease is critical for early prevention and for better government strategic planning. In this paper, we present a comprehensive study of different forecasting methods based on the monthly incidence of typhoid fever. The seasonal autoregressive integrated moving average (SARIMA) model and three different models inspired by neural networks, namely, back propagation neural networks (BPNN), radial basis function neural networks (RBFNN), and Elman recurrent neural networks (ERNN) were compared. The differences as well as the advantages and disadvantages, among the SARIMA model and the neural networks were summarized and discussed. The data obtained for 2005 to 2009 and for 2010 from the Chinese Center for Disease Control and Prevention were used as modeling and forecasting samples, respectively. The performances were evaluated based on three metrics: mean absolute error (MAE), mean absolute percentage error (MAPE), and mean square error (MSE). The results showed that RBFNN obtained the smallest MAE, MAPE and MSE in both the modeling and forecasting processes. The performances of the four models ranked in descending order were: RBFNN, ERNN, BPNN and the SARIMA model.

Comparative Study of Four Time Series Methods in Forecasting Typhoid Fever Incidence in China

PubMed Central

Zhang, Xingyu; Liu, Yuanyuan; Yang, Min; Zhang, Tao; Young, Alistair A.; Li, Xiaosong

2013-01-01

Accurate incidence forecasting of infectious disease is critical for early prevention and for better government strategic planning. In this paper, we present a comprehensive study of different forecasting methods based on the monthly incidence of typhoid fever. The seasonal autoregressive integrated moving average (SARIMA) model and three different models inspired by neural networks, namely, back propagation neural networks (BPNN), radial basis function neural networks (RBFNN), and Elman recurrent neural networks (ERNN) were compared. The differences as well as the advantages and disadvantages, among the SARIMA model and the neural networks were summarized and discussed. The data obtained for 2005 to 2009 and for 2010 from the Chinese Center for Disease Control and Prevention were used as modeling and forecasting samples, respectively. The performances were evaluated based on three metrics: mean absolute error (MAE), mean absolute percentage error (MAPE), and mean square error (MSE). The results showed that RBFNN obtained the smallest MAE, MAPE and MSE in both the modeling and forecasting processes. The performances of the four models ranked in descending order were: RBFNN, ERNN, BPNN and the SARIMA model. PMID:23650546

Global Surface Temperature Change and Uncertainties Since 1861

NASA Technical Reports Server (NTRS)

Shen, Samuel S. P.; Lau, William K. M. (Technical Monitor)

2002-01-01

The objective of this talk is to analyze the warming trend and its uncertainties of the global and hemi-spheric surface temperatures. By the method of statistical optimal averaging scheme, the land surface air temperature and sea surface temperature observational data are used to compute the spatial average annual mean surface air temperature. The optimal averaging method is derived from the minimization of the mean square error between the true and estimated averages and uses the empirical orthogonal functions. The method can accurately estimate the errors of the spatial average due to observational gaps and random measurement errors. In addition, quantified are three independent uncertainty factors: urbanization, change of the in situ observational practices and sea surface temperature data corrections. Based on these uncertainties, the best linear fit to annual global surface temperature gives an increase of 0.61 +/- 0.16 C between 1861 and 2000. This lecture will also touch the topics on the impact of global change on nature and environment. as well as the latest assessment methods for the attributions of global change.

Electrical conductance sensitivity functions for square and circular cloverleaf van der Pauw geometries

NASA Astrophysics Data System (ADS)

Koon, Daniel W.; Heřmanová, Martina; Náhlík, Josef

2015-11-01

We have undertaken the first systematic computational and experimental study of the sensitivity of charge transport measurement to local physical defects for van der Pauw circular and square cloverleafs with rounded internal corners and unclovered geometries, using copper-foil specimens. Cloverleafs with rounded internal corners are in common use and reduce sampling of the material near their boundaries, an advantage over sharp corners. We have defined two parameters for these cloverleafs, one of which, the ‘admittance’, is the best predictor of the sensitivity at the center of these specimens, with this sensitivity depending only weakly on the central ‘core’ size when its diameter is less than about 60% of the specimen’s lateral size. Resistive measurement errors in all four geometries are linear in areas for errors up to about 50% in sheet resistance, and superlinear above. An ASTM-based ‘standard’ cloverleaf geometry, in which the central core diameter of the specimen is 1/5 the overall length and the slit widths are 1/10 the overall length, narrows the effective area sampled by the resistive measurement by a factor of about 16  ×  in the small-hole limit and over 40  ×  for larger holes, relative to unclovered goemetries, whether square or circular, with a smooth transition in these numbers for geometries intermediate between the standard cloverleaf and unclovered specimens. We believe that this work will allow materials scientists to better estimate the impact of factors such as the uniformity of film thickness and of material purity on their measurements, and allow sensor designers to better choose an optimal specimen geometry.

Rapid investigation of α-glucosidase inhibitory activity of Phaleria macrocarpa extracts using FTIR-ATR based fingerprinting.

PubMed

Easmin, Sabina; Sarker, Md Zaidul Islam; Ghafoor, Kashif; Ferdosh, Sahena; Jaffri, Juliana; Ali, Md Eaqub; Mirhosseini, Hamed; Al-Juhaimi, Fahad Y; Perumal, Vikneswari; Khatib, Alfi

2017-04-01

Phaleria macrocarpa, known as "Mahkota Dewa", is a widely used medicinal plant in Malaysia. This study focused on the characterization of α-glucosidase inhibitory activity of P. macrocarpa extracts using Fourier transform infrared spectroscopy (FTIR)-based metabolomics. P. macrocarpa and its extracts contain thousands of compounds having synergistic effect. Generally, their variability exists, and there are many active components in meager amounts. Thus, the conventional measurement methods of a single component for the quality control are time consuming, laborious, expensive, and unreliable. It is of great interest to develop a rapid prediction method for herbal quality control to investigate the α-glucosidase inhibitory activity of P. macrocarpa by multicomponent analyses. In this study, a rapid and simple analytical method was developed using FTIR spectroscopy-based fingerprinting. A total of 36 extracts of different ethanol concentrations were prepared and tested on inhibitory potential and fingerprinted using FTIR spectroscopy, coupled with chemometrics of orthogonal partial least square (OPLS) at the 4000-400 cm -1 frequency region and resolution of 4 cm -1 . The OPLS model generated the highest regression coefficient with R 2 Y = 0.98 and Q 2 Y = 0.70, lowest root mean square error estimation = 17.17, and root mean square error of cross validation = 57.29. A five-component (1+4+0) predictive model was build up to correlate FTIR spectra with activity, and the responsible functional groups, such as -CH, -NH, -COOH, and -OH, were identified for the bioactivity. A successful multivariate model was constructed using FTIR-attenuated total reflection as a simple and rapid technique to predict the inhibitory activity. Copyright © 2016. Published by Elsevier B.V.

Optimal secondary source position in exterior spherical acoustical holophony

NASA Astrophysics Data System (ADS)

Pasqual, A. M.; Martin, V.

2012-02-01

Exterior spherical acoustical holophony is a branch of spatial audio reproduction that deals with the rendering of a given free-field radiation pattern (the primary field) by using a compact spherical loudspeaker array (the secondary source). More precisely, the primary field is known on a spherical surface surrounding the primary and secondary sources and, since the acoustic fields are described in spherical coordinates, they are naturally subjected to spherical harmonic analysis. Besides, the inverse problem of deriving optimal driving signals from a known primary field is ill-posed because the secondary source cannot radiate high-order spherical harmonics efficiently, especially in the low-frequency range. As a consequence, a standard least-squares solution will overload the transducers if the primary field contains such harmonics. Here, this is avoided by discarding the strongly decaying spherical waves, which are identified through inspection of the radiation efficiency curves of the secondary source. However, such an unavoidable regularization procedure increases the least-squares error, which also depends on the position of the secondary source. This paper deals with the above-mentioned questions in the context of far-field directivity reproduction at low and medium frequencies. In particular, an optimal secondary source position is sought, which leads to the lowest reproduction error in the least-squares sense without overloading the transducers. In order to address this issue, a regularization quality factor is introduced to evaluate the amount of regularization required. It is shown that the optimal position improves significantly the holophonic reconstruction and maximizes the regularization quality factor (minimizes the amount of regularization), which is the main general contribution of this paper. Therefore, this factor can also be used as a cost function to obtain the optimal secondary source position.

Evaluation of Interpolation Effects on Upsampling and Accuracy of Cost Functions-Based Optimized Automatic Image Registration

PubMed Central

Mahmoudzadeh, Amir Pasha; Kashou, Nasser H.

2013-01-01

Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR) grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order) and to compare the effect of cost functions (least squares (LS), normalized mutual information (NMI), normalized cross correlation (NCC), and correlation ratio (CR)) for optimized automatic image registration (OAIR) on 3D spoiled gradient recalled (SPGR) magnetic resonance images (MRI) of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method. PMID:24000283

Evaluation of interpolation effects on upsampling and accuracy of cost functions-based optimized automatic image registration.

PubMed

Mahmoudzadeh, Amir Pasha; Kashou, Nasser H

2013-01-01

Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR) grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order) and to compare the effect of cost functions (least squares (LS), normalized mutual information (NMI), normalized cross correlation (NCC), and correlation ratio (CR)) for optimized automatic image registration (OAIR) on 3D spoiled gradient recalled (SPGR) magnetic resonance images (MRI) of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method.

Validation of the Malay Version of the Inventory of Functional Status after Childbirth Questionnaire

PubMed Central

Noor, Norhayati Mohd; Aziz, Aniza Abd.; Mostapa, Mohd Rosmizaki; Awang, Zainudin

2015-01-01

Objective. This study was designed to examine the psychometric properties of Malay version of the Inventory of Functional Status after Childbirth (IFSAC). Design. A cross-sectional study. Materials and Methods. A total of 108 postpartum mothers attending Obstetrics and Gynaecology Clinic, in a tertiary teaching hospital in Malaysia, were involved. Construct validity and internal consistency were performed after the translation, content validity, and face validity process. The data were analyzed using Analysis of Moment Structure version 18 and Statistical Packages for the Social Sciences version 20. Results. The final model consists of four constructs, namely, infant care, personal care, household activities, and social and community activities, with 18 items demonstrating acceptable factor loadings, domain to domain correlation, and best fit (Chi-squared/degree of freedom = 1.678; Tucker-Lewis index = 0.923; comparative fit index = 0.936; and root mean square error of approximation = 0.080). Composite reliability and average variance extracted of the domains ranged from 0.659 to 0.921 and from 0.499 to 0.628, respectively. Conclusion. The study suggested that the four-factor model with 18 items of the Malay version of IFSAC was acceptable to be used to measure functional status after childbirth because it is valid, reliable, and simple. PMID:25667932

A Fast and On-Machine Measuring System Using the Laser Displacement Sensor for the Contour Parameters of the Drill Pipe Thread.

PubMed

Dong, Zhixu; Sun, Xingwei; Chen, Changzheng; Sun, Mengnan

2018-04-13

The inconvenient loading and unloading of a long and heavy drill pipe gives rise to the difficulty in measuring the contour parameters of its threads at both ends. To solve this problem, in this paper we take the SCK230 drill pipe thread-repairing machine tool as a carrier to design and achieve a fast and on-machine measuring system based on a laser probe. This system drives a laser displacement sensor to acquire the contour data of a certain axial section of the thread by using the servo function of a CNC machine tool. To correct the sensor's measurement errors caused by the measuring point inclination angle, an inclination error model is built to compensate data in real time. To better suppress random error interference and ensure real contour information, a new wavelet threshold function is proposed to process data through the wavelet threshold denoising. Discrete data after denoising is segmented according to the geometrical characteristics of the drill pipe thread, and the regression model of the contour data in each section is fitted by using the method of weighted total least squares (WTLS). Then, the thread parameters are calculated in real time to judge the processing quality. Inclination error experiments show that the proposed compensation model is accurate and effective, and it can improve the data acquisition accuracy of a sensor. Simulation results indicate that the improved threshold function is of better continuity and self-adaptability, which makes sure that denoising effects are guaranteed, and, meanwhile, the complete elimination of real data distorted in random errors is avoided. Additionally, NC50 thread-testing experiments show that the proposed on-machine measuring system can complete the measurement of a 25 mm thread in 7.8 s, with a measurement accuracy of ±8 μm and repeatability limit ≤ 4 μm (high repeatability), and hence the accuracy and efficiency of measurement are both improved.

A Fast and On-Machine Measuring System Using the Laser Displacement Sensor for the Contour Parameters of the Drill Pipe Thread

PubMed Central

Sun, Xingwei; Chen, Changzheng; Sun, Mengnan

2018-01-01

The inconvenient loading and unloading of a long and heavy drill pipe gives rise to the difficulty in measuring the contour parameters of its threads at both ends. To solve this problem, in this paper we take the SCK230 drill pipe thread-repairing machine tool as a carrier to design and achieve a fast and on-machine measuring system based on a laser probe. This system drives a laser displacement sensor to acquire the contour data of a certain axial section of the thread by using the servo function of a CNC machine tool. To correct the sensor’s measurement errors caused by the measuring point inclination angle, an inclination error model is built to compensate data in real time. To better suppress random error interference and ensure real contour information, a new wavelet threshold function is proposed to process data through the wavelet threshold denoising. Discrete data after denoising is segmented according to the geometrical characteristics of the drill pipe thread, and the regression model of the contour data in each section is fitted by using the method of weighted total least squares (WTLS). Then, the thread parameters are calculated in real time to judge the processing quality. Inclination error experiments show that the proposed compensation model is accurate and effective, and it can improve the data acquisition accuracy of a sensor. Simulation results indicate that the improved threshold function is of better continuity and self-adaptability, which makes sure that denoising effects are guaranteed, and, meanwhile, the complete elimination of real data distorted in random errors is avoided. Additionally, NC50 thread-testing experiments show that the proposed on-machine measuring system can complete the measurement of a 25 mm thread in 7.8 s, with a measurement accuracy of ±8 μm and repeatability limit ≤ 4 μm (high repeatability), and hence the accuracy and efficiency of measurement are both improved. PMID:29652836

Minimizing distortion and internal forces in truss structures by simulated annealing

NASA Technical Reports Server (NTRS)

Kincaid, Rex K.

1989-01-01

Inaccuracies in the length of members and the diameters of joints of large truss reflector backup structures may produce unacceptable levels of surface distortion and member forces. However, if the member lengths and joint diameters can be measured accurately it is possible to configure the members and joints so that root-mean-square (rms) surface error and/or rms member forces is minimized. Following Greene and Haftka (1989) it is assumed that the force vector f is linearly proportional to the member length errors e(sub M) of dimension NMEMB (the number of members) and joint errors e(sub J) of dimension NJOINT (the number of joints), and that the best-fit displacement vector d is a linear function of f. Let NNODES denote the number of positions on the surface of the truss where error influences are measured. The solution of the problem is discussed. To classify, this problem was compared to a similar combinatorial optimization problem. In particular, when only the member length errors are considered, minimizing d(sup 2)(sub rms) is equivalent to the quadratic assignment problem. The quadratic assignment problem is a well known NP-complete problem in operations research literature. Hence minimizing d(sup 2)(sub rms) is is also an NP-complete problem. The focus of the research is the development of a simulated annealing algorithm to reduce d(sup 2)(sub rms). The plausibility of this technique is its recent success on a variety of NP-complete combinatorial optimization problems including the quadratic assignment problem. A physical analogy for simulated annealing is the way liquids freeze and crystallize. All computational experiments were done on a MicroVAX. The two interchange heuristic is very fast but produces widely varying results. The two and three interchange heuristic provides less variability in the final objective function values but runs much more slowly. Simulated annealing produced the best objective function values for every starting configuration and was faster than the two and three interchange heuristic.

Determining the Uncertainty of X-Ray Absorption Measurements

PubMed Central

Wojcik, Gary S.

2004-01-01

X-ray absorption (or more properly, x-ray attenuation) techniques have been applied to study the moisture movement in and moisture content of materials like cement paste, mortar, and wood. An increase in the number of x-ray counts with time at a location in a specimen may indicate a decrease in moisture content. The uncertainty of measurements from an x-ray absorption system, which must be known to properly interpret the data, is often assumed to be the square root of the number of counts, as in a Poisson process. No detailed studies have heretofore been conducted to determine the uncertainty of x-ray absorption measurements or the effect of averaging data on the uncertainty. In this study, the Poisson estimate was found to adequately approximate normalized root mean square errors (a measure of uncertainty) of counts for point measurements and profile measurements of water specimens. The Poisson estimate, however, was not reliable in approximating the magnitude of the uncertainty when averaging data from paste and mortar specimens. Changes in uncertainty from differing averaging procedures were well-approximated by a Poisson process. The normalized root mean square errors decreased when the x-ray source intensity, integration time, collimator size, and number of scanning repetitions increased. Uncertainties in mean paste and mortar count profiles were kept below 2 % by averaging vertical profiles at horizontal spacings of 1 mm or larger with counts per point above 4000. Maximum normalized root mean square errors did not exceed 10 % in any of the tests conducted. PMID:27366627

Direct and simultaneous quantification of tannin mean degree of polymerization and percentage of galloylation in grape seeds using diffuse reflectance fourier transform-infrared spectroscopy.

PubMed

Pappas, Christos; Kyraleou, Maria; Voskidi, Eleni; Kotseridis, Yorgos; Taranilis, Petros A; Kallithraka, Stamatina

2015-02-01

The direct and simultaneous quantitative determination of the mean degree of polymerization (mDP) and the degree of galloylation (%G) in grape seeds were quantified using diffuse reflectance infrared Fourier transform spectroscopy and partial least squares (PLS). The results were compared with those obtained using the conventional analysis employing phloroglucinolysis as pretreatment followed by high performance liquid chromatography-UV and mass spectrometry detection. Infrared spectra were recorded in solid state samples after freeze drying. The 2nd derivative of the 1832 to 1416 and 918 to 739 cm(-1) spectral regions for the quantification of mDP, the 2nd derivative of the 1813 to 607 cm(-1) spectral region for the degree of %G determination and PLS regression were used. The determination coefficients (R(2) ) of mDP and %G were 0.99 and 0.98, respectively. The corresponding values of the root-mean-square error of calibration were found 0.506 and 0.692, the root-mean-square error of cross validation 0.811 and 0.921, and the root-mean-square error of prediction 0.612 and 0.801. The proposed method in comparison with the conventional method is simpler, less time consuming, more economical, and requires reduced quantities of chemical reagents and fewer sample pretreatment steps. It could be a starting point for the design of more specific models according to the requirements of the wineries. © 2015 Institute of Food Technologists®

Rapid discrimination between buffalo and cow milk and detection of adulteration of buffalo milk with cow milk using synchronous fluorescence spectroscopy in combination with multivariate methods.

PubMed

Durakli Velioglu, Serap; Ercioglu, Elif; Boyaci, Ismail Hakki

2017-05-01

This research paper describes the potential of synchronous fluorescence (SF) spectroscopy for authentication of buffalo milk, a favourable raw material in the production of some premium dairy products. Buffalo milk is subjected to fraudulent activities like many other high priced foodstuffs. The current methods widely used for the detection of adulteration of buffalo milk have various disadvantages making them unattractive for routine analysis. Thus, the aim of the present study was to assess the potential of SF spectroscopy in combination with multivariate methods for rapid discrimination between buffalo and cow milk and detection of the adulteration of buffalo milk with cow milk. SF spectra of cow and buffalo milk samples were recorded between 400-550 nm excitation range with Δλ of 10-100 nm, in steps of 10 nm. The data obtained for ∆λ = 10 nm were utilised to classify the samples using principal component analysis (PCA), and detect the adulteration level of buffalo milk with cow milk using partial least square (PLS) methods. Successful discrimination of samples and detection of adulteration of buffalo milk with limit of detection value (LOD) of 6% are achieved with the models having root mean square error of calibration (RMSEC) and the root mean square error of cross-validation (RMSECV) and root mean square error of prediction (RMSEP) values of 2, 7, and 4%, respectively. The results reveal the potential of SF spectroscopy for rapid authentication of buffalo milk.

Short-term forecasting of meteorological time series using Nonparametric Functional Data Analysis (NPFDA)

NASA Astrophysics Data System (ADS)

Curceac, S.; Ternynck, C.; Ouarda, T.

2015-12-01

Over the past decades, a substantial amount of research has been conducted to model and forecast climatic variables. In this study, Nonparametric Functional Data Analysis (NPFDA) methods are applied to forecast air temperature and wind speed time series in Abu Dhabi, UAE. The dataset consists of hourly measurements recorded for a period of 29 years, 1982-2010. The novelty of the Functional Data Analysis approach is in expressing the data as curves. In the present work, the focus is on daily forecasting and the functional observations (curves) express the daily measurements of the above mentioned variables. We apply a non-linear regression model with a functional non-parametric kernel estimator. The computation of the estimator is performed using an asymmetrical quadratic kernel function for local weighting based on the bandwidth obtained by a cross validation procedure. The proximities between functional objects are calculated by families of semi-metrics based on derivatives and Functional Principal Component Analysis (FPCA). Additionally, functional conditional mode and functional conditional median estimators are applied and the advantages of combining their results are analysed. A different approach employs a SARIMA model selected according to the minimum Akaike (AIC) and Bayessian (BIC) Information Criteria and based on the residuals of the model. The performance of the models is assessed by calculating error indices such as the root mean square error (RMSE), relative RMSE, BIAS and relative BIAS. The results indicate that the NPFDA models provide more accurate forecasts than the SARIMA models. Key words: Nonparametric functional data analysis, SARIMA, time series forecast, air temperature, wind speed

Photoacoustic signals denoising of the glucose aqueous solutions using an improved wavelet threshold method

NASA Astrophysics Data System (ADS)

Ren, Zhong; Liu, Guodong; Xiong, Zhihua

2016-10-01

The photoacoustic signals denoising of glucose is one of most important steps in the quality identification of the fruit because the real-time photoacoustic singals of glucose are easily interfered by all kinds of noises. To remove the noises and some useless information, an improved wavelet threshld function were proposed. Compared with the traditional wavelet hard and soft threshold functions, the improved wavelet threshold function can overcome the pseudo-oscillation effect of the denoised photoacoustic signals due to the continuity of the improved wavelet threshold function, and the error between the denoised signals and the original signals can be decreased. To validate the feasibility of the improved wavelet threshold function denoising, the denoising simulation experiments based on MATLAB programmimg were performed. In the simulation experiments, the standard test signal was used, and three different denoising methods were used and compared with the improved wavelet threshold function. The signal-to-noise ratio (SNR) and the root-mean-square error (RMSE) values were used to evaluate the performance of the improved wavelet threshold function denoising. The experimental results demonstrate that the SNR value of the improved wavelet threshold function is largest and the RMSE value is lest, which fully verifies that the improved wavelet threshold function denoising is feasible. Finally, the improved wavelet threshold function denoising was used to remove the noises of the photoacoustic signals of the glucose solutions. The denoising effect is also very good. Therefore, the improved wavelet threshold function denoising proposed by this paper, has a potential value in the field of denoising for the photoacoustic singals.

[Spectral quantitative analysis by nonlinear partial least squares based on neural network internal model for flue gas of thermal power plant].

PubMed

Cao, Hui; Li, Yao-Jiang; Zhou, Yan; Wang, Yan-Xia

2014-11-01

To deal with nonlinear characteristics of spectra data for the thermal power plant flue, a nonlinear partial least square (PLS) analysis method with internal model based on neural network is adopted in the paper. The latent variables of the independent variables and the dependent variables are extracted by PLS regression firstly, and then they are used as the inputs and outputs of neural network respectively to build the nonlinear internal model by train process. For spectra data of flue gases of the thermal power plant, PLS, the nonlinear PLS with the internal model of back propagation neural network (BP-NPLS), the non-linear PLS with the internal model of radial basis function neural network (RBF-NPLS) and the nonlinear PLS with the internal model of adaptive fuzzy inference system (ANFIS-NPLS) are compared. The root mean square error of prediction (RMSEP) of sulfur dioxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 16.96%, 16.60% and 19.55% than that of PLS, respectively. The RMSEP of nitric oxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 8.60%, 8.47% and 10.09% than that of PLS, respectively. The RMSEP of nitrogen dioxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 2.11%, 3.91% and 3.97% than that of PLS, respectively. Experimental results show that the nonlinear PLS is more suitable for the quantitative analysis of glue gas than PLS. Moreover, by using neural network function which can realize high approximation of nonlinear characteristics, the nonlinear partial least squares method with internal model mentioned in this paper have well predictive capabilities and robustness, and could deal with the limitations of nonlinear partial least squares method with other internal model such as polynomial and spline functions themselves under a certain extent. ANFIS-NPLS has the best performance with the internal model of adaptive fuzzy inference system having ability to learn more and reduce the residuals effectively. Hence, ANFIS-NPLS is an accurate and useful quantitative thermal power plant flue gas analysis method.

Local Linear Regression for Data with AR Errors.

PubMed

Li, Runze; Li, Yan

2009-07-01

In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.

A study of GPS measurement errors due to noise and multipath interference for CGADS

NASA Technical Reports Server (NTRS)

Axelrad, Penina; MacDoran, Peter F.; Comp, Christopher J.

1996-01-01

This report describes a study performed by the Colorado Center for Astrodynamics Research (CCAR) on GPS measurement errors in the Codeless GPS Attitude Determination System (CGADS) due to noise and multipath interference. Preliminary simulation models fo the CGADS receiver and orbital multipath are described. The standard FFT algorithms for processing the codeless data is described and two alternative algorithms - an auto-regressive/least squares (AR-LS) method, and a combined adaptive notch filter/least squares (ANF-ALS) method, are also presented. Effects of system noise, quantization, baseband frequency selection, and Doppler rates on the accuracy of phase estimates with each of the processing methods are shown. Typical electrical phase errors for the AR-LS method are 0.2 degrees, compared to 0.3 and 0.5 degrees for the FFT and ANF-ALS algorithms, respectively. Doppler rate was found to have the largest effect on the performance.

Linear regression in astronomy. II

NASA Technical Reports Server (NTRS)

Feigelson, Eric D.; Babu, Gutti J.

1992-01-01

A wide variety of least-squares linear regression procedures used in observational astronomy, particularly investigations of the cosmic distance scale, are presented and discussed. The classes of linear models considered are (1) unweighted regression lines, with bootstrap and jackknife resampling; (2) regression solutions when measurement error, in one or both variables, dominates the scatter; (3) methods to apply a calibration line to new data; (4) truncated regression models, which apply to flux-limited data sets; and (5) censored regression models, which apply when nondetections are present. For the calibration problem we develop two new procedures: a formula for the intercept offset between two parallel data sets, which propagates slope errors from one regression to the other; and a generalization of the Working-Hotelling confidence bands to nonstandard least-squares lines. They can provide improved error analysis for Faber-Jackson, Tully-Fisher, and similar cosmic distance scale relations.

Application of Adaptive Neuro-Fuzzy Inference System for Prediction of Neutron Yield of IR-IECF Facility in High Voltages

NASA Astrophysics Data System (ADS)

Adineh-Vand, A.; Torabi, M.; Roshani, G. H.; Taghipour, M.; Feghhi, S. A. H.; Rezaei, M.; Sadati, S. M.

2013-09-01

This paper presents a soft computing based artificial intelligent technique, adaptive neuro-fuzzy inference system (ANFIS) to predict the neutron production rate (NPR) of IR-IECF device in wide discharge current and voltage ranges. A hybrid learning algorithm consists of back-propagation and least-squares estimation is used for training the ANFIS model. The performance of the proposed ANFIS model is tested using the experimental data using four performance measures: correlation coefficient, mean absolute error, mean relative error percentage (MRE%) and root mean square error. The obtained results show that the proposed ANFIS model has achieved good agreement with the experimental results. In comparison to the experimental data the proposed ANFIS model has MRE% <1.53 and 2.85 % for training and testing data respectively. Therefore, this model can be used as an efficient tool to predict the NPR in the IR-IECF device.

Spectrophotometric determination of ternary mixtures of thiamin, riboflavin and pyridoxal in pharmaceutical and human plasma by least-squares support vector machines.

PubMed

Niazi, Ali; Zolgharnein, Javad; Afiuni-Zadeh, Somaie

2007-11-01

Ternary mixtures of thiamin, riboflavin and pyridoxal have been simultaneously determined in synthetic and real samples by applications of spectrophotometric and least-squares support vector machines. The calibration graphs were linear in the ranges of 1.0 - 20.0, 1.0 - 10.0 and 1.0 - 20.0 microg ml(-1) with detection limits of 0.6, 0.5 and 0.7 microg ml(-1) for thiamin, riboflavin and pyridoxal, respectively. The experimental calibration matrix was designed with 21 mixtures of these chemicals. The concentrations were varied between calibration graph concentrations of vitamins. The simultaneous determination of these vitamin mixtures by using spectrophotometric methods is a difficult problem, due to spectral interferences. The partial least squares (PLS) modeling and least-squares support vector machines were used for the multivariate calibration of the spectrophotometric data. An excellent model was built using LS-SVM, with low prediction errors and superior performance in relation to PLS. The root mean square errors of prediction (RMSEP) for thiamin, riboflavin and pyridoxal with PLS and LS-SVM were 0.6926, 0.3755, 0.4322 and 0.0421, 0.0318, 0.0457, respectively. The proposed method was satisfactorily applied to the rapid simultaneous determination of thiamin, riboflavin and pyridoxal in commercial pharmaceutical preparations and human plasma samples.

Optimization of wavefront coding imaging system using heuristic algorithms

NASA Astrophysics Data System (ADS)

González-Amador, E.; Padilla-Vivanco, A.; Toxqui-Quitl, C.; Zermeño-Loreto, O.

2017-08-01

Wavefront Coding (WFC) systems make use of an aspheric Phase-Mask (PM) and digital image processing to extend the Depth of Field (EDoF) of computational imaging systems. For years, several kinds of PM have been designed to produce a point spread function (PSF) near defocus-invariant. In this paper, the optimization of the phase deviation parameter is done by means of genetic algorithms (GAs). In this, the merit function minimizes the mean square error (MSE) between the diffraction limited Modulated Transfer Function (MTF) and the MTF of the system that is wavefront coded with different misfocus. WFC systems were simulated using the cubic, trefoil, and 4 Zernike polynomials phase-masks. Numerical results show defocus invariance aberration in all cases. Nevertheless, the best results are obtained by using the trefoil phase-mask, because the decoded image is almost free of artifacts.

Application of independent component analysis for speech-music separation using an efficient score function estimation

NASA Astrophysics Data System (ADS)

Pishravian, Arash; Aghabozorgi Sahaf, Masoud Reza

2012-12-01

In this paper speech-music separation using Blind Source Separation is discussed. The separating algorithm is based on the mutual information minimization where the natural gradient algorithm is used for minimization. In order to do that, score function estimation from observation signals (combination of speech and music) samples is needed. The accuracy and the speed of the mentioned estimation will affect on the quality of the separated signals and the processing time of the algorithm. The score function estimation in the presented algorithm is based on Gaussian mixture based kernel density estimation method. The experimental results of the presented algorithm on the speech-music separation and comparing to the separating algorithm which is based on the Minimum Mean Square Error estimator, indicate that it can cause better performance and less processing time

An estimator of the survival function based on the semi-Markov model under dependent censorship.

PubMed

Lee, Seung-Yeoun; Tsai, Wei-Yann

2005-06-01

Lee and Wolfe (Biometrics vol. 54 pp. 1176-1178, 1998) proposed the two-stage sampling design for testing the assumption of independent censoring, which involves further follow-up of a subset of lost-to-follow-up censored subjects. They also proposed an adjusted estimator for the survivor function for a proportional hazards model under the dependent censoring model. In this paper, a new estimator for the survivor function is proposed for the semi-Markov model under the dependent censorship on the basis of the two-stage sampling data. The consistency and the asymptotic distribution of the proposed estimator are derived. The estimation procedure is illustrated with an example of lung cancer clinical trial and simulation results are reported of the mean squared errors of estimators under a proportional hazards and two different nonproportional hazards models.

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

NASA Astrophysics Data System (ADS)

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; Birkholzer, Jens T.

2017-11-01

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1-D, 2-D, and 3-D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, td. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, td0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the first two terms for high-accuracy approximations (with less than 10-7 relative error) for 1-D isotropic (spheres, cylinders, slabs) and 2-D/3-D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1-D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2-D/3-D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

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

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1D, 2D, and 3D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, t d0. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, t d0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the firstmore » two terms for high-accuracy approximations (with less than 10-7 relative error) for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2D/3D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.« less

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

DOE PAGES

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; ...

2017-10-24

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1D, 2D, and 3D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, t d0. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, t d0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the firstmore » two terms for high-accuracy approximations (with less than 10-7 relative error) for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2D/3D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.« less

Modeling error analysis of stationary linear discrete-time filters

NASA Technical Reports Server (NTRS)

Patel, R.; Toda, M.

1977-01-01

The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a design can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices is available.