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Fitting nature's basic functions Part IV: The variable projection algorithm

COMPUTING IN SCIENCE & ENGINEERING 2003年第2期5卷 74-79页

作者： Rust, BW NIST Gaithersburg MD 20899 USA

For pt. III see ibid., vol. 4, no. 4, pp. 72-77 (2002). The author examines the variable projection algorithm, which often greatly simplifies nonlinear least squares calculations because it does not require iteration ... 详细信息

关键词： least squares approximations variable projection algorithm nonlinear least squares calculations iterative methods variable projection algorithms Nonlinear least squares MACHINE SHOP PRACTICE

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Battery state of health estimation using variable projection algorithm based on truncated variable order fractional gradient descent

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IONICS 2024年第2期30卷 863-874页

作者： Cheng, Lianyuan Pu, Yan Chen, Jing Liu, Qiang Jiangnan Univ Sch Sci Wuxi 214122 Jiangsu Peoples R China Minertech Technol Co Ltd Wuxi 214122 Jiangsu Peoples R China

Accurate estimation and prediction of battery state of health (SOH) is the focus of battery reliability research. Traditional algorithms ignore the coupling of linear and nonlinear parameters in the battery SOH model, leading to additional errors. To estimate the battery SOH more quickly and accurately, a variable projection algorithm based on truncated variable order fractional gradient descent (VP-TVF) is proposed in this paper. By choosing appropriate variable order constants, the VP-TVF algorithm can accurately estimate model parameters while converging quickly. The efficacy of our proposed algorithm is further substantiated through two comprehensive simulation examples.

关键词： Fractional derivative State of health variable order method variable projection algorithm

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Battery State of Health Model Estimation Based on variable projection algorithm Using Steffensen Acceleration Method

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JOURNAL OF THE ELECTROCHEMICAL SOCIETY 2023年第5期170卷 050509-050509页

作者： Cheng, Lianyuan Chen, Jing Pu, Yan Yin, Xia Jiangnan Univ Sch Sci Wuxi Jiangsu Peoples R China

In this paper, the variable projection based Steffensen acceleration (VP-SA) algorithm is proposed for battery state of health (SOH) estimation. The VP-SA algorithm exploits the separability of variables to reduce the dimensionality of the parameters, which can improve the estimation efficiency. In addition, based on the Steffensen acceleration method, the convergence rates of the VP algorithm can be increased. The simulation example shows the effectiveness of the proposed algorithm.

关键词： parameter estimation state of health variable projection algorithm Steffensen acceleration method

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Joint variable and variable projection algorithms for separable nonlinear models using Aitken acceleration technique

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2023年第3期42卷 202-210页

作者： Cheng, Lianyuan Chen, Jing Rong, Yingjiao Jiangnan Univ Sch Sci Wuxi 214122 Peoples R China Sci & Technol Near Surface Detect Lab Wuxi Peoples R China

This paper proposes a joint variable-based gradient descent algorithm (Joint-GD) and a variable projection (VP)-based gradient descent algorithm (VP-GD) for separable nonlinear models. The VP algorithm takes advantage of the separability property of variables to reduce the dimensionality of the parameters, which makes the convergence rates faster. In order to speed up the convergence of the gradient descent algorithm, the Aitken acceleration technique is introduced in the algorithms, which is second-order convergent. Moreover, the Aitken-based methods are robust to the step-size, therefore they can be widely used in engineering practices. The numerical simulation shows the effectiveness of the proposed algorithms.

关键词： variable projection algorithm joint variable algorithm gradient descent algorithm separable nonlinear model Aitken acceleration technique

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variable projection Methods for an Optimized Dynamic Mode Decomposition

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SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS 2018年第1期17卷 380-416页

作者： Askham, Travis Kutz, J. Nathan Univ Washington Dept Appl Math Seattle WA 98195 USA

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple algorithm for computing an optimized version of the DMD for data which may be collected at unevenly spaced sample times. By making use of the variable projection method for nonlinear least squares problems, the algorithm is capable of solving the underlying nonlinear optimization problem efficiently. We explore the performance of the algorithm with some numerical examples for synthetic and real data from dynamical systems and find that the resulting decomposition displays less bias in the presence of noise than standard DMD algorithms. Because of the flexibility of the algorithm, we also present some interesting new options for DMD-based analysis.

关键词： dynamic mode decomposition inverse linear systems variable projection algorithm inverse differential equations

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variable projections neural network training

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MATHEMATICS AND COMPUTERS IN SIMULATION 2006年第1-4期73卷 231-243页

作者： Pereyra, V. Scherer, G. Wong, F. Weidlinger Associates Inc Mountain View CA USA

The training of some types of neural networks leads to separable non-linear least squares problems. These problems may be ill-conditioned and require special techniques. A robust algorithm based on the variable projections method of Golub and Pereyra is designed for a class of feed-forward neural networks and tested on benchmark examples and real data. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： neural networks variable projection algorithm

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Estimation of material functions using system identification techniques

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CONTROL ENGINEERING PRACTICE 2012年第10期20卷 972-990页

作者： Soderstrom, Torsten Rensfelt, Agnes Uppsala Univ Dept Informat Technol Div Syst & Control SE-75105 Uppsala Sweden

Material properties of an elastic material are characterized by the elastic modulus, which is real-valued and constant. For viscoelastic materials, such as plastics and polymers, the relationship between stress and strain is instead dynamic, and characterized by the complex-valued and frequency-dependent complex modulus. It is in this paper described how system identification techniques can be used to determine the complex modulus using strain data from wave propagation experiments on a test specimen. Modeling, derivation of estimators, and analysis of their numerical and statistical properties are included. Identifiability and experimental design are examined in some detail. Several practical examples are presented using real-world data, and a number of extensions are outlined. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Material functions Complex modulus variable projection algorithm Wave propagation Identifiability Experiment design

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