Bounded Perturbation Regularization for Linear Least Squares Estimation

KAUST Repository

Ballal, Tarig; Suliman, Mohamed Abdalla Elhag; Al-Naffouri, Tareq Y.

2017-01-01

This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded

Multivariat least-squares methods applied to the quantitative spectral analysis of multicomponent samples

International Nuclear Information System (INIS)

Haaland, D.M.; Easterling, R.G.; Vopicka, D.A.

1985-01-01

In an extension of earlier work, weighted multivariate least-squares methods of quantitative FT-IR analysis have been developed. A linear least-squares approximation to nonlinearities in the Beer-Lambert law is made by allowing the reference spectra to be a set of known mixtures, The incorporation of nonzero intercepts in the relation between absorbance and concentration further improves the approximation of nonlinearities while simultaneously accounting for nonzero spectra baselines. Pathlength variations are also accommodated in the analysis, and under certain conditions, unknown sample pathlengths can be determined. All spectral data are used to improve the precision and accuracy of the estimated concentrations. During the calibration phase of the analysis, pure component spectra are estimated from the standard mixture spectra. These can be compared with the measured pure component spectra to determine which vibrations experience nonlinear behavior. In the predictive phase of the analysis, the calculated spectra are used in our previous least-squares analysis to estimate sample component concentrations. These methods were applied to the analysis of the IR spectra of binary mixtures of esters. Even with severely overlapping spectral bands and nonlinearities in the Beer-Lambert law, the average relative error in the estimated concentration was <1%

Parameter Estimation of Permanent Magnet Synchronous Motor Using Orthogonal Projection and Recursive Least Squares Combinatorial Algorithm

Directory of Open Access Journals (Sweden)

Iman Yousefi

2015-01-01

Full Text Available This paper presents parameter estimation of Permanent Magnet Synchronous Motor (PMSM using a combinatorial algorithm. Nonlinear fourth-order space state model of PMSM is selected. This model is rewritten to the linear regression form without linearization. Noise is imposed to the system in order to provide a real condition, and then combinatorial Orthogonal Projection Algorithm and Recursive Least Squares (OPA&RLS method is applied in the linear regression form to the system. Results of this method are compared to the Orthogonal Projection Algorithm (OPA and Recursive Least Squares (RLS methods to validate the feasibility of the proposed method. Simulation results validate the efficacy of the proposed algorithm.

Spectrum unfolding by the least-squares methods

International Nuclear Information System (INIS)

Perey, F.G.

1977-01-01

The method of least squares is briefly reviewed, and the conditions under which it may be used are stated. From this analysis, a least-squares approach to the solution of the dosimetry neutron spectrum unfolding problem is introduced. The mathematical solution to this least-squares problem is derived from the general solution. The existence of this solution is analyzed in some detail. A chi 2 -test is derived for the consistency of the input data which does not require the solution to be obtained first. The fact that the problem is technically nonlinear, but should be treated in general as a linear one, is argued. Therefore, the solution should not be obtained by iteration. Two interpretations are made for the solution of the code STAY'SL, which solves this least-squares problem. The relationship of the solution to this least-squares problem to those obtained currently by other methods of solving the dosimetry neutron spectrum unfolding problem is extensively discussed. It is shown that the least-squares method does not require more input information than would be needed by current methods in order to estimate the uncertainties in their solutions. From this discussion it is concluded that the proposed least-squares method does provide the best complete solution, with uncertainties, to the problem as it is understood now. Finally, some implications of this method are mentioned regarding future work required in order to exploit its potential fully

Performance improvement of shunt active power filter based on non-linear least-square approach

DEFF Research Database (Denmark)

Terriche, Yacine

2018-01-01

. This paper proposes an improved open loop strategy which is unconditionally stable and flexible. The proposed method which is based on non-linear least square (NLS) approach can extract the fundamental voltage and estimates its phase within only half cycle, even in the presence of odd harmonics and dc offset......). The synchronous reference frame (SRF) approach is widely used for generating the RCC due to its simplicity and computation efficiency. However, the SRF approach needs precise information of the voltage phase which becomes a challenge under adverse grid conditions. A typical solution to answer this need...

Online Parameter Identification and State of Charge Estimation of Lithium-Ion Batteries Based on Forgetting Factor Recursive Least Squares and Nonlinear Kalman Filter

Directory of Open Access Journals (Sweden)

Bizhong Xia

2017-12-01

Full Text Available State of charge (SOC estimation is the core of any battery management system. Most closed-loop SOC estimation algorithms are based on the equivalent circuit model with fixed parameters. However, the parameters of the equivalent circuit model will change as temperature or SOC changes, resulting in reduced SOC estimation accuracy. In this paper, two SOC estimation algorithms with online parameter identification are proposed to solve this problem based on forgetting factor recursive least squares (FFRLS and nonlinear Kalman filter. The parameters of a Thevenin model are constantly updated by FFRLS. The nonlinear Kalman filter is used to perform the recursive operation to estimate SOC. Experiments in variable temperature environments verify the effectiveness of the proposed algorithms. A combination of four driving cycles is loaded on lithium-ion batteries to test the adaptability of the approaches to different working conditions. Under certain conditions, the average error of the SOC estimation dropped from 5.6% to 1.1% after adding the online parameters identification, showing that the estimation accuracy of proposed algorithms is greatly improved. Besides, simulated measurement noise is added to the test data to prove the robustness of the algorithms.

New recursive-least-squares algorithms for nonlinear active control of sound and vibration using neural networks.

Science.gov (United States)

Bouchard, M

2001-01-01

In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.

Space-time least-squares Petrov-Galerkin projection in nonlinear model reduction.

Energy Technology Data Exchange (ETDEWEB)

Choi, Youngsoo [Sandia National Laboratories (SNL-CA), Livermore, CA (United States). Extreme-scale Data Science and Analytics Dept.; Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Carlberg, Kevin Thomas [Sandia National Laboratories (SNL-CA), Livermore, CA (United States). Extreme-scale Data Science and Analytics Dept.

2017-09-01

Our work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply Petrov-Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed method applies projection in space and time simultaneously. To accomplish this, the method first introduces a low-dimensional space-time trial subspace, which can be obtained by computing tensor decompositions of state-snapshot data. The method then computes discrete-optimal approximations in this space-time trial subspace by minimizing the residual arising after time discretization over all space and time in a weighted ℓ²-norm. This norm can be de ned to enable complexity reduction (i.e., hyper-reduction) in time, which leads to space-time collocation and space-time GNAT variants of the ST-LSPG method. Advantages of the approach relative to typical spatial-projection-based nonlinear model reduction methods such as Galerkin projection and least-squares Petrov-Galerkin projection include: (1) a reduction of both the spatial and temporal dimensions of the dynamical system, (2) the removal of spurious temporal modes (e.g., unstable growth) from the state space, and (3) error bounds that exhibit slower growth in time. Numerical examples performed on model problems in fluid dynamics demonstrate the ability of the method to generate orders-of-magnitude computational savings relative to spatial-projection-based reduced-order models without sacrificing accuracy.

Discussion About Nonlinear Time Series Prediction Using Least Squares Support Vector Machine

International Nuclear Information System (INIS)

Xu Ruirui; Bian Guoxing; Gao Chenfeng; Chen Tianlun

2005-01-01

The least squares support vector machine (LS-SVM) is used to study the nonlinear time series prediction. First, the parameter γ and multi-step prediction capabilities of the LS-SVM network are discussed. Then we employ clustering method in the model to prune the number of the support values. The learning rate and the capabilities of filtering noise for LS-SVM are all greatly improved.

A Weighted Least Squares Approach To Robustify Least Squares Estimates.

Science.gov (United States)

Lin, Chowhong; Davenport, Ernest C., Jr.

This study developed a robust linear regression technique based on the idea of weighted least squares. In this technique, a subsample of the full data of interest is drawn, based on a measure of distance, and an initial set of regression coefficients is calculated. The rest of the data points are then taken into the subsample, one after another,…

Algorithms for non-linear M-estimation

DEFF Research Database (Denmark)

Madsen, Kaj; Edlund, O; Ekblom, H

1997-01-01

In non-linear regression, the least squares method is most often used. Since this estimator is highly sensitive to outliers in the data, alternatives have became increasingly popular during the last decades. We present algorithms for non-linear M-estimation. A trust region approach is used, where...

Application of the Polynomial-Based Least Squares and Total Least Squares Models for the Attenuated Total Reflection Fourier Transform Infrared Spectra of Binary Mixtures of Hydroxyl Compounds.

Science.gov (United States)

Shan, Peng; Peng, Silong; Zhao, Yuhui; Tang, Liang

2016-03-01

An analysis of binary mixtures of hydroxyl compound by Attenuated Total Reflection Fourier transform infrared spectroscopy (ATR FT-IR) and classical least squares (CLS) yield large model error due to the presence of unmodeled components such as H-bonded components. To accommodate these spectral variations, polynomial-based least squares (LSP) and polynomial-based total least squares (TLSP) are proposed to capture the nonlinear absorbance-concentration relationship. LSP is based on assuming that only absorbance noise exists; while TLSP takes both absorbance noise and concentration noise into consideration. In addition, based on different solving strategy, two optimization algorithms (limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm and Levenberg-Marquardt (LM) algorithm) are combined with TLSP and then two different TLSP versions (termed as TLSP-LBFGS and TLSP-LM) are formed. The optimum order of each nonlinear model is determined by cross-validation. Comparison and analyses of the four models are made from two aspects: absorbance prediction and concentration prediction. The results for water-ethanol solution and ethanol-ethyl lactate solution show that LSP, TLSP-LBFGS, and TLSP-LM can, for both absorbance prediction and concentration prediction, obtain smaller root mean square error of prediction than CLS. Additionally, they can also greatly enhance the accuracy of estimated pure component spectra. However, from the view of concentration prediction, the Wilcoxon signed rank test shows that there is no statistically significant difference between each nonlinear model and CLS. © The Author(s) 2016.

An information geometric approach to least squares minimization

Science.gov (United States)

Transtrum, Mark; Machta, Benjamin; Sethna, James

2009-03-01

Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the origin. The standard algorithm for minimizing sums of squares, the Levenberg-Marquardt algorithm, also has geometric meaning. When the standard algorithm fails to efficiently find accurate fits to the data, geometric considerations suggest improvements. Problems involving large numbers of parameters, such as often arise in biological contexts, are notoriously difficult. We suggest an algorithm based on geodesic motion that may offer improvements over the standard algorithm for a certain class of problems.

Least Squares Data Fitting with Applications

DEFF Research Database (Denmark)

Hansen, Per Christian; Pereyra, Víctor; Scherer, Godela

As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data....... In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working...... with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems. Included are • an overview of computational methods together with their properties and advantages • topics from statistical regression analysis...

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

Science.gov (United States)

Rebillat, Marc; Schoukens, Maarten

2018-05-01

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

Support-Vector-based Least Squares for learning non-linear dynamics

NARCIS (Netherlands)

de Kruif, B.J.; de Vries, Theodorus J.A.

2002-01-01

A function approximator is introduced that is based on least squares support vector machines (LSSVM) and on least squares (LS). The potential indicators for the LS method are chosen as the kernel functions of all the training samples similar to LSSVM. By selecting these as indicator functions the

Decentralized Gauss-Newton method for nonlinear least squares on wide area network

Science.gov (United States)

Liu, Lanchao; Ling, Qing; Han, Zhu

2014-10-01

This paper presents a decentralized approach of Gauss-Newton (GN) method for nonlinear least squares (NLLS) on wide area network (WAN). In a multi-agent system, a centralized GN for NLLS requires the global GN Hessian matrix available at a central computing unit, which may incur large communication overhead. In the proposed decentralized alternative, each agent only needs local GN Hessian matrix to update iterates with the cooperation of neighbors. The detail formulation of decentralized NLLS on WAN is given, and the iteration at each agent is defined. The convergence property of the decentralized approach is analyzed, and numerical results validate the effectiveness of the proposed algorithm.

Implementation of the Least-Squares Lattice with Order and Forgetting Factor Estimation for FPGA

Czech Academy of Sciences Publication Activity Database

Pohl, Zdeněk; Tichý, Milan; Kadlec, Jiří

2008-01-01

Roč. 2008, č. 2008 (2008), s. 1-11 ISSN 1687-6172 R&D Projects: GA MŠk(CZ) 1M0567 EU Projects: European Commission(XE) 027611 - AETHER Program:FP6 Institutional research plan: CEZ:AV0Z10750506 Keywords : DSP * Least-squares lattice * order estimation * exponential forgetting factor estimation * FPGA implementation * scheduling * dynamic reconfiguration * microblaze Subject RIV: IN - Informatics, Computer Science Impact factor: 1.055, year: 2008 http://library.utia.cas.cz/separaty/2008/ZS/pohl-tichy-kadlec-implementation%20of%20the%20least-squares%20lattice%20with%20order%20and%20forgetting%20factor%20estimation%20for%20fpga.pdf

New methods of testing nonlinear hypothesis using iterative NLLS estimator

Science.gov (United States)

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

2017-11-01

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

A least-squares computational ``tool kit``. Nuclear data and measurements series

Energy Technology Data Exchange (ETDEWEB)

Smith, D.L.

1993-04-01

The information assembled in this report is intended to offer a useful computational ``tool kit`` to individuals who are interested in a variety of practical applications for the least-squares method of parameter estimation. The fundamental principles of Bayesian analysis are outlined first and these are applied to development of both the simple and the generalized least-squares conditions. Formal solutions that satisfy these conditions are given subsequently. Their application to both linear and non-linear problems is described in detail. Numerical procedures required to implement these formal solutions are discussed and two utility computer algorithms are offered for this purpose (codes LSIOD and GLSIOD written in FORTRAN). Some simple, easily understood examples are included to illustrate the use of these algorithms. Several related topics are then addressed, including the generation of covariance matrices, the role of iteration in applications of least-squares procedures, the effects of numerical precision and an approach that can be pursued in developing data analysis packages that are directed toward special applications.

Non-linear HVAC computations using least square support vector machines

International Nuclear Information System (INIS)

Kumar, Mahendra; Kar, I.N.

2009-01-01

This paper aims to demonstrate application of least square support vector machines (LS-SVM) to model two complex heating, ventilating and air-conditioning (HVAC) relationships. The two applications considered are the estimation of the predicted mean vote (PMV) for thermal comfort and the generation of psychrometric chart. LS-SVM has the potential for quick, exact representations and also possesses a structure that facilitates hardware implementation. The results show very good agreement between function values computed from conventional model and LS-SVM model in real time. The robustness of LS-SVM models against input noises has also been analyzed.

On structure-exploiting trust-region regularized nonlinear least squares algorithms for neural-network learning.

Science.gov (United States)

Mizutani, Eiji; Demmel, James W

2003-01-01

This paper briefly introduces our numerical linear algebra approaches for solving structured nonlinear least squares problems arising from 'multiple-output' neural-network (NN) models. Our algorithms feature trust-region regularization, and exploit sparsity of either the 'block-angular' residual Jacobian matrix or the 'block-arrow' Gauss-Newton Hessian (or Fisher information matrix in statistical sense) depending on problem scale so as to render a large class of NN-learning algorithms 'efficient' in both memory and operation costs. Using a relatively large real-world nonlinear regression application, we shall explain algorithmic strengths and weaknesses, analyzing simulation results obtained by both direct and iterative trust-region algorithms with two distinct NN models: 'multilayer perceptrons' (MLP) and 'complementary mixtures of MLP-experts' (or neuro-fuzzy modular networks).

Regularization Techniques for Linear Least-Squares Problems

KAUST Repository

Suliman, Mohamed

2016-04-01

Linear estimation is a fundamental branch of signal processing that deals with estimating the values of parameters from a corrupted measured data. Throughout the years, several optimization criteria have been used to achieve this task. The most astonishing attempt among theses is the linear least-squares. Although this criterion enjoyed a wide popularity in many areas due to its attractive properties, it appeared to suffer from some shortcomings. Alternative optimization criteria, as a result, have been proposed. These new criteria allowed, in one way or another, the incorporation of further prior information to the desired problem. Among theses alternative criteria is the regularized least-squares (RLS). In this thesis, we propose two new algorithms to find the regularization parameter for linear least-squares problems. In the constrained perturbation regularization algorithm (COPRA) for random matrices and COPRA for linear discrete ill-posed problems, an artificial perturbation matrix with a bounded norm is forced into the model matrix. This perturbation is introduced to enhance the singular value structure of the matrix. As a result, the new modified model is expected to provide a better stabilize substantial solution when used to estimate the original signal through minimizing the worst-case residual error function. Unlike many other regularization algorithms that go in search of minimizing the estimated data error, the two new proposed algorithms are developed mainly to select the artifcial perturbation bound and the regularization parameter in a way that approximately minimizes the mean-squared error (MSE) between the original signal and its estimate under various conditions. The first proposed COPRA method is developed mainly to estimate the regularization parameter when the measurement matrix is complex Gaussian, with centered unit variance (standard), and independent and identically distributed (i.i.d.) entries. Furthermore, the second proposed COPRA

Pressurized water reactor monitoring. Study of detection, diagnostic and estimation methods (least error squares and filtering)

International Nuclear Information System (INIS)

Gillet, M.

1986-07-01

This thesis presents a study for the surveillance of the ''primary coolant circuit inventory monitoring'' of a pressurized water reactor. A reference model is developed in view of an automatic system ensuring detection and diagnostic in real time. The methods used for the present application are statistical tests and a method related to pattern recognition. The estimation of failures detected, difficult owing to the non-linearity of the problem, is treated by the least error squares method of the predictor or corrector type, and by filtering. It is in this frame that a new optimized method with superlinear convergence is developed, and that a segmented linearization of the model is introduced, in view of a multiple filtering [fr

Least Squares Estimate of the Initial Phases in STFT based Speech Enhancement

DEFF Research Database (Denmark)

Nørholm, Sidsel Marie; Krawczyk-Becker, Martin; Gerkmann, Timo

2015-01-01

In this paper, we consider single-channel speech enhancement in the short time Fourier transform (STFT) domain. We suggest to improve an STFT phase estimate by estimating the initial phases. The method is based on the harmonic model and a model for the phase evolution over time. The initial phases...... are estimated by setting up a least squares problem between the noisy phase and the model for phase evolution. Simulations on synthetic and speech signals show a decreased error on the phase when an estimate of the initial phase is included compared to using the noisy phase as an initialisation. The error...... on the phase is decreased at input SNRs from -10 to 10 dB. Reconstructing the signal using the clean amplitude, the mean squared error is decreased and the PESQ score is increased....

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

Science.gov (United States)

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.

Least Squares Adjustment: Linear and Nonlinear Weighted Regression Analysis

DEFF Research Database (Denmark)

Nielsen, Allan Aasbjerg

2007-01-01

This note primarily describes the mathematics of least squares regression analysis as it is often used in geodesy including land surveying and satellite positioning applications. In these fields regression is often termed adjustment. The note also contains a couple of typical land surveying...... and satellite positioning application examples. In these application areas we are typically interested in the parameters in the model typically 2- or 3-D positions and not in predictive modelling which is often the main concern in other regression analysis applications. Adjustment is often used to obtain...... the clock error) and to obtain estimates of the uncertainty with which the position is determined. Regression analysis is used in many other fields of application both in the natural, the technical and the social sciences. Examples may be curve fitting, calibration, establishing relationships between...

Estimating Frequency by Interpolation Using Least Squares Support Vector Regression

Directory of Open Access Journals (Sweden)

Changwei Ma

2015-01-01

Full Text Available Discrete Fourier transform- (DFT- based maximum likelihood (ML algorithm is an important part of single sinusoid frequency estimation. As signal to noise ratio (SNR increases and is above the threshold value, it will lie very close to Cramer-Rao lower bound (CRLB, which is dependent on the number of DFT points. However, its mean square error (MSE performance is directly proportional to its calculation cost. As a modified version of support vector regression (SVR, least squares SVR (LS-SVR can not only still keep excellent capabilities for generalizing and fitting but also exhibit lower computational complexity. In this paper, therefore, LS-SVR is employed to interpolate on Fourier coefficients of received signals and attain high frequency estimation accuracy. Our results show that the proposed algorithm can make a good compromise between calculation cost and MSE performance under the assumption that the sample size, number of DFT points, and resampling points are already known.

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

Directory of Open Access Journals (Sweden)

Weiqiang Pan

2015-03-01

Full Text Available 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.

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

Science.gov (United States)

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.

A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems.

Science.gov (United States)

Kazemi, Mahdi; Arefi, Mohammad Mehdi

2017-03-01

In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Performance improvement of shunt active power filter based on non-linear least-square approach

DEFF Research Database (Denmark)

Terriche, Yacine

2018-01-01

Nowadays, the shunt active power filters (SAPFs) have become a popular solution for power quality issues. A crucial issue in controlling the SAPFs which is highly correlated with their accuracy, flexibility and dynamic behavior, is generating the reference compensating current (RCC). The synchron......Nowadays, the shunt active power filters (SAPFs) have become a popular solution for power quality issues. A crucial issue in controlling the SAPFs which is highly correlated with their accuracy, flexibility and dynamic behavior, is generating the reference compensating current (RCC......). The synchronous reference frame (SRF) approach is widely used for generating the RCC due to its simplicity and computation efficiency. However, the SRF approach needs precise information of the voltage phase which becomes a challenge under adverse grid conditions. A typical solution to answer this need....... This paper proposes an improved open loop strategy which is unconditionally stable and flexible. The proposed method which is based on non-linear least square (NLS) approach can extract the fundamental voltage and estimates its phase within only half cycle, even in the presence of odd harmonics and dc offset...

Analysis of total least squares in estimating the parameters of a mortar trajectory

Energy Technology Data Exchange (ETDEWEB)

Lau, D.L.; Ng, L.C.

1994-12-01

Least Squares (LS) is a method of curve fitting used with the assumption that error exists in the observation vector. The method of Total Least Squares (TLS) is more useful in cases where there is error in the data matrix as well as the observation vector. This paper describes work done in comparing the LS and TLS results for parameter estimation of a mortar trajectory based on a time series of angular observations. To improve the results, we investigated several derivations of the LS and TLS methods, and early findings show TLS provided slightly, 10%, improved results over the LS method.

Battery state-of-charge estimation using approximate least squares

Science.gov (United States)

Unterrieder, C.; Zhang, C.; Lunglmayr, M.; Priewasser, R.; Marsili, S.; Huemer, M.

2015-03-01

In recent years, much effort has been spent to extend the runtime of battery-powered electronic applications. In order to improve the utilization of the available cell capacity, high precision estimation approaches for battery-specific parameters are needed. In this work, an approximate least squares estimation scheme is proposed for the estimation of the battery state-of-charge (SoC). The SoC is determined based on the prediction of the battery's electromotive force. The proposed approach allows for an improved re-initialization of the Coulomb counting (CC) based SoC estimation method. Experimental results for an implementation of the estimation scheme on a fuel gauge system on chip are illustrated. Implementation details and design guidelines are presented. The performance of the presented concept is evaluated for realistic operating conditions (temperature effects, aging, standby current, etc.). For the considered test case of a GSM/UMTS load current pattern of a mobile phone, the proposed method is able to re-initialize the CC-method with a high accuracy, while state-of-the-art methods fail to perform a re-initialization.

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

Science.gov (United States)

Nair, S. P.; Righetti, R.

2015-05-01

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

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

Science.gov (United States)

Periaux, J.

1979-01-01

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Multivariate calibration with least-squares support vector machines.

NARCIS (Netherlands)

Thissen, U.M.J.; Ustun, B.; Melssen, W.J.; Buydens, L.M.C.

2004-01-01

This paper proposes the use of least-squares support vector machines (LS-SVMs) as a relatively new nonlinear multivariate calibration method, capable of dealing with ill-posed problems. LS-SVMs are an extension of "traditional" SVMs that have been introduced recently in the field of chemistry and

Fault Estimation for Fuzzy Delay Systems: A Minimum Norm Least Squares Solution Approach.

Science.gov (United States)

Huang, Sheng-Juan; Yang, Guang-Hong

2017-09-01

This paper mainly focuses on the problem of fault estimation for a class of Takagi-Sugeno fuzzy systems with state delays. A minimum norm least squares solution (MNLSS) approach is first introduced to establish a fault estimation compensator, which is able to optimize the fault estimator. Compared with most of the existing fault estimation methods, the MNLSS-based fault estimation method can effectively decrease the effect of state errors on the accuracy of fault estimation. Finally, three examples are given to illustrate the effectiveness and merits of the proposed method.

Robust regularized least-squares beamforming approach to signal estimation

KAUST Repository

Suliman, Mohamed Abdalla Elhag

2017-05-12

In this paper, we address the problem of robust adaptive beamforming of signals received by a linear array. The challenge associated with the beamforming problem is twofold. Firstly, the process requires the inversion of the usually ill-conditioned covariance matrix of the received signals. Secondly, the steering vector pertaining to the direction of arrival of the signal of interest is not known precisely. To tackle these two challenges, the standard capon beamformer is manipulated to a form where the beamformer output is obtained as a scaled version of the inner product of two vectors. The two vectors are linearly related to the steering vector and the received signal snapshot, respectively. The linear operator, in both cases, is the square root of the covariance matrix. A regularized least-squares (RLS) approach is proposed to estimate these two vectors and to provide robustness without exploiting prior information. Simulation results show that the RLS beamformer using the proposed regularization algorithm outperforms state-of-the-art beamforming algorithms, as well as another RLS beamformers using a standard regularization approaches.

Developing a local least-squares support vector machines-based neuro-fuzzy model for nonlinear and chaotic time series prediction.

Science.gov (United States)

Miranian, A; Abdollahzade, M

2013-02-01

Local modeling approaches, owing to their ability to model different operating regimes of nonlinear systems and processes by independent local models, seem appealing for modeling, identification, and prediction applications. In this paper, we propose a local neuro-fuzzy (LNF) approach based on the least-squares support vector machines (LSSVMs). The proposed LNF approach employs LSSVMs, which are powerful in modeling and predicting time series, as local models and uses hierarchical binary tree (HBT) learning algorithm for fast and efficient estimation of its parameters. The HBT algorithm heuristically partitions the input space into smaller subdomains by axis-orthogonal splits. In each partitioning, the validity functions automatically form a unity partition and therefore normalization side effects, e.g., reactivation, are prevented. Integration of LSSVMs into the LNF network as local models, along with the HBT learning algorithm, yield a high-performance approach for modeling and prediction of complex nonlinear time series. The proposed approach is applied to modeling and predictions of different nonlinear and chaotic real-world and hand-designed systems and time series. Analysis of the prediction results and comparisons with recent and old studies demonstrate the promising performance of the proposed LNF approach with the HBT learning algorithm for modeling and prediction of nonlinear and chaotic systems and time series.

TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods

Energy Technology Data Exchange (ETDEWEB)

Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science

1996-12-31

This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations.

Medium Band Least Squares Estimation of Fractional Cointegration in the Presence of Low-Frequency Contamination

DEFF Research Database (Denmark)

Christensen, Bent Jesper; Varneskov, Rasmus T.

band least squares (MBLS) estimator uses sample dependent trimming of frequencies in the vicinity of the origin to account for such contamination. Consistency and asymptotic normality of the MBLS estimator are established, a feasible inference procedure is proposed, and rigorous tools for assessing...

Status of the Monte Carlo library least-squares (MCLLS) approach for non-linear radiation analyzer problems

Science.gov (United States)

Gardner, Robin P.; Xu, Libai

2009-10-01

The Center for Engineering Applications of Radioisotopes (CEAR) has been working for over a decade on the Monte Carlo library least-squares (MCLLS) approach for treating non-linear radiation analyzer problems including: (1) prompt gamma-ray neutron activation analysis (PGNAA) for bulk analysis, (2) energy-dispersive X-ray fluorescence (EDXRF) analyzers, and (3) carbon/oxygen tool analysis in oil well logging. This approach essentially consists of using Monte Carlo simulation to generate the libraries of all the elements to be analyzed plus any other required background libraries. These libraries are then used in the linear library least-squares (LLS) approach with unknown sample spectra to analyze for all elements in the sample. Iterations of this are used until the LLS values agree with the composition used to generate the libraries. The current status of the methods (and topics) necessary to implement the MCLLS approach is reported. This includes: (1) the Monte Carlo codes such as CEARXRF, CEARCPG, and CEARCO for forward generation of the necessary elemental library spectra for the LLS calculation for X-ray fluorescence, neutron capture prompt gamma-ray analyzers, and carbon/oxygen tools; (2) the correction of spectral pulse pile-up (PPU) distortion by Monte Carlo simulation with the code CEARIPPU; (3) generation of detector response functions (DRF) for detectors with linear and non-linear responses for Monte Carlo simulation of pulse-height spectra; and (4) the use of the differential operator (DO) technique to make the necessary iterations for non-linear responses practical. In addition to commonly analyzed single spectra, coincidence spectra or even two-dimensional (2-D) coincidence spectra can also be used in the MCLLS approach and may provide more accurate results.

Non linear-least-squares fitting for pixe spectra

International Nuclear Information System (INIS)

Benamar, M.A.; Tchantchane, A.; Benouali, N.; Azbouche, A.; Tobbeche, S.

1992-10-01

An interactive computer program for the analysis of Pixe spectra is described. The fitting procedure consists of computing a function which approximates the experimental data. A nonlinear least-squares fitting is used to determine the parameters of the fit. The program takes into account the low energy tail and the escape peaks

Optimally weighted least-squares steganalysis

Science.gov (United States)

Ker, Andrew D.

2007-02-01

Quantitative steganalysis aims to estimate the amount of payload in a stego object, and such estimators seem to arise naturally in steganalysis of Least Significant Bit (LSB) replacement in digital images. However, as with all steganalysis, the estimators are subject to errors, and their magnitude seems heavily dependent on properties of the cover. In very recent work we have given the first derivation of estimation error, for a certain method of steganalysis (the Least-Squares variant of Sample Pairs Analysis) of LSB replacement steganography in digital images. In this paper we make use of our theoretical results to find an improved estimator and detector. We also extend the theoretical analysis to another (more accurate) steganalysis estimator (Triples Analysis) and hence derive an improved version of that estimator too. Experimental results show that the new steganalyzers have improved accuracy, particularly in the difficult case of never-compressed covers.

Data-adapted moving least squares method for 3-D image interpolation

International Nuclear Information System (INIS)

Jang, Sumi; Lee, Yeon Ju; Jeong, Byeongseon; Nam, Haewon; Lee, Rena; Yoon, Jungho

2013-01-01

In this paper, we present a nonlinear three-dimensional interpolation scheme for gray-level medical images. The scheme is based on the moving least squares method but introduces a fundamental modification. For a given evaluation point, the proposed method finds the local best approximation by reproducing polynomials of a certain degree. In particular, in order to obtain a better match to the local structures of the given image, we employ locally data-adapted least squares methods that can improve the classical one. Some numerical experiments are presented to demonstrate the performance of the proposed method. Five types of data sets are used: MR brain, MR foot, MR abdomen, CT head, and CT foot. From each of the five types, we choose five volumes. The scheme is compared with some well-known linear methods and other recently developed nonlinear methods. For quantitative comparison, we follow the paradigm proposed by Grevera and Udupa (1998). (Each slice is first assumed to be unknown then interpolated by each method. The performance of each interpolation method is assessed statistically.) The PSNR results for the estimated volumes are also provided. We observe that the new method generates better results in both quantitative and visual quality comparisons. (paper)

Time Scale in Least Square Method

Directory of Open Access Journals (Sweden)

Özgür Yeniay

2014-01-01

Full Text Available Study of dynamic equations in time scale is a new area in mathematics. Time scale tries to build a bridge between real numbers and integers. Two derivatives in time scale have been introduced and called as delta and nabla derivative. Delta derivative concept is defined as forward direction, and nabla derivative concept is defined as backward direction. Within the scope of this study, we consider the method of obtaining parameters of regression equation of integer values through time scale. Therefore, we implemented least squares method according to derivative definition of time scale and obtained coefficients related to the model. Here, there exist two coefficients originating from forward and backward jump operators relevant to the same model, which are different from each other. Occurrence of such a situation is equal to total number of values of vertical deviation between regression equations and observation values of forward and backward jump operators divided by two. We also estimated coefficients for the model using ordinary least squares method. As a result, we made an introduction to least squares method on time scale. We think that time scale theory would be a new vision in least square especially when assumptions of linear regression are violated.

LSL: a logarithmic least-squares adjustment method

International Nuclear Information System (INIS)

Stallmann, F.W.

1982-01-01

To meet regulatory requirements, spectral unfolding codes must not only provide reliable estimates for spectral parameters, but must also be able to determine the uncertainties associated with these parameters. The newer codes, which are more appropriately called adjustment codes, use the least squares principle to determine estimates and uncertainties. The principle is simple and straightforward, but there are several different mathematical models to describe the unfolding problem. In addition to a sound mathematical model, ease of use and range of options are important considerations in the construction of adjustment codes. Based on these considerations, a least squares adjustment code for neutron spectrum unfolding has been constructed some time ago and tentatively named LSL

Joint 2D-DOA and Frequency Estimation for L-Shaped Array Using Iterative Least Squares Method

Directory of Open Access Journals (Sweden)

Ling-yun Xu

2012-01-01

Full Text Available We introduce an iterative least squares method (ILS for estimating the 2D-DOA and frequency based on L-shaped array. The ILS iteratively finds direction matrix and delay matrix, then 2D-DOA and frequency can be obtained by the least squares method. Without spectral peak searching and pairing, this algorithm works well and pairs the parameters automatically. Moreover, our algorithm has better performance than conventional ESPRIT algorithm and propagator method. The useful behavior of the proposed algorithm is verified by simulations.

Recursive least squares method of regression coefficients estimation as a special case of Kalman filter

Science.gov (United States)

Borodachev, S. M.

2016-06-01

The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.

Parameter Estimation and Prediction of a Nonlinear Storage Model: an algebraic approach

NARCIS (Netherlands)

Doeswijk, T.G.; Keesman, K.J.

2005-01-01

Generally, parameters that are nonlinear in system models are estimated by nonlinear least-squares optimization algorithms. In this paper, if a nonlinear discrete-time model with a polynomial quotient structure in input, output, and parameters, a method is proposed to re-parameterize the model such

A Newton Algorithm for Multivariate Total Least Squares Problems

Directory of Open Access Journals (Sweden)

WANG Leyang

2016-04-01

Full Text Available In order to improve calculation efficiency of parameter estimation, an algorithm for multivariate weighted total least squares adjustment based on Newton method is derived. The relationship between the solution of this algorithm and that of multivariate weighted total least squares adjustment based on Lagrange multipliers method is analyzed. According to propagation of cofactor, 16 computational formulae of cofactor matrices of multivariate total least squares adjustment are also listed. The new algorithm could solve adjustment problems containing correlation between observation matrix and coefficient matrix. And it can also deal with their stochastic elements and deterministic elements with only one cofactor matrix. The results illustrate that the Newton algorithm for multivariate total least squares problems could be practiced and have higher convergence rate.

Partial least squares methods for spectrally estimating lunar soil FeO abundance: A stratified approach to revealing nonlinear effect and qualitative interpretation

Science.gov (United States)

Li, Lin

2008-12-01

Partial least squares (PLS) regressions were applied to lunar highland and mare soil data characterized by the Lunar Soil Characterization Consortium (LSCC) for spectral estimation of the abundance of lunar soil chemical constituents FeO and Al2O3. The LSCC data set was split into a number of subsets including the total highland, Apollo 16, Apollo 14, and total mare soils, and then PLS was applied to each to investigate the effect of nonlinearity on the performance of the PLS method. The weight-loading vectors resulting from PLS were analyzed to identify mineral species responsible for spectral estimation of the soil chemicals. The results from PLS modeling indicate that the PLS performance depends on the correlation of constituents of interest to their major mineral carriers, and the Apollo 16 soils are responsible for the large errors of FeO and Al2O3 estimates when the soils were modeled along with other types of soils. These large errors are primarily attributed to the degraded correlation FeO to pyroxene for the relatively mature Apollo 16 soils as a result of space weathering and secondary to the interference of olivine. PLS consistently yields very accurate fits to the two soil chemicals when applied to mare soils. Although Al2O3 has no spectrally diagnostic characteristics, this chemical can be predicted for all subset data by PLS modeling at high accuracies because of its correlation to FeO. This correlation is reflected in the symmetry of the PLS weight-loading vectors for FeO and Al2O3, which prove to be very useful for qualitative interpretation of the PLS results. However, this qualitative interpretation of PLS modeling cannot be achieved using principal component regression loading vectors.

Improved Accuracy of Nonlinear Parameter Estimation with LAV and Interval Arithmetic Methods

Directory of Open Access Journals (Sweden)

Humberto Muñoz

2009-06-01

Full Text Available The reliable solution of nonlinear parameter es- timation problems is an important computational problem in many areas of science and engineering, including such applications as real time optimization. Its goal is to estimate accurate model parameters that provide the best fit to measured data, despite small- scale noise in the data or occasional large-scale mea- surement errors (outliers. In general, the estimation techniques are based on some kind of least squares or maximum likelihood criterion, and these require the solution of a nonlinear and non-convex optimiza- tion problem. Classical solution methods for these problems are local methods, and may not be reliable for finding the global optimum, with no guarantee the best model parameters have been found. Interval arithmetic can be used to compute completely and reliably the global optimum for the nonlinear para- meter estimation problem. Finally, experimental re- sults will compare the least squares, l2, and the least absolute value, l1, estimates using interval arithmetic in a chemical engineering application.

New approach to breast cancer CAD using partial least squares and kernel-partial least squares

Science.gov (United States)

Land, Walker H., Jr.; Heine, John; Embrechts, Mark; Smith, Tom; Choma, Robert; Wong, Lut

2005-04-01

Breast cancer is second only to lung cancer as a tumor-related cause of death in women. Currently, the method of choice for the early detection of breast cancer is mammography. While sensitive to the detection of breast cancer, its positive predictive value (PPV) is low, resulting in biopsies that are only 15-34% likely to reveal malignancy. This paper explores the use of two novel approaches called Partial Least Squares (PLS) and Kernel-PLS (K-PLS) to the diagnosis of breast cancer. The approach is based on optimization for the partial least squares (PLS) algorithm for linear regression and the K-PLS algorithm for non-linear regression. Preliminary results show that both the PLS and K-PLS paradigms achieved comparable results with three separate support vector learning machines (SVLMs), where these SVLMs were known to have been trained to a global minimum. That is, the average performance of the three separate SVLMs were Az = 0.9167927, with an average partial Az (Az90) = 0.5684283. These results compare favorably with the K-PLS paradigm, which obtained an Az = 0.907 and partial Az = 0.6123. The PLS paradigm provided comparable results. Secondly, both the K-PLS and PLS paradigms out performed the ANN in that the Az index improved by about 14% (Az ~ 0.907 compared to the ANN Az of ~ 0.8). The "Press R squared" value for the PLS and K-PLS machine learning algorithms were 0.89 and 0.9, respectively, which is in good agreement with the other MOP values.

Distributed weighted least-squares estimation with fast convergence for large-scale systems☆

Science.gov (United States)

Marelli, Damián Edgardo; Fu, Minyue

2015-01-01

In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods. PMID:25641976

Distributed weighted least-squares estimation with fast convergence for large-scale systems.

Science.gov (United States)

Marelli, Damián Edgardo; Fu, Minyue

2015-01-01

In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods.

Decision-Directed Recursive Least Squares MIMO Channels Tracking

Directory of Open Access Journals (Sweden)

Karami Ebrahim

2006-01-01

Full Text Available A new approach for joint data estimation and channel tracking for multiple-input multiple-output (MIMO channels is proposed based on the decision-directed recursive least squares (DD-RLS algorithm. RLS algorithm is commonly used for equalization and its application in channel estimation is a novel idea. In this paper, after defining the weighted least squares cost function it is minimized and eventually the RLS MIMO channel estimation algorithm is derived. The proposed algorithm combined with the decision-directed algorithm (DDA is then extended for the blind mode operation. From the computational complexity point of view being versus the number of transmitter and receiver antennas, the proposed algorithm is very efficient. Through various simulations, the mean square error (MSE of the tracking of the proposed algorithm for different joint detection algorithms is compared with Kalman filtering approach which is one of the most well-known channel tracking algorithms. It is shown that the performance of the proposed algorithm is very close to Kalman estimator and that in the blind mode operation it presents a better performance with much lower complexity irrespective of the need to know the channel model.

Sparse least-squares reverse time migration using seislets

KAUST Repository

Dutta, Gaurav

2015-08-19

We propose sparse least-squares reverse time migration (LSRTM) using seislets as a basis for the reflectivity distribution. This basis is used along with a dip-constrained preconditioner that emphasizes image updates only along prominent dips during the iterations. These dips can be estimated from the standard migration image or from the gradient using plane-wave destruction filters or structural tensors. Numerical tests on synthetic datasets demonstrate the benefits of this method for mitigation of aliasing artifacts and crosstalk noise in multisource least-squares migration.

Generalized least squares and empirical Bayes estimation in regional partial duration series index-flood modeling

DEFF Research Database (Denmark)

Madsen, Henrik; Rosbjerg, Dan

1997-01-01

parameters is inferred from regional data using generalized least squares (GLS) regression. Two different Bayesian T-year event estimators are introduced: a linear estimator that requires only some moments of the prior distributions to be specified and a parametric estimator that is based on specified......A regional estimation procedure that combines the index-flood concept with an empirical Bayes method for inferring regional information is introduced. The model is based on the partial duration series approach with generalized Pareto (GP) distributed exceedances. The prior information of the model...

Partial Least Squares tutorial for analyzing neuroimaging data

Directory of Open Access Journals (Sweden)

Patricia Van Roon

2014-09-01

Full Text Available Partial least squares (PLS has become a respected and meaningful soft modeling analysis technique that can be applied to very large datasets where the number of factors or variables is greater than the number of observations. Current biometric studies (e.g., eye movements, EKG, body movements, EEG are often of this nature. PLS eliminates the multiple linear regression issues of over-fitting data by finding a few underlying or latent variables (factors that account for most of the variation in the data. In real-world applications, where linear models do not always apply, PLS can model the non-linear relationship well. This tutorial introduces two PLS methods, PLS Correlation (PLSC and PLS Regression (PLSR and their applications in data analysis which are illustrated with neuroimaging examples. Both methods provide straightforward and comprehensible techniques for determining and modeling relationships between two multivariate data blocks by finding latent variables that best describes the relationships. In the examples, the PLSC will analyze the relationship between neuroimaging data such as Event-Related Potential (ERP amplitude averages from different locations on the scalp with their corresponding behavioural data. Using the same data, the PLSR will be used to model the relationship between neuroimaging and behavioural data. This model will be able to predict future behaviour solely from available neuroimaging data. To find latent variables, Singular Value Decomposition (SVD for PLSC and Non-linear Iterative PArtial Least Squares (NIPALS for PLSR are implemented in this tutorial. SVD decomposes the large data block into three manageable matrices containing a diagonal set of singular values, as well as left and right singular vectors. For PLSR, NIPALS algorithms are used because it provides amore precise estimation of the latent variables. Mathematica notebooks are provided for each PLS method with clearly labeled sections and subsections. The

Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations

KAUST Repository

Carlberg, Kevin

2010-10-28

A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.

Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations

KAUST Repository

Carlberg, Kevin; Bou-Mosleh, Charbel; Farhat, Charbel

2010-01-01

A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.

Constrained least squares regularization in PET

International Nuclear Information System (INIS)

Choudhury, K.R.; O'Sullivan, F.O.

1996-01-01

Standard reconstruction methods used in tomography produce images with undesirable negative artifacts in background and in areas of high local contrast. While sophisticated statistical reconstruction methods can be devised to correct for these artifacts, their computational implementation is excessive for routine operational use. This work describes a technique for rapid computation of approximate constrained least squares regularization estimates. The unique feature of the approach is that it involves no iterative projection or backprojection steps. This contrasts with the familiar computationally intensive algorithms based on algebraic reconstruction (ART) or expectation-maximization (EM) methods. Experimentation with the new approach for deconvolution and mixture analysis shows that the root mean square error quality of estimators based on the proposed algorithm matches and usually dominates that of more elaborate maximum likelihood, at a fraction of the computational effort

A Bayesian least squares support vector machines based framework for fault diagnosis and failure prognosis

Science.gov (United States)

Khawaja, Taimoor Saleem

and any abnormal or novel data during real-time operation. The results of the scheme are interpreted as a posterior probability of health (1 - probability of fault). As shown through two case studies in Chapter 3, the scheme is well suited for diagnosing imminent faults in dynamical non-linear systems. Finally, the failure prognosis scheme is based on an incremental weighted Bayesian LS-SVR machine. It is particularly suited for online deployment given the incremental nature of the algorithm and the quick optimization problem solved in the LS-SVR algorithm. By way of kernelization and a Gaussian Mixture Modeling (GMM) scheme, the algorithm can estimate "possibly" non-Gaussian posterior distributions for complex non-linear systems. An efficient regression scheme associated with the more rigorous core algorithm allows for long-term predictions, fault growth estimation with confidence bounds and remaining useful life (RUL) estimation after a fault is detected. The leading contributions of this thesis are (a) the development of a novel Bayesian Anomaly Detector for efficient and reliable Fault Detection and Identification (FDI) based on Least Squares Support Vector Machines, (b) the development of a data-driven real-time architecture for long-term Failure Prognosis using Least Squares Support Vector Machines, (c) Uncertainty representation and management using Bayesian Inference for posterior distribution estimation and hyper-parameter tuning, and finally (d) the statistical characterization of the performance of diagnosis and prognosis algorithms in order to relate the efficiency and reliability of the proposed schemes.

Gravity Search Algorithm hybridized Recursive Least Square method for power system harmonic estimation

Directory of Open Access Journals (Sweden)

Santosh Kumar Singh

2017-06-01

Full Text Available This paper presents a new hybrid method based on Gravity Search Algorithm (GSA and Recursive Least Square (RLS, known as GSA-RLS, to solve the harmonic estimation problems in the case of time varying power signals in presence of different noises. GSA is based on the Newton’s law of gravity and mass interactions. In the proposed method, the searcher agents are a collection of masses that interact with each other using Newton’s laws of gravity and motion. The basic GSA algorithm strategy is combined with RLS algorithm sequentially in an adaptive way to update the unknown parameters (weights of the harmonic signal. Simulation and practical validation are made with the experimentation of the proposed algorithm with real time data obtained from a heavy paper industry. A comparative performance of the proposed algorithm is evaluated with other recently reported algorithms like, Differential Evolution (DE, Particle Swarm Optimization (PSO, Bacteria Foraging Optimization (BFO, Fuzzy-BFO (F-BFO hybridized with Least Square (LS and BFO hybridized with RLS algorithm, which reveals that the proposed GSA-RLS algorithm is the best in terms of accuracy, convergence and computational time.

Least-squares methods involving the H{sup -1} inner product

Energy Technology Data Exchange (ETDEWEB)

Pasciak, J.

1996-12-31

Least-squares methods are being shown to be an effective technique for the solution of elliptic boundary value problems. However, the methods differ depending on the norms in which they are formulated. For certain problems, it is much more natural to consider least-squares functionals involving the H{sup -1} norm. Such norms give rise to improved convergence estimates and better approximation to problems with low regularity solutions. In addition, fewer new variables need to be added and less stringent boundary conditions need to be imposed. In this talk, I will describe some recent developments involving least-squares methods utilizing the H{sup -1} inner product.

A Generalized Autocovariance Least-Squares Method for Kalman Filter Tuning

DEFF Research Database (Denmark)

Åkesson, Bernt Magnus; Jørgensen, John Bagterp; Poulsen, Niels Kjølstad

2008-01-01

This paper discusses a method for estimating noise covariances from process data. In linear stochastic state-space representations the true noise covariances are generally unknown in practical applications. Using estimated covariances a Kalman filter can be tuned in order to increase the accuracy...... of the state estimates. There is a linear relationship between covariances and autocovariance. Therefore, the covariance estimation problem can be stated as a least-squares problem, which can be solved as a symmetric semidefinite least-squares problem. This problem is convex and can be solved efficiently...... by interior-point methods. A numerical algorithm for solving the symmetric is able to handle systems with mutually correlated process noise and measurement noise. (c) 2007 Elsevier Ltd. All rights reserved....

Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR is an efficient tool for metamodelling of nonlinear dynamic models

Directory of Open Access Journals (Sweden)

Omholt Stig W

2011-06-01

Full Text Available Abstract Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs to variation in features of the trajectories of the state variables (outputs throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR, where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR and ordinary least squares (OLS regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

Science.gov (United States)

Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

2011-06-01

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for

Quantized kernel least mean square algorithm.

Science.gov (United States)

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.

Estimasi Model Seemingly Unrelated Regression (SUR dengan Metode Generalized Least Square (GLS

Directory of Open Access Journals (Sweden)

Ade Widyaningsih

2015-04-01

Full Text Available Regression analysis is a statistical tool that is used to determine the relationship between two or more quantitative variables so that one variable can be predicted from the other variables. A method that can used to obtain a good estimation in the regression analysis is ordinary least squares method. The least squares method is used to estimate the parameters of one or more regression but relationships among the errors in the response of other estimators are not allowed. One way to overcome this problem is Seemingly Unrelated Regression model (SUR in which parameters are estimated using Generalized Least Square (GLS. In this study, the author applies SUR model using GLS method on world gasoline demand data. The author obtains that SUR using GLS is better than OLS because SUR produce smaller errors than the OLS.

Estimasi Model Seemingly Unrelated Regression (SUR dengan Metode Generalized Least Square (GLS

Directory of Open Access Journals (Sweden)

Ade Widyaningsih

2014-06-01

Full Text Available Regression analysis is a statistical tool that is used to determine the relationship between two or more quantitative variables so that one variable can be predicted from the other variables. A method that can used to obtain a good estimation in the regression analysis is ordinary least squares method. The least squares method is used to estimate the parameters of one or more regression but relationships among the errors in the response of other estimators are not allowed. One way to overcome this problem is Seemingly Unrelated Regression model (SUR in which parameters are estimated using Generalized Least Square (GLS. In this study, the author applies SUR model using GLS method on world gasoline demand data. The author obtains that SUR using GLS is better than OLS because SUR produce smaller errors than the OLS.

Least-squares model-based halftoning

Science.gov (United States)

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

Estimation of active pharmaceutical ingredients content using locally weighted partial least squares and statistical wavelength selection.

OpenAIRE

Kim, Sanghong; Kano, Manabu; Nakagawa, Hiroshi; Hasebe, Shinji

2011-01-01

Development of quality estimation models using near infrared spectroscopy (NIRS) and multivariate analysis has been accelerated as a process analytical technology (PAT) tool in the pharmaceutical industry. Although linear regression methods such as partial least squares (PLS) are widely used, they cannot always achieve high estimation accuracy because physical and chemical properties of a measuring object have a complex effect on NIR spectra. In this research, locally weighted PLS (LW-PLS) wh...

On the Performance of Maximum Likelihood versus Means and Variance Adjusted Weighted Least Squares Estimation in CFA

Science.gov (United States)

Beauducel, Andre; Herzberg, Philipp Yorck

2006-01-01

This simulation study compared maximum likelihood (ML) estimation with weighted least squares means and variance adjusted (WLSMV) estimation. The study was based on confirmatory factor analyses with 1, 2, 4, and 8 factors, based on 250, 500, 750, and 1,000 cases, and on 5, 10, 20, and 40 variables with 2, 3, 4, 5, and 6 categories. There was no…

PROPOSED MODIFICATIONS OF K2-TEMPERATURE RELATION AND LEAST SQUARES ESTIMATES OF BOD (BIOCHEMICAL OXYGEN DEMAND) PARAMETERS

Science.gov (United States)

A technique is presented for finding the least squares estimates for the ultimate biochemical oxygen demand (BOD) and rate coefficient for the BOD reaction without resorting to complicated computer algorithms or subjective graphical methods. This may be used in stream water quali...

A nonlinear least-squares inverse analysis of strike-slip faulting with application to the San Andreas fault

Science.gov (United States)

Williams, Charles A.; Richardson, Randall M.

1988-01-01

A nonlinear weighted least-squares analysis was performed for a synthetic elastic layer over a viscoelastic half-space model of strike-slip faulting. Also, an inversion of strain rate data was attempted for the locked portions of the San Andreas fault in California. Based on an eigenvector analysis of synthetic data, it is found that the only parameter which can be resolved is the average shear modulus of the elastic layer and viscoelastic half-space. The other parameters were obtained by performing a suite of inversions for the fault. The inversions on data from the northern San Andreas resulted in predicted parameter ranges similar to those produced by inversions on data from the whole fault.

Direct integral linear least square regression method for kinetic evaluation of hepatobiliary scintigraphy

International Nuclear Information System (INIS)

Shuke, Noriyuki

1991-01-01

In hepatobiliary scintigraphy, kinetic model analysis, which provides kinetic parameters like hepatic extraction or excretion rate, have been done for quantitative evaluation of liver function. In this analysis, unknown model parameters are usually determined using nonlinear least square regression method (NLS method) where iterative calculation and initial estimate for unknown parameters are required. As a simple alternative to NLS method, direct integral linear least square regression method (DILS method), which can determine model parameters by a simple calculation without initial estimate, is proposed, and tested the applicability to analysis of hepatobiliary scintigraphy. In order to see whether DILS method could determine model parameters as good as NLS method, or to determine appropriate weight for DILS method, simulated theoretical data based on prefixed parameters were fitted to 1 compartment model using both DILS method with various weightings and NLS method. The parameter values obtained were then compared with prefixed values which were used for data generation. The effect of various weights on the error of parameter estimate was examined, and inverse of time was found to be the best weight to make the error minimum. When using this weight, DILS method could give parameter values close to those obtained by NLS method and both parameter values were very close to prefixed values. With appropriate weighting, the DILS method could provide reliable parameter estimate which is relatively insensitive to the data noise. In conclusion, the DILS method could be used as a simple alternative to NLS method, providing reliable parameter estimate. (author)

Review of the Palisades pressure vessel accumulated fluence estimate and of the least squares methodology employed

Energy Technology Data Exchange (ETDEWEB)

Griffin, P.J.

1998-05-01

This report provides a review of the Palisades submittal to the Nuclear Regulatory Commission requesting endorsement of their accumulated neutron fluence estimates based on a least squares adjustment methodology. This review highlights some minor issues in the applied methodology and provides some recommendations for future work. The overall conclusion is that the Palisades fluence estimation methodology provides a reasonable approach to a {open_quotes}best estimate{close_quotes} of the accumulated pressure vessel neutron fluence and is consistent with the state-of-the-art analysis as detailed in community consensus ASTM standards.

On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

Energy Technology Data Exchange (ETDEWEB)

Amini, Nina H. [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States); CNRS, Laboratoire des Signaux et Systemes (L2S) CentraleSupelec, Gif-sur-Yvette (France); Miao, Zibo; Pan, Yu; James, Matthew R. [Australian National University, ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Canberra, ACT (Australia); Mabuchi, Hideo [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States)

2015-12-15

The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice. (orig.)

Partial update least-square adaptive filtering

CERN Document Server

Xie, Bei

2014-01-01

Adaptive filters play an important role in the fields related to digital signal processing and communication, such as system identification, noise cancellation, channel equalization, and beamforming. In practical applications, the computational complexity of an adaptive filter is an important consideration. The Least Mean Square (LMS) algorithm is widely used because of its low computational complexity (O(N)) and simplicity in implementation. The least squares algorithms, such as Recursive Least Squares (RLS), Conjugate Gradient (CG), and Euclidean Direction Search (EDS), can converge faster a

Least square method of estimation of ecological half-lives of radionuclides in sediments

International Nuclear Information System (INIS)

Ranade, A.K.; Pandey, M.; Datta, D.; Ravi, P.M.

2012-01-01

Long term behavior of radionuclides in the environment is an important issue for estimating probable radiological consequences and associated risks. It is also useful for evaluating potential use of contaminated areas and the possible effectiveness of remediation activities. The long term behavior is quantified by means of ecological half life, a parameter that aggregates all processes except radioactive decay which causes a decrease of activity in a specific medium. The process involved in ecological half life depends upon the environmental condition of the medium involved. A fitting model based on least square regression approach was used to evaluate the ecological half life. This least square method has to run several times to evaluate the number of ecological half lives present in the medium for the radionuclide. The case study data considered here is for 137 Cs in Mumbai Harbour Bay. The study shows the trend of 137 Cs over the years at a location in Mumbai Harbour Bay. First iteration model illustrate the ecological half life as 4.94 y and subsequently it passes through a number of runs for more number of ecological half-life present by goodness of fit test. The paper presents a methodology for evaluating ecological half life and exemplifies it with a case study of 137 Cs. (author)

Joint Estimation of the Electric Vehicle Power Battery State of Charge Based on the Least Squares Method and the Kalman Filter Algorithm

Directory of Open Access Journals (Sweden)

Xiangwei Guo

2016-02-01

Full Text Available An estimation of the power battery state of charge (SOC is related to the energy management, the battery cycle life and the use cost of electric vehicles. When a lithium-ion power battery is used in an electric vehicle, the SOC displays a very strong time-dependent nonlinearity under the influence of random factors, such as the working conditions and the environment. Hence, research on estimating the SOC of a power battery for an electric vehicle is of great theoretical significance and application value. In this paper, according to the dynamic response of the power battery terminal voltage during a discharging process, the second-order RC circuit is first used as the equivalent model of the power battery. Subsequently, on the basis of this model, the least squares method (LS with a forgetting factor and the adaptive unscented Kalman filter (AUKF algorithm are used jointly in the estimation of the power battery SOC. Simulation experiments show that the joint estimation algorithm proposed in this paper has higher precision and convergence of the initial value error than a single AUKF algorithm.

Simplified neural networks for solving linear least squares and total least squares problems in real time.

Science.gov (United States)

Cichocki, A; Unbehauen, R

1994-01-01

In this paper a new class of simplified low-cost analog artificial neural networks with on chip adaptive learning algorithms are proposed for solving linear systems of algebraic equations in real time. The proposed learning algorithms for linear least squares (LS), total least squares (TLS) and data least squares (DLS) problems can be considered as modifications and extensions of well known algorithms: the row-action projection-Kaczmarz algorithm and/or the LMS (Adaline) Widrow-Hoff algorithms. The algorithms can be applied to any problem which can be formulated as a linear regression problem. The correctness and high performance of the proposed neural networks are illustrated by extensive computer simulation results.

Quantitative analysis of Fe and Co in Co-substituted magnetite using XPS: The application of non-linear least squares fitting (NLLSF)

Energy Technology Data Exchange (ETDEWEB)

Liu, Hongmei, E-mail: hmliu@gig.ac.cn [CAS Key Laboratory of Mineralogy and Metallogeny/Guangdong Provincial Key Laboratory of Mineral Physics and Materials, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou, 510640 (China); Wei, Gaoling [Guangdong Key Laboratory of Agricultural Environment Pollution Integrated Control, Guangdong Institute of Eco-Environmental and Soil Sciences, Guangzhou, 510650 (China); Xu, Zhen [School of Materials Science and Engineering, Central South University, Changsha, 410012 (China); Liu, Peng; Li, Ying [CAS Key Laboratory of Mineralogy and Metallogeny/Guangdong Provincial Key Laboratory of Mineral Physics and Materials, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou, 510640 (China); University of Chinese Academy of Sciences, Beijing, 100049 (China)

2016-12-15

Highlights: • XPS and Auger peak overlapping complicates Co-substituted magnetite quantification. • Disrurbance of Auger peaks was eliminated by non-linear least squares fitting. • Fitting greatly improved the accuracy of quantification for Co and Fe. • Catalytic activity of magnetite was enhanced with the increase of Co substitution. - Abstract: Quantitative analysis of Co and Fe using X-ray photoelectron spectroscopy (XPS) is of important for the evaluation of the catalytic ability of Co-substituted magnetite. However, the overlap of XPS peaks and Auger peaks for Co and Fe complicate quantification. In this study, non-linear least squares fitting (NLLSF) was used to calculate the relative Co and Fe contents of a series of synthesized Co-substituted magnetite samples with different Co doping levels. NLLSF separated the XPS peaks of Co 2p and Fe 2p from the Auger peaks of Fe and Co, respectively. Compared with a control group without fitting, the accuracy of quantification of Co and Fe was greatly improved after elimination by NLLSF of the disturbance of Auger peaks. A catalysis study confirmed that the catalytic activity of magnetite was enhanced with the increase of Co substitution. This study confirms the effectiveness and accuracy of the NLLSF method in XPS quantitative calculation of Fe and Co coexisting in a material.

On Perceptual Distortion Minimization and Nonlinear Least-Squares Frequency Estimation

DEFF Research Database (Denmark)

Christensen, Mads Græsbøll; Jensen, Søren Holdt

2006-01-01

In this paper, we present a framework for perceptual error minimization and sinusoidal frequency estimation based on a new perceptual distortion measure, and we state its optimal solution. Using this framework, we relate a number of well-known practical methods for perceptual sinusoidal parameter...

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

KAUST Repository

Migliorati, Giovanni

2015-08-28

We study the accuracy of the discrete least-squares approximation on a finite dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. The convergence estimates are given in mean-square sense with respect to the sampling measure. The noise may be correlated with the location of the evaluation and may have nonzero mean (offset). We consider both cases of bounded or square-integrable noise / offset. We prove conditions between the number of sampling points and the dimension of the underlying approximation space that ensure a stable and accurate approximation. Particular focus is on deriving estimates in probability within a given confidence level. We analyze how the best approximation error and the noise terms affect the convergence rate and the overall confidence level achieved by the convergence estimate. The proofs of our convergence estimates in probability use arguments from the theory of large deviations to bound the noise term. Finally we address the particular case of multivariate polynomial approximation spaces with any density in the beta family, including uniform and Chebyshev.

Review of the Palisades pressure vessel accumulated fluence estimate and of the least squares methodology employed

International Nuclear Information System (INIS)

Griffin, P.J.

1998-05-01

This report provides a review of the Palisades submittal to the Nuclear Regulatory Commission requesting endorsement of their accumulated neutron fluence estimates based on a least squares adjustment methodology. This review highlights some minor issues in the applied methodology and provides some recommendations for future work. The overall conclusion is that the Palisades fluence estimation methodology provides a reasonable approach to a open-quotes best estimateclose quotes of the accumulated pressure vessel neutron fluence and is consistent with the state-of-the-art analysis as detailed in community consensus ASTM standards

Comparison of least-squares vs. maximum likelihood estimation for standard spectrum technique of β−γ coincidence spectrum analysis

International Nuclear Information System (INIS)

Lowrey, Justin D.; Biegalski, Steven R.F.

2012-01-01

The spectrum deconvolution analysis tool (SDAT) software code was written and tested at The University of Texas at Austin utilizing the standard spectrum technique to determine activity levels of Xe-131m, Xe-133m, Xe-133, and Xe-135 in β–γ coincidence spectra. SDAT was originally written to utilize the method of least-squares to calculate the activity of each radionuclide component in the spectrum. Recently, maximum likelihood estimation was also incorporated into the SDAT tool. This is a robust statistical technique to determine the parameters that maximize the Poisson distribution likelihood function of the sample data. In this case it is used to parameterize the activity level of each of the radioxenon components in the spectra. A new test dataset was constructed utilizing Xe-131m placed on a Xe-133 background to compare the robustness of the least-squares and maximum likelihood estimation methods for low counting statistics data. The Xe-131m spectra were collected independently from the Xe-133 spectra and added to generate the spectra in the test dataset. The true independent counts of Xe-131m and Xe-133 are known, as they were calculated before the spectra were added together. Spectra with both high and low counting statistics are analyzed. Studies are also performed by analyzing only the 30 keV X-ray region of the β–γ coincidence spectra. Results show that maximum likelihood estimation slightly outperforms least-squares for low counting statistics data.

Wave-equation Q tomography and least-squares migration

KAUST Repository

Dutta, Gaurav

2016-03-01

This thesis designs new methods for Q tomography and Q-compensated prestack depth migration when the recorded seismic data suffer from strong attenuation. A motivation of this work is that the presence of gas clouds or mud channels in overburden structures leads to the distortion of amplitudes and phases in seismic waves propagating inside the earth. If the attenuation parameter Q is very strong, i.e., Q<30, ignoring the anelastic effects in imaging can lead to dimming of migration amplitudes and loss of resolution. This, in turn, adversely affects the ability to accurately predict reservoir properties below such layers. To mitigate this problem, I first develop an anelastic least-squares reverse time migration (Q-LSRTM) technique. I reformulate the conventional acoustic least-squares migration problem as a viscoacoustic linearized inversion problem. Using linearized viscoacoustic modeling and adjoint operators during the least-squares iterations, I show with numerical tests that Q-LSRTM can compensate for the amplitude loss and produce images with better balanced amplitudes than conventional migration. To estimate the background Q model that can be used for any Q-compensating migration algorithm, I then develop a wave-equation based optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early-arrivals. Through numerical tests on synthetic and field data, I show that noticeable improvements in the migration image quality can be obtained from Q models inverted using wave-equation Q tomography. A key feature of skeletonized inversion is that it is much less likely to get stuck in a local minimum than a standard waveform inversion method. Finally, I develop a preconditioning technique for least-squares migration using a directional Gabor-based preconditioning approach for isotropic

An Inequality Constrained Least-Squares Approach as an Alternative Estimation Procedure for Atmospheric Parameters from VLBI Observations

Science.gov (United States)

Halsig, Sebastian; Artz, Thomas; Iddink, Andreas; Nothnagel, Axel

2016-12-01

On its way through the atmosphere, radio signals are delayed and affected by bending and attenuation effects relative to a theoretical path in vacuum. In particular, the neutral part of the atmosphere contributes considerably to the error budget of space-geodetic observations. At the same time, space-geodetic techniques become more and more important in the understanding of the Earth's atmosphere, because atmospheric parameters can be linked to the water vapor content in the atmosphere. The tropospheric delay is usually taken into account by applying an adequate model for the hydrostatic component and by additionally estimating zenith wet delays for the highly variable wet component. Sometimes, the Ordinary Least Squares (OLS) approach leads to negative estimates, which would be equivalent to negative water vapor in the atmosphere and does, of course, not reflect meteorological and physical conditions in a plausible way. To cope with this phenomenon, we introduce an Inequality Constrained Least Squares (ICLS) method from the field of convex optimization and use inequality constraints to force the tropospheric parameters to be non-negative allowing for a more realistic tropospheric parameter estimation in a meteorological sense. Because deficiencies in the a priori hydrostatic modeling are almost fully compensated by the tropospheric estimates, the ICLS approach urgently requires suitable a priori hydrostatic delays. In this paper, we briefly describe the ICLS method and validate its impact with regard to station positions.

Three Least-Squares Minimization Approaches to Interpret Gravity Data Due to Dipping Faults

Science.gov (United States)

Abdelrahman, E. M.; Essa, K. S.

2015-02-01

We have developed three different least-squares minimization approaches to determine, successively, the depth, dip angle, and amplitude coefficient related to the thickness and density contrast of a buried dipping fault from first moving average residual gravity anomalies. By defining the zero-anomaly distance and the anomaly value at the origin of the moving average residual profile, the problem of depth determination is transformed into a constrained nonlinear gravity inversion. After estimating the depth of the fault, the dip angle is estimated by solving a nonlinear inverse problem. Finally, after estimating the depth and dip angle, the amplitude coefficient is determined using a linear equation. This method can be applied to residuals as well as to measured gravity data because it uses the moving average residual gravity anomalies to estimate the model parameters of the faulted structure. The proposed method was tested on noise-corrupted synthetic and real gravity data. In the case of the synthetic data, good results are obtained when errors are given in the zero-anomaly distance and the anomaly value at the origin, and even when the origin is determined approximately. In the case of practical data (Bouguer anomaly over Gazal fault, south Aswan, Egypt), the fault parameters obtained are in good agreement with the actual ones and with those given in the published literature.

Least-squares dual characterization for ROI assessment in emission tomography

International Nuclear Information System (INIS)

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

2013-01-01

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. (paper)

Least-squares dual characterization for ROI assessment in emission tomography

Science.gov (United States)

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.

Efectivity of Additive Spline for Partial Least Square Method in Regression Model Estimation

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Ahmad Bilfarsah

2005-04-01

Full Text Available Additive Spline of Partial Least Square method (ASPL as one generalization of Partial Least Square (PLS method. ASPLS method can be acommodation to non linear and multicollinearity case of predictor variables. As a principle, The ASPLS method approach is cahracterized by two idea. The first is to used parametric transformations of predictors by spline function; the second is to make ASPLS components mutually uncorrelated, to preserve properties of the linear PLS components. The performance of ASPLS compared with other PLS method is illustrated with the fisher economic application especially the tuna fish production.

Multi-frequency Phase Unwrap from Noisy Data: Adaptive Least Squares Approach

Science.gov (United States)

Katkovnik, Vladimir; Bioucas-Dias, José

2010-04-01

Multiple frequency interferometry is, basically, a phase acquisition strategy aimed at reducing or eliminating the ambiguity of the wrapped phase observations or, equivalently, reducing or eliminating the fringe ambiguity order. In multiple frequency interferometry, the phase measurements are acquired at different frequencies (or wavelengths) and recorded using the corresponding sensors (measurement channels). Assuming that the absolute phase to be reconstructed is piece-wise smooth, we use a nonparametric regression technique for the phase reconstruction. The nonparametric estimates are derived from a local least squares criterion, which, when applied to the multifrequency data, yields denoised (filtered) phase estimates with extended ambiguity (periodized), compared with the phase ambiguities inherent to each measurement frequency. The filtering algorithm is based on local polynomial (LPA) approximation for design of nonlinear filters (estimators) and adaptation of these filters to unknown smoothness of the spatially varying absolute phase [9]. For phase unwrapping, from filtered periodized data, we apply the recently introduced robust (in the sense of discontinuity preserving) PUMA unwrapping algorithm [1]. Simulations give evidence that the proposed algorithm yields state-of-the-art performance for continuous as well as for discontinues phase surfaces, enabling phase unwrapping in extraordinary difficult situations when all other algorithms fail.

Analysis of neutron and x-ray reflectivity data by constrained least-squares methods

DEFF Research Database (Denmark)

Pedersen, J.S.; Hamley, I.W.

1994-01-01

. The coefficients in the series are determined by constrained nonlinear least-squares methods, in which the smoothest solution that agrees with the data is chosen. In the second approach the profile is expressed as a series of sine and cosine terms. A smoothness constraint is used which reduces the coefficients...

Least median of squares filtering of locally optimal point matches for compressible flow image registration

International Nuclear Information System (INIS)

Castillo, Edward; Guerrero, Thomas; Castillo, Richard; White, Benjamin; Rojo, Javier

2012-01-01

Compressible flow based image registration operates under the assumption that the mass of the imaged material is conserved from one image to the next. Depending on how the mass conservation assumption is modeled, the performance of existing compressible flow methods is limited by factors such as image quality, noise, large magnitude voxel displacements, and computational requirements. The Least Median of Squares Filtered Compressible Flow (LFC) method introduced here is based on a localized, nonlinear least squares, compressible flow model that describes the displacement of a single voxel that lends itself to a simple grid search (block matching) optimization strategy. Spatially inaccurate grid search point matches, corresponding to erroneous local minimizers of the nonlinear compressible flow model, are removed by a novel filtering approach based on least median of squares fitting and the forward search outlier detection method. The spatial accuracy of the method is measured using ten thoracic CT image sets and large samples of expert determined landmarks (available at www.dir-lab.com). The LFC method produces an average error within the intra-observer error on eight of the ten cases, indicating that the method is capable of achieving a high spatial accuracy for thoracic CT registration. (paper)

The Use of Alternative Regression Methods in Social Sciences and the Comparison of Least Squares and M Estimation Methods in Terms of the Determination of Coefficient

Science.gov (United States)

Coskuntuncel, Orkun

2013-01-01

The purpose of this study is two-fold; the first aim being to show the effect of outliers on the widely used least squares regression estimator in social sciences. The second aim is to compare the classical method of least squares with the robust M-estimator using the "determination of coefficient" (R[superscript 2]). For this purpose,…

Deformation analysis with Total Least Squares

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M. Acar

2006-01-01

Full Text Available Deformation analysis is one of the main research fields in geodesy. Deformation analysis process comprises measurement and analysis phases. Measurements can be collected using several techniques. The output of the evaluation of the measurements is mainly point positions. In the deformation analysis phase, the coordinate changes in the point positions are investigated. Several models or approaches can be employed for the analysis. One approach is based on a Helmert or similarity coordinate transformation where the displacements and the respective covariance matrix are transformed into a unique datum. Traditionally a Least Squares (LS technique is used for the transformation procedure. Another approach that could be introduced as an alternative methodology is the Total Least Squares (TLS that is considerably a new approach in geodetic applications. In this study, in order to determine point displacements, 3-D coordinate transformations based on the Helmert transformation model were carried out individually by the Least Squares (LS and the Total Least Squares (TLS, respectively. The data used in this study was collected by GPS technique in a landslide area located nearby Istanbul. The results obtained from these two approaches have been compared.

An estimation of the height system bias parameter N (0) using least squares collocation from observed gravity and GPS-levelling data

DEFF Research Database (Denmark)

Sadiq, Muhammad; Tscherning, Carl C.; Ahmad, Zulfiqar

2009-01-01

This paper deals with the analysis of gravity anomaly and precise levelling in conjunction with GPS-Levelling data for the computation of a gravimetric geoid and an estimate of the height system bias parameter N-o for the vertical datum in Pakistan by means of least squares collocation technique...... covariance parameters has facilitated to achieve gravimetric height anomalies in a global geocentric datum. Residual terrain modeling (RTM) technique has been used in combination with the EGM96 for the reduction and smoothing of the gravity data. A value for the bias parameter N-o has been estimated...... with reference to the local GPS-Levelling datum that appears to be 0.705 m with 0.07 m mean square error. The gravimetric height anomalies were compared with height anomalies obtained from GPS-Levelling stations using least square collocation with and without bias adjustment. The bias adjustment minimizes...

Estimation of active pharmaceutical ingredients content using locally weighted partial least squares and statistical wavelength selection.

Science.gov (United States)

Kim, Sanghong; Kano, Manabu; Nakagawa, Hiroshi; Hasebe, Shinji

2011-12-15

Development of quality estimation models using near infrared spectroscopy (NIRS) and multivariate analysis has been accelerated as a process analytical technology (PAT) tool in the pharmaceutical industry. Although linear regression methods such as partial least squares (PLS) are widely used, they cannot always achieve high estimation accuracy because physical and chemical properties of a measuring object have a complex effect on NIR spectra. In this research, locally weighted PLS (LW-PLS) which utilizes a newly defined similarity between samples is proposed to estimate active pharmaceutical ingredient (API) content in granules for tableting. In addition, a statistical wavelength selection method which quantifies the effect of API content and other factors on NIR spectra is proposed. LW-PLS and the proposed wavelength selection method were applied to real process data provided by Daiichi Sankyo Co., Ltd., and the estimation accuracy was improved by 38.6% in root mean square error of prediction (RMSEP) compared to the conventional PLS using wavelengths selected on the basis of variable importance on the projection (VIP). The results clearly show that the proposed calibration modeling technique is useful for API content estimation and is superior to the conventional one. Copyright © 2011 Elsevier B.V. All rights reserved.

Microprocessor-controlled system for automatic acquisition of potentiometric data and their non-linear least-squares fit in equilibrium studies.

Science.gov (United States)

Gampp, H; Maeder, M; Zuberbühler, A D; Kaden, T A

1980-06-01

A microprocessor-controlled potentiometric titration apparatus for equilibrium studies is described. The microprocessor controls the stepwise addition of reagent, monitors the pH until it becomes constant and stores the constant value. The data are recorded on magnetic tape by a cassette recorder with an RS232 input-output interface. A non-linear least-squares program based on Marquardt's modification of the Newton-Gauss method is discussed and its performance in the calculation of equilibrium constants is exemplified. An HP 9821 desk-top computer accepts the data from the magnetic tape recorder. In addition to a fully automatic fitting procedure, the program allows manual adjustment of the parameters. Three examples are discussed with regard to performance and reproducibility.

Least mean square fourth based microgrid state estimation algorithm using the internet of things technology.

Science.gov (United States)

Rana, Md Masud

2017-01-01

This paper proposes an innovative internet of things (IoT) based communication framework for monitoring microgrid under the condition of packet dropouts in measurements. First of all, the microgrid incorporating the renewable distributed energy resources is represented by a state-space model. The IoT embedded wireless sensor network is adopted to sense the system states. Afterwards, the information is transmitted to the energy management system using the communication network. Finally, the least mean square fourth algorithm is explored for estimating the system states. The effectiveness of the developed approach is verified through numerical simulations.

Least-squares reverse time migration of multiples

KAUST Repository

Zhang, Dongliang; Schuster, Gerard T.

2013-01-01

The theory of least-squares reverse time migration of multiples (RTMM) is presented. In this method, least squares migration (LSM) is used to image free-surface multiples where the recorded traces are used as the time histories of the virtual

A least-squares minimization approach for model parameters estimate by using a new magnetic anomaly formula

Science.gov (United States)

Abo-Ezz, E. R.; Essa, K. S.

2016-04-01

A new linear least-squares approach is proposed to interpret magnetic anomalies of the buried structures by using a new magnetic anomaly formula. This approach depends on solving different sets of algebraic linear equations in order to invert the depth ( z), amplitude coefficient ( K), and magnetization angle ( θ) of buried structures using magnetic data. The utility and validity of the new proposed approach has been demonstrated through various reliable synthetic data sets with and without noise. In addition, the method has been applied to field data sets from USA and India. The best-fitted anomaly has been delineated by estimating the root-mean squared (rms). Judging satisfaction of this approach is done by comparing the obtained results with other available geological or geophysical information.

A new stabilized least-squares imaging condition

International Nuclear Information System (INIS)

Vivas, Flor A; Pestana, Reynam C; Ursin, Bjørn

2009-01-01

The classical deconvolution imaging condition consists of dividing the upgoing wave field by the downgoing wave field and summing over all frequencies and sources. The least-squares imaging condition consists of summing the cross-correlation of the upgoing and downgoing wave fields over all frequencies and sources, and dividing the result by the total energy of the downgoing wave field. This procedure is more stable than using the classical imaging condition, but it still requires stabilization in zones where the energy of the downgoing wave field is small. To stabilize the least-squares imaging condition, the energy of the downgoing wave field is replaced by its average value computed in a horizontal plane in poorly illuminated regions. Applications to the Marmousi and Sigsbee2A data sets show that the stabilized least-squares imaging condition produces better images than the least-squares and cross-correlation imaging conditions

An Incremental Weighted Least Squares Approach to Surface Lights Fields

Science.gov (United States)

Coombe, Greg; Lastra, Anselmo

An Image-Based Rendering (IBR) approach to appearance modelling enables the capture of a wide variety of real physical surfaces with complex reflectance behaviour. The challenges with this approach are handling the large amount of data, rendering the data efficiently, and previewing the model as it is being constructed. In this paper, we introduce the Incremental Weighted Least Squares approach to the representation and rendering of spatially and directionally varying illumination. Each surface patch consists of a set of Weighted Least Squares (WLS) node centers, which are low-degree polynomial representations of the anisotropic exitant radiance. During rendering, the representations are combined in a non-linear fashion to generate a full reconstruction of the exitant radiance. The rendering algorithm is fast, efficient, and implemented entirely on the GPU. The construction algorithm is incremental, which means that images are processed as they arrive instead of in the traditional batch fashion. This human-in-the-loop process enables the user to preview the model as it is being constructed and to adapt to over-sampling and under-sampling of the surface appearance.

Plane-wave Least-squares Reverse Time Migration

KAUST Repository

Dai, Wei

2012-11-04

Least-squares reverse time migration is formulated with a new parameterization, where the migration image of each shot is updated separately and a prestack image is produced with common image gathers. The advantage is that it can offer stable convergence for least-squares migration even when the migration velocity is not completely accurate. To significantly reduce computation cost, linear phase shift encoding is applied to hundreds of shot gathers to produce dozens of planes waves. A regularization term which penalizes the image difference between nearby angles are used to keep the prestack image consistent through all the angles. Numerical tests on a marine dataset is performed to illustrate the advantages of least-squares reverse time migration in the plane-wave domain. Through iterations of least-squares migration, the migration artifacts are reduced and the image resolution is improved. Empirical results suggest that the LSRTM in plane wave domain is an efficient method to improve the image quality and produce common image gathers.

Gompertz: A Scilab Program for Estimating Gompertz Curve Using Gauss-Newton Method of Least Squares

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Surajit Ghosh Dastidar

2006-04-01

Full Text Available A computer program for estimating Gompertz curve using Gauss-Newton method of least squares is described in detail. It is based on the estimation technique proposed in Reddy (1985. The program is developed using Scilab (version 3.1.1, a freely available scientific software package that can be downloaded from http://www.scilab.org/. Data is to be fed into the program from an external disk file which should be in Microsoft Excel format. The output will contain sample size, tolerance limit, a list of initial as well as the final estimate of the parameters, standard errors, value of Gauss-Normal equations namely GN1 GN2 and GN3 , No. of iterations, variance(σ2 , Durbin-Watson statistic, goodness of fit measures such as R2 , D value, covariance matrix and residuals. It also displays a graphical output of the estimated curve vis a vis the observed curve. It is an improved version of the program proposed in Dastidar (2005.

Gompertz: A Scilab Program for Estimating Gompertz Curve Using Gauss-Newton Method of Least Squares

Directory of Open Access Journals (Sweden)

Surajit Ghosh Dastidar

2006-04-01

Full Text Available A computer program for estimating Gompertz curve using Gauss-Newton method of least squares is described in detail. It is based on the estimation technique proposed in Reddy (1985. The program is developed using Scilab (version 3.1.1, a freely available scientific software package that can be downloaded from http://www.scilab.org/. Data is to be fed into the program from an external disk file which should be in Microsoft Excel format. The output will contain sample size, tolerance limit, a list of initial as well as the final estimate of the parameters, standard errors, value of Gauss-Normal equations namely GN1 GN2 and GN3, No. of iterations, variance(σ2, Durbin-Watson statistic, goodness of fit measures such as R2, D value, covariance matrix and residuals. It also displays a graphical output of the estimated curve vis a vis the observed curve. It is an improved version of the program proposed in Dastidar (2005.

Least mean square fourth based microgrid state estimation algorithm using the internet of things technology.

Directory of Open Access Journals (Sweden)

Md Masud Rana

Full Text Available This paper proposes an innovative internet of things (IoT based communication framework for monitoring microgrid under the condition of packet dropouts in measurements. First of all, the microgrid incorporating the renewable distributed energy resources is represented by a state-space model. The IoT embedded wireless sensor network is adopted to sense the system states. Afterwards, the information is transmitted to the energy management system using the communication network. Finally, the least mean square fourth algorithm is explored for estimating the system states. The effectiveness of the developed approach is verified through numerical simulations.

Pressurized water reactor monitoring. Study of detection, diagnostic and estimation (least squares and filtering) methods

International Nuclear Information System (INIS)

Gillet, M.

1986-07-01

This thesis presents a study for the surveillance of the Primary circuit water inventory of a pressurized water reactor. A reference model is developed for the development of an automatic system ensuring detection and real-time diagnostic. The methods to our application are statistical tests and adapted a pattern recognition method. The estimation of the detected anomalies is treated by the least square fit method, and by filtering. A new projected optimization method with superlinear convergence is developed in this framework, and a segmented linearization of the model is introduced, in view of a multiple filtering. 46 refs [fr

Least-Square Prediction for Backward Adaptive Video Coding

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Li Xin

2006-01-01

Full Text Available Almost all existing approaches towards video coding exploit the temporal redundancy by block-matching-based motion estimation and compensation. Regardless of its popularity, block matching still reflects an ad hoc understanding of the relationship between motion and intensity uncertainty models. In this paper, we present a novel backward adaptive approach, named "least-square prediction" (LSP, and demonstrate its potential in video coding. Motivated by the duality between edge contour in images and motion trajectory in video, we propose to derive the best prediction of the current frame from its causal past using least-square method. It is demonstrated that LSP is particularly effective for modeling video material with slow motion and can be extended to handle fast motion by temporal warping and forward adaptation. For typical QCIF test sequences, LSP often achieves smaller MSE than , full-search, quarter-pel block matching algorithm (BMA without the need of transmitting any overhead.

Nonlinear Estimation of Discrete-Time Signals Under Random Observation Delay

International Nuclear Information System (INIS)

Caballero-Aguila, R.; Jimenez-Lopez, J. D.; Hermoso-Carazo, A.; Linares-Perez, J.; Nakamori, S.

2008-01-01

This paper presents an approximation to the nonlinear least-squares estimation problem of discrete-time stochastic signals using nonlinear observations with additive white noise which can be randomly delayed by one sampling time. The observation delay is modelled by a sequence of independent Bernoulli random variables whose values, zero or one, indicate that the real observation arrives on time or it is delayed and, hence, the available measurement to estimate the signal is not up-to-date. Assuming that the state-space model generating the signal is unknown and only the covariance functions of the processes involved in the observation equation are ready for use, a filtering algorithm based on linear approximations of the real observations is proposed.

Least-squares methods for identifying biochemical regulatory networks from noisy measurements

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Heslop-Harrison Pat

2007-01-01

Full Text Available Abstract Background We consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS. The Total Least Squares (TLS technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks. Results The superior performance of the CTLS method in identifying network interactions is demonstrated on three examples: a genetic network containing four genes, a network describing p53 activity and mdm2 messenger RNA interactions, and a recently proposed kinetic model for interleukin (IL-6 and (IL-12b messenger RNA expression as a function of ATF3 and NF-κB promoter binding. For the first example, the CTLS significantly reduces the errors in the estimation of the Jacobian for the gene network. For the second, the CTLS reduces the errors from the measurements that are corrupted by white noise and the effect of neglected kinetics. For the third, it allows the correct identification, from noisy data, of the negative regulation of (IL-6 and (IL-12b by ATF3. Conclusion The significant improvements in performance demonstrated by the CTLS method under the wide range of conditions tested here, including different levels and types of measurement noise and different numbers of data points, suggests that its application will enable

Nonlinear partial least squares with Hellinger distance for nonlinear process monitoring

KAUST Repository

Harrou, Fouzi; Madakyaru, Muddu; Sun, Ying

2017-01-01

This paper proposes an efficient data-based anomaly detection method that can be used for monitoring nonlinear processes. The proposed method merges advantages of nonlinear projection to latent structures (NLPLS) modeling and those of Hellinger distance (HD) metric to identify abnormal changes in highly correlated multivariate data. Specifically, the HD is used to quantify the dissimilarity between current NLPLS-based residual and reference probability distributions. The performances of the developed anomaly detection using NLPLS-based HD technique is illustrated using simulated plug flow reactor data.

Nonlinear partial least squares with Hellinger distance for nonlinear process monitoring

KAUST Repository

Harrou, Fouzi

2017-02-16

This paper proposes an efficient data-based anomaly detection method that can be used for monitoring nonlinear processes. The proposed method merges advantages of nonlinear projection to latent structures (NLPLS) modeling and those of Hellinger distance (HD) metric to identify abnormal changes in highly correlated multivariate data. Specifically, the HD is used to quantify the dissimilarity between current NLPLS-based residual and reference probability distributions. The performances of the developed anomaly detection using NLPLS-based HD technique is illustrated using simulated plug flow reactor data.

Newton-Gauss Algorithm of Robust Weighted Total Least Squares Model

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WANG Bin

2015-06-01

Full Text Available Based on the Newton-Gauss iterative algorithm of weighted total least squares (WTLS, a robust WTLS (RWTLS model is presented. The model utilizes the standardized residuals to construct the weight factor function and the square root of the variance component estimator with robustness is obtained by introducing the median method. Therefore, the robustness in both the observation and structure spaces can be simultaneously achieved. To obtain standardized residuals, the linearly approximate cofactor propagation law is employed to derive the expression of the cofactor matrix of WTLS residuals. The iterative calculation steps for RWTLS are also described. The experiment indicates that the model proposed in this paper exhibits satisfactory robustness for gross errors handling problem of WTLS, the obtained parameters have no significant difference with the results of WTLS without gross errors. Therefore, it is superior to the robust weighted total least squares model directly constructed with residuals.

PENERAPAN METODE LEAST MEDIAN SQUARE-MINIMUM COVARIANCE DETERMINANT (LMS-MCD DALAM REGRESI KOMPONEN UTAMA

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I PUTU EKA IRAWAN

2013-11-01

Full Text Available Principal Component Regression is a method to overcome multicollinearity techniques by combining principal component analysis with regression analysis. The calculation of classical principal component analysis is based on the regular covariance matrix. The covariance matrix is optimal if the data originated from a multivariate normal distribution, but is very sensitive to the presence of outliers. Alternatives are used to overcome this problem the method of Least Median Square-Minimum Covariance Determinant (LMS-MCD. The purpose of this research is to conduct a comparison between Principal Component Regression (RKU and Method of Least Median Square - Minimum Covariance Determinant (LMS-MCD in dealing with outliers. In this study, Method of Least Median Square - Minimum Covariance Determinant (LMS-MCD has a bias and mean square error (MSE is smaller than the parameter RKU. Based on the difference of parameter estimators, still have a test that has a difference of parameter estimators method LMS-MCD greater than RKU method.

Least-squares Minimization Approaches to Interpret Total Magnetic Anomalies Due to Spheres

Science.gov (United States)

Abdelrahman, E. M.; El-Araby, T. M.; Soliman, K. S.; Essa, K. S.; Abo-Ezz, E. R.

2007-05-01

We have developed three different least-squares approaches to determine successively: the depth, magnetic angle, and amplitude coefficient of a buried sphere from a total magnetic anomaly. By defining the anomaly value at the origin and the nearest zero-anomaly distance from the origin on the profile, the problem of depth determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(z)=0. Knowing the depth and applying the least-squares method, the magnetic angle and amplitude coefficient are determined using two simple linear equations. In this way, the depth, magnetic angle, and amplitude coefficient are determined individually from all observed total magnetic data. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal, West Africa. In all cases, the depth solutions are in good agreement with the actual ones.

The reliability of nonlinear least-squares algorithm for data analysis of neural response activity during sinusoidal rotational stimulation in semicircular canal neurons.

Science.gov (United States)

Ren, Pengyu; Li, Bowen; Dong, Shiyao; Chen, Lin; Zhang, Yuelin

2018-01-01

Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system.

Linear least squares compartmental-model-independent parameter identification in PET

International Nuclear Information System (INIS)

Thie, J.A.; Smith, G.T.; Hubner, K.F.

1997-01-01

A simplified approach involving linear-regression straight-line parameter fitting of dynamic scan data is developed for both specific and nonspecific models. Where compartmental-model topologies apply, the measured activity may be expressed in terms of: its integrals, plasma activity and plasma integrals -- all in a linear expression with macroparameters as coefficients. Multiple linear regression, as in spreadsheet software, determines parameters for best data fits. Positron emission tomography (PET)-acquired gray-matter images in a dynamic scan are analyzed: both by this method and by traditional iterative nonlinear least squares. Both patient and simulated data were used. Regression and traditional methods are in expected agreement. Monte-Carlo simulations evaluate parameter standard deviations, due to data noise, and much smaller noise-induced biases. Unique straight-line graphical displays permit visualizing data influences on various macroparameters as changes in slopes. Advantages of regression fitting are: simplicity, speed, ease of implementation in spreadsheet software, avoiding risks of convergence failures or false solutions in iterative least squares, and providing various visualizations of the uptake process by straight line graphical displays. Multiparameter model-independent analyses on lesser understood systems is also made possible

Modeling and control of PEMFC based on least squares support vector machines

International Nuclear Information System (INIS)

Li Xi; Cao Guangyi; Zhu Xinjian

2006-01-01

The proton exchange membrane fuel cell (PEMFC) is one of the most important power supplies. The operating temperature of the stack is an important controlled variable, which impacts the performance of the PEMFC. In order to improve the generating performance of the PEMFC, prolong its life and guarantee safety, credibility and low cost of the PEMFC system, it must be controlled efficiently. A nonlinear predictive control algorithm based on a least squares support vector machine (LS-SVM) model is presented for a family of complex systems with severe nonlinearity, such as the PEMFC, in this paper. The nonlinear off line model of the PEMFC is built by a LS-SVM model with radial basis function (RBF) kernel so as to implement nonlinear predictive control of the plant. During PEMFC operation, the off line model is linearized at each sampling instant, and the generalized predictive control (GPC) algorithm is applied to the predictive control of the plant. Experimental results demonstrate the effectiveness and advantages of this approach

A Least Square-Based Self-Adaptive Localization Method for Wireless Sensor Networks

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Baoguo Yu

2016-01-01

Full Text Available In the wireless sensor network (WSN localization methods based on Received Signal Strength Indicator (RSSI, it is usually required to determine the parameters of the radio signal propagation model before estimating the distance between the anchor node and an unknown node with reference to their communication RSSI value. And finally we use a localization algorithm to estimate the location of the unknown node. However, this localization method, though high in localization accuracy, has weaknesses such as complex working procedure and poor system versatility. Concerning these defects, a self-adaptive WSN localization method based on least square is proposed, which uses the least square criterion to estimate the parameters of radio signal propagation model, which positively reduces the computation amount in the estimation process. The experimental results show that the proposed self-adaptive localization method outputs a high processing efficiency while satisfying the high localization accuracy requirement. Conclusively, the proposed method is of definite practical value.

An on-line modified least-mean-square algorithm for training neurofuzzy controllers.

Science.gov (United States)

Tan, Woei Wan

2007-04-01

The problem hindering the use of data-driven modelling methods for training controllers on-line is the lack of control over the amount by which the plant is excited. As the operating schedule determines the information available on-line, the knowledge of the process may degrade if the setpoint remains constant for an extended period. This paper proposes an identification algorithm that alleviates "learning interference" by incorporating fuzzy theory into the normalized least-mean-square update rule. The ability of the proposed methodology to achieve faster learning is examined by employing the algorithm to train a neurofuzzy feedforward controller for controlling a liquid level process. Since the proposed identification strategy has similarities with the normalized least-mean-square update rule and the recursive least-square estimator, the on-line learning rates of these algorithms are also compared.

Optimization Method of Fusing Model Tree into Partial Least Squares

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Yu Fang

2017-01-01

Full Text Available Partial Least Square (PLS can’t adapt to the characteristics of the data of many fields due to its own features multiple independent variables, multi-dependent variables and non-linear. However, Model Tree (MT has a good adaptability to nonlinear function, which is made up of many multiple linear segments. Based on this, a new method combining PLS and MT to analysis and predict the data is proposed, which build MT through the main ingredient and the explanatory variables(the dependent variable extracted from PLS, and extract residual information constantly to build Model Tree until well-pleased accuracy condition is satisfied. Using the data of the maxingshigan decoction of the monarch drug to treat the asthma or cough and two sample sets in the UCI Machine Learning Repository, the experimental results show that, the ability of explanation and predicting get improved in the new method.

A least-squares minimisation approach to depth determination from numerical second horizontal self-potential anomalies

Science.gov (United States)

Abdelrahman, El-Sayed Mohamed; Soliman, Khalid; Essa, Khalid Sayed; Abo-Ezz, Eid Ragab; El-Araby, Tarek Mohamed

2009-06-01

This paper develops a least-squares minimisation approach to determine the depth of a buried structure from numerical second horizontal derivative anomalies obtained from self-potential (SP) data using filters of successive window lengths. The method is based on using a relationship between the depth and a combination of observations at symmetric points with respect to the coordinate of the projection of the centre of the source in the plane of the measurement points with a free parameter (graticule spacing). The problem of depth determination from second derivative SP anomalies has been transformed into the problem of finding a solution to a non-linear equation of the form f(z)=0. Formulas have been derived for horizontal cylinders, spheres, and vertical cylinders. Procedures are also formulated to determine the electric dipole moment and the polarization angle. The proposed method was tested on synthetic noisy and real SP data. In the case of the synthetic data, the least-squares method determined the correct depths of the sources. In the case of practical data (SP anomalies over a sulfide ore deposit, Sariyer, Turkey and over a Malachite Mine, Jefferson County, Colorado, USA), the estimated depths of the buried structures are in good agreement with the results obtained from drilling and surface geology.

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

Science.gov (United States)

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.

A cross-correlation objective function for least-squares migration and visco-acoustic imaging

KAUST Repository

Dutta, Gaurav

2014-08-05

Conventional acoustic least-squares migration inverts for a reflectivity image that best matches the amplitudes of the observed data. However, for field data applications, it is not easy to match the recorded amplitudes because of the visco-elastic nature of the earth and inaccuracies in the estimation of source signature and strength at different shot locations. To relax the requirement for strong amplitude matching of least-squares migration, we use a normalized cross-correlation objective function that is only sensitive to the similarity between the predicted and the observed data. Such a normalized cross-correlation objective function is also equivalent to a time-domain phase inversion method where the main emphasis is only on matching the phase of the data rather than the amplitude. Numerical tests on synthetic and field data show that such an objective function can be used as an alternative to visco-acoustic least-squares reverse time migration (Qp-LSRTM) when there is strong attenuation in the subsurface and the estimation of the attenuation parameter Qp is insufficiently accurate.

A cross-correlation objective function for least-squares migration and visco-acoustic imaging

KAUST Repository

Dutta, Gaurav; Sinha, Mrinal; Schuster, Gerard T.

2014-01-01

Conventional acoustic least-squares migration inverts for a reflectivity image that best matches the amplitudes of the observed data. However, for field data applications, it is not easy to match the recorded amplitudes because of the visco-elastic nature of the earth and inaccuracies in the estimation of source signature and strength at different shot locations. To relax the requirement for strong amplitude matching of least-squares migration, we use a normalized cross-correlation objective function that is only sensitive to the similarity between the predicted and the observed data. Such a normalized cross-correlation objective function is also equivalent to a time-domain phase inversion method where the main emphasis is only on matching the phase of the data rather than the amplitude. Numerical tests on synthetic and field data show that such an objective function can be used as an alternative to visco-acoustic least-squares reverse time migration (Qp-LSRTM) when there is strong attenuation in the subsurface and the estimation of the attenuation parameter Qp is insufficiently accurate.

Bias correction for the least squares estimator of Weibull shape parameter with complete and censored data

International Nuclear Information System (INIS)

Zhang, L.F.; Xie, M.; Tang, L.C.

2006-01-01

Estimation of the Weibull shape parameter is important in reliability engineering. However, commonly used methods such as the maximum likelihood estimation (MLE) and the least squares estimation (LSE) are known to be biased. Bias correction methods for MLE have been studied in the literature. This paper investigates the methods for bias correction when model parameters are estimated with LSE based on probability plot. Weibull probability plot is very simple and commonly used by practitioners and hence such a study is useful. The bias of the LS shape parameter estimator for multiple censored data is also examined. It is found that the bias can be modeled as the function of the sample size and the censoring level, and is mainly dependent on the latter. A simple bias function is introduced and bias correcting formulas are proposed for both complete and censored data. Simulation results are also presented. The bias correction methods proposed are very easy to use and they can typically reduce the bias of the LSE of the shape parameter to less than half percent

A least squares approach to estimating the probability distribution of unobserved data in multiphoton microscopy

Science.gov (United States)

Salama, Paul

2008-02-01

Multi-photon microscopy has provided biologists with unprecedented opportunities for high resolution imaging deep into tissues. Unfortunately deep tissue multi-photon microscopy images are in general noisy since they are acquired at low photon counts. To aid in the analysis and segmentation of such images it is sometimes necessary to initially enhance the acquired images. One way to enhance an image is to find the maximum a posteriori (MAP) estimate of each pixel comprising an image, which is achieved by finding a constrained least squares estimate of the unknown distribution. In arriving at the distribution it is assumed that the noise is Poisson distributed, the true but unknown pixel values assume a probability mass function over a finite set of non-negative values, and since the observed data also assumes finite values because of low photon counts, the sum of the probabilities of the observed pixel values (obtained from the histogram of the acquired pixel values) is less than one. Experimental results demonstrate that it is possible to closely estimate the unknown probability mass function with these assumptions.

Iterative least-squares solvers for the Navier-Stokes equations

Energy Technology Data Exchange (ETDEWEB)

Bochev, P. [Univ. of Texas, Arlington, TX (United States)

1996-12-31

In the recent years finite element methods of least-squares type have attracted considerable attention from both mathematicians and engineers. This interest has been motivated, to a large extent, by several valuable analytic and computational properties of least-squares variational principles. In particular, finite element methods based on such principles circumvent Ladyzhenskaya-Babuska-Brezzi condition and lead to symmetric and positive definite algebraic systems. Thus, it is not surprising that numerical solution of fluid flow problems has been among the most promising and successful applications of least-squares methods. In this context least-squares methods offer significant theoretical and practical advantages in the algorithmic design, which makes resulting methods suitable, among other things, for large-scale numerical simulations.

Bayesian model averaging and weighted average least squares : Equivariance, stability, and numerical issues

NARCIS (Netherlands)

De Luca, G.; Magnus, J.R.

2011-01-01

In this article, we describe the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals, which implement, respectively, the exact Bayesian model-averaging estimator and the weighted-average least-squares

Robust methods and asymptotic theory in nonlinear econometrics

CERN Document Server

Bierens, Herman J

1981-01-01

This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non­ linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...

A new finite element formulation for CFD:VIII. The Galerkin/least-squares method for advective-diffusive equations

International Nuclear Information System (INIS)

Hughes, T.J.R.; Hulbert, G.M.; Franca, L.P.

1988-10-01

Galerkin/least-squares finite element methods are presented for advective-diffusive equations. Galerkin/least-squares represents a conceptual simplification of SUPG, and is in fact applicable to a wide variety of other problem types. A convergence analysis and error estimates are presented. (author) [pt

Block Least Mean Squares Algorithm over Distributed Wireless Sensor Network

Directory of Open Access Journals (Sweden)

T. Panigrahi

2012-01-01

Full Text Available In a distributed parameter estimation problem, during each sampling instant, a typical sensor node communicates its estimate either by the diffusion algorithm or by the incremental algorithm. Both these conventional distributed algorithms involve significant communication overheads and, consequently, defeat the basic purpose of wireless sensor networks. In the present paper, we therefore propose two new distributed algorithms, namely, block diffusion least mean square (BDLMS and block incremental least mean square (BILMS by extending the concept of block adaptive filtering techniques to the distributed adaptation scenario. The performance analysis of the proposed BDLMS and BILMS algorithms has been carried out and found to have similar performances to those offered by conventional diffusion LMS and incremental LMS algorithms, respectively. The convergence analyses of the proposed algorithms obtained from the simulation study are also found to be in agreement with the theoretical analysis. The remarkable and interesting aspect of the proposed block-based algorithms is that their communication overheads per node and latencies are less than those of the conventional algorithms by a factor as high as the block size used in the algorithms.

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

Science.gov (United States)

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

1997-01-01

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

Analysis of Nonlinear Dynamics by Square Matrix Method

Energy Technology Data Exchange (ETDEWEB)

Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II

2016-07-25

The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.

Regularization by truncated total least squares

DEFF Research Database (Denmark)

Hansen, Per Christian; Fierro, R.D; Golub, G.H

1997-01-01

The total least squares (TLS) method is a successful method for noise reduction in linear least squares problems in a number of applications. The TLS method is suited to problems in which both the coefficient matrix and the right-hand side are not precisely known. This paper focuses on the use...... schemes for relativistic hydrodynamical equations. Such an approximate Riemann solver is presented in this paper which treats all waves emanating from an initial discontinuity as themselves discontinuous. Therefore, jump conditions for shocks are approximately used for rarefaction waves. The solver...... is easy to implement in a Godunov scheme and converges rapidly for relativistic hydrodynamics. The fast convergence of the solver indicates the potential of a higher performance of a Godunov scheme in which the solver is used....

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

Science.gov (United States)

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.

Seismic time-lapse imaging using Interferometric least-squares migration

KAUST Repository

Sinha, Mrinal

2016-09-06

One of the problems with 4D surveys is that the environmental conditions change over time so that the experiment is insufficiently repeatable. To mitigate this problem, we propose the use of interferometric least-squares migration (ILSM) to estimate the migration image for the baseline and monitor surveys. Here, a known reflector is used as the reference reflector for ILSM. Results with synthetic and field data show that ILSM can eliminate artifacts caused by non-repeatability in time-lapse surveys.

Seismic time-lapse imaging using Interferometric least-squares migration

KAUST Repository

Sinha, Mrinal; Schuster, Gerard T.

2016-01-01

One of the problems with 4D surveys is that the environmental conditions change over time so that the experiment is insufficiently repeatable. To mitigate this problem, we propose the use of interferometric least-squares migration (ILSM) to estimate the migration image for the baseline and monitor surveys. Here, a known reflector is used as the reference reflector for ILSM. Results with synthetic and field data show that ILSM can eliminate artifacts caused by non-repeatability in time-lapse surveys.

Consistency of the least weighted squares under heteroscedasticity

Czech Academy of Sciences Publication Activity Database

Víšek, Jan Ámos

2011-01-01

Roč. 2011, č. 47 (2011), s. 179-206 ISSN 0023-5954 Grant - others:GA UK(CZ) GA402/09/055 Institutional research plan: CEZ:AV0Z10750506 Keywords : Regression * Consistency * The least weighted squares * Heteroscedasticity Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.454, year: 2011 http://library.utia.cas.cz/separaty/2011/SI/visek-consistency of the least weighted squares under heteroscedasticity.pdf

note: The least square nucleolus is a general nucleolus

OpenAIRE

Elisenda Molina; Juan Tejada

2000-01-01

This short note proves that the least square nucleolus (Ruiz et al. (1996)) and the lexicographical solution (Sakawa and Nishizaki (1994)) select the same imputation in each game with nonempty imputation set. As a consequence the least square nucleolus is a general nucleolus (Maschler et al. (1992)).

Feature extraction through least squares fit to a simple model

International Nuclear Information System (INIS)

Demuth, H.B.

1976-01-01

The Oak Ridge National Laboratory (ORNL) presented the Los Alamos Scientific Laboratory (LASL) with 18 radiographs of fuel rod test bundles. The problem is to estimate the thickness of the gap between some cylindrical rods and a flat wall surface. The edges of the gaps are poorly defined due to finite source size, x-ray scatter, parallax, film grain noise, and other degrading effects. The radiographs were scanned and the scan-line data were averaged to reduce noise and to convert the problem to one dimension. A model of the ideal gap, convolved with an appropriate point-spread function, was fit to the averaged data with a least squares program; and the gap width was determined from the final fitted-model parameters. The least squares routine did converge and the gaps obtained are of reasonable size. The method is remarkably insensitive to noise. This report describes the problem, the techniques used to solve it, and the results and conclusions. Suggestions for future work are also given

Non-linear partial least square regression increases the estimation accuracy of grass nitrogen and phosphorus using in situ hyperspectral and environmental data

CSIR Research Space (South Africa)

Ramoelo, Abel

2013-06-01

Full Text Available in situ hyperspectral and environmental variables yielded the highest grass N and P estimation accuracy (R2 = 0.81, root mean square error (RMSE) = 0.08, and R2 = 0.80, RMSE = 0.03, respectively) as compared to using remote sensing variables only...

Application of least-squares method to decay heat evaluation

International Nuclear Information System (INIS)

Schmittroth, F.; Schenter, R.E.

1976-01-01

Generalized least-squares methods are applied to decay-heat experiments and summation calculations to arrive at evaluated values and uncertainties for the fission-product decay-heat from the thermal fission of 235 U. Emphasis is placed on a proper treatment of both statistical and correlated uncertainties in the least-squares method

Multiples least-squares reverse time migration

KAUST Repository

Zhang, Dongliang; Zhan, Ge; Dai, Wei; Schuster, Gerard T.

2013-01-01

To enhance the image quality, we propose multiples least-squares reverse time migration (MLSRTM) that transforms each hydrophone into a virtual point source with a time history equal to that of the recorded data. Since each recorded trace is treated

Consistent Partial Least Squares Path Modeling via Regularization.

Science.gov (United States)

Jung, Sunho; Park, JaeHong

2018-01-01

Partial least squares (PLS) path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc), designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present.

Consistent Partial Least Squares Path Modeling via Regularization

Directory of Open Access Journals (Sweden)

Sunho Jung

2018-02-01

Full Text Available Partial least squares (PLS path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc, designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present.

A different approach to estimate nonlinear regression model using numerical methods

Science.gov (United States)

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

2017-11-01

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

Generalized Spatial Two Stage Least Squares Estimation of Spatial Autoregressive Models with Autoregressive Disturbances in the Presence of Endogenous Regressors and Many Instruments

Directory of Open Access Journals (Sweden)

Fei Jin

2013-05-01

Full Text Available This paper studies the generalized spatial two stage least squares (GS2SLS estimation of spatial autoregressive models with autoregressive disturbances when there are endogenous regressors with many valid instruments. Using many instruments may improve the efficiency of estimators asymptotically, but the bias might be large in finite samples, making the inference inaccurate. We consider the case that the number of instruments K increases with, but at a rate slower than, the sample size, and derive the approximate mean square errors (MSE that account for the trade-offs between the bias and variance, for both the GS2SLS estimator and a bias-corrected GS2SLS estimator. A criterion function for the optimal K selection can be based on the approximate MSEs. Monte Carlo experiments are provided to show the performance of our procedure of choosing K.

Expectile smoothing: new perspectives on asymmetric least squares. An application to life expectancy

NARCIS (Netherlands)

Schnabel, S.K.

2011-01-01

While initially motivated from a demographic application, this thesis develops methodology for expectile estimation. To this end first the basic model for expectile curves using least asymmetrically weighted squares (LAWS) was introduced as well as methods for smoothing in this context. The simple

Wind Tunnel Strain-Gage Balance Calibration Data Analysis Using a Weighted Least Squares Approach

Science.gov (United States)

Ulbrich, N.; Volden, T.

2017-01-01

A new approach is presented that uses a weighted least squares fit to analyze wind tunnel strain-gage balance calibration data. The weighted least squares fit is specifically designed to increase the influence of single-component loadings during the regression analysis. The weighted least squares fit also reduces the impact of calibration load schedule asymmetries on the predicted primary sensitivities of the balance gages. A weighting factor between zero and one is assigned to each calibration data point that depends on a simple count of its intentionally loaded load components or gages. The greater the number of a data point's intentionally loaded load components or gages is, the smaller its weighting factor becomes. The proposed approach is applicable to both the Iterative and Non-Iterative Methods that are used for the analysis of strain-gage balance calibration data in the aerospace testing community. The Iterative Method uses a reasonable estimate of the tare corrected load set as input for the determination of the weighting factors. The Non-Iterative Method, on the other hand, uses gage output differences relative to the natural zeros as input for the determination of the weighting factors. Machine calibration data of a six-component force balance is used to illustrate benefits of the proposed weighted least squares fit. In addition, a detailed derivation of the PRESS residuals associated with a weighted least squares fit is given in the appendices of the paper as this information could not be found in the literature. These PRESS residuals may be needed to evaluate the predictive capabilities of the final regression models that result from a weighted least squares fit of the balance calibration data.

Elastic least-squares reverse time migration

KAUST Repository

Feng, Zongcai

2017-03-08

We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTMsolves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional leastsquares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTMwill produce migration noise stronger than that seen in the RTM images.

Elastic least-squares reverse time migration

KAUST Repository

Feng, Zongcai; Schuster, Gerard T.

2017-01-01

We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTMsolves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional leastsquares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTMwill produce migration noise stronger than that seen in the RTM images.

Group-wise partial least square regression

NARCIS (Netherlands)

Camacho, José; Saccenti, Edoardo

2018-01-01

This paper introduces the group-wise partial least squares (GPLS) regression. GPLS is a new sparse PLS technique where the sparsity structure is defined in terms of groups of correlated variables, similarly to what is done in the related group-wise principal component analysis. These groups are

Multivariate estimation of the limit of detection by orthogonal partial least squares in temperature-modulated MOX sensors.

Science.gov (United States)

Burgués, Javier; Marco, Santiago

2018-08-17

Metal oxide semiconductor (MOX) sensors are usually temperature-modulated and calibrated with multivariate models such as partial least squares (PLS) to increase the inherent low selectivity of this technology. The multivariate sensor response patterns exhibit heteroscedastic and correlated noise, which suggests that maximum likelihood methods should outperform PLS. One contribution of this paper is the comparison between PLS and maximum likelihood principal components regression (MLPCR) in MOX sensors. PLS is often criticized by the lack of interpretability when the model complexity increases beyond the chemical rank of the problem. This happens in MOX sensors due to cross-sensitivities to interferences, such as temperature or humidity and non-linearity. Additionally, the estimation of fundamental figures of merit, such as the limit of detection (LOD), is still not standardized in multivariate models. Orthogonalization methods, such as orthogonal projection to latent structures (O-PLS), have been successfully applied in other fields to reduce the complexity of PLS models. In this work, we propose a LOD estimation method based on applying the well-accepted univariate LOD formulas to the scores of the first component of an orthogonal PLS model. The resulting LOD is compared to the multivariate LOD range derived from error-propagation. The methodology is applied to data extracted from temperature-modulated MOX sensors (FIS SB-500-12 and Figaro TGS 3870-A04), aiming at the detection of low concentrations of carbon monoxide in the presence of uncontrolled humidity (chemical noise). We found that PLS models were simpler and more accurate than MLPCR models. Average LOD values of 0.79 ppm (FIS) and 1.06 ppm (Figaro) were found using the approach described in this paper. These values were contained within the LOD ranges obtained with the error-propagation approach. The mean LOD increased to 1.13 ppm (FIS) and 1.59 ppm (Figaro) when considering validation samples

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

Energy Technology Data Exchange (ETDEWEB)

Verdoolaege, G., E-mail: geert.verdoolaege@ugent.be [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium); Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels (Belgium); Shabbir, A. [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium); Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching (Germany); Hornung, G. [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium)

2016-11-15

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 standard least squares.

New method to incorporate Type B uncertainty into least-squares procedures in radionuclide metrology

International Nuclear Information System (INIS)

Han, Jubong; Lee, K.B.; Lee, Jong-Man; Park, Tae Soon; Oh, J.S.; Oh, Pil-Jei

2016-01-01

We discuss a new method to incorporate Type B uncertainty into least-squares procedures. The new method is based on an extension of the likelihood function from which a conventional least-squares function is derived. The extended likelihood function is the product of the original likelihood function with additional PDFs (Probability Density Functions) that characterize the Type B uncertainties. The PDFs are considered to describe one's incomplete knowledge on correction factors being called nuisance parameters. We use the extended likelihood function to make point and interval estimations of parameters in the basically same way as the least-squares function used in the conventional least-squares method is derived. Since the nuisance parameters are not of interest and should be prevented from appearing in the final result, we eliminate such nuisance parameters by using the profile likelihood. As an example, we present a case study for a linear regression analysis with a common component of Type B uncertainty. In this example we compare the analysis results obtained from using our procedure with those from conventional methods. - Highlights: • A new method proposed to incorporate Type B uncertainty into least-squares method. • The method constructed from the likelihood function and PDFs of Type B uncertainty. • A case study performed to compare results from the new and the conventional method. • Fitted parameters are consistent but with larger uncertainties in the new method.

A constrained robust least squares approach for contaminant release history identification

Science.gov (United States)

Sun, Alexander Y.; Painter, Scott L.; Wittmeyer, Gordon W.

2006-04-01

Contaminant source identification is an important type of inverse problem in groundwater modeling and is subject to both data and model uncertainty. Model uncertainty was rarely considered in the previous studies. In this work, a robust framework for solving contaminant source recovery problems is introduced. The contaminant source identification problem is first cast into one of solving uncertain linear equations, where the response matrix is constructed using a superposition technique. The formulation presented here is general and is applicable to any porous media flow and transport solvers. The robust least squares (RLS) estimator, which originated in the field of robust identification, directly accounts for errors arising from model uncertainty and has been shown to significantly reduce the sensitivity of the optimal solution to perturbations in model and data. In this work, a new variant of RLS, the constrained robust least squares (CRLS), is formulated for solving uncertain linear equations. CRLS allows for additional constraints, such as nonnegativity, to be imposed. The performance of CRLS is demonstrated through one- and two-dimensional test problems. When the system is ill-conditioned and uncertain, it is found that CRLS gave much better performance than its classical counterpart, the nonnegative least squares. The source identification framework developed in this work thus constitutes a reliable tool for recovering source release histories in real applications.

Optimistic semi-supervised least squares classification

DEFF Research Database (Denmark)

Krijthe, Jesse H.; Loog, Marco

2017-01-01

The goal of semi-supervised learning is to improve supervised classifiers by using additional unlabeled training examples. In this work we study a simple self-learning approach to semi-supervised learning applied to the least squares classifier. We show that a soft-label and a hard-label variant ...

A negative-norm least-squares method for time-harmonic Maxwell equations

KAUST Repository

Copeland, Dylan M.

2012-04-01

This paper presents and analyzes a negative-norm least-squares finite element discretization method for the dimension-reduced time-harmonic Maxwell equations in the case of axial symmetry. The reduced equations are expressed in cylindrical coordinates, and the analysis consequently involves weighted Sobolev spaces based on the degenerate radial weighting. The main theoretical results established in this work include existence and uniqueness of the continuous and discrete formulations and error estimates for simple finite element functions. Numerical experiments confirm the error estimates and efficiency of the method for piecewise constant coefficients. © 2011 Elsevier Inc.

Distributed least-squares estimation of a remote chemical source via convex combination in wireless sensor networks.

Science.gov (United States)

Cao, Meng-Li; Meng, Qing-Hao; Zeng, Ming; Sun, Biao; Li, Wei; Ding, Cheng-Jun

2014-06-27

This paper investigates the problem of locating a continuous chemical source using the concentration measurements provided by a wireless sensor network (WSN). Such a problem exists in various applications: eliminating explosives or drugs, detecting the leakage of noxious chemicals, etc. The limited power and bandwidth of WSNs have motivated collaborative in-network processing which is the focus of this paper. We propose a novel distributed least-squares estimation (DLSE) method to solve the chemical source localization (CSL) problem using a WSN. The DLSE method is realized by iteratively conducting convex combination of the locally estimated chemical source locations in a distributed manner. Performance assessments of our method are conducted using both simulations and real experiments. In the experiments, we propose a fitting method to identify both the release rate and the eddy diffusivity. The results show that the proposed DLSE method can overcome the negative interference of local minima and saddle points of the objective function, which would hinder the convergence of local search methods, especially in the case of locating a remote chemical source.

Distributed Least-Squares Estimation of a Remote Chemical Source via Convex Combination in Wireless Sensor Networks

Directory of Open Access Journals (Sweden)

Meng-Li Cao

2014-06-01

Full Text Available This paper investigates the problem of locating a continuous chemical source using the concentration measurements provided by a wireless sensor network (WSN. Such a problem exists in various applications: eliminating explosives or drugs, detecting the leakage of noxious chemicals, etc. The limited power and bandwidth of WSNs have motivated collaborative in-network processing which is the focus of this paper. We propose a novel distributed least-squares estimation (DLSE method to solve the chemical source localization (CSL problem using a WSN. The DLSE method is realized by iteratively conducting convex combination of the locally estimated chemical source locations in a distributed manner. Performance assessments of our method are conducted using both simulations and real experiments. In the experiments, we propose a fitting method to identify both the release rate and the eddy diffusivity. The results show that the proposed DLSE method can overcome the negative interference of local minima and saddle points of the objective function, which would hinder the convergence of local search methods, especially in the case of locating a remote chemical source.

Application of Least-Squares Spectral Element Methods to Polynomial Chaos

NARCIS (Netherlands)

Vos, P.E.J.; Gerritsma, M.I.

2006-01-01

This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.

FC LSEI WNNLS, Least-Square Fitting Algorithms Using B Splines

International Nuclear Information System (INIS)

Hanson, R.J.; Haskell, K.H.

1989-01-01

1 - Description of problem or function: FC allows a user to fit dis- crete data, in a weighted least-squares sense, using piece-wise polynomial functions represented by B-Splines on a given set of knots. In addition to the least-squares fitting of the data, equality, inequality, and periodic constraints at a discrete, user-specified set of points can be imposed on the fitted curve or its derivatives. The subprograms LSEI and WNNLS solve the linearly-constrained least-squares problem. LSEI solves the class of problem with general inequality constraints, and, if requested, obtains a covariance matrix of the solution parameters. WNNLS solves the class of problem with non-negativity constraints. It is anticipated that most users will find LSEI suitable for their needs; however, users with inequalities that are single bounds on variables may wish to use WNNLS. 2 - Method of solution: The discrete data are fit by a linear combination of piece-wise polynomial curves which leads to a linear least-squares system of algebraic equations. Additional information is expressed as a discrete set of linear inequality and equality constraints on the fitted curve which leads to a linearly-constrained least-squares system of algebraic equations. The solution of this system is the main computational problem solved

Multi-source least-squares reverse time migration

KAUST Repository

Dai, Wei

2012-06-15

Least-squares migration has been shown to improve image quality compared to the conventional migration method, but its computational cost is often too high to be practical. In this paper, we develop two numerical schemes to implement least-squares migration with the reverse time migration method and the blended source processing technique to increase computation efficiency. By iterative migration of supergathers, which consist in a sum of many phase-encoded shots, the image quality is enhanced and the crosstalk noise associated with the encoded shots is reduced. Numerical tests on 2D HESS VTI data show that the multisource least-squares reverse time migration (LSRTM) algorithm suppresses migration artefacts, balances the amplitudes, improves image resolution and reduces crosstalk noise associated with the blended shot gathers. For this example, the multisource LSRTM is about three times faster than the conventional RTM method. For the 3D example of the SEG/EAGE salt model, with a comparable computational cost, multisource LSRTM produces images with more accurate amplitudes, better spatial resolution and fewer migration artefacts compared to conventional RTM. The empirical results suggest that multisource LSRTM can produce more accurate reflectivity images than conventional RTM does with a similar or less computational cost. The caveat is that the LSRTM image is sensitive to large errors in the migration velocity model. © 2012 European Association of Geoscientists & Engineers.

Multi-source least-squares reverse time migration

KAUST Repository

Dai, Wei; Fowler, Paul J.; Schuster, Gerard T.

2012-01-01

Least-squares migration has been shown to improve image quality compared to the conventional migration method, but its computational cost is often too high to be practical. In this paper, we develop two numerical schemes to implement least-squares migration with the reverse time migration method and the blended source processing technique to increase computation efficiency. By iterative migration of supergathers, which consist in a sum of many phase-encoded shots, the image quality is enhanced and the crosstalk noise associated with the encoded shots is reduced. Numerical tests on 2D HESS VTI data show that the multisource least-squares reverse time migration (LSRTM) algorithm suppresses migration artefacts, balances the amplitudes, improves image resolution and reduces crosstalk noise associated with the blended shot gathers. For this example, the multisource LSRTM is about three times faster than the conventional RTM method. For the 3D example of the SEG/EAGE salt model, with a comparable computational cost, multisource LSRTM produces images with more accurate amplitudes, better spatial resolution and fewer migration artefacts compared to conventional RTM. The empirical results suggest that multisource LSRTM can produce more accurate reflectivity images than conventional RTM does with a similar or less computational cost. The caveat is that the LSRTM image is sensitive to large errors in the migration velocity model. © 2012 European Association of Geoscientists & Engineers.

Application of new least-squares methods for the quantitative infrared analysis of multicomponent samples

International Nuclear Information System (INIS)

Haaland, D.M.; Easterling, R.G.

1982-01-01

Improvements have been made in previous least-squares regression analyses of infrared spectra for the quantitative estimation of concentrations of multicomponent mixtures. Spectral baselines are fitted by least-squares methods, and overlapping spectral features are accounted for in the fitting procedure. Selection of peaks above a threshold value reduces computation time and data storage requirements. Four weighted least-squares methods incorporating different baseline assumptions were investigated using FT-IR spectra of the three pure xylene isomers and their mixtures. By fitting only regions of the spectra that follow Beer's Law, accurate results can be obtained using three of the fitting methods even when baselines are not corrected to zero. Accurate results can also be obtained using one of the fits even in the presence of Beer's Law deviations. This is a consequence of pooling the weighted results for each spectral peak such that the greatest weighting is automatically given to those peaks that adhere to Beer's Law. It has been shown with the xylene spectra that semiquantitative results can be obtained even when all the major components are not known or when expected components are not present. This improvement over previous methods greatly expands the utility of quantitative least-squares analyses

Enhanced least squares Monte Carlo method for real-time decision optimizations for evolving natural hazards

DEFF Research Database (Denmark)

Anders, Annett; Nishijima, Kazuyoshi

The present paper aims at enhancing a solution approach proposed by Anders & Nishijima (2011) to real-time decision problems in civil engineering. The approach takes basis in the Least Squares Monte Carlo method (LSM) originally proposed by Longstaff & Schwartz (2001) for computing American option...... prices. In Anders & Nishijima (2011) the LSM is adapted for a real-time operational decision problem; however it is found that further improvement is required in regard to the computational efficiency, in order to facilitate it for practice. This is the focus in the present paper. The idea behind...... the improvement of the computational efficiency is to “best utilize” the least squares method; i.e. least squares method is applied for estimating the expected utility for terminal decisions, conditional on realizations of underlying random phenomena at respective times in a parametric way. The implementation...

Multi-source least-squares migration of marine data

KAUST Repository

Wang, Xin

2012-11-04

Kirchhoff based multi-source least-squares migration (MSLSM) is applied to marine streamer data. To suppress the crosstalk noise from the excitation of multiple sources, a dynamic encoding function (including both time-shifts and polarity changes) is applied to the receiver side traces. Results show that the MSLSM images are of better quality than the standard Kirchhoff migration and reverse time migration images; moreover, the migration artifacts are reduced and image resolution is significantly improved. The computational cost of MSLSM is about the same as conventional least-squares migration, but its IO cost is significantly decreased.

semPLS: Structural Equation Modeling Using Partial Least Squares

Directory of Open Access Journals (Sweden)

Armin Monecke

2012-05-01

Full Text Available Structural equation models (SEM are very popular in many disciplines. The partial least squares (PLS approach to SEM offers an alternative to covariance-based SEM, which is especially suited for situations when data is not normally distributed. PLS path modelling is referred to as soft-modeling-technique with minimum demands regarding mea- surement scales, sample sizes and residual distributions. The semPLS package provides the capability to estimate PLS path models within the R programming environment. Different setups for the estimation of factor scores can be used. Furthermore it contains modular methods for computation of bootstrap confidence intervals, model parameters and several quality indices. Various plot functions help to evaluate the model. The well known mobile phone dataset from marketing research is used to demonstrate the features of the package.

Plane-wave Least-squares Reverse Time Migration

KAUST Repository

Dai, Wei; Schuster, Gerard T.

2012-01-01

convergence for least-squares migration even when the migration velocity is not completely accurate. To significantly reduce computation cost, linear phase shift encoding is applied to hundreds of shot gathers to produce dozens of planes waves. A

Regularized plane-wave least-squares Kirchhoff migration

KAUST Repository

Wang, Xin; Dai, Wei; Schuster, Gerard T.

2013-01-01

A Kirchhoff least-squares migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images. A regularization term is included that accounts for mispositioning of reflectors due to errors in the velocity

Least squares reverse time migration of controlled order multiples

Science.gov (United States)

Liu, Y.

2016-12-01

Imaging using the reverse time migration of multiples generates inherent crosstalk artifacts due to the interference among different order multiples. Traditionally, least-square fitting has been used to address this issue by seeking the best objective function to measure the amplitude differences between the predicted and observed data. We have developed an alternative objective function by decomposing multiples into different orders to minimize the difference between Born modeling predicted multiples and specific-order multiples from observational data in order to attenuate the crosstalk. This method is denoted as the least-squares reverse time migration of controlled order multiples (LSRTM-CM). Our numerical examples demonstrated that the LSRTM-CM can significantly improve image quality compared with reverse time migration of multiples and least-square reverse time migration of multiples. Acknowledgments This research was funded by the National Nature Science Foundation of China (Grant Nos. 41430321 and 41374138).

Total least squares for anomalous change detection

Science.gov (United States)

Theiler, James; Matsekh, Anna M.

2010-04-01

A family of subtraction-based anomalous change detection algorithms is derived from a total least squares (TLSQ) framework. This provides an alternative to the well-known chronochrome algorithm, which is derived from ordinary least squares. In both cases, the most anomalous changes are identified with the pixels that exhibit the largest residuals with respect to the regression of the two images against each other. The family of TLSQbased anomalous change detectors is shown to be equivalent to the subspace RX formulation for straight anomaly detection, but applied to the stacked space. However, this family is not invariant to linear coordinate transforms. On the other hand, whitened TLSQ is coordinate invariant, and special cases of it are equivalent to canonical correlation analysis and optimized covariance equalization. What whitened TLSQ offers is a generalization of these algorithms with the potential for better performance.

COMPARISON OF RECURSIVE ESTIMATION TECHNIQUES FOR POSITION TRACKING RADIOACTIVE SOURCES

International Nuclear Information System (INIS)

Muske, K.; Howse, J.

2000-01-01

This paper compares the performance of recursive state estimation techniques for tracking the physical location of a radioactive source within a room based on radiation measurements obtained from a series of detectors at fixed locations. Specifically, the extended Kalman filter, algebraic observer, and nonlinear least squares techniques are investigated. The results of this study indicate that recursive least squares estimation significantly outperforms the other techniques due to the severe model nonlinearity

Accurate human limb angle measurement: sensor fusion through Kalman, least mean squares and recursive least-squares adaptive filtering

Science.gov (United States)

Olivares, A.; Górriz, J. M.; Ramírez, J.; Olivares, G.

2011-02-01

Inertial sensors are widely used in human body motion monitoring systems since they permit us to determine the position of the subject's limbs. Limb angle measurement is carried out through the integration of the angular velocity measured by a rate sensor and the decomposition of the components of static gravity acceleration measured by an accelerometer. Different factors derived from the sensors' nature, such as the angle random walk and dynamic bias, lead to erroneous measurements. Dynamic bias effects can be reduced through the use of adaptive filtering based on sensor fusion concepts. Most existing published works use a Kalman filtering sensor fusion approach. Our aim is to perform a comparative study among different adaptive filters. Several least mean squares (LMS), recursive least squares (RLS) and Kalman filtering variations are tested for the purpose of finding the best method leading to a more accurate and robust limb angle measurement. A new angle wander compensation sensor fusion approach based on LMS and RLS filters has been developed.

Accurate human limb angle measurement: sensor fusion through Kalman, least mean squares and recursive least-squares adaptive filtering

International Nuclear Information System (INIS)

Olivares, A; Olivares, G; Górriz, J M; Ramírez, J

2011-01-01

Inertial sensors are widely used in human body motion monitoring systems since they permit us to determine the position of the subject's limbs. Limb angle measurement is carried out through the integration of the angular velocity measured by a rate sensor and the decomposition of the components of static gravity acceleration measured by an accelerometer. Different factors derived from the sensors' nature, such as the angle random walk and dynamic bias, lead to erroneous measurements. Dynamic bias effects can be reduced through the use of adaptive filtering based on sensor fusion concepts. Most existing published works use a Kalman filtering sensor fusion approach. Our aim is to perform a comparative study among different adaptive filters. Several least mean squares (LMS), recursive least squares (RLS) and Kalman filtering variations are tested for the purpose of finding the best method leading to a more accurate and robust limb angle measurement. A new angle wander compensation sensor fusion approach based on LMS and RLS filters has been developed

Solution of a Complex Least Squares Problem with Constrained Phase.

Science.gov (United States)

Bydder, Mark

2010-12-30

The least squares solution of a complex linear equation is in general a complex vector with independent real and imaginary parts. In certain applications in magnetic resonance imaging, a solution is desired such that each element has the same phase. A direct method for obtaining the least squares solution to the phase constrained problem is described.

Iterative methods for weighted least-squares

Energy Technology Data Exchange (ETDEWEB)

Bobrovnikova, E.Y.; Vavasis, S.A. [Cornell Univ., Ithaca, NY (United States)

1996-12-31

A weighted least-squares problem with a very ill-conditioned weight matrix arises in many applications. Because of round-off errors, the standard conjugate gradient method for solving this system does not give the correct answer even after n iterations. In this paper we propose an iterative algorithm based on a new type of reorthogonalization that converges to the solution.

Emulating facial biomechanics using multivariate partial least squares surrogate models.

Science.gov (United States)

Wu, Tim; Martens, Harald; Hunter, Peter; Mithraratne, Kumar

2014-11-01

A detailed biomechanical model of the human face driven by a network of muscles is a useful tool in relating the muscle activities to facial deformations. However, lengthy computational times often hinder its applications in practical settings. The objective of this study is to replace precise but computationally demanding biomechanical model by a much faster multivariate meta-model (surrogate model), such that a significant speedup (to real-time interactive speed) can be achieved. Using a multilevel fractional factorial design, the parameter space of the biomechanical system was probed from a set of sample points chosen to satisfy maximal rank optimality and volume filling. The input-output relationship at these sampled points was then statistically emulated using linear and nonlinear, cross-validated, partial least squares regression models. It was demonstrated that these surrogate models can mimic facial biomechanics efficiently and reliably in real-time. Copyright © 2014 John Wiley & Sons, Ltd.

Least Squares Inference on Integrated Volatility and the Relationship between Efficient Prices and Noise

OpenAIRE

Nolte, Ingmar; Voev, Valeri

2009-01-01

The expected value of sums of squared intraday returns (realized variance)gives rise to a least squares regression which adapts itself to the assumptions ofthe noise process and allows for a joint inference on integrated volatility (IV),noise moments and price-noise relations. In the iid noise case we derive theasymptotic variance of the regression parameter estimating the IV, show thatit is consistent and compare its asymptotic efficiency against alternative consistentIV measures. In case of...

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

KAUST Repository

Chkifa, Abdellah

2015-04-08

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that in the univariate case, the least-squares method is quasi-optimal in expectation in [A. Cohen, M A. Davenport and D. Leviatan. Found. Comput. Math. 13 (2013) 819–834] and in probability in [G. Migliorati, F. Nobile, E. von Schwerin, R. Tempone, Found. Comput. Math. 14 (2014) 419–456], under suitable conditions that relate the number of samples with respect to the dimension of the polynomial space. Here “quasi-optimal” means that the accuracy of the least-squares approximation is comparable with that of the best approximation in the given polynomial space. In this paper, we discuss the quasi-optimality of the polynomial least-squares method in arbitrary dimension. Our analysis applies to any arbitrary multivariate polynomial space (including tensor product, total degree or hyperbolic crosses), under the minimal requirement that its associated index set is downward closed. The optimality criterion only involves the relation between the number of samples and the dimension of the polynomial space, independently of the anisotropic shape and of the number of variables. We extend our results to the approximation of Hilbert space-valued functions in order to apply them to the approximation of parametric and stochastic elliptic PDEs. As a particular case, we discuss “inclusion type” elliptic PDE models, and derive an exponential convergence estimate for the least-squares method. Numerical results confirm our estimate, yet pointing out a gap between the condition necessary to achieve optimality in the theory, and the condition that in practice yields the optimal convergence rate.

Computing ordinary least-squares parameter estimates for the National Descriptive Model of Mercury in Fish

Science.gov (United States)

Donato, David I.

2013-01-01

A specialized technique is used to compute weighted ordinary least-squares (OLS) estimates of the parameters of the National Descriptive Model of Mercury in Fish (NDMMF) in less time using less computer memory than general methods. The characteristics of the NDMMF allow the two products X'X and X'y in the normal equations to be filled out in a second or two of computer time during a single pass through the N data observations. As a result, the matrix X does not have to be stored in computer memory and the computationally expensive matrix multiplications generally required to produce X'X and X'y do not have to be carried out. The normal equations may then be solved to determine the best-fit parameters in the OLS sense. The computational solution based on this specialized technique requires O(8p2+16p) bytes of computer memory for p parameters on a machine with 8-byte double-precision numbers. This publication includes a reference implementation of this technique and a Gaussian-elimination solver in preliminary custom software.

Hourly cooling load forecasting using time-indexed ARX models with two-stage weighted least squares regression

International Nuclear Information System (INIS)

Guo, Yin; Nazarian, Ehsan; Ko, Jeonghan; Rajurkar, Kamlakar

2014-01-01

Highlights: • Developed hourly-indexed ARX models for robust cooling-load forecasting. • Proposed a two-stage weighted least-squares regression approach. • Considered the effect of outliers as well as trend of cooling load and weather patterns. • Included higher order terms and day type patterns in the forecasting models. • Demonstrated better accuracy compared with some ARX and ANN models. - Abstract: This paper presents a robust hourly cooling-load forecasting method based on time-indexed autoregressive with exogenous inputs (ARX) models, in which the coefficients are estimated through a two-stage weighted least squares regression. The prediction method includes a combination of two separate time-indexed ARX models to improve prediction accuracy of the cooling load over different forecasting periods. The two-stage weighted least-squares regression approach in this study is robust to outliers and suitable for fast and adaptive coefficient estimation. The proposed method is tested on a large-scale central cooling system in an academic institution. The numerical case studies show the proposed prediction method performs better than some ANN and ARX forecasting models for the given test data set

Least Squares Methods for Equidistant Tree Reconstruction

OpenAIRE

Fahey, Conor; Hosten, Serkan; Krieger, Nathan; Timpe, Leslie

2008-01-01

UPGMA is a heuristic method identifying the least squares equidistant phylogenetic tree given empirical distance data among $n$ taxa. We study this classic algorithm using the geometry of the space of all equidistant trees with $n$ leaves, also known as the Bergman complex of the graphical matroid for the complete graph $K_n$. We show that UPGMA performs an orthogonal projection of the data onto a maximal cell of the Bergman complex. We also show that the equidistant tree with the least (Eucl...

A weak Galerkin least-squares finite element method for div-curl systems

Science.gov (United States)

Li, Jichun; Ye, Xiu; Zhang, Shangyou

2018-06-01

In this paper, we introduce a weak Galerkin least-squares method for solving div-curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.

Multilevel solvers of first-order system least-squares for Stokes equations

Energy Technology Data Exchange (ETDEWEB)

Lai, Chen-Yao G. [National Chung Cheng Univ., Chia-Yi (Taiwan, Province of China)

1996-12-31

Recently, The use of first-order system least squares principle for the approximate solution of Stokes problems has been extensively studied by Cai, Manteuffel, and McCormick. In this paper, we study multilevel solvers of first-order system least-squares method for the generalized Stokes equations based on the velocity-vorticity-pressure formulation in three dimensions. The least-squares functionals is defined to be the sum of the L{sup 2}-norms of the residuals, which is weighted appropriately by the Reynolds number. We develop convergence analysis for additive and multiplicative multilevel methods applied to the resulting discrete equations.

The possibilities of least-squares migration of internally scattered seismic energy

KAUST Repository

Aldawood, Ali

2015-05-26

Approximate images of the earth’s subsurface structures are usually obtained by migrating surface seismic data. Least-squares migration, under the single-scattering assumption, is used as an iterative linearized inversion scheme to suppress migration artifacts, deconvolve the source signature, mitigate the acquisition fingerprint, and enhance the spatial resolution of migrated images. The problem with least-squares migration of primaries, however, is that it may not be able to enhance events that are mainly illuminated by internal multiples, such as vertical and nearly vertical faults or salt flanks. To alleviate this problem, we adopted a linearized inversion framework to migrate internally scattered energy. We apply the least-squares migration of first-order internal multiples to image subsurface vertical fault planes. Tests on synthetic data demonstrated the ability of the proposed method to resolve vertical fault planes, which are poorly illuminated by the least-squares migration of primaries only. The proposed scheme is robust in the presence of white Gaussian observational noise and in the case of imaging the fault planes using inaccurate migration velocities. Our results suggested that the proposed least-squares imaging, under the double-scattering assumption, still retrieved the vertical fault planes when imaging the scattered data despite a slight defocusing of these events due to the presence of noise or velocity errors.

The possibilities of least-squares migration of internally scattered seismic energy

KAUST Repository

Aldawood, Ali; Hoteit, Ibrahim; Zuberi, Mohammad; Turkiyyah, George; Alkhalifah, Tariq Ali

2015-01-01

Approximate images of the earth’s subsurface structures are usually obtained by migrating surface seismic data. Least-squares migration, under the single-scattering assumption, is used as an iterative linearized inversion scheme to suppress migration artifacts, deconvolve the source signature, mitigate the acquisition fingerprint, and enhance the spatial resolution of migrated images. The problem with least-squares migration of primaries, however, is that it may not be able to enhance events that are mainly illuminated by internal multiples, such as vertical and nearly vertical faults or salt flanks. To alleviate this problem, we adopted a linearized inversion framework to migrate internally scattered energy. We apply the least-squares migration of first-order internal multiples to image subsurface vertical fault planes. Tests on synthetic data demonstrated the ability of the proposed method to resolve vertical fault planes, which are poorly illuminated by the least-squares migration of primaries only. The proposed scheme is robust in the presence of white Gaussian observational noise and in the case of imaging the fault planes using inaccurate migration velocities. Our results suggested that the proposed least-squares imaging, under the double-scattering assumption, still retrieved the vertical fault planes when imaging the scattered data despite a slight defocusing of these events due to the presence of noise or velocity errors.

Penalized linear regression for discrete ill-posed problems: A hybrid least-squares and mean-squared error approach

KAUST Repository

Suliman, Mohamed Abdalla Elhag

2016-12-19

This paper proposes a new approach to find the regularization parameter for linear least-squares discrete ill-posed problems. In the proposed approach, an artificial perturbation matrix with a bounded norm is forced into the discrete ill-posed model matrix. This perturbation is introduced to enhance the singular-value (SV) structure of the matrix and hence to provide a better solution. The proposed approach is derived to select the regularization parameter in a way that minimizes the mean-squared error (MSE) of the estimator. Numerical results demonstrate that the proposed approach outperforms a set of benchmark methods in most cases when applied to different scenarios of discrete ill-posed problems. Jointly, the proposed approach enjoys the lowest run-time and offers the highest level of robustness amongst all the tested methods.

Fast Dating Using Least-Squares Criteria and Algorithms.

Science.gov (United States)

To, Thu-Hien; Jung, Matthieu; Lycett, Samantha; Gascuel, Olivier

2016-01-01

Phylogenies provide a useful way to understand the evolutionary history of genetic samples, and data sets with more than a thousand taxa are becoming increasingly common, notably with viruses (e.g., human immunodeficiency virus (HIV)). Dating ancestral events is one of the first, essential goals with such data. However, current sophisticated probabilistic approaches struggle to handle data sets of this size. Here, we present very fast dating algorithms, based on a Gaussian model closely related to the Langley-Fitch molecular-clock model. We show that this model is robust to uncorrelated violations of the molecular clock. Our algorithms apply to serial data, where the tips of the tree have been sampled through times. They estimate the substitution rate and the dates of all ancestral nodes. When the input tree is unrooted, they can provide an estimate for the root position, thus representing a new, practical alternative to the standard rooting methods (e.g., midpoint). Our algorithms exploit the tree (recursive) structure of the problem at hand, and the close relationships between least-squares and linear algebra. We distinguish between an unconstrained setting and the case where the temporal precedence constraint (i.e., an ancestral node must be older that its daughter nodes) is accounted for. With rooted trees, the former is solved using linear algebra in linear computing time (i.e., proportional to the number of taxa), while the resolution of the latter, constrained setting, is based on an active-set method that runs in nearly linear time. With unrooted trees the computing time becomes (nearly) quadratic (i.e., proportional to the square of the number of taxa). In all cases, very large input trees (>10,000 taxa) can easily be processed and transformed into time-scaled trees. We compare these algorithms to standard methods (root-to-tip, r8s version of Langley-Fitch method, and BEAST). Using simulated data, we show that their estimation accuracy is similar to that

Elastic least-squares reverse time migration

KAUST Repository

Feng, Zongcai; Schuster, Gerard T.

2016-01-01

Elastic least-squares reverse time migration (LSRTM) is used to invert synthetic particle-velocity data and crosswell pressure field data. The migration images consist of both the P- and Svelocity perturbation images. Numerical tests on synthetic and field data illustrate the advantages of elastic LSRTM over elastic reverse time migration (RTM). In addition, elastic LSRTM images are better focused and have better reflector continuity than do the acoustic LSRTM images.

Elastic least-squares reverse time migration

KAUST Repository

Feng, Zongcai

2016-09-06

Elastic least-squares reverse time migration (LSRTM) is used to invert synthetic particle-velocity data and crosswell pressure field data. The migration images consist of both the P- and Svelocity perturbation images. Numerical tests on synthetic and field data illustrate the advantages of elastic LSRTM over elastic reverse time migration (RTM). In addition, elastic LSRTM images are better focused and have better reflector continuity than do the acoustic LSRTM images.

8th International Conference on Partial Least Squares and Related Methods

CERN Document Server

Vinzi, Vincenzo; Russolillo, Giorgio; Saporta, Gilbert; Trinchera, Laura

2016-01-01

This volume presents state of the art theories, new developments, and important applications of Partial Least Square (PLS) methods. The text begins with the invited communications of current leaders in the field who cover the history of PLS, an overview of methodological issues, and recent advances in regression and multi-block approaches. The rest of the volume comprises selected, reviewed contributions from the 8th International Conference on Partial Least Squares and Related Methods held in Paris, France, on 26-28 May, 2014. They are organized in four coherent sections: 1) new developments in genomics and brain imaging, 2) new and alternative methods for multi-table and path analysis, 3) advances in partial least square regression (PLSR), and 4) partial least square path modeling (PLS-PM) breakthroughs and applications. PLS methods are very versatile methods that are now used in areas as diverse as engineering, life science, sociology, psychology, brain imaging, genomics, and business among both academics ...

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

Science.gov (United States)

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

Small-kernel constrained-least-squares restoration of sampled image data

Science.gov (United States)

Hazra, Rajeeb; Park, Stephen K.

1992-10-01

Constrained least-squares image restoration, first proposed by Hunt twenty years ago, is a linear image restoration technique in which the restoration filter is derived by maximizing the smoothness of the restored image while satisfying a fidelity constraint related to how well the restored image matches the actual data. The traditional derivation and implementation of the constrained least-squares restoration filter is based on an incomplete discrete/discrete system model which does not account for the effects of spatial sampling and image reconstruction. For many imaging systems, these effects are significant and should not be ignored. In a recent paper Park demonstrated that a derivation of the Wiener filter based on the incomplete discrete/discrete model can be extended to a more comprehensive end-to-end, continuous/discrete/continuous model. In a similar way, in this paper, we show that a derivation of the constrained least-squares filter based on the discrete/discrete model can also be extended to this more comprehensive continuous/discrete/continuous model and, by so doing, an improved restoration filter is derived. Building on previous work by Reichenbach and Park for the Wiener filter, we also show that this improved constrained least-squares restoration filter can be efficiently implemented as a small-kernel convolution in the spatial domain.

Solving linear inequalities in a least squares sense

Energy Technology Data Exchange (ETDEWEB)

Bramley, R.; Winnicka, B. [Indiana Univ., Bloomington, IN (United States)

1994-12-31

Let A {element_of} {Re}{sup mxn} be an arbitrary real matrix, and let b {element_of} {Re}{sup m} a given vector. A familiar problem in computational linear algebra is to solve the system Ax = b in a least squares sense; that is, to find an x* minimizing {parallel}Ax {minus} b{parallel}, where {parallel} {center_dot} {parallel} refers to the vector two-norm. Such an x* solves the normal equations A{sup T}(Ax {minus} b) = 0, and the optimal residual r* = b {minus} Ax* is unique (although x* need not be). The least squares problem is usually interpreted as corresponding to multiple observations, represented by the rows of A and b, on a vector of data x. The observations may be inconsistent, and in this case a solution is sought that minimizes the norm of the residuals. A less familiar problem to numerical linear algebraists is the solution of systems of linear inequalities Ax {le} b in a least squares sense, but the motivation is similar: if a set of observations places upper or lower bounds on linear combinations of variables, the authors want to find x* minimizing {parallel} (Ax {minus} b){sub +} {parallel}, where the i{sup th} component of the vector v{sub +} is the maximum of zero and the i{sup th} component of v.

Global Search Strategies for Solving Multilinear Least-Squares Problems

Directory of Open Access Journals (Sweden)

Mats Andersson

2012-04-01

Full Text Available The multilinear least-squares (MLLS problem is an extension of the linear least-squares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by the results of numerical experiments performed for some problems related to the design of filter networks.

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

KAUST Repository

Migliorati, Giovanni; Nobile, Fabio; Tempone, Raul

2015-01-01

We study the accuracy of the discrete least-squares approximation on a finite dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability

Stable Galerkin versus equal-order Galerkin least-squares elements for the stokes flow problem

International Nuclear Information System (INIS)

Franca, L.P.; Frey, S.L.; Sampaio, R.

1989-11-01

Numerical experiments are performed for the stokes flow problem employing a stable Galerkin method and a Galerkin/Least-squares method with equal-order elements. Error estimates for the methods tested herein are reviewed. The numerical results presented attest the good stability properties of all methods examined herein. (A.C.A.S.) [pt

Uncertainty analysis of pollutant build-up modelling based on a Bayesian weighted least squares approach

International Nuclear Information System (INIS)

Haddad, Khaled; Egodawatta, Prasanna; Rahman, Ataur; Goonetilleke, Ashantha

2013-01-01

Reliable pollutant build-up prediction plays a critical role in the accuracy of urban stormwater quality modelling outcomes. However, water quality data collection is resource demanding compared to streamflow data monitoring, where a greater quantity of data is generally available. Consequently, available water quality datasets span only relatively short time scales unlike water quantity data. Therefore, the ability to take due consideration of the variability associated with pollutant processes and natural phenomena is constrained. This in turn gives rise to uncertainty in the modelling outcomes as research has shown that pollutant loadings on catchment surfaces and rainfall within an area can vary considerably over space and time scales. Therefore, the assessment of model uncertainty is an essential element of informed decision making in urban stormwater management. This paper presents the application of a range of regression approaches such as ordinary least squares regression, weighted least squares regression and Bayesian weighted least squares regression for the estimation of uncertainty associated with pollutant build-up prediction using limited datasets. The study outcomes confirmed that the use of ordinary least squares regression with fixed model inputs and limited observational data may not provide realistic estimates. The stochastic nature of the dependent and independent variables need to be taken into consideration in pollutant build-up prediction. It was found that the use of the Bayesian approach along with the Monte Carlo simulation technique provides a powerful tool, which attempts to make the best use of the available knowledge in prediction and thereby presents a practical solution to counteract the limitations which are otherwise imposed on water quality modelling. - Highlights: ► Water quality data spans short time scales leading to significant model uncertainty. ► Assessment of uncertainty essential for informed decision making in water

Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction

International Nuclear Information System (INIS)

Carlberg, Kevin Thomas; Barone, Matthew F.; Antil, Harbir

2016-01-01

Least-squares Petrov–Galerkin (LSPG) model-reduction techniques such as the Gauss–Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible flow problems where standard Galerkin techniques have failed. Furthermore, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform optimal projection associated with residual minimization at the time-continuous level, while LSPG techniques do so at the time-discrete level. This work provides a detailed theoretical and computational comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge–Kutta schemes. We present a number of new findings, including conditions under which the LSPG ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and computationally that decreasing the time step does not necessarily decrease the error for the LSPG ROM; instead, the time step should be ‘matched’ to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible-flow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the LSPG reduced-order model by an order of magnitude.

Making the most out of least-squares migration

KAUST Repository

Huang, Yunsong; Dutta, Gaurav; Dai, Wei; Wang, Xin; Schuster, Gerard T.; Yu, Jianhua

2014-01-01

) weak amplitudes resulting from geometric spreading, attenuation, and defocusing. These problems can be remedied in part by least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), which aims to linearly

Simultaneous estimation of cross-validation errors in least squares collocation applied for statistical testing and evaluation of the noise variance components

Science.gov (United States)

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

Bubble-Enriched Least-Squares Finite Element Method for Transient Advective Transport

Directory of Open Access Journals (Sweden)

Rajeev Kumar

2008-01-01

Full Text Available The least-squares finite element method (LSFEM has received increasing attention in recent years due to advantages over the Galerkin finite element method (GFEM. The method leads to a minimization problem in the L2-norm and thus results in a symmetric and positive definite matrix, even for first-order differential equations. In addition, the method contains an implicit streamline upwinding mechanism that prevents the appearance of oscillations that are characteristic of the Galerkin method. Thus, the least-squares approach does not require explicit stabilization and the associated stabilization parameters required by the Galerkin method. A new approach, the bubble enriched least-squares finite element method (BELSFEM, is presented and compared with the classical LSFEM. The BELSFEM requires a space-time element formulation and employs bubble functions in space and time to increase the accuracy of the finite element solution without degrading computational performance. We apply the BELSFEM and classical least-squares finite element methods to benchmark problems for 1D and 2D linear transport. The accuracy and performance are compared.

Multi-source least-squares migration of marine data

KAUST Repository

Wang, Xin; Schuster, Gerard T.

2012-01-01

Kirchhoff based multi-source least-squares migration (MSLSM) is applied to marine streamer data. To suppress the crosstalk noise from the excitation of multiple sources, a dynamic encoding function (including both time-shifts and polarity changes

Weighted least-squares criteria for electrical impedance tomography

International Nuclear Information System (INIS)

Kallman, J.S.; Berryman, J.G.

1992-01-01

Methods are developed for design of electrical impedance tomographic reconstruction algorithms with specified properties. Assuming a starting model with constant conductivity or some other specified background distribution, an algorithm with the following properties is found: (1) the optimum constant for the starting model is determined automatically; (2) the weighted least-squares error between the predicted and measured power dissipation data is as small as possible; (3) the variance of the reconstructed conductivity from the starting model is minimized; (4) potential distributions with the largest volume integral of gradient squared have the least influence on the reconstructed conductivity, and therefore distributions most likely to be corrupted by contact impedance effects are deemphasized; (5) cells that dissipate the most power during the current injection tests tend to deviate least from the background value. The resulting algorithm maps the reconstruction problem into a vector space where the contribution to the inversion from the background conductivity remains invariant, while the optimum contributions in orthogonal directions are found. For a starting model with nonconstant conductivity, the reconstruction algorithm has analogous properties

And still, a new beginning: the Galerkin least-squares gradient method

International Nuclear Information System (INIS)

Franca, L.P.; Carmo, E.G.D. do

1988-08-01

A finite element method is proposed to solve a scalar singular diffusion problem. The method is constructed by adding to the standard Galerkin a mesh-dependent term obtained by taking the gradient of the Euler-lagrange equation and multiplying it by its least-squares. For the one-dimensional homogeneous problem the method is designed to develop nodal exact solution. An error estimate shows that the method converges optimaly for any value of the singular parameter. Numerical results demonstrate the good stability and accuracy properties of the method. (author) [pt

3D plane-wave least-squares Kirchhoff migration

KAUST Repository

Wang, Xin; Dai, Wei; Huang, Yunsong; Schuster, Gerard T.

2014-01-01

A three dimensional least-squares Kirchhoff migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images and the computational efficiency. Due to the limitation of current 3D marine acquisition

Estimating the Acquisition Price of Enshi Yulu Young Tea Shoots Using Near-Infrared Spectroscopy by the Back Propagation Artificial Neural Network Model in Conjunction with Backward Interval Partial Least Squares Algorithm

Science.gov (United States)

Wang, Sh.-P.; Gong, Z.-M.; Su, X.-Zh.; Liao, J.-Zh.

2017-09-01

Near infrared spectroscopy and the back propagation artificial neural network model in conjunction with backward interval partial least squares algorithm were used to estimate the purchasing price of Enshi yulu young tea shoots. The near-infrared spectra regions most relevant to the tea shoots price model (5700.5-5935.8, 7613.6-7848.9, 8091.8-8327.1, 8331-8566.2, 9287.5-9522.5, and 9526.6-9761.9 cm-1) were selected using backward interval partial least squares algorithm. The first five principal components that explained 99.96% of the variability in those selected spectral data were then used to calibrate the back propagation artificial neural tea shoots purchasing price model. The performance of this model (coefficient of determination for prediction 0.9724; root-mean-square error of prediction 4.727) was superior to those of the back propagation artificial neural model (coefficient of determination for prediction 0.8653, root-mean-square error of prediction 5.125) and the backward interval partial least squares model (coefficient of determination for prediction 0.5932, root-mean-square error of prediction 25.125). The acquisition price model with the combined backward interval partial least squares-back propagation artificial neural network algorithms can evaluate the price of Enshi yulu tea shoots accurately, quickly and objectively.

Least squares analysis of fission neutron standard fields

International Nuclear Information System (INIS)

Griffin, P.J.; Williams, J.G.

1997-01-01

A least squares analysis of fission neutron standard fields has been performed using the latest dosimetry cross sections. Discrepant nuclear data are identified and adjusted spectra for 252 Cf spontaneous fission and 235 U thermal fission fields are presented

Soft sensor modelling by time difference, recursive partial least squares and adaptive model updating

International Nuclear Information System (INIS)

Fu, Y; Xu, O; Yang, W; Zhou, L; Wang, J

2017-01-01

To investigate time-variant and nonlinear characteristics in industrial processes, a soft sensor modelling method based on time difference, moving-window recursive partial least square (PLS) and adaptive model updating is proposed. In this method, time difference values of input and output variables are used as training samples to construct the model, which can reduce the effects of the nonlinear characteristic on modelling accuracy and retain the advantages of recursive PLS algorithm. To solve the high updating frequency of the model, a confidence value is introduced, which can be updated adaptively according to the results of the model performance assessment. Once the confidence value is updated, the model can be updated. The proposed method has been used to predict the 4-carboxy-benz-aldehyde (CBA) content in the purified terephthalic acid (PTA) oxidation reaction process. The results show that the proposed soft sensor modelling method can reduce computation effectively, improve prediction accuracy by making use of process information and reflect the process characteristics accurately. (paper)

Least squares autoregressive (maximum entropy) spectral estimation for Fourier spectroscopy and its application to the electron cyclotron emission from plasma

International Nuclear Information System (INIS)

Iwama, N.; Inoue, A.; Tsukishima, T.; Sato, M.; Kawahata, K.

1981-07-01

A new procedure for the maximum entropy spectral estimation is studied for the purpose of data processing in Fourier transform spectroscopy. The autoregressive model fitting is examined under a least squares criterion based on the Yule-Walker equations. An AIC-like criterion is suggested for selecting the model order. The principal advantage of the new procedure lies in the enhanced frequency resolution particularly for small values of the maximum optical path-difference of the interferogram. The usefulness of the procedure is ascertained by some numerical simulations and further by experiments with respect to a highly coherent submillimeter wave and the electron cyclotron emission from a stellarator plasma. (author)

Least-squares finite element discretizations of neutron transport equations in 3 dimensions

Energy Technology Data Exchange (ETDEWEB)

Manteuffel, T.A [Univ. of Colorado, Boulder, CO (United States); Ressel, K.J. [Interdisciplinary Project Center for Supercomputing, Zurich (Switzerland); Starkes, G. [Universtaet Karlsruhe (Germany)

1996-12-31

The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.

Simultaneous determination of penicillin G salts by infrared spectroscopy: Evaluation of combining orthogonal signal correction with radial basis function-partial least squares regression

Science.gov (United States)

Talebpour, Zahra; Tavallaie, Roya; Ahmadi, Seyyed Hamid; Abdollahpour, Assem

2010-09-01

In this study, a new method for the simultaneous determination of penicillin G salts in pharmaceutical mixture via FT-IR spectroscopy combined with chemometrics was investigated. The mixture of penicillin G salts is a complex system due to similar analytical characteristics of components. Partial least squares (PLS) and radial basis function-partial least squares (RBF-PLS) were used to develop the linear and nonlinear relation between spectra and components, respectively. The orthogonal signal correction (OSC) preprocessing method was used to correct unexpected information, such as spectral overlapping and scattering effects. In order to compare the influence of OSC on PLS and RBF-PLS models, the optimal linear (PLS) and nonlinear (RBF-PLS) models based on conventional and OSC preprocessed spectra were established and compared. The obtained results demonstrated that OSC clearly enhanced the performance of both RBF-PLS and PLS calibration models. Also in the case of some nonlinear relation between spectra and component, OSC-RBF-PLS gave satisfactory results than OSC-PLS model which indicated that the OSC was helpful to remove extrinsic deviations from linearity without elimination of nonlinear information related to component. The chemometric models were tested on an external dataset and finally applied to the analysis commercialized injection product of penicillin G salts.

A Least Squares Collocation Approach with GOCE gravity gradients for regional Moho-estimation

Science.gov (United States)

Rieser, Daniel; Mayer-Guerr, Torsten

2014-05-01

The depth of the Moho discontinuity is commonly derived by either seismic observations, gravity measurements or combinations of both. In this study, we aim to use the gravity gradient measurements of the GOCE satellite mission in a Least Squares Collocation (LSC) approach for the estimation of the Moho depth on regional scale. Due to its mission configuration and measurement setup, GOCE is able to contribute valuable information in particular in the medium wavelengths of the gravity field spectrum, which is also of special interest for the crust-mantle boundary. In contrast to other studies we use the full information of the gradient tensor in all three dimensions. The problem outline is formulated as isostatically compensated topography according to the Airy-Heiskanen model. By using a topography model in spherical harmonics representation the topographic influences can be reduced from the gradient observations. Under the assumption of constant mantle and crustal densities, surface densities are directly derived by LSC on regional scale, which in turn are converted in Moho depths. First investigations proofed the ability of this method to resolve the gravity inversion problem already with a small amount of GOCE data and comparisons with other seismic and gravitmetric Moho models for the European region show promising results. With the recently reprocessed GOCE gradients, an improved data set shall be used for the derivation of the Moho depth. In this contribution the processing strategy will be introduced and the most recent developments and results using the currently available GOCE data shall be presented.

Nonlinear temperature compensation of fluxgate magnetometers with a least-squares support vector machine

International Nuclear Information System (INIS)

Pang, Hongfeng; Chen, Dixiang; Pan, Mengchun; Luo, Shitu; Zhang, Qi; Luo, Feilu

2012-01-01

Fluxgate magnetometers are widely used for magnetic field measurement. However, their accuracy is influenced by temperature. In this paper, a new method was proposed to compensate the temperature drift of fluxgate magnetometers, in which a least-squares support vector machine (LSSVM) is utilized. The compensation performance was analyzed by simulation, which shows that the LSSVM has better performance and less training time than backpropagation and radical basis function neural networks. The temperature characteristics of a DM fluxgate magnetometer were measured with a temperature experiment box. Forty-five measured data under different magnetic fields and temperatures were obtained and divided into 36 training data and nine test data. The training data were used to obtain the parameters of the LSSVM model, and the compensation performance of the LSSVM model was verified by the test data. Experimental results show that the temperature drift of magnetometer is reduced from 109.3 to 3.3 nT after compensation, which suggests that this compensation method is effective for the accuracy improvement of fluxgate magnetometers. (paper)

Nonlinear temperature compensation of fluxgate magnetometers with a least-squares support vector machine

Science.gov (United States)

Pang, Hongfeng; Chen, Dixiang; Pan, Mengchun; Luo, Shitu; Zhang, Qi; Luo, Feilu

2012-02-01

Fluxgate magnetometers are widely used for magnetic field measurement. However, their accuracy is influenced by temperature. In this paper, a new method was proposed to compensate the temperature drift of fluxgate magnetometers, in which a least-squares support vector machine (LSSVM) is utilized. The compensation performance was analyzed by simulation, which shows that the LSSVM has better performance and less training time than backpropagation and radical basis function neural networks. The temperature characteristics of a DM fluxgate magnetometer were measured with a temperature experiment box. Forty-five measured data under different magnetic fields and temperatures were obtained and divided into 36 training data and nine test data. The training data were used to obtain the parameters of the LSSVM model, and the compensation performance of the LSSVM model was verified by the test data. Experimental results show that the temperature drift of magnetometer is reduced from 109.3 to 3.3 nT after compensation, which suggests that this compensation method is effective for the accuracy improvement of fluxgate magnetometers.

Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method

Directory of Open Access Journals (Sweden)

Reza Ezzati

2014-08-01

Full Text Available In this paper, we propose the least square method for computing the positive solution of a non-square fully fuzzy linear system. To this end, we use Kaffman' arithmetic operations on fuzzy numbers \\cite{17}. Here, considered existence of exact solution using pseudoinverse, if they are not satisfy in positive solution condition, we will compute fuzzy vector core and then we will obtain right and left spreads of positive fuzzy vector by introducing constrained least squares problem. Using our proposed method, non-square fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.

LEAST SQUARE APPROACH FOR ESTIMATING OF LAND SURFACE TEMPERATURE FROM LANDSAT-8 SATELLITE DATA USING RADIATIVE TRANSFER EQUATION

Directory of Open Access Journals (Sweden)

Y. Jouybari-Moghaddam

2017-09-01

Full Text Available Land Surface Temperature (LST is one of the significant variables measured by remotely sensed data, and it is applied in many environmental and Geoscience studies. The main aim of this study is to develop an algorithm to retrieve the LST from Landsat-8 satellite data using Radiative Transfer Equation (RTE. However, LST can be retrieved from RTE, but, since the RTE has two unknown parameters including LST and surface emissivity, estimating LST from RTE is an under the determined problem. In this study, in order to solve this problem, an approach is proposed an equation set includes two RTE based on Landsat-8 thermal bands (i.e.: band 10 and 11 and two additional equations based on the relation between the Normalized Difference Vegetation Index (NDVI and emissivity of Landsat-8 thermal bands by using simulated data for Landsat-8 bands. The iterative least square approach was used for solving the equation set. The LST derived from proposed algorithm is evaluated by the simulated dataset, built up by MODTRAN. The result shows the Root Mean Squared Error (RMSE is less than 1.18°K. Therefore; the proposed algorithm can be a suitable and robust method to retrieve the LST from Landsat-8 satellite data.

Least Square Approach for Estimating of Land Surface Temperature from LANDSAT-8 Satellite Data Using Radiative Transfer Equation

Science.gov (United States)

Jouybari-Moghaddam, Y.; Saradjian, M. R.; Forati, A. M.

2017-09-01

Land Surface Temperature (LST) is one of the significant variables measured by remotely sensed data, and it is applied in many environmental and Geoscience studies. The main aim of this study is to develop an algorithm to retrieve the LST from Landsat-8 satellite data using Radiative Transfer Equation (RTE). However, LST can be retrieved from RTE, but, since the RTE has two unknown parameters including LST and surface emissivity, estimating LST from RTE is an under the determined problem. In this study, in order to solve this problem, an approach is proposed an equation set includes two RTE based on Landsat-8 thermal bands (i.e.: band 10 and 11) and two additional equations based on the relation between the Normalized Difference Vegetation Index (NDVI) and emissivity of Landsat-8 thermal bands by using simulated data for Landsat-8 bands. The iterative least square approach was used for solving the equation set. The LST derived from proposed algorithm is evaluated by the simulated dataset, built up by MODTRAN. The result shows the Root Mean Squared Error (RMSE) is less than 1.18°K. Therefore; the proposed algorithm can be a suitable and robust method to retrieve the LST from Landsat-8 satellite data.

Baseline configuration for GNSS attitude determination with an analytical least-squares solution

International Nuclear Information System (INIS)

Chang, Guobin; Wang, Qianxin; Xu, Tianhe

2016-01-01

The GNSS attitude determination using carrier phase measurements with 4 antennas is studied on condition that the integer ambiguities have been resolved. The solution to the nonlinear least-squares is often obtained iteratively, however an analytical solution can exist for specific baseline configurations. The main aim of this work is to design this class of configurations. Both single and double difference measurements are treated which refer to the dedicated and non-dedicated receivers respectively. More realistic error models are employed in which the correlations between different measurements are given full consideration. The desired configurations are worked out. The configurations are rotation and scale equivariant and can be applied to both the dedicated and non-dedicated receivers. For these configurations, the analytical and optimal solution for the attitude is also given together with its error variance–covariance matrix. (paper)

From least squares to multilevel modeling: A graphical introduction to Bayesian inference

Science.gov (United States)

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.

Normalization Ridge Regression in Practice I: Comparisons Between Ordinary Least Squares, Ridge Regression and Normalization Ridge Regression.

Science.gov (United States)

Bulcock, J. W.

The problem of model estimation when the data are collinear was examined. Though the ridge regression (RR) outperforms ordinary least squares (OLS) regression in the presence of acute multicollinearity, it is not a problem free technique for reducing the variance of the estimates. It is a stochastic procedure when it should be nonstochastic and it…

Moving least squares simulation of free surface flows

DEFF Research Database (Denmark)

Felter, C. L.; Walther, Jens Honore; Henriksen, Christian

2014-01-01

In this paper a Moving Least Squares method (MLS) for the simulation of 2D free surface flows is presented. The emphasis is on the governing equations, the boundary conditions, and the numerical implementation. The compressible viscous isothermal Navier–Stokes equations are taken as the starting ...

Linearized least-square imaging of internally scattered data

KAUST Repository

Aldawood, Ali; Hoteit, Ibrahim; Turkiyyah, George M.; Zuberi, M. A H; Alkhalifah, Tariq Ali

2014-01-01

Internal multiples deteriorate the quality of the migrated image obtained conventionally by imaging single scattering energy. However, imaging internal multiples properly has the potential to enhance the migrated image because they illuminate zones in the subsurface that are poorly illuminated by single-scattering energy such as nearly vertical faults. Standard migration of these multiples provide subsurface reflectivity distributions with low spatial resolution and migration artifacts due to the limited recording aperture, coarse sources and receivers sampling, and the band-limited nature of the source wavelet. Hence, we apply a linearized least-square inversion scheme to mitigate the effect of the migration artifacts, enhance the spatial resolution, and provide more accurate amplitude information when imaging internal multiples. Application to synthetic data demonstrated the effectiveness of the proposed inversion in imaging a reflector that is poorly illuminated by single-scattering energy. The least-square inversion of doublescattered data helped delineate that reflector with minimal acquisition fingerprint.

Source allocation by least-squares hydrocarbon fingerprint matching

Energy Technology Data Exchange (ETDEWEB)

William A. Burns; Stephen M. Mudge; A. Edward Bence; Paul D. Boehm; John S. Brown; David S. Page; Keith R. Parker [W.A. Burns Consulting Services LLC, Houston, TX (United States)

2006-11-01

There has been much controversy regarding the origins of the natural polycyclic aromatic hydrocarbon (PAH) and chemical biomarker background in Prince William Sound (PWS), Alaska, site of the 1989 Exxon Valdez oil spill. Different authors have attributed the sources to various proportions of coal, natural seep oil, shales, and stream sediments. The different probable bioavailabilities of hydrocarbons from these various sources can affect environmental damage assessments from the spill. This study compares two different approaches to source apportionment with the same data (136 PAHs and biomarkers) and investigate whether increasing the number of coal source samples from one to six increases coal attributions. The constrained least-squares (CLS) source allocation method that fits concentrations meets geologic and chemical constraints better than partial least-squares (PLS) which predicts variance. The field data set was expanded to include coal samples reported by others, and CLS fits confirm earlier findings of low coal contributions to PWS. 15 refs., 5 figs.

Efficient Model Selection for Sparse Least-Square SVMs

Directory of Open Access Journals (Sweden)

Xiao-Lei Xia

2013-01-01

Full Text Available The Forward Least-Squares Approximation (FLSA SVM is a newly-emerged Least-Square SVM (LS-SVM whose solution is extremely sparse. The algorithm uses the number of support vectors as the regularization parameter and ensures the linear independency of the support vectors which span the solution. This paper proposed a variant of the FLSA-SVM, namely, Reduced FLSA-SVM which is of reduced computational complexity and memory requirements. The strategy of “contexts inheritance” is introduced to improve the efficiency of tuning the regularization parameter for both the FLSA-SVM and the RFLSA-SVM algorithms. Experimental results on benchmark datasets showed that, compared to the SVM and a number of its variants, the RFLSA-SVM solutions contain a reduced number of support vectors, while maintaining competitive generalization abilities. With respect to the time cost for tuning of the regularize parameter, the RFLSA-SVM algorithm was empirically demonstrated fastest compared to FLSA-SVM, the LS-SVM, and the SVM algorithms.

Simplified Least Squares Shadowing sensitivity analysis for chaotic ODEs and PDEs

Energy Technology Data Exchange (ETDEWEB)

Chater, Mario, E-mail: chaterm@mit.edu; Ni, Angxiu, E-mail: niangxiu@mit.edu; Wang, Qiqi, E-mail: qiqi@mit.edu

2017-01-15

This paper develops a variant of the Least Squares Shadowing (LSS) method, which has successfully computed the derivative for several chaotic ODEs and PDEs. The development in this paper aims to simplify Least Squares Shadowing method by improving how time dilation is treated. Instead of adding an explicit time dilation term as in the original method, the new variant uses windowing, which can be more efficient and simpler to implement, especially for PDEs.

Strong source heat transfer simulations based on a GalerKin/Gradient - least - squares method

International Nuclear Information System (INIS)

Franca, L.P.; Carmo, E.G.D. do.

1989-05-01

Heat conduction problems with temperature-dependent strong sources are modeled by an equation with a laplacian term, a linear term and a given source distribution term. When the linear-temperature-dependent source term is much larger than the laplacian term, we have a singular perturbation problem. In this case, boundary layers are formed to satisfy the Dirichlet boundary conditions. Although this is an elliptic equation, the standard Galerkin method solution is contaminated by spurious oscillations in the neighborhood of the boundary layers. Herein we employ a Galerkin/Gradient-least-squares method which eliminates all pathological phenomena of the Galerkin method. The method is constructed by adding to the Galerkin method a mesh-dependent term obtained by the least-squares form of the gradient of the Euler-Lagrange equation. Error estimates, numerical simulations in one-and multi-dimensions are given that attest the good stability and accuracy properties of the method [pt

Least-mean-square spatial filter for IR sensors.

Science.gov (United States)

Takken, E H; Friedman, D; Milton, A F; Nitzberg, R

1979-12-15

A new least-mean-square filter is defined for signal-detection problems. The technique is proposed for scanning IR surveillance systems operating in poorly characterized but primarily low-frequency clutter interference. Near-optimal detection of point-source targets is predicted both for continuous-time and sampled-data systems.

The crux of the method: assumptions in ordinary least squares and logistic regression.

Science.gov (United States)

Long, Rebecca G

2008-10-01

Logistic regression has increasingly become the tool of choice when analyzing data with a binary dependent variable. While resources relating to the technique are widely available, clear discussions of why logistic regression should be used in place of ordinary least squares regression are difficult to find. The current paper compares and contrasts the assumptions of ordinary least squares with those of logistic regression and explains why logistic regression's looser assumptions make it adept at handling violations of the more important assumptions in ordinary least squares.

Regression model of support vector machines for least squares prediction of crystallinity of cracking catalysts by infrared spectroscopy

International Nuclear Information System (INIS)

Comesanna Garcia, Yumirka; Dago Morales, Angel; Talavera Bustamante, Isneri

2010-01-01

The recently introduction of the least squares support vector machines method for regression purposes in the field of Chemometrics has provided several advantages to linear and nonlinear multivariate calibration methods. The objective of the paper was to propose the use of the least squares support vector machine as an alternative multivariate calibration method for the prediction of the percentage of crystallinity of fluidized catalytic cracking catalysts, by means of Fourier transform mid-infrared spectroscopy. A linear kernel was used in the calculations of the regression model. The optimization of its gamma parameter was carried out using the leave-one-out cross-validation procedure. The root mean square error of prediction was used to measure the performance of the model. The accuracy of the results obtained with the application of the method is in accordance with the uncertainty of the X-ray powder diffraction reference method. To compare the generalization capability of the developed method, a comparison study was carried out, taking into account the results achieved with the new model and those reached through the application of linear calibration methods. The developed method can be easily implemented in refinery laboratories

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

International Nuclear Information System (INIS)

Xu, Yu-Lin.

1988-01-01

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 the orbit problem. 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 this problem. The normal equations were first solved by Newton's scheme. 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

Penalized weighted least-squares approach for low-dose x-ray computed tomography

Science.gov (United States)

Wang, Jing; Li, Tianfang; Lu, Hongbing; Liang, Zhengrong

2006-03-01

The noise of low-dose computed tomography (CT) sinogram follows approximately a Gaussian distribution with nonlinear dependence between the sample mean and variance. The noise is statistically uncorrelated among detector bins at any view angle. However the correlation coefficient matrix of data signal indicates a strong signal correlation among neighboring views. Based on above observations, Karhunen-Loeve (KL) transform can be used to de-correlate the signal among the neighboring views. In each KL component, a penalized weighted least-squares (PWLS) objective function can be constructed and optimal sinogram can be estimated by minimizing the objective function, followed by filtered backprojection (FBP) for CT image reconstruction. In this work, we compared the KL-PWLS method with an iterative image reconstruction algorithm, which uses the Gauss-Seidel iterative calculation to minimize the PWLS objective function in image domain. We also compared the KL-PWLS with an iterative sinogram smoothing algorithm, which uses the iterated conditional mode calculation to minimize the PWLS objective function in sinogram space, followed by FBP for image reconstruction. Phantom experiments show a comparable performance of these three PWLS methods in suppressing the noise-induced artifacts and preserving resolution in reconstructed images. Computer simulation concurs with the phantom experiments in terms of noise-resolution tradeoff and detectability in low contrast environment. The KL-PWLS noise reduction may have the advantage in computation for low-dose CT imaging, especially for dynamic high-resolution studies.

Plane-wave least-squares reverse-time migration

KAUST Repository

Dai, Wei

2013-06-03

A plane-wave least-squares reverse-time migration (LSRTM) is formulated with a new parameterization, where the migration image of each shot gather is updated separately and an ensemble of prestack images is produced along with common image gathers. The merits of plane-wave prestack LSRTM are the following: (1) plane-wave prestack LSRTM can sometimes offer stable convergence even when the migration velocity has bulk errors of up to 5%; (2) to significantly reduce computation cost, linear phase-shift encoding is applied to hundreds of shot gathers to produce dozens of plane waves. Unlike phase-shift encoding with random time shifts applied to each shot gather, plane-wave encoding can be effectively applied to data with a marine streamer geometry. (3) Plane-wave prestack LSRTM can provide higher-quality images than standard reverse-time migration. Numerical tests on the Marmousi2 model and a marine field data set are performed to illustrate the benefits of plane-wave LSRTM. Empirical results show that LSRTM in the plane-wave domain, compared to standard reversetime migration, produces images efficiently with fewer artifacts and better spatial resolution. Moreover, the prestack image ensemble accommodates more unknowns to makes it more robust than conventional least-squares migration in the presence of migration velocity errors. © 2013 Society of Exploration Geophysicists.

Flexible aluminum tubes and a least square multi-objective non-linear optimization scheme

International Nuclear Information System (INIS)

Endelt, Benny; Nielsen, Karl Brian; Olsen, Soeren

2004-01-01

The automotive industry currently uses rubber hoses as the media carrier between e.g. the radiator and the engine, and the basic idea is to replace the rubber hoses with flexible aluminum tubes.A good quality is defined through several quality measurements, i.e. in the current case the key objective is to produce a flexible convolution through optimization of the tool geometry, but the process should also be stable, and the process stability is evaluated through Forming Limit Diagrams. Typically the defined objectives are conflicting, i.e. the optimized configuration represents therefore a trade-off between the individual objectives, in this case flexibility versus process stability.The optimization problem is solved through iteratively minimizing the object function. A second-order least square scheme is used for the approximation of the quadratic model, and the change in the design parameters is evaluated through the trust region scheme and box constraints are introduced within the trust region framework. Furthermore, the object function is minimized by applying the non-monotone scheme, and the trust region subproblem is solved by applying the Cholesky factorization scheme.An optimal bell shaped geometry is identified and the design is verified experimentally

Output-only modal parameter estimator of linear time-varying structural systems based on vector TAR model and least squares support vector machine

Science.gov (United States)

Zhou, Si-Da; Ma, Yuan-Chen; Liu, Li; Kang, Jie; Ma, Zhi-Sai; Yu, Lei

2018-01-01

Identification of time-varying modal parameters contributes to the structural health monitoring, fault detection, vibration control, etc. of the operational time-varying structural systems. However, it is a challenging task because there is not more information for the identification of the time-varying systems than that of the time-invariant systems. This paper presents a vector time-dependent autoregressive model and least squares support vector machine based modal parameter estimator for linear time-varying structural systems in case of output-only measurements. To reduce the computational cost, a Wendland's compactly supported radial basis function is used to achieve the sparsity of the Gram matrix. A Gamma-test-based non-parametric approach of selecting the regularization factor is adapted for the proposed estimator to replace the time-consuming n-fold cross validation. A series of numerical examples have illustrated the advantages of the proposed modal parameter estimator on the suppression of the overestimate and the short data. A laboratory experiment has further validated the proposed estimator.

Least Squares Problems with Absolute Quadratic Constraints

Directory of Open Access Journals (Sweden)

R. Schöne

2012-01-01

Full Text Available This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.

Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

Science.gov (United States)

Liu, L. H.; Tan, J. Y.

2007-02-01

A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media.

Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

International Nuclear Information System (INIS)

Liu, L.H.; Tan, J.Y.

2007-01-01

A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media

Making the most out of the least (squares migration)

KAUST Repository

Dutta, Gaurav; Huang, Yunsong; Dai, Wei; Wang, Xin; Schuster, Gerard T.

2014-01-01

) ringiness caused by a ringy source wavelet. To partly remedy these problems, least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), proposes to linearly invert seismic data for the reflectivity distribution

Concerning an application of the method of least squares with a variable weight matrix

Science.gov (United States)

Sukhanov, A. A.

1979-01-01

An estimate of a state vector for a physical system when the weight matrix in the method of least squares is a function of this vector is considered. An iterative procedure is proposed for calculating the desired estimate. Conditions for the existence and uniqueness of the limit of this procedure are obtained, and a domain is found which contains the limit estimate. A second method for calculating the desired estimate which reduces to the solution of a system of algebraic equations is proposed. The question of applying Newton's method of tangents to solving the given system of algebraic equations is considered and conditions for the convergence of the modified Newton's method are obtained. Certain properties of the estimate obtained are presented together with an example.

A Constrained Least Squares Approach to Mobile Positioning: Algorithms and Optimality

Science.gov (United States)

Cheung, KW; So, HC; Ma, W.-K.; Chan, YT

2006-12-01

The problem of locating a mobile terminal has received significant attention in the field of wireless communications. Time-of-arrival (TOA), received signal strength (RSS), time-difference-of-arrival (TDOA), and angle-of-arrival (AOA) are commonly used measurements for estimating the position of the mobile station. In this paper, we present a constrained weighted least squares (CWLS) mobile positioning approach that encompasses all the above described measurement cases. The advantages of CWLS include performance optimality and capability of extension to hybrid measurement cases (e.g., mobile positioning using TDOA and AOA measurements jointly). Assuming zero-mean uncorrelated measurement errors, we show by mean and variance analysis that all the developed CWLS location estimators achieve zero bias and the Cramér-Rao lower bound approximately when measurement error variances are small. The asymptotic optimum performance is also confirmed by simulation results.

A Novel Method for Lithium-Ion Battery Online Parameter Identification Based on Variable Forgetting Factor Recursive Least Squares

Directory of Open Access Journals (Sweden)

Zizhou Lao

2018-05-01

Full Text Available For model-based state of charge (SOC estimation methods, the battery model parameters change with temperature, SOC, and so forth, causing the estimation error to increase. Constantly updating model parameters during battery operation, also known as online parameter identification, can effectively solve this problem. In this paper, a lithium-ion battery is modeled using the Thevenin model. A variable forgetting factor (VFF strategy is introduced to improve forgetting factor recursive least squares (FFRLS to variable forgetting factor recursive least squares (VFF-RLS. A novel method based on VFF-RLS for the online identification of the Thevenin model is proposed. Experiments verified that VFF-RLS gives more stable online parameter identification results than FFRLS. Combined with an unscented Kalman filter (UKF algorithm, a joint algorithm named VFF-RLS-UKF is proposed for SOC estimation. In a variable-temperature environment, a battery SOC estimation experiment was performed using the joint algorithm. The average error of the SOC estimation was as low as 0.595% in some experiments. Experiments showed that VFF-RLS can effectively track the changes in model parameters. The joint algorithm improved the SOC estimation accuracy compared to the method with the fixed forgetting factor.

Making the most out of least-squares migration

KAUST Repository

Huang, Yunsong

2014-09-01

Standard migration images can suffer from (1) migration artifacts caused by an undersampled acquisition geometry, (2) poor resolution resulting from a limited recording aperture, (3) ringing artifacts caused by ripples in the source wavelet, and (4) weak amplitudes resulting from geometric spreading, attenuation, and defocusing. These problems can be remedied in part by least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), which aims to linearly invert seismic data for the reflectivity distribution. Given a sufficiently accurate migration velocity model, LSM can mitigate many of the above problems and can produce more resolved migration images, sometimes with more than twice the spatial resolution of standard migration. However, LSM faces two challenges: The computational cost can be an order of magnitude higher than that of standard migration, and the resulting image quality can fail to improve for migration velocity errors of about 5% or more. It is possible to obtain the most from least-squares migration by reducing the cost and velocity sensitivity of LSM.

State Estimation of Permanent Magnet Synchronous Motor Using Improved Square Root UKF

Directory of Open Access Journals (Sweden)

Bo Xu

2016-06-01

Full Text Available This paper focuses on an improved square root unscented Kalman filter (SRUKF and its application for rotor speed and position estimation of permanent magnet synchronous motor (PMSM. The approach, which combines the SRUKF and strong tracking filter, uses the minimal skew simplex transformation to reduce the number of the sigma points, and utilizes the square root filtering to reduce computational errors. The time-varying fading factor and softening factor are introduced to self-adjust the gain matrices and the state forecast covariance square root matrix, which can realize the residuals orthogonality and force the SRUKF to track the real state rapidly. The theoretical analysis of the improved SRUKF and implementation details for PMSM state estimation are examined. The simulation results show that the improved SRUKF has higher nonlinear approximation accuracy, stronger numerical stability and computational efficiency, and it is an effective and powerful tool for PMSM state estimation under the conditions of step response or load disturbance.

A Bayesian least-squares support vector machine method for predicting the remaining useful life of a microwave component

Directory of Open Access Journals (Sweden)

Fuqiang Sun

2017-01-01

Full Text Available Rapid and accurate lifetime prediction of critical components in a system is important to maintaining the system’s reliable operation. To this end, many lifetime prediction methods have been developed to handle various failure-related data collected in different situations. Among these methods, machine learning and Bayesian updating are the most popular ones. In this article, a Bayesian least-squares support vector machine method that combines least-squares support vector machine with Bayesian inference is developed for predicting the remaining useful life of a microwave component. A degradation model describing the change in the component’s power gain over time is developed, and the point and interval remaining useful life estimates are obtained considering a predefined failure threshold. In our case study, the radial basis function neural network approach is also implemented for comparison purposes. The results indicate that the Bayesian least-squares support vector machine method is more precise and stable in predicting the remaining useful life of this type of components.

Status of software for PGNAA bulk analysis by the Monte Carlo - Library Least-Squares (MCLLS) approach

International Nuclear Information System (INIS)

Gardner, R.P.; Zhang, W.; Metwally, W.A.

2005-01-01

The Center for Engineering Applications of Radioisotopes (CEAR) has been working for about ten years on the Monte Carlo - Library Least-Squares (MCLLS) approach for treating the nonlinear inverse analysis problem for PGNAA bulk analysis. This approach consists essentially of using Monte Carlo simulation to generate the libraries of all the elements to be analyzed plus any other required libraries. These libraries are then used in the linear Library Least-Squares (LLS) approach with unknown sample spectra to analyze for all elements in the sample. The other libraries include all sources of background which includes: (1) gamma-rays emitted by the neutron source, (2) prompt gamma-rays produced in the analyzer construction materials, (3) natural gamma-rays from K-40 and the uranium and thorium decay chains, and (4) prompt and decay gamma-rays produced in the NaI detector by neutron activation. A number of unforeseen problems have arisen in pursuing this approach including: (1) the neutron activation of the most common detector (NaI) used in bulk analysis PGNAA systems, (2) the nonlinearity of this detector, and (3) difficulties in obtaining detector response functions for this (and other) detectors. These problems have been addressed by CEAR recently and have either been solved or are almost solved at the present time. Development of Monte Carlo simulation for all of the libraries has been finished except the prompt gamma-ray library from the activation of the NaI detector. Treatment for the coincidence schemes for Na and particularly I must be first determined to complete the Monte Carlo simulation of this last library. (author)

Least Squares Neural Network-Based Wireless E-Nose System Using an SnO₂ Sensor Array.

Science.gov (United States)

Shahid, Areej; Choi, Jong-Hyeok; Rana, Abu Ul Hassan Sarwar; Kim, Hyun-Seok

2018-05-06

Over the last few decades, the development of the electronic nose (E-nose) for detection and quantification of dangerous and odorless gases, such as methane (CH₄) and carbon monoxide (CO), using an array of SnO₂ gas sensors has attracted considerable attention. This paper addresses sensor cross sensitivity by developing a classifier and estimator using an artificial neural network (ANN) and least squares regression (LSR), respectively. Initially, the ANN was implemented using a feedforward pattern recognition algorithm to learn the collective behavior of an array as the signature of a particular gas. In the second phase, the classified gas was quantified by minimizing the mean square error using LSR. The combined approach produced 98.7% recognition probability, with 95.5 and 94.4% estimated gas concentration accuracies for CH₄ and CO, respectively. The classifier and estimator parameters were deployed in a remote microcontroller for the actualization of a wireless E-nose system.

A Generalized Least Squares Regression Approach for Computing Effect Sizes in Single-Case Research: Application Examples

Science.gov (United States)

Maggin, Daniel M.; Swaminathan, Hariharan; Rogers, Helen J.; O'Keeffe, Breda V.; Sugai, George; Horner, Robert H.

2011-01-01

A new method for deriving effect sizes from single-case designs is proposed. The strategy is applicable to small-sample time-series data with autoregressive errors. The method uses Generalized Least Squares (GLS) to model the autocorrelation of the data and estimate regression parameters to produce an effect size that represents the magnitude of…

Fishery landing forecasting using EMD-based least square support vector machine models

Science.gov (United States)

Shabri, Ani

2015-05-01

In this paper, the novel hybrid ensemble learning paradigm integrating ensemble empirical mode decomposition (EMD) and least square support machine (LSSVM) is proposed to improve the accuracy of fishery landing forecasting. This hybrid is formulated specifically to address in modeling fishery landing, which has high nonlinear, non-stationary and seasonality time series which can hardly be properly modelled and accurately forecasted by traditional statistical models. In the hybrid model, EMD is used to decompose original data into a finite and often small number of sub-series. The each sub-series is modeled and forecasted by a LSSVM model. Finally the forecast of fishery landing is obtained by aggregating all forecasting results of sub-series. To assess the effectiveness and predictability of EMD-LSSVM, monthly fishery landing record data from East Johor of Peninsular Malaysia, have been used as a case study. The result shows that proposed model yield better forecasts than Autoregressive Integrated Moving Average (ARIMA), LSSVM and EMD-ARIMA models on several criteria..

Comparison of some nonlinear smoothing methods

International Nuclear Information System (INIS)

Bell, P.R.; Dillon, R.S.

1977-01-01

Due to the poor quality of many nuclear medicine images, computer-driven smoothing procedures are frequently employed to enhance the diagnostic utility of these images. While linear methods were first tried, it was discovered that nonlinear techniques produced superior smoothing with little detail suppression. We have compared four methods: Gaussian smoothing (linear), two-dimensional least-squares smoothing (linear), two-dimensional least-squares bounding (nonlinear), and two-dimensional median smoothing (nonlinear). The two dimensional least-squares procedures have yielded the most satisfactorily enhanced images, with the median smoothers providing quite good images, even in the presence of widely aberrant points

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Internal displacement and strain measurement using digital volume correlation: a least-squares framework

International Nuclear Information System (INIS)

Pan, Bing; Wu, Dafang; Wang, Zhaoyang

2012-01-01

As a novel tool for quantitative 3D internal deformation measurement throughout the interior of a material or tissue, digital volume correlation (DVC) has increasingly gained attention and application in the fields of experimental mechanics, material research and biomedical engineering. However, the practical implementation of DVC involves important challenges such as implementation complexity, calculation accuracy and computational efficiency. In this paper, a least-squares framework is presented for 3D internal displacement and strain field measurement using DVC. The proposed DVC combines a practical linear-intensity-change model with an easy-to-implement iterative least-squares (ILS) algorithm to retrieve 3D internal displacement vector field with sub-voxel accuracy. Because the linear-intensity-change model is capable of accounting for both the possible intensity changes and the relative geometric transform of the target subvolume, the presented DVC thus provides the highest sub-voxel registration accuracy and widest applicability. Furthermore, as the ILS algorithm uses only first-order spatial derivatives of the deformed volumetric image, the developed DVC thus significantly reduces computational complexity. To further extract 3D strain distributions from the 3D discrete displacement vectors obtained by the ILS algorithm, the presented DVC employs a pointwise least-squares algorithm to estimate the strain components for each measurement point. Computer-simulated volume images with controlled displacements are employed to investigate the performance of the proposed DVC method in terms of mean bias error and standard deviation error. Results reveal that the present technique is capable of providing accurate measurements in an easy-to-implement manner, and can be applied to practical 3D internal displacement and strain calculation. (paper)

Application of pulse pile-up correction spectrum to the library least-squares method

Energy Technology Data Exchange (ETDEWEB)

Lee, Sang Hoon [Kyungpook National Univ., Daegu (Korea, Republic of)

2006-12-15

The Monte Carlo simulation code CEARPPU has been developed and updated to provide pulse pile-up correction spectra for high counting rate cases. For neutron activation analysis, CEARPPU correction spectra were used in library least-squares method to give better isotopic activity results than the convention library least-squares fitting with uncorrected spectra.

A library least-squares approach for scatter correction in gamma-ray tomography

Science.gov (United States)

Meric, Ilker; Anton Johansen, Geir; Valgueiro Malta Moreira, Icaro

2015-03-01

Scattered radiation is known to lead to distortion in reconstructed images in Computed Tomography (CT). The effects of scattered radiation are especially more pronounced in non-scanning, multiple source systems which are preferred for flow imaging where the instantaneous density distribution of the flow components is of interest. In this work, a new method based on a library least-squares (LLS) approach is proposed as a means of estimating the scatter contribution and correcting for this. The validity of the proposed method is tested using the 85-channel industrial gamma-ray tomograph previously developed at the University of Bergen (UoB). The results presented here confirm that the LLS approach can effectively estimate the amounts of transmission and scatter components in any given detector in the UoB gamma-ray tomography system.

Performance Evaluation of the Ordinary Least Square (OLS) and ...

African Journals Online (AJOL)

Nana Kwasi Peprah

1Deparment of Geomatic Engineering, University of Mines and Technology, ... precise, accurate and can be used to execute any engineering works due to ..... and Ordinary Least Squares Methods”, Journal of Geomatics and Planning, Vol ... Technology”, Unpublished BSc Project Report, University of Mines and Technology ...

MINPACK-1, Subroutine Library for Nonlinear Equation System

International Nuclear Information System (INIS)

Garbow, Burton S.

1984-01-01

1 - Description of problem or function: MINPACK1 is a package of FORTRAN subprograms for the numerical solution of systems of non- linear equations and nonlinear least-squares problems. The individual programs are: Identification/Description: - CHKDER: Check gradients for consistency with functions, - DOGLEG: Determine combination of Gauss-Newton and gradient directions, - DPMPAR: Provide double precision machine parameters, - ENORM: Calculate Euclidean norm of vector, - FDJAC1: Calculate difference approximation to Jacobian (nonlinear equations), - FDJAC2: Calculate difference approximation to Jacobian (least squares), - HYBRD: Solve system of nonlinear equations (approximate Jacobian), - HYBRD1: Easy-to-use driver for HYBRD, - HYBRJ: Solve system of nonlinear equations (analytic Jacobian), - HYBRJ1: Easy-to-use driver for HYBRJ, - LMDER: Solve nonlinear least squares problem (analytic Jacobian), - LMDER1: Easy-to-use driver for LMDER, - LMDIF: Solve nonlinear least squares problem (approximate Jacobian), - LMDIF1: Easy-to-use driver for LMDIF, - LMPAR: Determine Levenberg-Marquardt parameter - LMSTR: Solve nonlinear least squares problem (analytic Jacobian, storage conserving), - LMSTR1: Easy-to-use driver for LMSTR, - QFORM: Accumulate orthogonal matrix from QR factorization QRFAC Compute QR factorization of rectangular matrix, - QRSOLV: Complete solution of least squares problem, - RWUPDT: Update QR factorization after row addition, - R1MPYQ: Apply orthogonal transformations from QR factorization, - R1UPDT: Update QR factorization after rank-1 addition, - SPMPAR: Provide single precision machine parameters. 4. Method of solution - MINPACK1 uses the modified Powell hybrid method and the Levenberg-Marquardt algorithm

Temporal gravity field modeling based on least square collocation with short-arc approach

Science.gov (United States)

ran, jiangjun; Zhong, Min; Xu, Houze; Liu, Chengshu; Tangdamrongsub, Natthachet

2014-05-01

After the launch of the Gravity Recovery And Climate Experiment (GRACE) in 2002, several research centers have attempted to produce the finest gravity model based on different approaches. In this study, we present an alternative approach to derive the Earth's gravity field, and two main objectives are discussed. Firstly, we seek the optimal method to estimate the accelerometer parameters, and secondly, we intend to recover the monthly gravity model based on least square collocation method. The method has been paid less attention compared to the least square adjustment method because of the massive computational resource's requirement. The positions of twin satellites are treated as pseudo-observations and unknown parameters at the same time. The variance covariance matrices of the pseudo-observations and the unknown parameters are valuable information to improve the accuracy of the estimated gravity solutions. Our analyses showed that introducing a drift parameter as an additional accelerometer parameter, compared to using only a bias parameter, leads to a significant improvement of our estimated monthly gravity field. The gravity errors outside the continents are significantly reduced based on the selected set of the accelerometer parameters. We introduced the improved gravity model namely the second version of Institute of Geodesy and Geophysics, Chinese Academy of Sciences (IGG-CAS 02). The accuracy of IGG-CAS 02 model is comparable to the gravity solutions computed from the Geoforschungszentrum (GFZ), the Center for Space Research (CSR) and the NASA Jet Propulsion Laboratory (JPL). In term of the equivalent water height, the correlation coefficients over the study regions (the Yangtze River valley, the Sahara desert, and the Amazon) among four gravity models are greater than 0.80.

Tensor hypercontraction. II. Least-squares renormalization

Science.gov (United States)

Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

2012-12-01

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

A Two-Layer Least Squares Support Vector Machine Approach to Credit Risk Assessment

Science.gov (United States)

Liu, Jingli; Li, Jianping; Xu, Weixuan; Shi, Yong

Least squares support vector machine (LS-SVM) is a revised version of support vector machine (SVM) and has been proved to be a useful tool for pattern recognition. LS-SVM had excellent generalization performance and low computational cost. In this paper, we propose a new method called two-layer least squares support vector machine which combines kernel principle component analysis (KPCA) and linear programming form of least square support vector machine. With this method sparseness and robustness is obtained while solving large dimensional and large scale database. A U.S. commercial credit card database is used to test the efficiency of our method and the result proved to be a satisfactory one.

Chaos characteristics and least squares support vector machines based online pipeline small leakages detection

International Nuclear Information System (INIS)

Liu, Jinhai; Su, Hanguang; Ma, Yanjuan; Wang, Gang; Wang, Yuan; Zhang, Kun

2016-01-01

Small leakages are severe threats to the long distance pipeline transportation. An online small leakage detection method based on chaos characteristics and Least Squares Support Vector Machines (LS-SVMs) is proposed in this paper. For the first time, the relationship between the chaos characteristics of pipeline inner pressures and the small leakages is investigated and applied in the pipeline detection method. Firstly, chaos in the pipeline inner pressure is found. Relevant chaos characteristics are estimated by the nonlinear time series analysis package (TISEAN). Then LS-SVM with a hybrid kernel is built and named as hybrid kernel LS-SVM (HKLS-SVM). It is applied to analyze the chaos characteristics and distinguish the negative pressure waves (NPWs) caused by small leaks. A new leak location method is also expounded. Finally, data of the chaotic Logistic-Map system is used in the simulation. A comparison between HKLS-SVM and other methods, in terms of the identification accuracy and computing efficiency, is made. The simulation result shows that HKLS-SVM gets the best performance and is effective in error analysis of chaotic systems. When real pipeline data is used in the test, the ultimate identification accuracy of HKLS-SVM reaches 97.38% and the position accuracy is 99.28%, indicating that the method proposed in this paper has good performance in detecting and locating small pipeline leaks.

A FORTRAN program for a least-square fitting

International Nuclear Information System (INIS)

Yamazaki, Tetsuo

1978-01-01

A practical FORTRAN program for a least-squares fitting is presented. Although the method is quite usual, the program calculates not only the most satisfactory set of values of unknowns but also the plausible errors associated with them. As an example, a measured lateral absorbed-dose distribution in water for a narrow 25-MeV electron beam is fitted to a Gaussian distribution. (auth.)

A deterministic iterative least-squares algorithm for beam weight optimization in conformal radiotherapy

International Nuclear Information System (INIS)

Chen Yan; Michalski, Darek; Houser, Christopher; Galvin, James M.

2002-01-01

Currently, inverse treatment planning in conformal radiotherapy is, in part, a trial-and-error process due to the interplay of many competing criteria for obtaining a clinically acceptable dose distribution. A new method is developed for beam weight optimization that incorporates clinically relevant nonlinear and linear constraints. The process is driven by a nonlinear, quasi-quadratic objective function and the solution space is defined by a set of linear constraints. At each step of iteration, the optimization problem is linearized by a self-consistent approximation that is local to the existing dose distribution. The dose distribution is then improved by solving a series of constrained least-squares problems using an established method until all prescribed constraints are satisfied. This differs from the current approaches in that it does not rely on the search for the global minimum of a specific objective function. Essentially, our proposed objective function can be construed as a functional that comprises a class of dose-based quadratic objective functions. Empirical adjustment for appropriate model parameters in the construction of objective function is minimized, since these parameters are in effect adaptively adjusted during optimization. The method is robust in solving difficult clinical cases using either aperture or pencil beam based planning techniques for intensity-modulated radiation therapy. (author)

Making the most out of the least (squares migration)

KAUST Repository

Dutta, Gaurav

2014-08-05

Standard migration images can suffer from migration artifacts due to 1) poor source-receiver sampling, 2) weak amplitudes caused by geometric spreading, 3) attenuation, 4) defocusing, 5) poor resolution due to limited source-receiver aperture, and 6) ringiness caused by a ringy source wavelet. To partly remedy these problems, least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), proposes to linearly invert seismic data for the reflectivity distribution. If the migration velocity model is sufficiently accurate, then LSM can mitigate many of the above problems and lead to a more resolved migration image, sometimes with twice the spatial resolution. However, there are two problems with LSM: the cost can be an order of magnitude more than standard migration and the quality of the LSM image is no better than the standard image for velocity errors of 5% or more. We now show how to get the most from least-squares migration by reducing the cost and velocity sensitivity of LSM.

Least squares orthogonal polynomial approximation in several independent variables

International Nuclear Information System (INIS)

Caprari, R.S.

1992-06-01

This paper begins with an exposition of a systematic technique for generating orthonormal polynomials in two independent variables by application of the Gram-Schmidt orthogonalization procedure of linear algebra. It is then demonstrated how a linear least squares approximation for experimental data or an arbitrary function can be generated from these polynomials. The least squares coefficients are computed without recourse to matrix arithmetic, which ensures both numerical stability and simplicity of implementation as a self contained numerical algorithm. The Gram-Schmidt procedure is then utilised to generate a complete set of orthogonal polynomials of fourth degree. A theory for the transformation of the polynomial representation from an arbitrary basis into the familiar sum of products form is presented, together with a specific implementation for fourth degree polynomials. Finally, the computational integrity of this algorithm is verified by reconstructing arbitrary fourth degree polynomials from their values at randomly chosen points in their domain. 13 refs., 1 tab

Least-squares reverse time migration of multiples

KAUST Repository

Zhang, Dongliang

2013-12-06

The theory of least-squares reverse time migration of multiples (RTMM) is presented. In this method, least squares migration (LSM) is used to image free-surface multiples where the recorded traces are used as the time histories of the virtual sources at the hydrophones and the surface-related multiples are the observed data. For a single source, the entire free-surface becomes an extended virtual source where the downgoing free-surface multiples more fully illuminate the subsurface compared to the primaries. Since each recorded trace is treated as the time history of a virtual source, knowledge of the source wavelet is not required and the ringy time series for each source is automatically deconvolved. If the multiples can be perfectly separated from the primaries, numerical tests on synthetic data for the Sigsbee2B and Marmousi2 models show that least-squares reverse time migration of multiples (LSRTMM) can significantly improve the image quality compared to RTMM or standard reverse time migration (RTM) of primaries. However, if there is imperfect separation and the multiples are strongly interfering with the primaries then LSRTMM images show no significant advantage over the primary migration images. In some cases, they can be of worse quality. Applying LSRTMM to Gulf of Mexico data shows higher signal-to-noise imaging of the salt bottom and top compared to standard RTM images. This is likely attributed to the fact that the target body is just below the sea bed so that the deep water multiples do not have strong interference with the primaries. Migrating a sparsely sampled version of the Marmousi2 ocean bottom seismic data shows that LSM of primaries and LSRTMM provides significantly better imaging than standard RTM. A potential liability of LSRTMM is that multiples require several round trips between the reflector and the free surface, so that high frequencies in the multiples suffer greater attenuation compared to the primary reflections. This can lead to lower

Spectral mimetic least-squares method for div-curl systems

NARCIS (Netherlands)

Gerritsma, Marc; Palha, Artur; Lirkov, I.; Margenov, S.

2018-01-01

In this paper the spectral mimetic least-squares method is applied to a two-dimensional div-curl system. A test problem is solved on orthogonal and curvilinear meshes and both h- and p-convergence results are presented. The resulting solutions will be pointwise divergence-free for these test

Fitting of two and three variate polynomials from experimental data through the least squares method

International Nuclear Information System (INIS)

Sanchez-Miro, J.J.; Sanz-Martin, J.C.

1994-01-01

Obtaining polynomial fittings from observational data in two and three dimensions is an interesting and practical task. Such an arduous problem suggests the development of an automatic code. The main novelty we provide lies in the generalization of the classical least squares method in three FORTRAN 77 programs usable in any sampling problem. Furthermore, we introduce the orthogonal 2D-Legendre function in the fitting process. These FORTRAN 77 programs are equipped with the options to calculate the approximation quality standard indicators, obviously generalized to two and three dimensions (correlation nonlinear factor, confidence intervals, cuadratic mean error, and so on). The aim of this paper is to rectify the absence of fitting algorithms for more than one independent variable in mathematical libraries

Nonnegative least-squares image deblurring: improved gradient projection approaches

Science.gov (United States)

Benvenuto, F.; Zanella, R.; Zanni, L.; Bertero, M.

2010-02-01

The least-squares approach to image deblurring leads to an ill-posed problem. The addition of the nonnegativity constraint, when appropriate, does not provide regularization, even if, as far as we know, a thorough investigation of the ill-posedness of the resulting constrained least-squares problem has still to be done. Iterative methods, converging to nonnegative least-squares solutions, have been proposed. Some of them have the 'semi-convergence' property, i.e. early stopping of the iteration provides 'regularized' solutions. In this paper we consider two of these methods: the projected Landweber (PL) method and the iterative image space reconstruction algorithm (ISRA). Even if they work well in many instances, they are not frequently used in practice because, in general, they require a large number of iterations before providing a sensible solution. Therefore, the main purpose of this paper is to refresh these methods by increasing their efficiency. Starting from the remark that PL and ISRA require only the computation of the gradient of the functional, we propose the application to these algorithms of special acceleration techniques that have been recently developed in the area of the gradient methods. In particular, we propose the application of efficient step-length selection rules and line-search strategies. Moreover, remarking that ISRA is a scaled gradient algorithm, we evaluate its behaviour in comparison with a recent scaled gradient projection (SGP) method for image deblurring. Numerical experiments demonstrate that the accelerated methods still exhibit the semi-convergence property, with a considerable gain both in the number of iterations and in the computational time; in particular, SGP appears definitely the most efficient one.

On-line scheme for parameter estimation of nonlinear lithium ion battery equivalent circuit models using the simplified refined instrumental variable method for a modified Wiener continuous-time model

International Nuclear Information System (INIS)

Allafi, Walid; Uddin, Kotub; Zhang, Cheng; Mazuir Raja Ahsan Sha, Raja; Marco, James

2017-01-01

Highlights: •Off-line estimation approach for continuous-time domain for non-invertible function. •Model reformulated to multi-input-single-output; nonlinearity described by sigmoid. •Method directly estimates parameters of nonlinear ECM from the measured-data. •Iterative on-line technique leads to smoother convergence. •The model is validated off-line and on-line using NCA battery. -- Abstract: The accuracy of identifying the parameters of models describing lithium ion batteries (LIBs) in typical battery management system (BMS) applications is critical to the estimation of key states such as the state of charge (SoC) and state of health (SoH). In applications such as electric vehicles (EVs) where LIBs are subjected to highly demanding cycles of operation and varying environmental conditions leading to non-trivial interactions of ageing stress factors, this identification is more challenging. This paper proposes an algorithm that directly estimates the parameters of a nonlinear battery model from measured input and output data in the continuous time-domain. The simplified refined instrumental variable method is extended to estimate the parameters of a Wiener model where there is no requirement for the nonlinear function to be invertible. To account for nonlinear battery dynamics, in this paper, the typical linear equivalent circuit model (ECM) is enhanced by a block-oriented Wiener configuration where the nonlinear memoryless block following the typical ECM is defined to be a sigmoid static nonlinearity. The nonlinear Weiner model is reformulated in the form of a multi-input, single-output linear model. This linear form allows the parameters of the nonlinear model to be estimated using any linear estimator such as the well-established least squares (LS) algorithm. In this paper, the recursive least square (RLS) method is adopted for online parameter estimation. The approach was validated on experimental data measured from an 18650-type Graphite

Attenuation compensation in least-squares reverse time migration using the visco-acoustic wave equation

KAUST Repository

Dutta, Gaurav

2013-08-20

Attenuation leads to distortion of amplitude and phase of seismic waves propagating inside the earth. Conventional acoustic and least-squares reverse time migration do not account for this distortion which leads to defocusing of migration images in highly attenuative geological environments. To account for this distortion, we propose to use the visco-acoustic wave equation for least-squares reverse time migration. Numerical tests on synthetic data show that least-squares reverse time migration with the visco-acoustic wave equation corrects for this distortion and produces images with better balanced amplitudes compared to the conventional approach. © 2013 SEG.

A method for nonlinear exponential regression analysis

Science.gov (United States)

Junkin, B. G.

1971-01-01

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

Estimating the shadow prices of SO2 and NOx for U.S. coal power plants: A convex nonparametric least squares approach

International Nuclear Information System (INIS)

Mekaroonreung, Maethee; Johnson, Andrew L.

2012-01-01

Weak disposability between outputs and pollutants, defined as a simultaneous proportional reduction of both outputs and pollutants, assumes that pollutants are byproducts of the output generation process and that a firm can “freely dispose” of both by scaling down production levels, leaving some inputs idle. Based on the production axioms of monotonicity, convexity and weak disposability, we formulate a convex nonparametric least squares (CNLS) quadratic optimization problem to estimate a frontier production function assuming either a deterministic disturbance term consisting only of inefficiency, or a composite disturbance term composed of both inefficiency and noise. The suggested methodology extends the stochastic semi-nonparametric envelopment of data (StoNED) described in Kuosmanen and Kortelainen (2011). Applying the method to estimate the shadow prices of SO 2 and NO x generated by U.S. coal power plants, we conclude that the weak disposability StoNED method provides more consistent estimates of market prices. - Highlights: ► Develops methodology to estimate shadow prices for SO 2 and NO x in the U.S. coal power plants. ► Extends CNLS and StoNED methods to include the weak disposability assumption. ► Estimates the range of SO 2 and NO x shadow prices as 201–343 $/ton and 409–1352 $/ton. ► StoNED method provides more accurate estimates of shadow prices than deterministic frontier.

Track Circuit Fault Diagnosis Method based on Least Squares Support Vector

Science.gov (United States)

Cao, Yan; Sun, Fengru

2018-01-01

In order to improve the troubleshooting efficiency and accuracy of the track circuit, track circuit fault diagnosis method was researched. Firstly, the least squares support vector machine was applied to design the multi-fault classifier of the track circuit, and then the measured track data as training samples was used to verify the feasibility of the methods. Finally, the results based on BP neural network fault diagnosis methods and the methods used in this paper were compared. Results shows that the track fault classifier based on least squares support vector machine can effectively achieve the five track circuit fault diagnosis with less computing time.

Parameter estimation of a three-axis spacecraft simulator using recursive least-squares approach with tracking differentiator and Extended Kalman Filter

Science.gov (United States)

Xu, Zheyao; Qi, Naiming; Chen, Yukun

2015-12-01

Spacecraft simulators are widely used to study the dynamics, guidance, navigation, and control of a spacecraft on the ground. A spacecraft simulator can have three rotational degrees of freedom by using a spherical air-bearing to simulate a frictionless and micro-gravity space environment. The moment of inertia and center of mass are essential for control system design of ground-based three-axis spacecraft simulators. Unfortunately, they cannot be known precisely. This paper presents two approaches, i.e. a recursive least-squares (RLS) approach with tracking differentiator (TD) and Extended Kalman Filter (EKF) method, to estimate inertia parameters. The tracking differentiator (TD) filter the noise coupled with the measured signals and generate derivate of the measured signals. Combination of two TD filters in series obtains the angular accelerations that are required in RLS (TD-TD-RLS). Another method that does not need to estimate the angular accelerations is using the integrated form of dynamics equation. An extended TD (ETD) filter which can also generate the integration of the function of signals is presented for RLS (denoted as ETD-RLS). States and inertia parameters are estimated simultaneously using EKF. The observability is analyzed. All proposed methods are illustrated by simulations and experiments.

A task specific uncertainty analysis method for least-squares-based form characterization of ultra-precision freeform surfaces

International Nuclear Information System (INIS)

Ren, M J; Cheung, C F; Kong, L B

2012-01-01

In the measurement of ultra-precision freeform surfaces, least-squares-based form characterization methods are widely used to evaluate the form error of the measured surfaces. Although many methodologies have been proposed in recent years to improve the efficiency of the characterization process, relatively little research has been conducted on the analysis of associated uncertainty in the characterization results which may result from those characterization methods being used. As a result, this paper presents a task specific uncertainty analysis method with application in the least-squares-based form characterization of ultra-precision freeform surfaces. That is, the associated uncertainty in the form characterization results is estimated when the measured data are extracted from a specific surface with specific sampling strategy. Three factors are considered in this study which include measurement error, surface form error and sample size. The task specific uncertainty analysis method has been evaluated through a series of experiments. The results show that the task specific uncertainty analysis method can effectively estimate the uncertainty of the form characterization results for a specific freeform surface measurement

A suggested procedure for resolving an anomaly in least-squares data analysis known as ''Peelle's Pertinent Puzzle'' and the general implications for nuclear data evaluation

International Nuclear Information System (INIS)

Chiba, Satoshi; Smith, D.L.

1991-09-01

Modern nuclear-data evaluation methodology is based largely on statistical inference, with the least-squares technique being chosen most often to generate best estimates for physical quantities and their uncertainties. It has been observed that those least-squares evaluations which employ covariance matrices based on absolute errors that are derived directly from the reported experimental data often tend to produce results which appear to be too low. This anomaly is discussed briefly in this report, and a procedure for resolving it is suggested. The method involves employing data uncertainties which are derived from errors expressed in percent. These percent errors are used, in conjunction with reasonable a priori estimates for the quantities to be evaluated, to derive the covariance matrices which are required for applications of the least-squares procedure. This approach appears to lead to more rational weighting of the experimental data and, thus, to more realistic evaluated results than are obtained when the errors are based on the actual data. The procedure is very straightforward when only one parameter must be estimated. However, for those evaluation exercises involving more than one parameter, this technique demands that a priori estimates be provided at the outset for all of the parameters in question. Then, the least-squares method is applied iteratively to produce a sequence of sets of estimated values which are anticipated to convergence toward a particular set of parameters which one then designates as the ''best'' evaluated results from the exercise. It is found that convergence usually occurs very rapidly when the a priori estimates approximate the final solution reasonably well

A comparison of two least-squared random coefficient autoregressive models: with and without autocorrelated errors

OpenAIRE

Autcha Araveeporn

2013-01-01

This paper compares a Least-Squared Random Coefficient Autoregressive (RCA) model with a Least-Squared RCA model based on Autocorrelated Errors (RCA-AR). We looked at only the first order models, denoted RCA(1) and RCA(1)-AR(1). The efficiency of the Least-Squared method was checked by applying the models to Brownian motion and Wiener process, and the efficiency followed closely the asymptotic properties of a normal distribution. In a simulation study, we compared the performance of RCA(1) an...

Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem

Energy Technology Data Exchange (ETDEWEB)

Yoo, Jaechil [Univ. of Wisconsin, Madison, WI (United States)

1996-12-31

Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included.

Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

Czech Academy of Sciences Publication Activity Database

Bru, R.; Marín, J.; Mas, J.; Tůma, Miroslav

2014-01-01

Roč. 36, č. 4 (2014), A2002-A2022 ISSN 1064-8275 Institutional support: RVO:67985807 Keywords : preconditioned iterative methods * incomplete decompositions * approximate inverses * linear least squares Subject RIV: BA - General Mathematics Impact factor: 1.854, year: 2014

Determination of calibration equations by means of the generalized least squares method

International Nuclear Information System (INIS)

Zijp, W.L.

1984-12-01

For the determination of two-dimensional calibration curves (e.g. in tank calibration procedures) or of three dimensional calibration equations (e.g. for the calibration of NDA equipment for enrichment measurements) one performs measurements under well chosen conditions, where all observables of interest (inclusive the values of the standard material) are subject to measurement uncertainties. Moreover correlations in several measurements may occur. This document describes the mathematical-statistical approach to determine the values of the model parameters and their covariance matrix, which fit best to the mathematical model for the calibration equation. The formulae are based on the method of generalized least squares where the term generalized implies that non-linear equations in the unknown parameters and also covariance matrices of the measurement data of the calibration can be taken into account. In the general case an iteration procedure is required. No iteration is required when the model is linear in the parameters and the covariance matrices for the measurements of co-ordinates of the calibration points are proportional to each other

Analysis of quantile regression as alternative to ordinary least squares

OpenAIRE

Ibrahim Abdullahi; Abubakar Yahaya

2015-01-01

In this article, an alternative to ordinary least squares (OLS) regression based on analytical solution in the Statgraphics software is considered, and this alternative is no other than quantile regression (QR) model. We also present goodness of fit statistic as well as approximate distributions of the associated test statistics for the parameters. Furthermore, we suggest a goodness of fit statistic called the least absolute deviation (LAD) coefficient of determination. The procedure is well ...

Comparison of ERBS orbit determination accuracy using batch least-squares and sequential methods

Science.gov (United States)

Oza, D. H.; Jones, T. L.; Fabien, S. M.; Mistretta, G. D.; Hart, R. C.; Doll, C. E.

1991-10-01

The Flight Dynamics Div. (FDD) at NASA-Goddard commissioned a study to develop the Real Time Orbit Determination/Enhanced (RTOD/E) system as a prototype system for sequential orbit determination of spacecraft on a DOS based personal computer (PC). An overview is presented of RTOD/E capabilities and the results are presented of a study to compare the orbit determination accuracy for a Tracking and Data Relay Satellite System (TDRSS) user spacecraft obtained using RTOS/E on a PC with the accuracy of an established batch least squares system, the Goddard Trajectory Determination System (GTDS), operating on a mainframe computer. RTOD/E was used to perform sequential orbit determination for the Earth Radiation Budget Satellite (ERBS), and the Goddard Trajectory Determination System (GTDS) was used to perform the batch least squares orbit determination. The estimated ERBS ephemerides were obtained for the Aug. 16 to 22, 1989, timeframe, during which intensive TDRSS tracking data for ERBS were available. Independent assessments were made to examine the consistencies of results obtained by the batch and sequential methods. Comparisons were made between the forward filtered RTOD/E orbit solutions and definitive GTDS orbit solutions for ERBS; the solution differences were less than 40 meters after the filter had reached steady state.

Comparison of ERBS orbit determination accuracy using batch least-squares and sequential methods

Science.gov (United States)

Oza, D. H.; Jones, T. L.; Fabien, S. M.; Mistretta, G. D.; Hart, R. C.; Doll, C. E.

1991-01-01

The Flight Dynamics Div. (FDD) at NASA-Goddard commissioned a study to develop the Real Time Orbit Determination/Enhanced (RTOD/E) system as a prototype system for sequential orbit determination of spacecraft on a DOS based personal computer (PC). An overview is presented of RTOD/E capabilities and the results are presented of a study to compare the orbit determination accuracy for a Tracking and Data Relay Satellite System (TDRSS) user spacecraft obtained using RTOS/E on a PC with the accuracy of an established batch least squares system, the Goddard Trajectory Determination System (GTDS), operating on a mainframe computer. RTOD/E was used to perform sequential orbit determination for the Earth Radiation Budget Satellite (ERBS), and the Goddard Trajectory Determination System (GTDS) was used to perform the batch least squares orbit determination. The estimated ERBS ephemerides were obtained for the Aug. 16 to 22, 1989, timeframe, during which intensive TDRSS tracking data for ERBS were available. Independent assessments were made to examine the consistencies of results obtained by the batch and sequential methods. Comparisons were made between the forward filtered RTOD/E orbit solutions and definitive GTDS orbit solutions for ERBS; the solution differences were less than 40 meters after the filter had reached steady state.

Spectral/hp least-squares finite element formulation for the Navier-Stokes equations

International Nuclear Information System (INIS)

Pontaza, J.P.; Reddy, J.N.

2003-01-01

We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier-Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L 2 least-squares functional and L 2 error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier-Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation

Growth kinetics of borided layers: Artificial neural network and least square approaches

Science.gov (United States)

Campos, I.; Islas, M.; Ramírez, G.; VillaVelázquez, C.; Mota, C.

2007-05-01

The present study evaluates the growth kinetics of the boride layer Fe 2B in AISI 1045 steel, by means of neural networks and the least square techniques. The Fe 2B phase was formed at the material surface using the paste boriding process. The surface boron potential was modified considering different boron paste thicknesses, with exposure times of 2, 4 and 6 h, and treatment temperatures of 1193, 1223 and 1273 K. The neural network and the least square models were set by the layer thickness of Fe 2B phase, and assuming that the growth of the boride layer follows a parabolic law. The reliability of the techniques used is compared with a set of experiments at a temperature of 1223 K with 5 h of treatment time and boron potentials of 2, 3, 4 and 5 mm. The results of the Fe 2B layer thicknesses show a mean error of 5.31% for the neural network and 3.42% for the least square method.

Unweighted least squares phase unwrapping by means of multigrid techniques

Science.gov (United States)

Pritt, Mark D.

1995-11-01

We present a multigrid algorithm for unweighted least squares phase unwrapping. This algorithm applies Gauss-Seidel relaxation schemes to solve the Poisson equation on smaller, coarser grids and transfers the intermediate results to the finer grids. This approach forms the basis of our multigrid algorithm for weighted least squares phase unwrapping, which is described in a separate paper. The key idea of our multigrid approach is to maintain the partial derivatives of the phase data in separate arrays and to correct these derivatives at the boundaries of the coarser grids. This maintains the boundary conditions necessary for rapid convergence to the correct solution. Although the multigrid algorithm is an iterative algorithm, we demonstrate that it is nearly as fast as the direct Fourier-based method. We also describe how to parallelize the algorithm for execution on a distributed-memory parallel processor computer or a network-cluster of workstations.

Efficient Levenberg-Marquardt minimization of the maximum likelihood estimator for Poisson deviates

International Nuclear Information System (INIS)

Laurence, T.; Chromy, B.

2010-01-01

Histograms of counted events are Poisson distributed, but are typically fitted without justification using nonlinear least squares fitting. The more appropriate maximum likelihood estimator (MLE) for Poisson distributed data is seldom used. We extend the use of the Levenberg-Marquardt algorithm commonly used for nonlinear least squares minimization for use with the MLE for Poisson distributed data. In so doing, we remove any excuse for not using this more appropriate MLE. We demonstrate the use of the algorithm and the superior performance of the MLE using simulations and experiments in the context of fluorescence lifetime imaging. Scientists commonly form histograms of counted events from their data, and extract parameters by fitting to a specified model. Assuming that the probability of occurrence for each bin is small, event counts in the histogram bins will be distributed according to the Poisson distribution. We develop here an efficient algorithm for fitting event counting histograms using the maximum likelihood estimator (MLE) for Poisson distributed data, rather than the non-linear least squares measure. This algorithm is a simple extension of the common Levenberg-Marquardt (L-M) algorithm, is simple to implement, quick and robust. Fitting using a least squares measure is most common, but it is the maximum likelihood estimator only for Gaussian-distributed data. Non-linear least squares methods may be applied to event counting histograms in cases where the number of events is very large, so that the Poisson distribution is well approximated by a Gaussian. However, it is not easy to satisfy this criterion in practice - which requires a large number of events. It has been well-known for years that least squares procedures lead to biased results when applied to Poisson-distributed data; a recent paper providing extensive characterization of these biases in exponential fitting is given. The more appropriate measure based on the maximum likelihood estimator (MLE

Non-linear least squares curve fitting of a simple theoretical model to radioimmunoassay dose-response data using a mini-computer

International Nuclear Information System (INIS)

Wilkins, T.A.; Chadney, D.C.; Bryant, J.; Palmstroem, S.H.; Winder, R.L.

1977-01-01

Using the simple univalent antigen univalent-antibody equilibrium model the dose-response curve of a radioimmunoassay (RIA) may be expressed as a function of Y, X and the four physical parameters of the idealised system. A compact but powerful mini-computer program has been written in BASIC for rapid iterative non-linear least squares curve fitting and dose interpolation with this function. In its simplest form the program can be operated in an 8K byte mini-computer. The program has been extensively tested with data from 10 different assay systems (RIA and CPBA) for measurement of drugs and hormones ranging in molecular size from thyroxine to insulin. For each assay system the results have been analysed in terms of (a) curve fitting biases and (b) direct comparison with manual fitting. In all cases the quality of fitting was remarkably good in spite of the fact that the chemistry of each system departed significantly from one or more of the assumptions implicit in the model used. A mathematical analysis of departures from the model's principal assumption has provided an explanation for this somewhat unexpected observation. The essential features of this analysis are presented in this paper together with the statistical analyses of the performance of the program. From these and the results obtained to date in the routine quality control of these 10 assays, it is concluded that the method of curve fitting and dose interpolation presented in this paper is likely to be of general applicability. (orig.) [de

A library least-squares approach for scatter correction in gamma-ray tomography

International Nuclear Information System (INIS)

Meric, Ilker; Anton Johansen, Geir; Valgueiro Malta Moreira, Icaro

2015-01-01

Scattered radiation is known to lead to distortion in reconstructed images in Computed Tomography (CT). The effects of scattered radiation are especially more pronounced in non-scanning, multiple source systems which are preferred for flow imaging where the instantaneous density distribution of the flow components is of interest. In this work, a new method based on a library least-squares (LLS) approach is proposed as a means of estimating the scatter contribution and correcting for this. The validity of the proposed method is tested using the 85-channel industrial gamma-ray tomograph previously developed at the University of Bergen (UoB). The results presented here confirm that the LLS approach can effectively estimate the amounts of transmission and scatter components in any given detector in the UoB gamma-ray tomography system. - Highlights: • A LLS approach is proposed for scatter correction in gamma-ray tomography. • The validity of the LLS approach is tested through experiments. • Gain shift and pulse pile-up affect the accuracy of the LLS approach. • The LLS approach successfully estimates scatter profiles

Economic Optimization of Spray Dryer Operation using Nonlinear Model Predictive Control with State Estimation

DEFF Research Database (Denmark)

Petersen, Lars Norbert; Jørgensen, John Bagterp; Rawlings, James B.

2015-01-01

In this paper, we develop an economically optimizing Nonlinear Model Predictive Controller (E-NMPC) for a complete spray drying plant with multiple stages. In the E-NMPC the initial state is estimated by an extended Kalman Filter (EKF) with noise covariances estimated by an autocovariance least...... squares method (ALS). We present a model for the spray drying plant and use this model for simulation as well as for prediction in the E-NMPC. The open-loop optimal control problem in the E-NMPC is solved using the single-shooting method combined with a quasi-Newton Sequential Quadratic programming (SQP......) algorithm and the adjoint method for computation of gradients. We evaluate the economic performance when unmeasured disturbances are present. By simulation, we demonstrate that the E-NMPC improves the profit of spray drying by 17% compared to conventional PI control....

BRGLM, Interactive Linear Regression Analysis by Least Square Fit

International Nuclear Information System (INIS)

Ringland, J.T.; Bohrer, R.E.; Sherman, M.E.

1985-01-01

1 - Description of program or function: BRGLM is an interactive program written to fit general linear regression models by least squares and to provide a variety of statistical diagnostic information about the fit. Stepwise and all-subsets regression can be carried out also. There are facilities for interactive data management (e.g. setting missing value flags, data transformations) and tools for constructing design matrices for the more commonly-used models such as factorials, cubic Splines, and auto-regressions. 2 - Method of solution: The least squares computations are based on the orthogonal (QR) decomposition of the design matrix obtained using the modified Gram-Schmidt algorithm. 3 - Restrictions on the complexity of the problem: The current release of BRGLM allows maxima of 1000 observations, 99 variables, and 3000 words of main memory workspace. For a problem with N observations and P variables, the number of words of main memory storage required is MAX(N*(P+6), N*P+P*P+3*N, and 3*P*P+6*N). Any linear model may be fit although the in-memory workspace will have to be increased for larger problems

Combining Approach in Stages with Least Squares for fits of data in hyperelasticity

Science.gov (United States)

Beda, Tibi

2006-10-01

The present work concerns a method of continuous approximation by block of a continuous function; a method of approximation combining the Approach in Stages with the finite domains Least Squares. An identification procedure by sub-domains: basic generating functions are determined step-by-step permitting their weighting effects to be felt. This procedure allows one to be in control of the signs and to some extent of the optimal values of the parameters estimated, and consequently it provides a unique set of solutions that should represent the real physical parameters. Illustrations and comparisons are developed in rubber hyperelastic modeling. To cite this article: T. Beda, C. R. Mecanique 334 (2006).

Estimation of the in-cylinder air/fuel ratio of an internal combustion engine by the use of pressure sensors

Energy Technology Data Exchange (ETDEWEB)

Tunestaal, Per

2000-03-01

This thesis investigates the use of cylinder pressure measurements for estimation of the in-cylinder air/fuel ratio in a spark ignited internal combustion engine. An estimation model which uses the net heat release profile for estimating the cylinder air/fuel ratio of a spark ignition engine is developed. The net heat release profile is computed from the cylinder pressure trace and quantifies the conversion of chemical energy of the reactants in the charge into thermal energy. The net heat release profile does not take heat- or mass transfer into account. Cycle-averaged air/fuel ratio estimates over a range of engine speeds and loads show an RMS error of 4.1% compared to measurements in the exhaust. A thermochemical model of the combustion process in an internal combustion engine is developed. It uses a simple chemical combustion reaction, polynominal fits of internal energy as function of temperature, and the first law of thermodynamics to derive a relationship between measured cylinder pressure and the progress of the combustion process. Simplifying assumptions are made to arrive at an equation which relates the net heat release to the cylinder pressure. Two methods for estimating the sensor offset of a cylinder pressure transducer are developed. Both methods fit the pressure data during the pre-combustion phase of the compression stroke to a polytropic curve. The first method assumes a known polytropic exponent, and the other estimates the polytropic exponent. The first method results in a linear least-squares problem, and the second method results in a nonlinear least-squares problem. The nonlinear least-squares problem is solved by separating out the nonlinear dependence and solving the single-variable minimization problem. For this, a finite difference Newton method is derived. Using this method, the cost of solving the nonlinear least-squares problem is only slightly higher than solving the linear least-squares problem. Both methods show good statistical

Estimation of bone Calcium-to-Phosphorous mass ratio using dual-energy nonlinear polynomial functions

International Nuclear Information System (INIS)

Sotiropoulou, P; Koukou, V; Martini, N; Nikiforidis, G; Michail, C; Kandarakis, I; Fountos, G; Kounadi, E

2015-01-01

In this study an analytical approximation of dual-energy inverse functions is presented for the estimation of the calcium-to-phosphorous (Ca/P) mass ratio, which is a crucial parameter in bone health. Bone quality could be examined by the X-ray dual-energy method (XDEM), in terms of bone tissue material properties. Low- and high-energy, log- intensity measurements were combined by using a nonlinear function, to cancel out the soft tissue structures and generate the dual energy bone Ca/P mass ratio. The dual-energy simulated data were obtained using variable Ca and PO 4 thicknesses on a fixed total tissue thickness. The XDEM simulations were based on a bone phantom. Inverse fitting functions with least-squares estimation were used to obtain the fitting coefficients and to calculate the thickness of each material. The examined inverse mapping functions were linear, quadratic, and cubic. For every thickness, the nonlinear quadratic function provided the optimal fitting accuracy while requiring relative few terms. The dual-energy method, simulated in this work could be used to quantify bone Ca/P mass ratio with photon-counting detectors. (paper)

Constrained Balancing of Two Industrial Rotor Systems: Least Squares and Min-Max Approaches

Directory of Open Access Journals (Sweden)

Bin Huang

2009-01-01

Full Text Available Rotor vibrations caused by rotor mass unbalance distributions are a major source of maintenance problems in high-speed rotating machinery. Minimizing this vibration by balancing under practical constraints is quite important to industry. This paper considers balancing of two large industrial rotor systems by constrained least squares and min-max balancing methods. In current industrial practice, the weighted least squares method has been utilized to minimize rotor vibrations for many years. One of its disadvantages is that it cannot guarantee that the maximum value of vibration is below a specified value. To achieve better balancing performance, the min-max balancing method utilizing the Second Order Cone Programming (SOCP with the maximum correction weight constraint, the maximum residual response constraint as well as the weight splitting constraint has been utilized for effective balancing. The min-max balancing method can guarantee a maximum residual vibration value below an optimum value and is shown by simulation to significantly outperform the weighted least squares method.

A Collocation Method by Moving Least Squares Applicable to European Option Pricing

Directory of Open Access Journals (Sweden)

M. Amirfakhrian

2016-05-01

Full Text Available The subject matter of the present inquiry is the pricing of European options in the actual form of numbers. To assess the numerical prices of European options, a scheme independent of any kind of mesh but rather powered by moving least squares (MLS estimation is made. In practical terms, first the discretion of time variable is implemented and then, an MLS-powered method is applied for spatial approximation. As, unlike other methods, these courses of action mentioned here don't rely on a mesh, one can firmly claim they are to be categorized under mesh-less methods. And, of course, at the end of the paper, various experiments are offered to prove how efficient and how powerful the introduced approach is.

Geodesic least squares regression for scaling studies in magnetic confinement fusion

International Nuclear Information System (INIS)

Verdoolaege, Geert

2015-01-01

In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority of the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices

Analysis of a plane stress wave by the moving least squares method

Directory of Open Access Journals (Sweden)

Wojciech Dornowski

2014-08-01

Full Text Available A meshless method based on the moving least squares approximation is applied to stress wave propagation analysis. Two kinds of node meshes, the randomly generated mesh and the regular mesh are used. The nearest neighbours’ problem is developed from a triangulation that satisfies minimum edges length conditions. It is found that this method of neighbours’ choice significantly improves the solution accuracy. The reflection of stress waves from the free edge is modelled using fictitious nodes (outside the plate. The comparison with the finite difference results also demonstrated the accuracy of the proposed approach.[b]Keywords[/b]: civil engineering, meshless method, moving least squares method, elastic waves

Regularized plane-wave least-squares Kirchhoff migration

KAUST Repository

Wang, Xin

2013-09-22

A Kirchhoff least-squares migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images. A regularization term is included that accounts for mispositioning of reflectors due to errors in the velocity model. Both synthetic and field results show that: 1) LSM with a reflectivity model common for all the plane-wave gathers provides the best image when the migration velocity model is accurate, but it is more sensitive to the velocity errors, 2) the regularized plane-wave LSM is more robust in the presence of velocity errors, and 3) LSM achieves both computational and IO saving by plane-wave encoding compared to shot-domain LSM for the models tested.

Multiples least-squares reverse time migration

KAUST Repository

Zhang, Dongliang

2013-01-01

To enhance the image quality, we propose multiples least-squares reverse time migration (MLSRTM) that transforms each hydrophone into a virtual point source with a time history equal to that of the recorded data. Since each recorded trace is treated as a virtual source, knowledge of the source wavelet is not required. Numerical tests on synthetic data for the Sigsbee2B model and field data from Gulf of Mexico show that MLSRTM can improve the image quality by removing artifacts, balancing amplitudes, and suppressing crosstalk compared to standard migration of the free-surface multiples. The potential liability of this method is that multiples require several roundtrips between the reflector and the free surface, so that high frequencies in the multiples are attenuated compared to the primary reflections. This can lead to lower resolution in the migration image compared to that computed from primaries.

Penalized linear regression for discrete ill-posed problems: A hybrid least-squares and mean-squared error approach

KAUST Repository

Suliman, Mohamed Abdalla Elhag; Ballal, Tarig; Kammoun, Abla; Al-Naffouri, Tareq Y.

2016-01-01

This paper proposes a new approach to find the regularization parameter for linear least-squares discrete ill-posed problems. In the proposed approach, an artificial perturbation matrix with a bounded norm is forced into the discrete ill-posed model

Pemodelan Peningkatan Akurasi Estimasi Biaya Dengan Metode Structural Equation Modeling-Partial Least Square Pada Proyek Jalan Provinsi Kalimantan Tengah

Directory of Open Access Journals (Sweden)

Yanda Christian

2018-01-01

Full Text Available Acceleration of national development increases the number of construction projects in Indonesia, including road projects. The contractor as the service provider in the implementation of the construction work shall have a detailed implementation schedule and project cost budget plan so that the construction work shall not be subject to delays and cost overrun. The main thing that can cause cost overrun is the error in cost estimation. In this study discusses the modeling of increasing the accuracy of cost estimation as well as the development of factors that can improve the accuracy of cost estimation. Validation of research variables was done to experts using Analytical Hierarchy Process (AHP method and modeling using Structural Equation ModelingPartial Least Square (SEM-PLS method to project contractor of Public Works Department of Central Kalimantan Province and National Road Implementation Center XI Unit Work of Central Kalimantan with contract value of project worth 20 Billion to 50 Billion Rupiah Year 2016. The result of variable validation shows the competence variable of estimator, survey, availability of information, calculation of cost estimation and internal company is variable which influence estimation The obtained modeling equation is AEB = 0,129 KE + 0.466 S + 0,191 KI + 0,153 PEB + 0,069 IP + 0,181 ζ. The development of cost estimation is done by improving each influential indicator in each variable and applying development strategies to increase the estimated cost estimation based on SWOT analysis. Keywords : Analytical Hierarchy Process (AHP, cost estimation, road, Structural Equation Modeling-Partial Least Square (SEM-PLS, SWOT analysis.

Discrete least squares polynomial approximation with random evaluations - application to PDEs with Random parameters

KAUST Repository

Nobile, Fabio

2015-01-07

We consider a general problem F(u, y) = 0 where u is the unknown solution, possibly Hilbert space valued, and y a set of uncertain parameters. We specifically address the situation in which the parameterto-solution map u(y) is smooth, however y could be very high (or even infinite) dimensional. In particular, we are interested in cases in which F is a differential operator, u a Hilbert space valued function and y a distributed, space and/or time varying, random field. We aim at reconstructing the parameter-to-solution map u(y) from random noise-free or noisy observations in random points by discrete least squares on polynomial spaces. The noise-free case is relevant whenever the technique is used to construct metamodels, based on polynomial expansions, for the output of computer experiments. In the case of PDEs with random parameters, the metamodel is then used to approximate statistics of the output quantity. We discuss the stability of discrete least squares on random points show convergence estimates both in expectation and probability. We also present possible strategies to select, either a-priori or by adaptive algorithms, sequences of approximating polynomial spaces that allow to reduce, and in some cases break, the curse of dimensionality

Least squares shadowing sensitivity analysis of a modified Kuramoto–Sivashinsky equation

International Nuclear Information System (INIS)

Blonigan, Patrick J.; Wang, Qiqi

2014-01-01

Highlights: •Modifying the Kuramoto–Sivashinsky equation and changing its boundary conditions make it an ergodic dynamical system. •The modified Kuramoto–Sivashinsky equation exhibits distinct dynamics for three different ranges of system parameters. •Least squares shadowing sensitivity analysis computes accurate gradients for a wide range of system parameters. - Abstract: Computational methods for sensitivity analysis are invaluable tools for scientists and engineers investigating a wide range of physical phenomena. However, many of these methods fail when applied to chaotic systems, such as the Kuramoto–Sivashinsky (K–S) equation, which models a number of different chaotic systems found in nature. The following paper discusses the application of a new sensitivity analysis method developed by the authors to a modified K–S equation. We find that least squares shadowing sensitivity analysis computes accurate gradients for solutions corresponding to a wide range of system parameters

Online Identification of Multivariable Discrete Time Delay Systems Using a Recursive Least Square Algorithm

Directory of Open Access Journals (Sweden)

Saïda Bedoui

2013-01-01

Full Text Available This paper addresses the problem of simultaneous identification of linear discrete time delay multivariable systems. This problem involves both the estimation of the time delays and the dynamic parameters matrices. In fact, we suggest a new formulation of this problem allowing defining the time delay and the dynamic parameters in the same estimated vector and building the corresponding observation vector. Then, we use this formulation to propose a new method to identify the time delays and the parameters of these systems using the least square approach. Convergence conditions and statistics properties of the proposed method are also developed. Simulation results are presented to illustrate the performance of the proposed method. An application of the developed approach to compact disc player arm is also suggested in order to validate simulation results.

First-order system least-squares for second-order elliptic problems with discontinuous coefficients: Further results

Energy Technology Data Exchange (ETDEWEB)

Bloechle, B.; Manteuffel, T.; McCormick, S.; Starke, G.

1996-12-31

Many physical phenomena are modeled as scalar second-order elliptic boundary value problems with discontinuous coefficients. The first-order system least-squares (FOSLS) methodology is an alternative to standard mixed finite element methods for such problems. The occurrence of singularities at interface corners and cross-points requires that care be taken when implementing the least-squares finite element method in the FOSLS context. We introduce two methods of handling the challenges resulting from singularities. The first method is based on a weighted least-squares functional and results in non-conforming finite elements. The second method is based on the use of singular basis functions and results in conforming finite elements. We also share numerical results comparing the two approaches.

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

Science.gov (United States)

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%.

Non-stationary least-squares complex decomposition for microseismic noise attenuation

Science.gov (United States)

Chen, Yangkang

2018-06-01

Microseismic data processing and imaging are crucial for subsurface real-time monitoring during hydraulic fracturing process. Unlike the active-source seismic events or large-scale earthquake events, the microseismic event is usually of very small magnitude, which makes its detection challenging. The biggest trouble of microseismic data is the low signal-to-noise ratio issue. Because of the small energy difference between effective microseismic signal and ambient noise, the effective signals are usually buried in strong random noise. I propose a useful microseismic denoising algorithm that is based on decomposing a microseismic trace into an ensemble of components using least-squares inversion. Based on the predictive property of useful microseismic event along the time direction, the random noise can be filtered out via least-squares fitting of multiple damping exponential components. The method is flexible and almost automated since the only parameter needed to be defined is a decomposition number. I use some synthetic and real data examples to demonstrate the potential of the algorithm in processing complicated microseismic data sets.

Sensitivity equation for quantitative analysis with multivariate curve resolution-alternating least-squares: theoretical and experimental approach.

Science.gov (United States)

Bauza, María C; Ibañez, Gabriela A; Tauler, Romà; Olivieri, Alejandro C

2012-10-16

A new equation is derived for estimating the sensitivity when the multivariate curve resolution-alternating least-squares (MCR-ALS) method is applied to second-order multivariate calibration data. The validity of the expression is substantiated by extensive Monte Carlo noise addition simulations. The multivariate selectivity can be derived from the new sensitivity expression. Other important figures of merit, such as limit of detection, limit of quantitation, and concentration uncertainty of MCR-ALS quantitative estimations can be easily estimated from the proposed sensitivity expression and the instrumental noise. An experimental example involving the determination of an analyte in the presence of uncalibrated interfering agents is described in detail, involving second-order time-decaying sensitized lanthanide luminescence excitation spectra. The estimated figures of merit are reasonably correlated with the analytical features of the analyzed experimental system.

Skeletonized Least Squares Wave Equation Migration

KAUST Repository

Zhan, Ge

2010-10-17

The theory for skeletonized least squares wave equation migration (LSM) is presented. The key idea is, for an assumed velocity model, the source‐side Green\\'s function and the geophone‐side Green\\'s function are computed by a numerical solution of the wave equation. Only the early‐arrivals of these Green\\'s functions are saved and skeletonized to form the migration Green\\'s function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF for every trial image point. The key to an efficient implementation of iterative LSM is that at each conjugate gradient iteration, the MGF is reused and no new finitedifference (FD) simulations are needed to get the updated migration image. It is believed that this procedure combined with phase‐encoded multi‐source technology will allow for the efficient computation of wave equation LSM images in less time than that of conventional reverse time migration (RTM).

A robust regression based on weighted LSSVM and penalized trimmed squares

International Nuclear Information System (INIS)

Liu, Jianyong; Wang, Yong; Fu, Chengqun; Guo, Jie; Yu, Qin

2016-01-01

Least squares support vector machine (LS-SVM) for nonlinear regression is sensitive to outliers in the field of machine learning. Weighted LS-SVM (WLS-SVM) overcomes this drawback by adding weight to each training sample. However, as the number of outliers increases, the accuracy of WLS-SVM may decrease. In order to improve the robustness of WLS-SVM, a new robust regression method based on WLS-SVM and penalized trimmed squares (WLSSVM–PTS) has been proposed. The algorithm comprises three main stages. The initial parameters are obtained by least trimmed squares at first. Then, the significant outliers are identified and eliminated by the Fast-PTS algorithm. The remaining samples with little outliers are estimated by WLS-SVM at last. The statistical tests of experimental results carried out on numerical datasets and real-world datasets show that the proposed WLSSVM–PTS is significantly robust than LS-SVM, WLS-SVM and LSSVM–LTS.

Estimation of Nonlinear Functions of State Vector for Linear Systems with Time-Delays and Uncertainties

Directory of Open Access Journals (Sweden)

Il Young Song

2015-01-01

Full Text Available This paper focuses on estimation of a nonlinear function of state vector (NFS in discrete-time linear systems with time-delays and model uncertainties. The NFS represents a multivariate nonlinear function of state variables, which can indicate useful information of a target system for control. The optimal nonlinear estimator of an NFS (in mean square sense represents a function of the receding horizon estimate and its error covariance. The proposed receding horizon filter represents the standard Kalman filter with time-delays and special initial horizon conditions described by the Lyapunov-like equations. In general case to calculate an optimal estimator of an NFS we propose using the unscented transformation. Important class of polynomial NFS is considered in detail. In the case of polynomial NFS an optimal estimator has a closed-form computational procedure. The subsequent application of the proposed receding horizon filter and nonlinear estimator to a linear stochastic system with time-delays and uncertainties demonstrates their effectiveness.

Time-Series INSAR: An Integer Least-Squares Approach For Distributed Scatterers

Science.gov (United States)

Samiei-Esfahany, Sami; Hanssen, Ramon F.

2012-01-01

The objective of this research is to extend the geode- tic mathematical model which was developed for persistent scatterers to a model which can exploit distributed scatterers (DS). The main focus is on the integer least- squares framework, and the main challenge is to include the decorrelation effect in the mathematical model. In order to adapt the integer least-squares mathematical model for DS we altered the model from a single master to a multi-master configuration and introduced the decorrelation effect stochastically. This effect is described in our model by a full covariance matrix. We propose to de- rive this covariance matrix by numerical integration of the (joint) probability distribution function (PDF) of interferometric phases. This PDF is a function of coherence values and can be directly computed from radar data. We show that the use of this model can improve the performance of temporal phase unwrapping of distributed scatterers.

Adaptive Noise Canceling Menggunakan Algoritma Least Mean Square (Lms)

OpenAIRE

Nardiana, Anita; Sumaryono, Sari Sujoko

2011-01-01

Noise is inevitable in communication system. In some cases, noise can disturb signal. It is veryannoying as the received signal is jumbled with the noise itself. To reduce or remove noise, filter lowpass,highpass or bandpass can solve the problems, but this method cannot reach a maximum standard. One ofthe alternatives to solve the problem is by using adaptive filter. Adaptive algorithm frequently used is LeastMean Square (LMS) Algorithm which is compatible to Finite Impulse Response (FIR). T...

Evaluation of Ordinary Least Square (OLS) and Geographically Weighted Regression (GWR) for Water Quality Monitoring: A Case Study for the Estimation of Salinity

Science.gov (United States)

Nazeer, Majid; Bilal, Muhammad

2018-04-01

Landsat-5 Thematic Mapper (TM) dataset have been used to estimate salinity in the coastal area of Hong Kong. Four adjacent Landsat TM images were used in this study, which was atmospherically corrected using the Second Simulation of the Satellite Signal in the Solar Spectrum (6S) radiative transfer code. The atmospherically corrected images were further used to develop models for salinity using Ordinary Least Square (OLS) regression and Geographically Weighted Regression (GWR) based on in situ data of October 2009. Results show that the coefficient of determination ( R 2) of 0.42 between the OLS estimated and in situ measured salinity is much lower than that of the GWR model, which is two times higher ( R 2 = 0.86). It indicates that the GWR model has more ability than the OLS regression model to predict salinity and show its spatial heterogeneity better. It was observed that the salinity was high in Deep Bay (north-western part of Hong Kong) which might be due to the industrial waste disposal, whereas the salinity was estimated to be constant (32 practical salinity units) towards the open sea.

Lameness detection challenges in automated milking systems addressed with partial least squares discriminant analysis

DEFF Research Database (Denmark)

Garcia, Emanuel; Klaas, Ilka Christine; Amigo Rubio, Jose Manuel

2014-01-01

Lameness is prevalent in dairy herds. It causes decreased animal welfare and leads to higher production costs. This study explored data from an automatic milking system (AMS) to model on-farm gait scoring from a commercial farm. A total of 88 cows were gait scored once per week, for 2 5-wk periods......). The reference gait scoring error was estimated in the first week of the study and was, on average, 15%. Two partial least squares discriminant analysis models were fitted to parity 1 and parity 2 groups, respectively, to assign the lameness class according to the predicted probability of being lame (score 3...

Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients

Directory of Open Access Journals (Sweden)

Nauman Raza

2016-01-01

Full Text Available The nonlinear Klein-Gordon equation (KGE models many nonlinear phenomena. In this paper, we propose a scheme for numerical approximation of solutions of the one-dimensional nonlinear KGE. A common approach to find a solution of a nonlinear system is to first linearize the equations by successive substitution or the Newton iteration method and then solve a linear least squares problem. Here, we show that it can be advantageous to form a sum of squared residuals of the nonlinear problem and then find a zero of the gradient. Our scheme is based on the Sobolev gradient method for solving a nonlinear least square problem directly. The numerical results are compared with Lattice Boltzmann Method (LBM. The L2, L∞, and Root-Mean-Square (RMS values indicate better accuracy of the proposed method with less computational effort.

The consistency of ordinary least-squares and generalized least-squares polynomial regression on characterizing the mechanomyographic amplitude versus torque relationship

International Nuclear Information System (INIS)

Herda, Trent J; Ryan, Eric D; Costa, Pablo B; DeFreitas, Jason M; Walter, Ashley A; Stout, Jeffrey R; Beck, Travis W; Cramer, Joel T; Housh, Terry J; Weir, Joseph P

2009-01-01

The primary purpose of this study was to examine the consistency of ordinary least-squares (OLS) and generalized least-squares (GLS) polynomial regression analyses utilizing linear, quadratic and cubic models on either five or ten data points that characterize the mechanomyographic amplitude (MMG RMS ) versus isometric torque relationship. The secondary purpose was to examine the consistency of OLS and GLS polynomial regression utilizing only linear and quadratic models (excluding cubic responses) on either ten or five data points. Eighteen participants (mean ± SD age = 24 ± 4 yr) completed ten randomly ordered isometric step muscle actions from 5% to 95% of the maximal voluntary contraction (MVC) of the right leg extensors during three separate trials. MMG RMS was recorded from the vastus lateralis during the MVCs and each submaximal muscle action. MMG RMS versus torque relationships were analyzed on a subject-by-subject basis using OLS and GLS polynomial regression. When using ten data points, only 33% and 27% of the subjects were fitted with the same model (utilizing linear, quadratic and cubic models) across all three trials for OLS and GLS, respectively. After eliminating the cubic model, there was an increase to 55% of the subjects being fitted with the same model across all trials for both OLS and GLS regression. Using only five data points (instead of ten data points), 55% of the subjects were fitted with the same model across all trials for OLS and GLS regression. Overall, OLS and GLS polynomial regression models were only able to consistently describe the torque-related patterns of response for MMG RMS in 27–55% of the subjects across three trials. Future studies should examine alternative methods for improving the consistency and reliability of the patterns of response for the MMG RMS versus isometric torque relationship

Precision PEP-II optics measurement with an SVD-enhanced Least-Square fitting

Science.gov (United States)

Yan, Y. T.; Cai, Y.

2006-03-01

A singular value decomposition (SVD)-enhanced Least-Square fitting technique is discussed. By automatic identifying, ordering, and selecting dominant SVD modes of the derivative matrix that responds to the variations of the variables, the converging process of the Least-Square fitting is significantly enhanced. Thus the fitting speed can be fast enough for a fairly large system. This technique has been successfully applied to precision PEP-II optics measurement in which we determine all quadrupole strengths (both normal and skew components) and sextupole feed-downs as well as all BPM gains and BPM cross-plane couplings through Least-Square fitting of the phase advances and the Local Green's functions as well as the coupling ellipses among BPMs. The local Green's functions are specified by 4 local transfer matrix components R12, R34, R32, R14. These measurable quantities (the Green's functions, the phase advances and the coupling ellipse tilt angles and axis ratios) are obtained by analyzing turn-by-turn Beam Position Monitor (BPM) data with a high-resolution model-independent analysis (MIA). Once all of the quadrupoles and sextupole feed-downs are determined, we obtain a computer virtual accelerator which matches the real accelerator in linear optics. Thus, beta functions, linear coupling parameters, and interaction point (IP) optics characteristics can be measured and displayed.

An Inverse Function Least Square Fitting Approach of the Buildup Factor for Radiation Shielding Analysis

Energy Technology Data Exchange (ETDEWEB)

Park, Chang Je [Sejong Univ., Seoul (Korea, Republic of); Alkhatee, Sari; Roh, Gyuhong; Lee, Byungchul [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2014-05-15

Dose absorption and energy absorption buildup factors are widely used in the shielding analysis. The dose rate of the medium is main concern in the dose buildup factor, however energy absorption is an important parameter in the energy buildup factors. ANSI/ANS-6.4.3-1991 standard data is widely used based on interpolation and extrapolation by means of an approximation method. Recently, Yoshida's geometric progression (GP) formulae are also popular and it is already implemented in QAD code. In the QAD code, two buildup factors are notated as DOSE for standard air exposure response and ENG for the response of the energy absorbed in the material itself. In this paper, a new least square fitting method is suggested to obtain a reliable buildup factors proposed since 1991. Total 4 datasets of air exposure buildup factors are used for evaluation including ANSI/ANS-6.4.3-1991, Taylor, Berger, and GP data. The standard deviation of the fitted data are analyzed based on the results. A new reverse least square fitting method is proposed in this study in order to reduce the fitting uncertainties. It adapts an inverse function rather than the original function by the distribution slope of dataset. Some quantitative comparisons are provided for concrete and lead in this paper, too. This study is focused on the least square fitting of existing buildup factors to be utilized in the point-kernel code for radiation shielding analysis. The inverse least square fitting method is suggested to obtain more reliable results of concave shaped dataset such as concrete. In the concrete case, the variance and residue are decreased significantly, too. However, the convex shaped case of lead can be applied to the usual least square fitting method. In the future, more datasets will be tested by using the least square fitting. And the fitted data could be implemented to the existing point-kernel codes.

Gauss’s, Cholesky’s and Banachiewicz’s Contributions to Least Squares

DEFF Research Database (Denmark)

Gustavson, Fred G.; Wasniewski, Jerzy

This paper describes historically Gauss’s contributions to the area of Least Squares. Also mentioned are Cholesky’s and Banachiewicz’s contributions to linear algebra. The material given is backup information to a Tutorial given at PPAM 2011 to honor Cholesky on the hundred anniversary of his...

Partial least squares path modeling basic concepts, methodological issues and applications

CERN Document Server

Noonan, Richard

2017-01-01

This edited book presents the recent developments in partial least squares-path modeling (PLS-PM) and provides a comprehensive overview of the current state of the most advanced research related to PLS-PM. The first section of this book emphasizes the basic concepts and extensions of the PLS-PM method. The second section discusses the methodological issues that are the focus of the recent development of the PLS-PM method. The third part discusses the real world application of the PLS-PM method in various disciplines. The contributions from expert authors in the field of PLS focus on topics such as the factor-based PLS-PM, the perfect match between a model and a mode, quantile composite-based path modeling (QC-PM), ordinal consistent partial least squares (OrdPLSc), non-symmetrical composite-based path modeling (NSCPM), modern view for mediation analysis in PLS-PM, a multi-method approach for identifying and treating unobserved heterogeneity, multigroup analysis (PLS-MGA), the assessment of the common method b...

Mean Square Synchronization of Stochastic Nonlinear Delayed Coupled Complex Networks

Directory of Open Access Journals (Sweden)

Chengrong Xie

2013-01-01

Full Text Available We investigate the problem of adaptive mean square synchronization for nonlinear delayed coupled complex networks with stochastic perturbation. Based on the LaSalle invariance principle and the properties of the Weiner process, the controller and adaptive laws are designed to ensure achieving stochastic synchronization and topology identification of complex networks. Sufficient conditions are given to ensure the complex networks to be mean square synchronization. Furthermore, numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.

Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

Energy Technology Data Exchange (ETDEWEB)

Lee, Kookjin [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science; Carlberg, Kevin [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Elman, Howard C. [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science and Inst. for Advanced Computer Studies

2018-03-29

Here, we consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weighted $\\ell^2$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $\\ell^2$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.

Square Root Unscented Kalman Filters for State Estimation of Induction Motor Drives

DEFF Research Database (Denmark)

Lascu, Cristian; Jafarzadeh, Saeed; Fadali, M.Sami

2013-01-01

This paper investigates the application, design, and implementation of the square root unscented Kalman filter (UKF) (SRUKF) for induction motor (IM) sensorless drives. The UKF uses nonlinear unscented transforms (UTs) in the prediction step in order to preserve the stochastic characteristics...... of a nonlinear system. The advantage of using the UT is its ability to capture the nonlinear behavior of the system, unlike the extended Kalman filter (EKF) that uses linearized models. The SRUKF implements the UKF using square root filtering to reduce computational errors. We discuss the theoretical aspects...

ESTIMATION OF CONSTANT AND TIME-VARYING DYNAMIC PARAMETERS OF HIV INFECTION IN A NONLINEAR DIFFERENTIAL EQUATION MODEL.

Science.gov (United States)

Liang, Hua; Miao, Hongyu; Wu, Hulin

2010-03-01

Modeling viral dynamics in HIV/AIDS studies has resulted in deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper, we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies. We applied the proposed techniques to estimate the key HIV viral dynamic parameters for two individual AIDS patients treated with antiretroviral therapies. We demonstrate that HIV viral dynamics can be well characterized and

A Monte Carlo Library Least Square approach in the Neutron Inelastic-scattering and Thermal-capture Analysis (NISTA) process in bulk coal samples

Science.gov (United States)

Reyhancan, Iskender Atilla; Ebrahimi, Alborz; Çolak, Üner; Erduran, M. Nizamettin; Angin, Nergis

2017-01-01

A new Monte-Carlo Library Least Square (MCLLS) approach for treating non-linear radiation analysis problem in Neutron Inelastic-scattering and Thermal-capture Analysis (NISTA) was developed. 14 MeV neutrons were produced by a neutron generator via the 3H (2H , n) 4He reaction. The prompt gamma ray spectra from bulk samples of seven different materials were measured by a Bismuth Germanate (BGO) gamma detection system. Polyethylene was used as neutron moderator along with iron and lead as neutron and gamma ray shielding, respectively. The gamma detection system was equipped with a list mode data acquisition system which streams spectroscopy data directly to the computer, event-by-event. A GEANT4 simulation toolkit was used for generating the single-element libraries of all the elements of interest. These libraries were then used in a Linear Library Least Square (LLLS) approach with an unknown experimental sample spectrum to fit it with the calculated elemental libraries. GEANT4 simulation results were also used for the selection of the neutron shielding material.

Least squares methodology applied to LWR-PV damage dosimetry, experience and expectations

International Nuclear Information System (INIS)

Wagschal, J.J.; Broadhead, B.L.; Maerker, R.E.

1979-01-01

The development of an advanced methodology for Light Water Reactors (LWR) Pressure Vessel (PV) damage dosimetry applications is the subject of an ongoing EPRI-sponsored research project at ORNL. This methodology includes a generalized least squares approach to a combination of data. The data include measured foil activations, evaluated cross sections and calculated fluxes. The uncertainties associated with the data as well as with the calculational methods are an essential component of this methodology. Activation measurements in two NBS benchmark neutron fields ( 252 Cf ISNF) and in a prototypic reactor field (Oak Ridge Pool Critical Assembly - PCA) are being analyzed using a generalized least squares method. The sensitivity of the results to the representation of the uncertainties (covariances) was carefully checked. Cross element covariances were found to be of utmost importance

Positive Scattering Cross Sections using Constrained Least Squares

International Nuclear Information System (INIS)

Dahl, J.A.; Ganapol, B.D.; Morel, J.E.

1999-01-01

A method which creates a positive Legendre expansion from truncated Legendre cross section libraries is presented. The cross section moments of order two and greater are modified by a constrained least squares algorithm, subject to the constraints that the zeroth and first moments remain constant, and that the standard discrete ordinate scattering matrix is positive. A method using the maximum entropy representation of the cross section which reduces the error of these modified moments is also presented. These methods are implemented in PARTISN, and numerical results from a transport calculation using highly anisotropic scattering cross sections with the exponential discontinuous spatial scheme is presented

A modified Generalized Least Squares method for large scale nuclear data evaluation

Energy Technology Data Exchange (ETDEWEB)

Schnabel, Georg [Irfu, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette (France); Atominstitut, TU Wien, Vienna (Austria); Leeb, Helmut [Atominstitut, TU Wien, Vienna (Austria)

2017-01-01

Nuclear data evaluation aims to provide estimates and uncertainties in the form of covariance matrices of cross sections and related quantities. Many practitioners use the Generalized Least Squares (GLS) formulas to combine experimental data and results of model calculations in order to determine reliable estimates and covariance matrices. A prerequisite to apply the GLS formulas is the construction of a prior covariance matrix for the observables from a set of model calculations. Modern nuclear model codes are able to provide predictions for a large number of observables. However, the inclusion of all observables may lead to a prior covariance matrix of intractable size. Therefore, we introduce mathematically equivalent versions of the GLS formulas to avoid the construction of the prior covariance matrix. Experimental data can be incrementally incorporated into the evaluation process, hence there is no upper limit on their amount. We demonstrate the modified GLS method in a tentative evaluation involving about three million observables using the code TALYS. The revised scheme is well suited as building block of a database application providing evaluated nuclear data. Updating with new experimental data is feasible and users can query estimates and correlations of arbitrary subsets of the observables stored in the database.

Least-squares finite-element method for shallow-water equations with source terms

Institute of Scientific and Technical Information of China (English)

Shin-Jye Liang; Tai-Wen Hsu

2009-01-01

Numerical solution of shallow-water equations (SWE) has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include: the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.

A Precise Lane Detection Algorithm Based on Top View Image Transformation and Least-Square Approaches

Directory of Open Access Journals (Sweden)

Byambaa Dorj

2016-01-01

Full Text Available The next promising key issue of the automobile development is a self-driving technique. One of the challenges for intelligent self-driving includes a lane-detecting and lane-keeping capability for advanced driver assistance systems. This paper introduces an efficient and lane detection method designed based on top view image transformation that converts an image from a front view to a top view space. After the top view image transformation, a Hough transformation technique is integrated by using a parabolic model of a curved lane in order to estimate a parametric model of the lane in the top view space. The parameters of the parabolic model are estimated by utilizing a least-square approach. The experimental results show that the newly proposed lane detection method with the top view transformation is very effective in estimating a sharp and curved lane leading to a precise self-driving capability.

Least-squares reverse time migration of marine data with frequency-selection encoding

KAUST Repository

Dai, Wei; Huang, Yunsong; Schuster, Gerard T.

2013-01-01

The phase-encoding technique can sometimes increase the efficiency of the least-squares reverse time migration (LSRTM) by more than one order of magnitude. However, traditional random encoding functions require all the encoded shots to share

Handbook of Partial Least Squares Concepts, Methods and Applications

CERN Document Server

Vinzi, Vincenzo Esposito; Henseler, Jörg

2010-01-01

This handbook provides a comprehensive overview of Partial Least Squares (PLS) methods with specific reference to their use in marketing and with a discussion of the directions of current research and perspectives. It covers the broad area of PLS methods, from regression to structural equation modeling applications, software and interpretation of results. The handbook serves both as an introduction for those without prior knowledge of PLS and as a comprehensive reference for researchers and practitioners interested in the most recent advances in PLS methodology.

Robust design optimization using the price of robustness, robust least squares and regularization methods

Science.gov (United States)

Bukhari, Hassan J.

2017-12-01

In this paper a framework for robust optimization of mechanical design problems and process systems that have parametric uncertainty is presented using three different approaches. Robust optimization problems are formulated so that the optimal solution is robust which means it is minimally sensitive to any perturbations in parameters. The first method uses the price of robustness approach which assumes the uncertain parameters to be symmetric and bounded. The robustness for the design can be controlled by limiting the parameters that can perturb.The second method uses the robust least squares method to determine the optimal parameters when data itself is subjected to perturbations instead of the parameters. The last method manages uncertainty by restricting the perturbation on parameters to improve sensitivity similar to Tikhonov regularization. The methods are implemented on two sets of problems; one linear and the other non-linear. This methodology will be compared with a prior method using multiple Monte Carlo simulation runs which shows that the approach being presented in this paper results in better performance.

On the use of a penalized least squares method to process kinematic full-field measurements

International Nuclear Information System (INIS)

Moulart, Raphaël; Rotinat, René

2014-01-01

This work is aimed at exploring the performances of an alternative procedure to smooth and differentiate full-field displacement measurements. After recalling the strategies currently used by the experimental mechanics community, a short overview of the available smoothing algorithms is drawn up and the requirements that such an algorithm has to fulfil to be applicable to process kinematic measurements are listed. A comparative study of the chosen algorithm is performed including the 2D penalized least squares method and two other commonly implemented strategies. The results obtained by penalized least squares are comparable in terms of quality to those produced by the two other algorithms, while the penalized least squares method appears to be the fastest and the most flexible. Unlike both the other considered methods, it is possible with penalized least squares to automatically choose the parameter governing the amount of smoothing to apply. Unfortunately, it appears that this automation is not suitable for the proposed application since it does not lead to optimal strain maps. Finally, it is possible with this technique to perform the derivation to obtain strain maps before smoothing them (while the smoothing is normally applied to displacement maps before the differentiation), which can lead in some cases to a more effective reconstruction of the strain fields. (paper)

Partial Least Square with Savitzky Golay Derivative in Predicting Blood Hemoglobin Using Near Infrared Spectrum

Directory of Open Access Journals (Sweden)

Mohd Idrus Mohd Nazrul Effendy

2018-01-01

Full Text Available Near infrared spectroscopy (NIRS is a reliable technique that widely used in medical fields. Partial least square was developed to predict blood hemoglobin concentration using NIRS. The aims of this paper are (i to develop predictive model for near infrared spectroscopic analysis in blood hemoglobin prediction, (ii to establish relationship between blood hemoglobin and near infrared spectrum using a predictive model, (iii to evaluate the predictive accuracy of a predictive model based on root mean squared error (RMSE and coefficient of determination rp2. Partial least square with first order Savitzky Golay (SG derivative preprocessing (PLS-SGd1 showed the higher performance of predictions with RMSE = 0.7965 and rp2= 0.9206 in K-fold cross validation. Optimum number of latent variable (LV and frame length (f were 32 and 27 nm, respectively. These findings suggest that the relationship between blood hemoglobin and near infrared spectrum is strong, and the partial least square with first order SG derivative is able to predict the blood hemoglobin using near infrared spectral data.

The Short-Term Power Load Forecasting Based on Sperm Whale Algorithm and Wavelet Least Square Support Vector Machine with DWT-IR for Feature Selection

Directory of Open Access Journals (Sweden)

Jin-peng Liu

2017-07-01

Full Text Available Short-term power load forecasting is an important basis for the operation of integrated energy system, and the accuracy of load forecasting directly affects the economy of system operation. To improve the forecasting accuracy, this paper proposes a load forecasting system based on wavelet least square support vector machine and sperm whale algorithm. Firstly, the methods of discrete wavelet transform and inconsistency rate model (DWT-IR are used to select the optimal features, which aims to reduce the redundancy of input vectors. Secondly, the kernel function of least square support vector machine LSSVM is replaced by wavelet kernel function for improving the nonlinear mapping ability of LSSVM. Lastly, the parameters of W-LSSVM are optimized by sperm whale algorithm, and the short-term load forecasting method of W-LSSVM-SWA is established. Additionally, the example verification results show that the proposed model outperforms other alternative methods and has a strong effectiveness and feasibility in short-term power load forecasting.

Improved prediction of drug-target interactions using regularized least squares integrating with kernel fusion technique

Energy Technology Data Exchange (ETDEWEB)

Hao, Ming; Wang, Yanli, E-mail: ywang@ncbi.nlm.nih.gov; Bryant, Stephen H., E-mail: bryant@ncbi.nlm.nih.gov

2016-02-25

Identification of drug-target interactions (DTI) is a central task in drug discovery processes. In this work, a simple but effective regularized least squares integrating with nonlinear kernel fusion (RLS-KF) algorithm is proposed to perform DTI predictions. Using benchmark DTI datasets, our proposed algorithm achieves the state-of-the-art results with area under precision–recall curve (AUPR) of 0.915, 0.925, 0.853 and 0.909 for enzymes, ion channels (IC), G protein-coupled receptors (GPCR) and nuclear receptors (NR) based on 10 fold cross-validation. The performance can further be improved by using a recalculated kernel matrix, especially for the small set of nuclear receptors with AUPR of 0.945. Importantly, most of the top ranked interaction predictions can be validated by experimental data reported in the literature, bioassay results in the PubChem BioAssay database, as well as other previous studies. Our analysis suggests that the proposed RLS-KF is helpful for studying DTI, drug repositioning as well as polypharmacology, and may help to accelerate drug discovery by identifying novel drug targets. - Graphical abstract: Flowchart of the proposed RLS-KF algorithm for drug-target interaction predictions. - Highlights: • A nonlinear kernel fusion algorithm is proposed to perform drug-target interaction predictions. • Performance can further be improved by using the recalculated kernel. • Top predictions can be validated by experimental data.

Improved prediction of drug-target interactions using regularized least squares integrating with kernel fusion technique

International Nuclear Information System (INIS)

Hao, Ming; Wang, Yanli; Bryant, Stephen H.

2016-01-01

Identification of drug-target interactions (DTI) is a central task in drug discovery processes. In this work, a simple but effective regularized least squares integrating with nonlinear kernel fusion (RLS-KF) algorithm is proposed to perform DTI predictions. Using benchmark DTI datasets, our proposed algorithm achieves the state-of-the-art results with area under precision–recall curve (AUPR) of 0.915, 0.925, 0.853 and 0.909 for enzymes, ion channels (IC), G protein-coupled receptors (GPCR) and nuclear receptors (NR) based on 10 fold cross-validation. The performance can further be improved by using a recalculated kernel matrix, especially for the small set of nuclear receptors with AUPR of 0.945. Importantly, most of the top ranked interaction predictions can be validated by experimental data reported in the literature, bioassay results in the PubChem BioAssay database, as well as other previous studies. Our analysis suggests that the proposed RLS-KF is helpful for studying DTI, drug repositioning as well as polypharmacology, and may help to accelerate drug discovery by identifying novel drug targets. - Graphical abstract: Flowchart of the proposed RLS-KF algorithm for drug-target interaction predictions. - Highlights: • A nonlinear kernel fusion algorithm is proposed to perform drug-target interaction predictions. • Performance can further be improved by using the recalculated kernel. • Top predictions can be validated by experimental data.

ANYOLS, Least Square Fit by Stepwise Regression

International Nuclear Information System (INIS)

Atwoods, C.L.; Mathews, S.

1986-01-01

Description of program or function: ANYOLS is a stepwise program which fits data using ordinary or weighted least squares. Variables are selected for the model in a stepwise way based on a user- specified input criterion or a user-written subroutine. The order in which variables are entered can be influenced by user-defined forcing priorities. Instead of stepwise selection, ANYOLS can try all possible combinations of any desired subset of the variables. Automatic output for the final model in a stepwise search includes plots of the residuals, 'studentized' residuals, and leverages; if the model is not too large, the output also includes partial regression and partial leverage plots. A data set may be re-used so that several selection criteria can be tried. Flexibility is increased by allowing the substitution of user-written subroutines for several default subroutines

Least Squares Inference on Integrated Volatility and the Relationship between Efficient Prices and Noise

DEFF Research Database (Denmark)

Nolte, Ingmar; Voev, Valeri

The expected value of sums of squared intraday returns (realized variance) gives rise to a least squares regression which adapts itself to the assumptions of the noise process and allows for a joint inference on integrated volatility (IV), noise moments and price-noise relations. In the iid noise...

The output least-squares approach to estimating Lamé moduli

Science.gov (United States)

Gockenbach, Mark S.

2007-12-01

The Lamé moduli of a heterogeneous, isotropic, planar membrane can be estimated by observing the displacement of the membrane under a known edge traction, and choosing estimates of the moduli that best predict the observed displacement under a finite-element simulation. This algorithm converges to the exact moduli given pointwise measurements of the displacement on an increasingly fine mesh. The error estimates that prove this convergence also show the instability of the inverse problem.

Preprocessing in Matlab Inconsistent Linear System for a Meaningful Least Squares Solution

Science.gov (United States)

Sen, Symal K.; Shaykhian, Gholam Ali

2011-01-01

Mathematical models of many physical/statistical problems are systems of linear equations Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the . minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

A least squares calculational method: application to e±-H elastic scattering

International Nuclear Information System (INIS)

Das, J.N.; Chakraborty, S.

1989-01-01

The least squares calcualtional method proposed by Das has been applied for the e ± -H elastic scattering problems for intermediate energies. Some important conclusions are made on the basis of the calculation. (author). 7 refs ., 2 tabs

Regularized Partial Least Squares with an Application to NMR Spectroscopy

OpenAIRE

Allen, Genevera I.; Peterson, Christine; Vannucci, Marina; Maletic-Savatic, Mirjana

2012-01-01

High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension reduction techniques in the context of supervised data analysis. We introduce a framework for Regularized PLS by solving a relaxation of the SIMPLS optimization problem with penalties on the PLS loadings vectors. Our approach enjoys many advantages including flexi...

Multisource Least-squares Reverse Time Migration

KAUST Repository

Dai, Wei

2012-12-01

Least-squares migration has been shown to be able to produce high quality migration images, but its computational cost is considered to be too high for practical imaging. In this dissertation, a multisource least-squares reverse time migration algorithm (LSRTM) is proposed to increase by up to 10 times the computational efficiency by utilizing the blended sources processing technique. There are three main chapters in this dissertation. In Chapter 2, the multisource LSRTM algorithm is implemented with random time-shift and random source polarity encoding functions. Numerical tests on the 2D HESS VTI data show that the multisource LSRTM algorithm suppresses migration artifacts, balances the amplitudes, improves image resolution, and reduces crosstalk noise associated with the blended shot gathers. For this example, multisource LSRTM is about three times faster than the conventional RTM method. For the 3D example of the SEG/EAGE salt model, with comparable computational cost, multisource LSRTM produces images with more accurate amplitudes, better spatial resolution, and fewer migration artifacts compared to conventional RTM. The empirical results suggest that the multisource LSRTM can produce more accurate reflectivity images than conventional RTM does with similar or less computational cost. The caveat is that LSRTM image is sensitive to large errors in the migration velocity model. In Chapter 3, the multisource LSRTM algorithm is implemented with frequency selection encoding strategy and applied to marine streamer data, for which traditional random encoding functions are not applicable. The frequency-selection encoding functions are delta functions in the frequency domain, so that all the encoded shots have unique non-overlapping frequency content. Therefore, the receivers can distinguish the wavefield from each shot according to the frequencies. With the frequency-selection encoding method, the computational efficiency of LSRTM is increased so that its cost is

Quantitative analysis of Ni2+/Ni3+ in Li[NixMnyCoz]O2 cathode materials: Non-linear least-squares fitting of XPS spectra

Science.gov (United States)

Fu, Zewei; Hu, Juntao; Hu, Wenlong; Yang, Shiyu; Luo, Yunfeng

2018-05-01

Quantitative analysis of Ni2+/Ni3+ using X-ray photoelectron spectroscopy (XPS) is important for evaluating the crystal structure and electrochemical performance of Lithium-nickel-cobalt-manganese oxide (Li[NixMnyCoz]O2, NMC). However, quantitative analysis based on Gaussian/Lorentzian (G/L) peak fitting suffers from the challenges of reproducibility and effectiveness. In this study, the Ni2+ and Ni3+ standard samples and a series of NMC samples with different Ni doping levels were synthesized. The Ni2+/Ni3+ ratios in NMC were quantitatively analyzed by non-linear least-squares fitting (NLLSF). Two Ni 2p overall spectra of synthesized Li [Ni0.33Mn0.33Co0.33]O2(NMC111) and bulk LiNiO2 were used as the Ni2+ and Ni3+ reference standards. Compared to G/L peak fitting, the fitting parameters required no adjustment, meaning that the spectral fitting process was free from operator dependence and the reproducibility was improved. Comparison of residual standard deviation (STD) showed that the fitting quality of NLLSF was superior to that of G/L peaks fitting. Overall, these findings confirmed the reproducibility and effectiveness of the NLLSF method in XPS quantitative analysis of Ni2+/Ni3+ ratio in Li[NixMnyCoz]O2 cathode materials.

Ordinary Least Squares and Quantile Regression: An Inquiry-Based Learning Approach to a Comparison of Regression Methods

Science.gov (United States)

Helmreich, James E.; Krog, K. Peter

2018-01-01

We present a short, inquiry-based learning course on concepts and methods underlying ordinary least squares (OLS), least absolute deviation (LAD), and quantile regression (QR). Students investigate squared, absolute, and weighted absolute distance functions (metrics) as location measures. Using differential calculus and properties of convex…

Calculating the parameters of experimental data Gauss distribution using the least square fit method and evaluation of their accuracy

International Nuclear Information System (INIS)

Guseva, E.V.; Peregudov, V.N.

1982-01-01

The FITGAV program for calculation of parameters of the Gauss curve describing experimental data is considered. The calculations are based on the least square fit method. The estimations of errors in the parameter determination as a function of experimental data sample volume and their statistical significance are obtained. The curve fit using 100 points occupies less than 1 s at the SM-4 type computer

DEM4-26, Least Square Fit for IBM PC by Deming Method

International Nuclear Information System (INIS)

Rinard, P.M.; Bosler, G.E.

1989-01-01

1 - Description of program or function: DEM4-26 is a generalized least square fitting program based on Deming's method. Functions built into the program for fitting include linear, quadratic, cubic, power, Howard's, exponential, and Gaussian; others can easily be added. The program has the following capabilities: (1) entry, editing, and saving of data; (2) fitting of any of the built-in functions or of a user-supplied function; (3) plotting the data and fitted function on the display screen, with error limits if requested, and with the option of copying the plot to the printer; (4) interpolation of x or y values from the fitted curve with error estimates based on error limits selected by the user; and (5) plotting the residuals between the y data values and the fitted curve, with the option copying the plot to the printer. 2 - Method of solution: Deming's method

A rigid-body least-squares program with angular and translation scan facilities

CERN Document Server

Kutschabsky, L

1981-01-01

The described computer program, written in CERN Fortran, is designed to enlarge the convergence radius of the rigid-body least-squares method by allowing a stepwise change of the angular and/or translational parameters within a chosen range. (6 refs).

Harmonic tidal analysis at a few stations using the least squares method

Digital Repository Service at National Institute of Oceanography (India)

Fernandes, A.A.; Das, V.K.; Bahulayan, N.

Using the least squares method, harmonic analysis has been performed on hourly water level records of 29 days at several stations depicting different types of non-tidal noise. For a tidal record at Mormugao, which was free from storm surges (low...

A high order compact least-squares reconstructed discontinuous Galerkin method for the steady-state compressible flows on hybrid grids

Science.gov (United States)

Cheng, Jian; Zhang, Fan; Liu, Tiegang

2018-06-01

In this paper, a class of new high order reconstructed DG (rDG) methods based on the compact least-squares (CLS) reconstruction [23,24] is developed for simulating the two dimensional steady-state compressible flows on hybrid grids. The proposed method combines the advantages of the DG discretization with the flexibility of the compact least-squares reconstruction, which exhibits its superior potential in enhancing the level of accuracy and reducing the computational cost compared to the underlying DG methods with respect to the same number of degrees of freedom. To be specific, a third-order compact least-squares rDG(p1p2) method and a fourth-order compact least-squares rDG(p2p3) method are developed and investigated in this work. In this compact least-squares rDG method, the low order degrees of freedom are evolved through the underlying DG(p1) method and DG(p2) method, respectively, while the high order degrees of freedom are reconstructed through the compact least-squares reconstruction, in which the constitutive relations are built by requiring the reconstructed polynomial and its spatial derivatives on the target cell to conserve the cell averages and the corresponding spatial derivatives on the face-neighboring cells. The large sparse linear system resulted by the compact least-squares reconstruction can be solved relatively efficient when it is coupled with the temporal discretization in the steady-state simulations. A number of test cases are presented to assess the performance of the high order compact least-squares rDG methods, which demonstrates their potential to be an alternative approach for the high order numerical simulations of steady-state compressible flows.

Iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) imaging of multiple myeloma: initial clinical efficiency results

International Nuclear Information System (INIS)

Takasu, Miyuki; Tani, Chihiro; Sakoda, Yasuko; Ishikawa, Miho; Tanitame, Keizo; Date, Shuji; Akiyama, Yuji; Awai, Kazuo; Sakai, Akira; Asaoku, Hideki; Kajima, Toshio

2012-01-01

To evaluate the effectiveness of the iterative decomposition of water and fat with echo asymmetric and least-squares estimation (IDEAL) MRI to quantify tumour infiltration into the lumbar vertebrae in myeloma patients without visible focal lesions. The lumbar spine was examined with 3 T MRI in 24 patients with multiple myeloma and in 26 controls. The fat-signal fraction was calculated as the mean value from three vertebral bodies. A post hoc test was used to compare the fat-signal fraction in controls and patients with monoclonal gammopathy of undetermined significance (MGUS), asymptomatic myeloma or symptomatic myeloma. Differences were considered significant at P 2 -microglobulin-to-albumin ratio were entered into the discriminant analysis. Fat-signal fractions were significantly lower in patients with symptomatic myelomas (43.9 ±19.7%, P 2 -microglobulin-to-albumin ratio facilitated discrimination of symptomatic myeloma from non-symptomatic myeloma in patients without focal bone lesions. circle A new magnetic resonance technique (IDEAL) offers new insights in multiple myeloma. (orig.)

Time-domain least-squares migration using the Gaussian beam summation method

Science.gov (United States)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-04-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modeling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modeling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a preconditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

A Hybrid Least Square Support Vector Machine Model with Parameters Optimization for Stock Forecasting

Directory of Open Access Journals (Sweden)

Jian Chai

2015-01-01

Full Text Available This paper proposes an EMD-LSSVM (empirical mode decomposition least squares support vector machine model to analyze the CSI 300 index. A WD-LSSVM (wavelet denoising least squares support machine is also proposed as a benchmark to compare with the performance of EMD-LSSVM. Since parameters selection is vital to the performance of the model, different optimization methods are used, including simplex, GS (grid search, PSO (particle swarm optimization, and GA (genetic algorithm. Experimental results show that the EMD-LSSVM model with GS algorithm outperforms other methods in predicting stock market movement direction.

Updating QR factorization procedure for solution of linear least squares problem with equality constraints.

Science.gov (United States)

Zeb, Salman; Yousaf, Muhammad

2017-01-01

In this article, we present a QR updating procedure as a solution approach for linear least squares problem with equality constraints. We reduce the constrained problem to unconstrained linear least squares and partition it into a small subproblem. The QR factorization of the subproblem is calculated and then we apply updating techniques to its upper triangular factor R to obtain its solution. We carry out the error analysis of the proposed algorithm to show that it is backward stable. We also illustrate the implementation and accuracy of the proposed algorithm by providing some numerical experiments with particular emphasis on dense problems.

Least square regularized regression in sum space.

Science.gov (United States)

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.

Prediction of toxicity of nitrobenzenes using ab initio and least squares support vector machines

International Nuclear Information System (INIS)

Niazi, Ali; Jameh-Bozorghi, Saeed; Nori-Shargh, Davood

2008-01-01

A quantitative structure-property relationship (QSPR) study is suggested for the prediction of toxicity (IGC 50 ) of nitrobenzenes. Ab initio theory was used to calculate some quantum chemical descriptors including electrostatic potentials and local charges at each atom, HOMO and LUMO energies, etc. Modeling of the IGC 50 of nitrobenzenes as a function of molecular structures was established by means of the least squares support vector machines (LS-SVM). This model was applied for the prediction of the toxicity (IGC 50 ) of nitrobenzenes, which were not in the modeling procedure. The resulted model showed high prediction ability with root mean square error of prediction of 0.0049 for LS-SVM. Results have shown that the introduction of LS-SVM for quantum chemical descriptors drastically enhances the ability of prediction in QSAR studies superior to multiple linear regression and partial least squares

The least weighted squares I. The asymptotic linearity of normal equations

Czech Academy of Sciences Publication Activity Database

Víšek, Jan Ámos

2002-01-01

Roč. 9, č. 15 (2002), s. 31-58 ISSN 1212-074X R&D Projects: GA AV ČR KSK1019101 Grant - others:GA UK(CZ) 255/2002/A EK /FSV Institutional research plan: CEZ:AV0Z1075907 Keywords : the least weighted squares * robust regression * asymptotic normality and representation Subject RIV: BA - General Mathematics

A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity

International Nuclear Information System (INIS)

Aziz, A.; Bouaziz, M.N.

2011-01-01

Highlights: → Analytical solutions for a rectangular fin with temperature dependent heat generation and thermal conductivity. → Graphs give temperature distributions and fin efficiency. → Comparison of analytical and numerical solutions. → Method of least squares used for the analytical solutions. - Abstract: Approximate but highly accurate solutions for the temperature distribution, fin efficiency, and optimum fin parameter for a constant area longitudinal fin with temperature dependent internal heat generation and thermal conductivity are derived analytically. The method of least squares recently used by the authors is applied to treat the two nonlinearities, one associated with the temperature dependent internal heat generation and the other due to temperature dependent thermal conductivity. The solution is built from the classical solution for a fin with uniform internal heat generation and constant thermal conductivity. The results are presented graphically and compared with the direct numerical solutions. The analytical solutions retain their accuracy (within 1% of the numerical solution) even when there is a 60% increase in thermal conductivity and internal heat generation at the base temperature from their corresponding values at the sink temperature. The present solution is simple (involves hyperbolic functions only) compared with the fairly complex approximate solutions based on the homotopy perturbation method, variational iteration method, and the double series regular perturbation method and offers high accuracy. The simple analytical expressions for the temperature distribution, the fin efficiency and the optimum fin parameter are convenient for use by engineers dealing with the design and analysis of heat generating fins operating with a large temperature difference between the base and the environment.

Multilevel weighted least squares polynomial approximation

KAUST Repository

Haji-Ali, Abdul-Lateef

2017-06-30

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.

Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems

Czech Academy of Sciences Publication Activity Database

Morikuni, Keiichi; Hayami, K.

2015-01-01

Roč. 36, č. 1 (2015), s. 225-250 ISSN 0895-4798 Institutional support: RVO:67985807 Keywords : least squares problem * iterative methods * preconditioner * inner-outer iteration * GMRES method * stationary iterative method * rank-deficient problem Subject RIV: BA - General Mathematics Impact factor: 1.883, year: 2015

Least-squares approximation of an improper correlation matrix by a proper one

NARCIS (Netherlands)

Knol, Dirk L.; ten Berge, Jos M.F.

1989-01-01

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based upon a solution for Mosier's oblique Procrustes rotation problem offered by ten Berge and Nevels. A necessary and

Weighted Least Squares Techniques for Improved Received Signal Strength Based Localization

Directory of Open Access Journals (Sweden)

José R. Casar

2011-09-01

Full Text Available The practical deployment of wireless positioning systems requires minimizing the calibration procedures while improving the location estimation accuracy. Received Signal Strength localization techniques using propagation channel models are the simplest alternative, but they are usually designed under the assumption that the radio propagation model is to be perfectly characterized a priori. In practice, this assumption does not hold and the localization results are affected by the inaccuracies of the theoretical, roughly calibrated or just imperfect channel models used to compute location. In this paper, we propose the use of weighted multilateration techniques to gain robustness with respect to these inaccuracies, reducing the dependency of having an optimal channel model. In particular, we propose two weighted least squares techniques based on the standard hyperbolic and circular positioning algorithms that specifically consider the accuracies of the different measurements to obtain a better estimation of the position. These techniques are compared to the standard hyperbolic and circular positioning techniques through both numerical simulations and an exhaustive set of real experiments on different types of wireless networks (a wireless sensor network, a WiFi network and a Bluetooth network. The algorithms not only produce better localization results with a very limited overhead in terms of computational cost but also achieve a greater robustness to inaccuracies in channel modeling.

Multi-Gaussian fitting for pulse waveform using Weighted Least Squares and multi-criteria decision making method.

Science.gov (United States)

Wang, Lu; Xu, Lisheng; Feng, Shuting; Meng, Max Q-H; Wang, Kuanquan

2013-11-01

Analysis of pulse waveform is a low cost, non-invasive method for obtaining vital information related to the conditions of the cardiovascular system. In recent years, different Pulse Decomposition Analysis (PDA) methods have been applied to disclose the pathological mechanisms of the pulse waveform. All these methods decompose single-period pulse waveform into a constant number (such as 3, 4 or 5) of individual waves. Furthermore, those methods do not pay much attention to the estimation error of the key points in the pulse waveform. The estimation of human vascular conditions depends on the key points' positions of pulse wave. In this paper, we propose a Multi-Gaussian (MG) model to fit real pulse waveforms using an adaptive number (4 or 5 in our study) of Gaussian waves. The unknown parameters in the MG model are estimated by the Weighted Least Squares (WLS) method and the optimized weight values corresponding to different sampling points are selected by using the Multi-Criteria Decision Making (MCDM) method. Performance of the MG model and the WLS method has been evaluated by fitting 150 real pulse waveforms of five different types. The resulting Normalized Root Mean Square Error (NRMSE) was less than 2.0% and the estimation accuracy for the key points was satisfactory, demonstrating that our proposed method is effective in compressing, synthesizing and analyzing pulse waveforms. Copyright © 2013 Elsevier Ltd. All rights reserved.

Efficient design of gain-flattened multi-pump Raman fiber amplifiers using least squares support vector regression

Science.gov (United States)

Chen, Jing; Qiu, Xiaojie; Yin, Cunyi; Jiang, Hao

2018-02-01

An efficient method to design the broadband gain-flattened Raman fiber amplifier with multiple pumps is proposed based on least squares support vector regression (LS-SVR). A multi-input multi-output LS-SVR model is introduced to replace the complicated solving process of the nonlinear coupled Raman amplification equation. The proposed approach contains two stages: offline training stage and online optimization stage. During the offline stage, the LS-SVR model is trained. Owing to the good generalization capability of LS-SVR, the net gain spectrum can be directly and accurately obtained when inputting any combination of the pump wavelength and power to the well-trained model. During the online stage, we incorporate the LS-SVR model into the particle swarm optimization algorithm to find the optimal pump configuration. The design results demonstrate that the proposed method greatly shortens the computation time and enhances the efficiency of the pump parameter optimization for Raman fiber amplifier design.

On Solution of Total Least Squares Problems with Multiple Right-hand Sides

Czech Academy of Sciences Publication Activity Database

Hnětynková, I.; Plešinger, Martin; Strakoš, Zdeněk

2008-01-01

Roč. 8, č. 1 (2008), s. 10815-10816 ISSN 1617-7061 R&D Projects: GA AV ČR IAA100300802 Institutional research plan: CEZ:AV0Z10300504 Keywords : total least squares problem * multiple right-hand sides * linear approximation problem Subject RIV: BA - General Mathematics

Method for exploiting bias in factor analysis using constrained alternating least squares algorithms

Science.gov (United States)

Keenan, Michael R.

2008-12-30

Bias plays an important role in factor analysis and is often implicitly made use of, for example, to constrain solutions to factors that conform to physical reality. However, when components are collinear, a large range of solutions may exist that satisfy the basic constraints and fit the data equally well. In such cases, the introduction of mathematical bias through the application of constraints may select solutions that are less than optimal. The biased alternating least squares algorithm of the present invention can offset mathematical bias introduced by constraints in the standard alternating least squares analysis to achieve factor solutions that are most consistent with physical reality. In addition, these methods can be used to explicitly exploit bias to provide alternative views and provide additional insights into spectral data sets.

Least-squares migration of multisource data with a deblurring filter

KAUST Repository

Dai, Wei; Wang, Xin; Schuster, Gerard T.

2011-01-01

Least-squares migration (LSM) has been shown to be able to produce high-quality migration images, but its computational cost is considered to be too high for practical imaging. We have developed a multisource least-squares migration algorithm (MLSM) to increase the computational efficiency by using the blended sources processing technique. To expedite convergence, a multisource deblurring filter is used as a preconditioner to reduce the data residual. This MLSM algorithm is applicable with Kirchhoff migration, wave-equation migration, or reverse time migration, and the gain in computational efficiency depends on the choice of migration method. Numerical results with Kirchhoff LSM on the 2D SEG/EAGE salt model show that an accurate image is obtained by migrating a supergather of 320 phase-encoded shots. When the encoding functions are the same for every iteration, the input/output cost of MLSM is reduced by 320 times. Empirical results show that the crosstalk noise introduced by blended sources is more effectively reduced when the encoding functions are changed at every iteration. The analysis of signal-to-noise ratio (S/N) suggests that not too many iterations are needed to enhance the S/N to an acceptable level. Therefore, when implemented with wave-equation migration or reverse time migration methods, the MLSM algorithm can be more efficient than the conventional migration method. © 2011 Society of Exploration Geophysicists.

Least-squares migration of multisource data with a deblurring filter

KAUST Repository

Dai, Wei

2011-09-01

Least-squares migration (LSM) has been shown to be able to produce high-quality migration images, but its computational cost is considered to be too high for practical imaging. We have developed a multisource least-squares migration algorithm (MLSM) to increase the computational efficiency by using the blended sources processing technique. To expedite convergence, a multisource deblurring filter is used as a preconditioner to reduce the data residual. This MLSM algorithm is applicable with Kirchhoff migration, wave-equation migration, or reverse time migration, and the gain in computational efficiency depends on the choice of migration method. Numerical results with Kirchhoff LSM on the 2D SEG/EAGE salt model show that an accurate image is obtained by migrating a supergather of 320 phase-encoded shots. When the encoding functions are the same for every iteration, the input/output cost of MLSM is reduced by 320 times. Empirical results show that the crosstalk noise introduced by blended sources is more effectively reduced when the encoding functions are changed at every iteration. The analysis of signal-to-noise ratio (S/N) suggests that not too many iterations are needed to enhance the S/N to an acceptable level. Therefore, when implemented with wave-equation migration or reverse time migration methods, the MLSM algorithm can be more efficient than the conventional migration method. © 2011 Society of Exploration Geophysicists.

Vis-NIR spectrometric determination of Brix and sucrose in sugar production samples using kernel partial least squares with interval selection based on the successive projections algorithm.

Science.gov (United States)

de Almeida, Valber Elias; de Araújo Gomes, Adriano; de Sousa Fernandes, David Douglas; Goicoechea, Héctor Casimiro; Galvão, Roberto Kawakami Harrop; Araújo, Mario Cesar Ugulino

2018-05-01

This paper proposes a new variable selection method for nonlinear multivariate calibration, combining the Successive Projections Algorithm for interval selection (iSPA) with the Kernel Partial Least Squares (Kernel-PLS) modelling technique. The proposed iSPA-Kernel-PLS algorithm is employed in a case study involving a Vis-NIR spectrometric dataset with complex nonlinear features. The analytical problem consists of determining Brix and sucrose content in samples from a sugar production system, on the basis of transflectance spectra. As compared to full-spectrum Kernel-PLS, the iSPA-Kernel-PLS models involve a smaller number of variables and display statistically significant superiority in terms of accuracy and/or bias in the predictions. Published by Elsevier B.V.

Mitigation of defocusing by statics and near-surface velocity errors by interferometric least-squares migration

KAUST Repository

Sinha, Mrinal

2015-08-19

We propose an interferometric least-squares migration method that can significantly reduce migration artifacts due to statics and errors in the near-surface velocity model. We first choose a reference reflector whose topography is well known from the, e.g., well logs. Reflections from this reference layer are correlated with the traces associated with reflections from deeper interfaces to get crosscorrelograms. These crosscorrelograms are then migrated using interferometric least-squares migration (ILSM). In this way statics and velocity errors at the near surface are largely eliminated for the examples in our paper.

Least-Squares Approximation of an Improper Correlation Matrix by a Proper One.

Science.gov (United States)

Knol, Dirk L.; ten Berge, Jos M. F.

1989-01-01

An algorithm, based on a solution for C. I. Mosier's oblique Procrustes rotation problem, is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. Results are of interest for missing value and tetrachoric correlation, indefinite matrix correlation, and constrained…

A Fortran 77 computer code for damped least-squares inversion of Slingram electromagnetic anomalies over thin tabular conductors

Science.gov (United States)

Dondurur, Derman; Sarı, Coşkun

2004-07-01

A FORTRAN 77 computer code is presented that permits the inversion of Slingram electromagnetic anomalies to an optimal conductor model. Damped least-squares inversion algorithm is used to estimate the anomalous body parameters, e.g. depth, dip and surface projection point of the target. Iteration progress is controlled by maximum relative error value and iteration continued until a tolerance value was satisfied, while the modification of Marquardt's parameter is controlled by sum of the squared errors value. In order to form the Jacobian matrix, the partial derivatives of theoretical anomaly expression with respect to the parameters being optimised are calculated by numerical differentiation by using first-order forward finite differences. A theoretical and two field anomalies are inserted to test the accuracy and applicability of the present inversion program. Inversion of the field data indicated that depth and the surface projection point parameters of the conductor are estimated correctly, however, considerable discrepancies appeared on the estimated dip angles. It is therefore concluded that the most important factor resulting in the misfit between observed and calculated data is due to the fact that the theory used for computing Slingram anomalies is valid for only thin conductors and this assumption might have caused incorrect dip estimates in the case of wide conductors.

An improved partial least-squares regression method for Raman spectroscopy

Science.gov (United States)

Momenpour Tehran Monfared, Ali; Anis, Hanan

2017-10-01

It is known that the performance of partial least-squares (PLS) regression analysis can be improved using the backward variable selection method (BVSPLS). In this paper, we further improve the BVSPLS based on a novel selection mechanism. The proposed method is based on sorting the weighted regression coefficients, and then the importance of each variable of the sorted list is evaluated using root mean square errors of prediction (RMSEP) criterion in each iteration step. Our Improved BVSPLS (IBVSPLS) method has been applied to leukemia and heparin data sets and led to an improvement in limit of detection of Raman biosensing ranged from 10% to 43% compared to PLS. Our IBVSPLS was also compared to the jack-knifing (simpler) and Genetic Algorithm (more complex) methods. Our method was consistently better than the jack-knifing method and showed either a similar or a better performance compared to the genetic algorithm.

[Main Components of Xinjiang Lavender Essential Oil Determined by Partial Least Squares and Near Infrared Spectroscopy].

Science.gov (United States)

Liao, Xiang; Wang, Qing; Fu, Ji-hong; Tang, Jun

2015-09-01

This work was undertaken to establish a quantitative analysis model which can rapid determinate the content of linalool, linalyl acetate of Xinjiang lavender essential oil. Totally 165 lavender essential oil samples were measured by using near infrared absorption spectrum (NIR), after analyzing the near infrared spectral absorption peaks of all samples, lavender essential oil have abundant chemical information and the interference of random noise may be relatively low on the spectral intervals of 7100~4500 cm(-1). Thus, the PLS models was constructed by using this interval for further analysis. 8 abnormal samples were eliminated. Through the clustering method, 157 lavender essential oil samples were divided into 105 calibration set samples and 52 validation set samples. Gas chromatography mass spectrometry (GC-MS) was used as a tool to determine the content of linalool and linalyl acetate in lavender essential oil. Then the matrix was established with the GC-MS raw data of two compounds in combination with the original NIR data. In order to optimize the model, different pretreatment methods were used to preprocess the raw NIR spectral to contrast the spectral filtering effect, after analysizing the quantitative model results of linalool and linalyl acetate, the root mean square error prediction (RMSEP) of orthogonal signal transformation (OSC) was 0.226, 0.558, spectrally, it was the optimum pretreatment method. In addition, forward interval partial least squares (FiPLS) method was used to exclude the wavelength points which has nothing to do with determination composition or present nonlinear correlation, finally 8 spectral intervals totally 160 wavelength points were obtained as the dataset. Combining the data sets which have optimized by OSC-FiPLS with partial least squares (PLS) to establish a rapid quantitative analysis model for determining the content of linalool and linalyl acetate in Xinjiang lavender essential oil, numbers of hidden variables of two

Stable Parameter Estimation for Autoregressive Equations with Random Coefficients

Directory of Open Access Journals (Sweden)

V. B. Goryainov

2014-01-01

Full Text Available In recent yearsthere has been a growing interest in non-linear time series models. They are more flexible than traditional linear models and allow more adequate description of real data. Among these models a autoregressive model with random coefficients plays an important role. It is widely used in various fields of science and technology, for example, in physics, biology, economics and finance. The model parameters are the mean values of autoregressive coefficients. Their evaluation is the main task of model identification. The basic method of estimation is still the least squares method, which gives good results for Gaussian time series, but it is quite sensitive to even small disturbancesin the assumption of Gaussian observations. In this paper we propose estimates, which generalize the least squares estimate in the sense that the quadratic objective function is replaced by an arbitrary convex and even function. Reasonable choice of objective function allows you to keep the benefits of the least squares estimate and eliminate its shortcomings. In particular, you can make it so that they will be almost as effective as the least squares estimate in the Gaussian case, but almost never loose in accuracy with small deviations of the probability distribution of the observations from the Gaussian distribution.The main result is the proof of consistency and asymptotic normality of the proposed estimates in the particular case of the one-parameter model describing the stationary process with finite variance. Another important result is the finding of the asymptotic relative efficiency of the proposed estimates in relation to the least squares estimate. This allows you to compare the two estimates, depending on the probability distribution of innovation process and of autoregressive coefficients. The results can be used to identify an autoregressive process, especially with nonGaussian nature, and/or of autoregressive processes observed with gross

A wavelet and least square filter based spatial-spectral denoising approach of hyperspectral imagery

Science.gov (United States)

Li, Ting; Chen, Xiao-Mei; Chen, Gang; Xue, Bo; Ni, Guo-Qiang

2009-11-01

Noise reduction is a crucial step in hyperspectral imagery pre-processing. Based on sensor characteristics, the noise of hyperspectral imagery represents in both spatial and spectral domain. However, most prevailing denosing techniques process the imagery in only one specific domain, which have not utilized multi-domain nature of hyperspectral imagery. In this paper, a new spatial-spectral noise reduction algorithm is proposed, which is based on wavelet analysis and least squares filtering techniques. First, in the spatial domain, a new stationary wavelet shrinking algorithm with improved threshold function is utilized to adjust the noise level band-by-band. This new algorithm uses BayesShrink for threshold estimation, and amends the traditional soft-threshold function by adding shape tuning parameters. Comparing with soft or hard threshold function, the improved one, which is first-order derivable and has a smooth transitional region between noise and signal, could save more details of image edge and weaken Pseudo-Gibbs. Then, in the spectral domain, cubic Savitzky-Golay filter based on least squares method is used to remove spectral noise and artificial noise that may have been introduced in during the spatial denoising. Appropriately selecting the filter window width according to prior knowledge, this algorithm has effective performance in smoothing the spectral curve. The performance of the new algorithm is experimented on a set of Hyperion imageries acquired in 2007. The result shows that the new spatial-spectral denoising algorithm provides more significant signal-to-noise-ratio improvement than traditional spatial or spectral method, while saves the local spectral absorption features better.

Q-Least Squares Reverse Time Migration with Viscoacoustic Deblurring Filters

KAUST Repository

Chen, Yuqing; Dutta, Gaurav; Dai, Wei; Schuster, Gerard T.

2017-01-01

Viscoacoustic least-squares reverse time migration (Q-LSRTM) linearly inverts for the subsurface reflectivity model from lossy data. Compared to the conventional migration methods, it can compensate for the amplitude loss in the migrated images because of the strong subsurface attenuation and can produce reflectors that are accurately positioned in depth. However, the adjoint Q propagators used for backward propagating the residual data are also attenuative. Thus, the inverted images from Q-LSRTM are often observed to have lower resolution when compared to the benchmark acoustic LSRTM images from acoustic data. To increase the resolution and accelerate the convergence of Q-LSRTM, we propose using viscoacoustic deblurring filters as a preconditioner for Q-LSRTM. These filters can be estimated by matching a simulated migration image to its reference reflectivity model. Numerical tests on synthetic and field data demonstrate that Q-LSRTM combined with viscoacoustic deblurring filters can produce images with higher resolution and more balanced amplitudes than images from acoustic RTM, acoustic LSRTM and Q-LSRTM when there is strong attenuation in the background medium. The proposed preconditioning method is also shown to improve the convergence rate of Q-LSRTM by more than 30 percent in some cases and significantly compensate for the lossy artifacts in RTM images.

Q-Least Squares Reverse Time Migration with Viscoacoustic Deblurring Filters

KAUST Repository

Chen, Yuqing

2017-08-02

Viscoacoustic least-squares reverse time migration (Q-LSRTM) linearly inverts for the subsurface reflectivity model from lossy data. Compared to the conventional migration methods, it can compensate for the amplitude loss in the migrated images because of the strong subsurface attenuation and can produce reflectors that are accurately positioned in depth. However, the adjoint Q propagators used for backward propagating the residual data are also attenuative. Thus, the inverted images from Q-LSRTM are often observed to have lower resolution when compared to the benchmark acoustic LSRTM images from acoustic data. To increase the resolution and accelerate the convergence of Q-LSRTM, we propose using viscoacoustic deblurring filters as a preconditioner for Q-LSRTM. These filters can be estimated by matching a simulated migration image to its reference reflectivity model. Numerical tests on synthetic and field data demonstrate that Q-LSRTM combined with viscoacoustic deblurring filters can produce images with higher resolution and more balanced amplitudes than images from acoustic RTM, acoustic LSRTM and Q-LSRTM when there is strong attenuation in the background medium. The proposed preconditioning method is also shown to improve the convergence rate of Q-LSRTM by more than 30 percent in some cases and significantly compensate for the lossy artifacts in RTM images.

Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem

Directory of Open Access Journals (Sweden)

Baiyu Wang

2014-01-01

Full Text Available This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.

Space-time coupled spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Pontaza, J.P.; Reddy, J.N.

2004-01-01

We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least-squares

Incoherent dictionary learning for reducing crosstalk noise in least-squares reverse time migration

Science.gov (United States)

Wu, Juan; Bai, Min

2018-05-01

We propose to apply a novel incoherent dictionary learning (IDL) algorithm for regularizing the least-squares inversion in seismic imaging. The IDL is proposed to overcome the drawback of traditional dictionary learning algorithm in losing partial texture information. Firstly, the noisy image is divided into overlapped image patches, and some random patches are extracted for dictionary learning. Then, we apply the IDL technology to minimize the coherency between atoms during dictionary learning. Finally, the sparse representation problem is solved by a sparse coding algorithm, and image is restored by those sparse coefficients. By reducing the correlation among atoms, it is possible to preserve most of the small-scale features in the image while removing much of the long-wavelength noise. The application of the IDL method to regularization of seismic images from least-squares reverse time migration shows successful performance.

Small-kernel, constrained least-squares restoration of sampled image data

Science.gov (United States)

Hazra, Rajeeb; Park, Stephen K.

1992-01-01

Following the work of Park (1989), who extended a derivation of the Wiener filter based on the incomplete discrete/discrete model to a more comprehensive end-to-end continuous/discrete/continuous model, it is shown that a derivation of the constrained least-squares (CLS) filter based on the discrete/discrete model can also be extended to this more comprehensive continuous/discrete/continuous model. This results in an improved CLS restoration filter, which can be efficiently implemented as a small-kernel convolution in the spatial domain.

Error analysis of some Galerkin - least squares methods for the elasticity equations

International Nuclear Information System (INIS)

Franca, L.P.; Stenberg, R.

1989-05-01

We consider the recent technique of stabilizing mixed finite element methods by augmenting the Galerkin formulation with least squares terms calculated separately on each element. The error analysis is performed in a unified manner yielding improved results for some methods introduced earlier. In addition, a new formulation is introduced and analyzed [pt

COMPARISON OF PARTIAL LEAST SQUARES REGRESSION METHOD ALGORITHMS: NIPALS AND PLS-KERNEL AND AN APPLICATION

Directory of Open Access Journals (Sweden)

ELİF BULUT

2013-06-01

Full Text Available Partial Least Squares Regression (PLSR is a multivariate statistical method that consists of partial least squares and multiple linear regression analysis. Explanatory variables, X, having multicollinearity are reduced to components which explain the great amount of covariance between explanatory and response variable. These components are few in number and they don’t have multicollinearity problem. Then multiple linear regression analysis is applied to those components to model the response variable Y. There are various PLSR algorithms. In this study NIPALS and PLS-Kernel algorithms will be studied and illustrated on a real data set.

Fully Modified Narrow-Band Least Squares Estimation of Weak Fractional Cointegration

DEFF Research Database (Denmark)

Nielsen, Morten Ørregaard; Frederiksen, Per

regressors and errors at the zero frequency. We show that in the absence of this condition, the NBLS estimator is asymptotically biased, and also that the bias can be consistently estimated. Consequently, we introduce a fully modi…ed NBLS estimator which eliminates the bias, and indeed enjoys a faster rate...

Establishment of regression dependences. Linear and nonlinear dependences

International Nuclear Information System (INIS)

Onishchenko, A.M.

1994-01-01

The main problems of determination of linear and 19 types of nonlinear regression dependences are completely discussed. It is taken into consideration that total dispersions are the sum of measurement dispersions and parameter variation dispersions themselves. Approaches to all dispersions determination are described. It is shown that the least square fit gives inconsistent estimation for industrial objects and processes. The correction methods by taking into account comparable measurement errors for both variable give an opportunity to obtain consistent estimation for the regression equation parameters. The condition of the correction technique application expediency is given. The technique for determination of nonlinear regression dependences taking into account the dependence form and comparable errors of both variables is described. 6 refs., 1 tab

Stability and square integrability of solutions of nonlinear fourth order differential equations

Directory of Open Access Journals (Sweden)

Moussadek Remili

2016-05-01

Full Text Available The aim of the present paper is to establish a new result, which guarantees the asymptotic stability of zero solution and square integrability of solutions and their derivatives to nonlinear differential equations of fourth order.

Optimization of sequential decisions by least squares Monte Carlo method

DEFF Research Database (Denmark)

Nishijima, Kazuyoshi; Anders, Annett

change adaptation measures, and evacuation of people and assets in the face of an emerging natural hazard event. Focusing on the last example, an efficient solution scheme is proposed by Anders and Nishijima (2011). The proposed solution scheme takes basis in the least squares Monte Carlo method, which...... is proposed by Longstaff and Schwartz (2001) for pricing of American options. The present paper formulates the decision problem in a more general manner and explains how the solution scheme proposed by Anders and Nishijima (2011) is implemented for the optimization of the formulated decision problem...

Least-squares resolution of gamma-ray spectra in environmental samples

International Nuclear Information System (INIS)

Kanipe, L.G.; Seale, S.K.; Liggett, W.S.

1977-08-01

The use of ALPHA-M, a least squares computer program for analyzing NaI (Tl) gamma spectra of environmental samples, is evaluated. Included is a comprehensive set of program instructions, listings, and flowcharts. Two other programs, GEN4 and SIMSPEC, are also described. GEN4 is used to create standard libraries for ALPHA-M, and SIMSPEC is used to simulate spectra for ALPHA-M analysis. Tests to evaluate the standard libraries selected for use in analyzing environmental samples are provided. An evaluation of the results of sample analyses is discussed

Canonical Least-Squares Monte Carlo Valuation of American Options: Convergence and Empirical Pricing Analysis

Directory of Open Access Journals (Sweden)

Xisheng Yu

2014-01-01

Full Text Available The paper by Liu (2010 introduces a method termed the canonical least-squares Monte Carlo (CLM which combines a martingale-constrained entropy model and a least-squares Monte Carlo algorithm to price American options. In this paper, we first provide the convergence results of CLM and numerically examine the convergence properties. Then, the comparative analysis is empirically conducted using a large sample of the S&P 100 Index (OEX puts and IBM puts. The results on the convergence show that choosing the shifted Legendre polynomials with four regressors is more appropriate considering the pricing accuracy and the computational cost. With this choice, CLM method is empirically demonstrated to be superior to the benchmark methods of binominal tree and finite difference with historical volatilities.

A measurement fusion method for nonlinear system identification using a cooperative learning algorithm.

Science.gov (United States)

Xia, Youshen; Kamel, Mohamed S

2007-06-01

Identification of a general nonlinear noisy system viewed as an estimation of a predictor function is studied in this article. A measurement fusion method for the predictor function estimate is proposed. In the proposed scheme, observed data are first fused by using an optimal fusion technique, and then the optimal fused data are incorporated in a nonlinear function estimator based on a robust least squares support vector machine (LS-SVM). A cooperative learning algorithm is proposed to implement the proposed measurement fusion method. Compared with related identification methods, the proposed method can minimize both the approximation error and the noise error. The performance analysis shows that the proposed optimal measurement fusion function estimate has a smaller mean square error than the LS-SVM function estimate. Moreover, the proposed cooperative learning algorithm can converge globally to the optimal measurement fusion function estimate. Finally, the proposed measurement fusion method is applied to ARMA signal and spatial temporal signal modeling. Experimental results show that the proposed measurement fusion method can provide a more accurate model.

Weighted least-square approach for simultaneous measurement of multiple reflective surfaces

Science.gov (United States)

Tang, Shouhong; Bills, Richard E.; Freischlad, Klaus

2007-09-01

Phase shifting interferometry (PSI) is a highly accurate method for measuring the nanometer-scale relative surface height of a semi-reflective test surface. PSI is effectively used in conjunction with Fizeau interferometers for optical testing, hard disk inspection, and semiconductor wafer flatness. However, commonly-used PSI algorithms are unable to produce an accurate phase measurement if more than one reflective surface is present in the Fizeau interferometer test cavity. Examples of test parts that fall into this category include lithography mask blanks and their protective pellicles, and plane parallel optical beam splitters. The plane parallel surfaces of these parts generate multiple interferograms that are superimposed in the recording plane of the Fizeau interferometer. When using wavelength shifting in PSI the phase shifting speed of each interferogram is proportional to the optical path difference (OPD) between the two reflective surfaces. The proposed method is able to differentiate each underlying interferogram from each other in an optimal manner. In this paper, we present a method for simultaneously measuring the multiple test surfaces of all underlying interferograms from these superimposed interferograms through the use of a weighted least-square fitting technique. The theoretical analysis of weighted least-square technique and the measurement results will be described in this paper.

Influence of the least-squares phase on optical vortices in strongly scintillated beams

CSIR Research Space (South Africa)

Chen, M

2009-06-01

Full Text Available , the average total number of vortices is reduced further. However, the reduction becomes smaller for each succes- sive step. This indicates that the ability of getting rid of optical vortices by removing the least-squares phase becomes progressively less...

Solitary heat waves in nonlinear lattices with squared on-site potential

Indian Academy of Sciences (India)

A model Hamiltonian is proposed for heat conduction in a nonlinear lattice with squared on-site potential using the second quantized operators and averaging the same using a suitable wave function, equations are derived in discrete form for the field amplitude and the properties of heat transfer are examined theoretically.

Ordinary least square regression, orthogonal regression, geometric mean regression and their applications in aerosol science

International Nuclear Information System (INIS)

Leng Ling; Zhang Tianyi; Kleinman, Lawrence; Zhu Wei

2007-01-01

Regression analysis, especially the ordinary least squares method which assumes that errors are confined to the dependent variable, has seen a fair share of its applications in aerosol science. The ordinary least squares approach, however, could be problematic due to the fact that atmospheric data often does not lend itself to calling one variable independent and the other dependent. Errors often exist for both measurements. In this work, we examine two regression approaches available to accommodate this situation. They are orthogonal regression and geometric mean regression. Comparisons are made theoretically as well as numerically through an aerosol study examining whether the ratio of organic aerosol to CO would change with age

Calculation of Credit Valuation Adjustment Based on Least Square Monte Carlo Methods

Directory of Open Access Journals (Sweden)

Qian Liu

2015-01-01

Full Text Available Counterparty credit risk has become one of the highest-profile risks facing participants in the financial markets. Despite this, relatively little is known about how counterparty credit risk is actually priced mathematically. We examine this issue using interest rate swaps. This largely traded financial product allows us to well identify the risk profiles of both institutions and their counterparties. Concretely, Hull-White model for rate and mean-reverting model for default intensity have proven to be in correspondence with the reality and to be well suited for financial institutions. Besides, we find that least square Monte Carlo method is quite efficient in the calculation of credit valuation adjustment (CVA, for short as it avoids the redundant step to generate inner scenarios. As a result, it accelerates the convergence speed of the CVA estimators. In the second part, we propose a new method to calculate bilateral CVA to avoid double counting in the existing bibliographies, where several copula functions are adopted to describe the dependence of two first to default times.

Linear least squares approach for evaluating crack tip fracture parameters using isochromatic and isoclinic data from digital photoelasticity

Science.gov (United States)

Patil, Prataprao; Vyasarayani, C. P.; Ramji, M.

2017-06-01

In this work, digital photoelasticity technique is used to estimate the crack tip fracture parameters for different crack configurations. Conventionally, only isochromatic data surrounding the crack tip is used for SIF estimation, but with the advent of digital photoelasticity, pixel-wise availability of both isoclinic and isochromatic data could be exploited for SIF estimation in a novel way. A linear least square approach is proposed to estimate the mixed-mode crack tip fracture parameters by solving the multi-parameter stress field equation. The stress intensity factor (SIF) is extracted from those estimated fracture parameters. The isochromatic and isoclinic data around the crack tip is estimated using the ten-step phase shifting technique. To get the unwrapped data, the adaptive quality guided phase unwrapping algorithm (AQGPU) has been used. The mixed mode fracture parameters, especially SIF are estimated for specimen configurations like single edge notch (SEN), center crack and straight crack ahead of inclusion using the proposed algorithm. The experimental SIF values estimated using the proposed method are compared with analytical/finite element analysis (FEA) results, and are found to be in good agreement.

Hyperspectral analysis of soil organic matter in coal mining regions using wavelets, correlations, and partial least squares regression.

Science.gov (United States)

Lin, Lixin; Wang, Yunjia; Teng, Jiyao; Wang, Xuchen

2016-02-01

Hyperspectral estimation of soil organic matter (SOM) in coal mining regions is an important tool for enhancing fertilization in soil restoration programs. The correlation--partial least squares regression (PLSR) method effectively solves the information loss problem of correlation--multiple linear stepwise regression, but results of the correlation analysis must be optimized to improve precision. This study considers the relationship between spectral reflectance and SOM based on spectral reflectance curves of soil samples collected from coal mining regions. Based on the major absorption troughs in the 400-1006 nm spectral range, PLSR analysis was performed using 289 independent bands of the second derivative (SDR) with three levels and measured SOM values. A wavelet-correlation-PLSR (W-C-PLSR) model was then constructed. By amplifying useful information that was previously obscured by noise, the W-C-PLSR model was optimal for estimating SOM content, with smaller prediction errors in both calibration (R(2) = 0.970, root mean square error (RMSEC) = 3.10, and mean relative error (MREC) = 8.75) and validation (RMSEV = 5.85 and MREV = 14.32) analyses, as compared with other models. Results indicate that W-C-PLSR has great potential to estimate SOM in coal mining regions.

Solitary heat waves in nonlinear lattices with squared on-site potential

Indian Academy of Sciences (India)

Abstract. A model Hamiltonian is proposed for heat conduction in a nonlinear lattice with squared on-site potential using the second quantized operators and averaging the same using a suitable wave function, equations are derived in discrete form for the field amplitude and the prop- erties of heat transfer are examined ...

Least median of squares and iteratively re-weighted least squares as robust linear regression methods for fluorimetric determination of α-lipoic acid in capsules in ideal and non-ideal cases of linearity.

Science.gov (United States)

Korany, Mohamed A; Gazy, Azza A; Khamis, Essam F; Ragab, Marwa A A; Kamal, Miranda F

2018-03-26

This study outlines two robust regression approaches, namely least median of squares (LMS) and iteratively re-weighted least squares (IRLS) to investigate their application in instrument analysis of nutraceuticals (that is, fluorescence quenching of merbromin reagent upon lipoic acid addition). These robust regression methods were used to calculate calibration data from the fluorescence quenching reaction (∆F and F-ratio) under ideal or non-ideal linearity conditions. For each condition, data were treated using three regression fittings: Ordinary Least Squares (OLS), LMS and IRLS. Assessment of linearity, limits of detection (LOD) and quantitation (LOQ), accuracy and precision were carefully studied for each condition. LMS and IRLS regression line fittings showed significant improvement in correlation coefficients and all regression parameters for both methods and both conditions. In the ideal linearity condition, the intercept and slope changed insignificantly, but a dramatic change was observed for the non-ideal condition and linearity intercept. Under both linearity conditions, LOD and LOQ values after the robust regression line fitting of data were lower than those obtained before data treatment. The results obtained after statistical treatment indicated that the linearity ranges for drug determination could be expanded to lower limits of quantitation by enhancing the regression equation parameters after data treatment. Analysis results for lipoic acid in capsules, using both fluorimetric methods, treated by parametric OLS and after treatment by robust LMS and IRLS were compared for both linearity conditions. Copyright © 2018 John Wiley & Sons, Ltd.

DEM GENERATION FROM HIGH RESOLUTION SATELLITE IMAGES THROUGH A NEW 3D LEAST SQUARES MATCHING ALGORITHM

Directory of Open Access Journals (Sweden)

T. Kim

2012-09-01

Full Text Available Automated generation of digital elevation models (DEMs from high resolution satellite images (HRSIs has been an active research topic for many years. However, stereo matching of HRSIs, in particular based on image-space search, is still difficult due to occlusions and building facades within them. Object-space matching schemes, proposed to overcome these problem, often are very time consuming and critical to the dimensions of voxels. In this paper, we tried a new least square matching (LSM algorithm that works in a 3D object space. The algorithm starts with an initial height value on one location of the object space. From this 3D point, the left and right image points are projected. The true height is calculated by iterative least squares estimation based on the grey level differences between the left and right patches centred on the projected left and right points. We tested the 3D LSM to the Worldview images over 'Terrassa Sud' provided by the ISPRS WG I/4. We also compared the performance of the 3D LSM with the correlation matching based on 2D image space and the correlation matching based on 3D object space. The accuracy of the DEM from each method was analysed against the ground truth. Test results showed that 3D LSM offers more accurate DEMs over the conventional matching algorithms. Results also showed that 3D LSM is sensitive to the accuracy of initial height value to start the estimation. We combined the 3D COM and 3D LSM for accurate and robust DEM generation from HRSIs. The major contribution of this paper is that we proposed and validated that LSM can be applied to object space and that the combination of 3D correlation and 3D LSM can be a good solution for automated DEM generation from HRSIs.

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

Science.gov (United States)

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.

Single Directional SMO Algorithm for Least Squares Support Vector Machines

Directory of Open Access Journals (Sweden)

Xigao Shao

2013-01-01

Full Text Available Working set selection is a major step in decomposition methods for training least squares support vector machines (LS-SVMs. In this paper, a new technique for the selection of working set in sequential minimal optimization- (SMO- type decomposition methods is proposed. By the new method, we can select a single direction to achieve the convergence of the optimality condition. A simple asymptotic convergence proof for the new algorithm is given. Experimental comparisons demonstrate that the classification accuracy of the new method is not largely different from the existing methods, but the training speed is faster than existing ones.

Attenuation compensation in least-squares reverse time migration using the visco-acoustic wave equation

KAUST Repository

Dutta, Gaurav; Lu, Kai; Wang, Xin; Schuster, Gerard T.

2013-01-01

Attenuation leads to distortion of amplitude and phase of seismic waves propagating inside the earth. Conventional acoustic and least-squares reverse time migration do not account for this distortion which leads to defocusing of migration images

On the vibrations of a simply supported square plate on a weakly nonlinear elastic foundation

NARCIS (Netherlands)

Zarubinskaya, M.A.; Van Horssen, W.T.

2003-01-01

In this paper an initial-boundary value problem for a weakly nonlinear plate equation with a quadratic nonlinearity will be studied. This initial-boundary value problem can be regarded as a simple model describing free oscillations of a simply supported square plate on an elastic foundation. It is

Comparison of multiple linear regression, partial least squares and artificial neural networks for prediction of gas chromatographic relative retention times of trimethylsilylated anabolic androgenic steroids.

Science.gov (United States)

Fragkaki, A G; Farmaki, E; Thomaidis, N; Tsantili-Kakoulidou, A; Angelis, Y S; Koupparis, M; Georgakopoulos, C

2012-09-21

The comparison among different modelling techniques, such as multiple linear regression, partial least squares and artificial neural networks, has been performed in order to construct and evaluate models for prediction of gas chromatographic relative retention times of trimethylsilylated anabolic androgenic steroids. The performance of the quantitative structure-retention relationship study, using the multiple linear regression and partial least squares techniques, has been previously conducted. In the present study, artificial neural networks models were constructed and used for the prediction of relative retention times of anabolic androgenic steroids, while their efficiency is compared with that of the models derived from the multiple linear regression and partial least squares techniques. For overall ranking of the models, a novel procedure [Trends Anal. Chem. 29 (2010) 101-109] based on sum of ranking differences was applied, which permits the best model to be selected. The suggested models are considered useful for the estimation of relative retention times of designer steroids for which no analytical data are available. Copyright © 2012 Elsevier B.V. All rights reserved.

Flow Applications of the Least Squares Finite Element Method

Science.gov (United States)

Jiang, Bo-Nan

1998-01-01

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Dual stacked partial least squares for analysis of near-infrared spectra

Energy Technology Data Exchange (ETDEWEB)

Bi, Yiming [Institute of Automation, Chinese Academy of Sciences, 100190 Beijing (China); Xie, Qiong, E-mail: yimbi@163.com [Institute of Automation, Chinese Academy of Sciences, 100190 Beijing (China); Peng, Silong; Tang, Liang; Hu, Yong; Tan, Jie [Institute of Automation, Chinese Academy of Sciences, 100190 Beijing (China); Zhao, Yuhui [School of Economics and Business, Northeastern University at Qinhuangdao, 066000 Qinhuangdao City (China); Li, Changwen [Food Research Institute of Tianjin Tasly Group, 300410 Tianjin (China)

2013-08-20

Graphical abstract: -- Highlights: •Dual stacking steps are used for multivariate calibration of near-infrared spectra. •A selective weighting strategy is introduced that only a subset of all available sub-models is used for model fusion. •Using two public near-infrared datasets, the proposed method achieved competitive results. •The method can be widely applied in many fields, such as Mid-infrared spectra data and Raman spectra data. -- Abstract: A new ensemble learning algorithm is presented for quantitative analysis of near-infrared spectra. The algorithm contains two steps of stacked regression and Partial Least Squares (PLS), termed Dual Stacked Partial Least Squares (DSPLS) algorithm. First, several sub-models were generated from the whole calibration set. The inner-stack step was implemented on sub-intervals of the spectrum. Then the outer-stack step was used to combine these sub-models. Several combination rules of the outer-stack step were analyzed for the proposed DSPLS algorithm. In addition, a novel selective weighting rule was also involved to select a subset of all available sub-models. Experiments on two public near-infrared datasets demonstrate that the proposed DSPLS with selective weighting rule provided superior prediction performance and outperformed the conventional PLS algorithm. Compared with the single model, the new ensemble model can provide more robust prediction result and can be considered an alternative choice for quantitative analytical applications.

Dual stacked partial least squares for analysis of near-infrared spectra

International Nuclear Information System (INIS)

Bi, Yiming; Xie, Qiong; Peng, Silong; Tang, Liang; Hu, Yong; Tan, Jie; Zhao, Yuhui; Li, Changwen

2013-01-01

Graphical abstract: -- Highlights: •Dual stacking steps are used for multivariate calibration of near-infrared spectra. •A selective weighting strategy is introduced that only a subset of all available sub-models is used for model fusion. •Using two public near-infrared datasets, the proposed method achieved competitive results. •The method can be widely applied in many fields, such as Mid-infrared spectra data and Raman spectra data. -- Abstract: A new ensemble learning algorithm is presented for quantitative analysis of near-infrared spectra. The algorithm contains two steps of stacked regression and Partial Least Squares (PLS), termed Dual Stacked Partial Least Squares (DSPLS) algorithm. First, several sub-models were generated from the whole calibration set. The inner-stack step was implemented on sub-intervals of the spectrum. Then the outer-stack step was used to combine these sub-models. Several combination rules of the outer-stack step were analyzed for the proposed DSPLS algorithm. In addition, a novel selective weighting rule was also involved to select a subset of all available sub-models. Experiments on two public near-infrared datasets demonstrate that the proposed DSPLS with selective weighting rule provided superior prediction performance and outperformed the conventional PLS algorithm. Compared with the single model, the new ensemble model can provide more robust prediction result and can be considered an alternative choice for quantitative analytical applications

Speed control of induction motor using fuzzy recursive least squares technique

OpenAIRE

Santiago Sánchez; Eduardo Giraldo

2008-01-01

A simple adaptive controller design is presented in this paper, the control system uses the adaptive fuzzy logic, sliding modes and is trained with the recursive least squares technique. The problem of parameter variation is solved with the adaptive controller; the use of an internal PI regulator produces that the speed control of the induction motor be achieved by the stator currents instead the input voltage. The rotor-flux oriented coordinated system model is used to develop and test the c...

Derivation of decay heat benchmarks for U235 and Pu239 by a least squares fit to measured data

International Nuclear Information System (INIS)

Tobias, A.

1989-05-01

A least squares technique used by previous authors has been applied to an extended set of available decay heat measurements for both U235 and Pu239 to yield simultaneous fits to the corresponding beta, gamma and total decay heat. The analysis takes account of both systematic and statistical uncertainties, including correlations, via calculations which use covariance matrices constructed for the measured data. The results of the analysis are given in the form of beta, gamma and total decay heat estimates following fission pulses and a range of irradiation times in both U235 and Pu239. These decay heat estimates are considered to form a consistent set of benchmarks for use in the assessment of summation calculations. (author)

State of charge estimation of lithium-ion batteries based on an improved parameter identification method

International Nuclear Information System (INIS)

Xia, Bizhong; Chen, Chaoren; Tian, Yong; Wang, Mingwang; Sun, Wei; Xu, Zhihui

2015-01-01

The SOC (state of charge) is the most important index of the battery management systems. However, it cannot be measured directly with sensors and must be estimated with mathematical techniques. An accurate battery model is crucial to exactly estimate the SOC. In order to improve the model accuracy, this paper presents an improved parameter identification method. Firstly, the concept of polarization depth is proposed based on the analysis of polarization characteristics of the lithium-ion batteries. Then, the nonlinear least square technique is applied to determine the model parameters according to data collected from pulsed discharge experiments. The results show that the proposed method can reduce the model error as compared with the conventional approach. Furthermore, a nonlinear observer presented in the previous work is utilized to verify the validity of the proposed parameter identification method in SOC estimation. Finally, experiments with different levels of discharge current are carried out to investigate the influence of polarization depth on SOC estimation. Experimental results show that the proposed method can improve the SOC estimation accuracy as compared with the conventional approach, especially under the conditions of large discharge current. - Highlights: • The polarization characteristics of lithium-ion batteries are analyzed. • The concept of polarization depth is proposed to improve model accuracy. • A nonlinear least square technique is applied to determine the model parameters. • A nonlinear observer is used as the SOC estimation algorithm. • The validity of the proposed method is verified by experimental results.