Fuzzy identification of nonlinear dynamic system based on selection of important input variables

doi:10.23919/JSEE.2022.000027

Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (3): 737-747.doi: 10.23919/JSEE.2022.000027

收稿日期:2020-03-22 出版日期:2022-06-18 发布日期:2022-06-24

Fuzzy identification of nonlinear dynamic system based on selection of important input variables

Jinfeng LYU^1,²(), Fucai LIU^1,*(), Yaxue REN¹()

¹ Engineering Research Center of the Ministry of Education for Intelligent Control System and Intelligent Equipment, Yanshan University, Qinhuangdao 066004, China
² School of Mathematics and Information Science and Technology, Hebei Normal University of Science and Technology, Qinhuangdao 066004, China

Received:2020-03-22 Online:2022-06-18 Published:2022-06-24
Contact: Fucai LIU E-mail:xfyy0308@163.com;lfc@ysu.edu.cn;2592863354@qq.com
About author:|LYU Jinfeng was born in 1977. She is currently a Ph.D. candidate in Automation Department of Yanshan University and an associate professor in Hebei Normal University of Science and Technology. Her main research interests are identification and control of nonlinear systems. E-mail: xfyy0308@163.com||LIU Fucai was born in 1966. He received his master degree from the Automatic Control Department of Northeast Institute of Heavy Machinery in 1994, and his Ph.D. degree from the Control Science and Engineering Department of Harbin Institute of Technology in 2003. He is now the director of Automation Department of Yanshan University. His main research interests are nonlinear system fuzzy identification and predictive control, and space robot control technology. E-mail: lfc@ysu.edu.cn||REN Yaxue was born in 1995. She received her bachelor degree in measurement and control technology and instrument from Hebei University, and master degree in control science and engineering from Yanshan University. She is currently a Ph.D. student in instrument science and technology at Yanshan University. Her main research interest is plane array capacitance detection technology. E-mail: 2592863354@qq.com
Supported by:
This work was supported by the Natural Science Foundation of Hebei Province (F2019203505)

摘要/Abstract

Abstract:

Input variables selection (IVS) is proved to be pivotal in nonlinear dynamic system modeling. In order to optimize the model of the nonlinear dynamic system, a fuzzy modeling method for determining the premise structure by selecting important inputs of the system is studied. Firstly, a simplified two stage fuzzy curves method is proposed, which is employed to sort all possible inputs by their relevance with outputs, select the important input variables of the system and identify the structure. Secondly, in order to reduce the complexity of the model, the standard fuzzy c-means clustering algorithm and the recursive least squares algorithm are used to identify the premise parameters and conclusion parameters, respectively. Then, the effectiveness of IVS is verified by two well-known issues. Finally, the proposed identification method is applied to a realistic variable load pneumatic system. The simulation experiments indicate that the IVS method in this paper has a positive influence on the approximation performance of the Takagi-Sugeno (T-S) fuzzy modeling.

Key words: Takagi-Sugeno (T-S) fuzzy modeling, input variable selection (IVS), fuzzy identification, fuzzy c-means clustering algorithm

. [J]. Journal of Systems Engineering and Electronics, 2022, 33(3): 737-747.

Jinfeng LYU, Fucai LIU, Yaxue REN. Fuzzy identification of nonlinear dynamic system based on selection of important input variables[J]. Journal of Systems Engineering and Electronics, 2022, 33(3): 737-747.

图/表 14

参考文献 38

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Model	Number of rules	Training MSE (×10^?4)	Testing MSE (×10^?4)
Guo et al. [11]	?	9.61	10.24
Masoumi et al. [33]	?	4.84	7.29
Zou et al. [13]	10	5.0216	6.7449
Liu [34]	2	0.6377	0.6518
Our model	2	0.41627	0.42957

Model	Input variables	Number of rules	MSE
FCM	$y(k - 1)$ , $u(k)$	2	0.4243
TSFC+FCM	$y(k - 1)$ , $u(k - 4)$	2	0.1655
FCM	$y(k - 1)$ , $y(k - 2)$ , $u(k)$ , $u(k - 1)$	2	0.0757
TSFC+FCM	$y(k - 1)$ , $y(k - 2)$ , $u(k - 3),$ $u(k - 4)$	2	0.0609
FCM	$y(k - 1)$ , $y(k - 2)$ , $y(k - 3)$ , $u(k)$ , $u(k - 1)$ , $u(k - 2)$	2	0.0570
TSFC+FCM	$y(k - 1)$ , $y(k - 2)$ , $y(k - 3)$ , $u(k - 2)$ , $u(k - 3),$ $u(k - 4)$	2	0.0545

Model	Input	c	MSE1 (Train)	MSE2 (Test)
FCM	$y(k - 1)$ , $u(k)$	2	0.3252	0.9611
TSFC+FCM	$y(k - 1)$ , $u(k - 4)$	2	0.0801	0.3803
FCM	$y(k - 1)$ , $y(k - 2)$ , $u(k)$ , $u(k - 1)$	2	0.0305	0.5387
TSFC+FCM	$y(k - 1)$ , $y(k - 2)$ , $u(k - 3),$ $u(k - 4)$	2	0.0164	0.1679
FCM	$y(k - 1)$ , $y(k - 2)$ , $y(k - 3)$ , $u(k)$ , $u(k - 1)$ , $u(k - 2)$	2	0.0171	0.1438
TSFC+FCM	$y(k - 1)$ , $y(k - 2)$ , $y(k - 3)$ , $u(k - 2)$ , $u(k - 3),$ $u(k - 4)$	2	0.0152	0.1707

Model	Number of inputs	c	Training MSE
Tsekouras [28]	6	8	0.075
Liu [34]	6	2	0.0561
Li et al. [8]	6	4	0.0498
Li et al. [37]	6	3	0.0560
Li et al. [36]	6	3	0.0534
Our model	6	2	0.0545

Model	Number of rules	MSE1 (Train)	MSE2 (Test)
Tsekouras [28]	7	0.022	0.236
Li et al. [37]	3	0.0159	0.1255
Li et al. [36]	3	0.0150	0.1470
Luo et al. [10]	2	0.0254	0.1243
Yan et al. [15]	2	0.0168	0.1402
Li et al. [14]	3	0.0149	0.1324
Our model	2	0.0152	0.1707
Our model	3	0.0150	0.1567

Fuzzy identification of nonlinear dynamic system based on selection of important input variables

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Model	Input	Number of rules	MSE
FCM	$u(t - 1)$ , $u(t)$ , $y(t - 1)$ , $y(t - 2)$	3	24.4626
TSFC-FCM	$u(t - 1)$ , $u(t - 2)$ , $u(t - 3)$ , $y(t - 1)$	3	3.0505
FCM	$u(t - 2)$ , $u(t - 1)$ , $u(t)$ , $y(t - 1)$ , $y(t - 2)$	3	14.8809
TSFC-FCM	$u(t - 1)$ , $u(t - 2)$ , $u(t - 3)$ , $u(t - 4)$ , $y(t - 1)$	3	2.0168