A regularised fast recursive algorithm for fraction model identification of nonlinear dynamic systems

The fraction model has been widely used to represent a range of engineering systems. To accurately identify the fraction model is however challenging, and this paper presents a regularised fast recursive algorithm (RFRA) to identify both the true fraction model structure and the associated unknown m...

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Published in:	International journal of systems science Vol. 54; no. 7; pp. 1616 - 1638
Main Authors:	Zhang, Li, Li, Kang, Du, Dajun, Li, Yihuan, Fei, Minrui
Format:	Journal Article
Language:	English
Published:	London Taylor & Francis 19.05.2023 Taylor & Francis Ltd
Subjects:	Algorithms Cost function Dynamical systems fraction models Linear transformations Nonlinear dynamics nonlinear model identification Nonlinear systems Regularisation regularised fast recursive algorithm Regularization
ISSN:	0020-7721, 1464-5319
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Abstract	The fraction model has been widely used to represent a range of engineering systems. To accurately identify the fraction model is however challenging, and this paper presents a regularised fast recursive algorithm (RFRA) to identify both the true fraction model structure and the associated unknown model parameters. This is achieved first by transforming the fraction form to a linear combination of nonlinear model terms. Then the terms in the denominator are used to form a regularisation term in the cost function to offset the bias induced by the linear transformation. According to the structural risk minimisation principle based on the new cost function, the model terms are selected based on their contributions to the cost function and the coefficients are then identified recursively without explicitly solving the inverse matrix. The proposed method is proved to have low computational complexity. Simulation results confirm the efficacy of the method in fast identification of the true fraction models for the targeted nonlinear systems.
AbstractList	The fraction model has been widely used to represent a range of engineering systems. To accurately identify the fraction model is however challenging, and this paper presents a regularised fast recursive algorithm (RFRA) to identify both the true fraction model structure and the associated unknown model parameters. This is achieved first by transforming the fraction form to a linear combination of nonlinear model terms. Then the terms in the denominator are used to form a regularisation term in the cost function to offset the bias induced by the linear transformation. According to the structural risk minimisation principle based on the new cost function, the model terms are selected based on their contributions to the cost function and the coefficients are then identified recursively without explicitly solving the inverse matrix. The proposed method is proved to have low computational complexity. Simulation results confirm the efficacy of the method in fast identification of the true fraction models for the targeted nonlinear systems.
Author	Du, Dajun Li, Yihuan Li, Kang Fei, Minrui Zhang, Li
Author_xml	– sequence: 1 givenname: Li surname: Zhang fullname: Zhang, Li organization: Shanghai University – sequence: 2 givenname: Kang surname: Li fullname: Li, Kang email: k.li1@leeds.ac.uk organization: University of Leeds – sequence: 3 givenname: Dajun orcidid: 0000-0003-2979-1507 surname: Du fullname: Du, Dajun email: ddj@i.shu.edu.cn organization: Shanghai University – sequence: 4 givenname: Yihuan surname: Li fullname: Li, Yihuan organization: North China Electric Power University – sequence: 5 givenname: Minrui surname: Fei fullname: Fei, Minrui organization: Shanghai University
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Snippet	The fraction model has been widely used to represent a range of engineering systems. To accurately identify the fraction model is however challenging, and this...
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SubjectTerms	Algorithms Cost function Dynamical systems fraction models Linear transformations Nonlinear dynamics nonlinear model identification Nonlinear systems Regularisation regularised fast recursive algorithm Regularization
Title	A regularised fast recursive algorithm for fraction model identification of nonlinear dynamic systems
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