Multistage parameter estimation algorithms for identification of bilinear systems
In this paper, two methods for parameter estimation of bilinear state-space systems with colored noise, which are expressed by ARMA model, are proposed. Using the hierarchical identification principle and gradient method, to reduce the computational cost, both the four-stage recursive least squares...
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| Vydáno v: | Nonlinear dynamics Ročník 110; číslo 3; s. 2635 - 2655 |
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| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Dordrecht
Springer Netherlands
01.11.2022
Springer Nature B.V |
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| ISSN: | 0924-090X, 1573-269X |
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| Abstract | In this paper, two methods for parameter estimation of bilinear state-space systems with colored noise, which are expressed by ARMA model, are proposed. Using the hierarchical identification principle and gradient method, to reduce the computational cost, both the four-stage recursive least squares algorithm and the four-stage stochastic gradient algorithm are exploited by which parameter estimation error is reduced and the speed of convergence of parameters is increased. In addition, a bilinear state observer for state estimation is designed to make use of the estimated states in the four-stage recursive least squares and the four-stage stochastic gradient algorithms. Finally, a numerical example and a practical example are provided to indicate the superiority of the proposed methods. The results show that due to the data length increase, the estimation error of the parameters is reduced. Furthermore, the estimated parameters converge to the actual values in a short time. |
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| AbstractList | In this paper, two methods for parameter estimation of bilinear state-space systems with colored noise, which are expressed by ARMA model, are proposed. Using the hierarchical identification principle and gradient method, to reduce the computational cost, both the four-stage recursive least squares algorithm and the four-stage stochastic gradient algorithm are exploited by which parameter estimation error is reduced and the speed of convergence of parameters is increased. In addition, a bilinear state observer for state estimation is designed to make use of the estimated states in the four-stage recursive least squares and the four-stage stochastic gradient algorithms. Finally, a numerical example and a practical example are provided to indicate the superiority of the proposed methods. The results show that due to the data length increase, the estimation error of the parameters is reduced. Furthermore, the estimated parameters converge to the actual values in a short time. |
| Author | Yin, Shen Arefi, Mohammad Mehdi Luo, Hao Shahriari, Fatemeh |
| Author_xml | – sequence: 1 givenname: Fatemeh surname: Shahriari fullname: Shahriari, Fatemeh organization: Department of Power and Control Engineering, School of Electrical and Computer Engineering, Shiraz University – sequence: 2 givenname: Mohammad Mehdi orcidid: 0000-0003-3986-8205 surname: Arefi fullname: Arefi, Mohammad Mehdi email: arefi@shirazu.ac.ir organization: Department of Power and Control Engineering, School of Electrical and Computer Engineering, Shiraz University – sequence: 3 givenname: Hao surname: Luo fullname: Luo, Hao organization: Department of Control Science and Engineering, School of Astronautics, Harbin Institute of Technology – sequence: 4 givenname: Shen surname: Yin fullname: Yin, Shen organization: Department of Mechanical and Industrial Engineering, Faculty of Engineering, Norwegian University of Science and Technology |
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| Keywords | Gradient search Parameter estimation Bilinear systems Hierarchical identification |
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| SubjectTerms | Accuracy Algorithms Automotive Engineering Classical Mechanics Control Convergence Decomposition Design Dynamical Systems Engineering Error reduction Identification Iterative methods Kalman filters Least squares Mechanical Engineering Methods Original Paper Parameter estimation Parameter identification State estimation State observers Vibration |
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