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Modified Kalman filtering based multi-step-length gradient iterative algorithm for ARX models with random missing outputs

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AUTOMATICA 2020年 118卷 109034-109034页

作者： Chen, Jing Zhu, Quanmin Liu, Yanjun Jiangnan Univ Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Jiangsu Peoples R China Jiangnan Univ Sch Sci Wuxi 214122 Jiangsu Peoples R China Univ West England Dept Engn Design & Math Bristol BS16 1QY Avon England

This study presents a modified Kalman filtering-based multi-step-length gradient iterative algorithm to identify ARX models with missing outputs. The Kalman filtering method is modified to enhance the estimation of unmeasurable outputs, laying the foundation for enabling the multi-step-length gradient iterative algorithm to update effectively the ARX model parameter estimation through the estimated outputs. Compared to the classical gradient iterative algorithm, this study improves the estimation accuracy of the missing outputs by introducing a modified Kalman filter, and the parameter estimation convergence rate by deriving a new multi-step-length formulation. To validate the framework and the algorithm developed, a series of bench tests were conducted with computational experiments. The simulated numerical results are consistent with the analytically derived results in terms of the feasibility and effectiveness of the proposed procedure. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Parameter estimation gradient iterative algorithm Multi-step-length Modified Kalman filter ARX model

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A shift-splitting Jacobi-gradient iterative algorithm for solving the matrix equation Aν - (ν)over-barB = C

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OPTIMAL CONTROL APPLICATIONS & METHODS 2024年第4期45卷 1593-1602页

作者： Bayoumi, Ahmed M. E. Ain Shams Univ Fac Educ Dept Math Cairo Egypt

To improve the convergence of the gradient iterative (GI) algorithm and the Jacobi-gradient iterative (JGI) algorithm [Bayoumi, Appl Math Inf Sci, 2021], a shift-splitting Jacobi-gradient iterative (SSJGI) algorithm for solving the matrix equation A nu - (nu) over barB = C is presented in this paper, which is based on the splitting of the coefficient matrices. The proposed algorithm converges to the exact solution for any initial value with some conditions. To demonstrate the effectiveness of the SSJGI algorithm and to compare it to the GI algorithm and the JGI algorithm [Bayoumi, Appl Math Inf Sci, 2021], numerical examples are provided.

关键词： convergence gradient iterative algorithm Jacobi-gradient iterative algorithm matrix equation shift-splitting Jacobi-gradient

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Interval Error Correction Auxiliary Model Based gradient iterative algorithms for Multirate ARX Models

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2020年第10期65卷 4385-4392页

作者： Chen, Jing Ding, Feng Zhu, Quanmin Liu, Yanjun Jiangnan Univ Minist Educ Key Lab Adv Proc Control Light Ind Wuxi 214122 Jiangsu Peoples R China Jiangnan Univ Sch Sci Wuxi 214122 Jiangsu Peoples R China Univ West England Dept Engn Design & Math Bristol BS16 1QY Avon England

To improve the identification efficiency of the auxiliary model based gradient iterative algorithm, this article derives a couple of interval error correction auxiliary model based gradient iterative (IEC-AM-GI) algorithms for multirate AutoRegressive eXogenous (ARX) models. The unmeasurable outputs between two measured outputs are estimated by two interval error correction auxiliary models. Unlike the AM-GI algorithm, the IEC-AM-GI algorithms can estimate the missing outputs by the auxiliary model and further fine tune through the measurable outputs, which thus are more efficient and accurate than those by only using the auxiliary model. In addition, this article makes a comparison between these two interval error correction auxiliary model methods and through which the optimal interval error correction auxiliary model method for the unmeasurable outputs can be chosen. The effectiveness of the proposed algorithms is demonstrated by the simulation results.

关键词： Error correction Data models iterative methods Measurement uncertainty Random variables Estimation error Auxiliary model gradient iterative algorithm interval error correction multirate AutoRegressive eXogenous (ARX) model parameter estimation

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Separable Synchronous gradient-Based iterative algorithms for the Nonlinear ExpARX System

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2024年第12期38卷 3801-3818页

作者： Gu, Ya Hou, Yuting Li, Chuanjiang Zhu, Yanfei Shanghai Normal Univ Coll Informat Mech & Elect Engn Shanghai Peoples R China

This article is aimed to study the parameter identification of the ExpARX system. To overcome the computational complexity associated with a large number of feature parameters, a parameter separation scheme based on the different features of the identification model is introduced. In terms of the phenomenon that the coupling parameters lead to the inability of algorithms, a separable synchronous interactive estimation method is introduced to eliminate the coupling parameters and perform parameter estimation in accordance with the hierarchical principle. For the purpose of achieving high-accuracy performance and reducing complexity, a separable synchronous gradient iterative algorithm is derived by means of gradient search. In order to improve the identification accuracy, a separable synchronous multi-innovation gradient iterative algorithm is proposed by introducing the multi-innovation identification theory. In order to improve the convergence speed, a separable synchronous multi-innovation conjugate gradient iterative algorithm is proposed by introducing the conjugate gradient theory. Finally, a simulation example and a real-life example of piezoelectric ceramics are used to verify the effectiveness of the proposed algorithm.

关键词： gradient iterative algorithm hierarchical identification multi-innovation identification nonlinear ExpARX system parameter estimation

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gradient iterative-based kernel method for exponential autoregressive models

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INTERNATIONAL JOURNAL OF COMPUTER APPLICATIONS IN TECHNOLOGY 2021年第2-3期67卷 224-231页

作者： Lu, Jianwei Changzhou Inst Ind Technol Sch Informat Engn Changzhou 213164 Jiangsu Peoples R China

Two kernel method-based gradient iterative algorithms are proposed for exponential autoregressive (ExpAR) models in this study. A polynomial kernel function is utilised to transform the ExpAR model into a linear-parameter model. Since the order of the linear-parameter model is large, a momentum stochastic gradient algorithm and an adaptive step-length gradient iterative algorithm are developed. Both these two algorithms can estimate the parameters with less computational efforts. Finally, a simulation example shows that the proposed algorithms are effective.

关键词： ExpAR model kernel method linear-parameter model momentum stochastic gradient algorithm adaptive step-length gradient iterative algorithm

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Parameter identification of fractional-order Wiener system based on FF-ESG and GI algorithms

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ASIAN JOURNAL OF CONTROL 2023年第6期25卷 4512-4524页

作者： Li, Junhong Zhang, Hongrui Gu, Juping Hua, Liang Nantong Univ Sch Elect Engn Nantong Jiangsu Peoples R China Nantong Univ Nantong Jiangsu Peoples R China

Fractional-order calculus has broad application scenarios in engineering and physics. Unlike integer-order calculus, fractional-order calculus has the ability to analyze nonclassical phenomena in science and engineering. For industrial processes with strong nonlinear characteristics, nonlinear models such as the Wiener model have become research hotspots. This paper studies the parameter identification of the fractional-order Wiener system. In this paper, the forgetting factor extended stochastic gradient (FF-ESG) algorithm and the gradient iterative (GI) algorithm are proposed to identify the parameters of the fractional-order Wiener system. Then, the convergence of the FF-ESG algorithm for the fractional-order Wiener system is analyzed. Both proposed algorithms can obtain exact parameter estimates, which are verified by a numerical example and a case study of a fluid control valve.

关键词： forgetting factor extended stochastic gradient algorithm fractional-order Wiener system gradient iterative algorithm parameter estimation

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Accelerated identification algorithms for rational models based on the vector transformation

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OPTIMAL CONTROL APPLICATIONS & METHODS 2022年第3期43卷 740-756页

作者： Pu, Yan Chen, Jing Yang, Yongqing Zhu, Quanmin Jiangnan Univ Sch Sci Wuxi 214122 Jiangsu Peoples R China Univ West England Dept Engn Design & Math Bristol Avon England

An accelerated algorithm, termed as Gram-Schmidt orthogonalization gradient-based iterative algorithm, is proposed for rational models in this article. The algorithm can obtain the optimal parameter estimates in one iteration for the reason that the information vectors obtained by using the vector transformation are independent of each other. Compared to the least squares algorithm and the traditional gradient-based iterative algorithm, the proposed algorithm does not require the matrix inversion and eigenvalue calculation, thus it can be applied to nonlinear systems with complex structures or large-scale systems. Since the information vector of the rational models contains the latest output that is correlated with the noise, a bias-compensated Gram-Schmidt orthogonalization gradient-based iterative algorithm is introduced, by which the unbiased parameter estimates can be obtained. Two simulated examples are applied to demonstrate the efficiency of the proposed algorithm.

关键词： bias compensation gradient iterative algorithm rational model vector transformation

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Several structure pool based identification algorithms for ARX models: order and parameter estimation

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2020年第3期36卷 233-239页

作者： Lu, Jianwei Changzhou Inst Ind Technol Sch Informat Engn Changzhou 213164 Jiangsu Peoples R China

Several structure pool based identification algorithms are proposed for autoregressive exogenous (ARX) models with unknown order in this study. Since the order of the ARX model is unknown, a structure pool which contains various different information products is provided, and then the gradient iterative and two-direction stochastic gradient algorithms are provided to estimate the order and the unknown parameters simultaneously. The proposed algorithms can be applied for systems with unknown orders and parameters, thus are more promising in engineering practice. The simulation example is utilised to validate the efficiency of the proposed algorithms.

关键词： order identification gradient iterative algorithm ARX model two-direction stochastic gradient algorithm parameter estimation structure pool

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A novel reduced-order algorithm for rational models based on Arnoldi process and Krylov subspace

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AUTOMATICA 2021年 129卷 109663-109663页

作者： Chen, Jing Huang, Biao Gan, Min Chen, C. L. Philip Jiangnan Univ Sch Sci Wuxi 214122 Jiangsu Peoples R China Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2G6 Canada Qingdao Univ Coll Comp Sci & Technol Qingdao 266071 Peoples R China South China Univ Technol Sch Comp Sci & Engn Guangzhou 511442 Peoples R China

This paper presents a novel reduced-order algorithm for identifying rational models. From the Arnoldi process, an orthonormal basis of the Krylov subspace is constructed. Based on the Krylov subspace, a high-order cost function is transformed into a low-order one, thereby significantly reducing the computational efforts. This algorithm can be considered as a reduced-order least squares (LS) algorithm or an extension of the traditional gradient iterative (GI) algorithm for different Krylov subspaces, and it presents several advantages over the traditional LS and GI algorithms. The simulated numerical results/figures are consistent with the analytically derived results in terms of the feasibility and effectiveness of the proposed algorithm. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Rational model Arnoldi's method Krylov subspace Least squares algorithm gradient iterative algorithm Reduced-order algorithm

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