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

• CONTROL THEORY AND APPLICATION • Previous Articles Next Articles

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)

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

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.

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References 38

1	SNIEDER E, SHAKIR R, KHAN U T. A comprehensive comparison of four input variable selection methods for artificial neural network flow forecasting models. Journal of Hydrology, 2019. DOI: 10.1016/j.jhydrol.2019.124299.
2	CHEN S F, GU H, TU M Y, et al Robust variable selection based on bagging classification tree for support vector machine in metabonomic data analysis. Journal of Chemometrics, 2018, 32 (11): e2921. doi: 10.1002/cem.2921
3	KANG R, ZHANG X K, LIU H J, et al Selection of optimal combinations of inputs in a partial least squares model for prediction of soil organic matter. Spectroscopy Letters, 2018, 51 (7): 373- 381. doi: 10.1080/00387010.2018.1485706
4	WANG Y X, JIA Z H, YANG J A variable selection method of the significance multivariate correlation competitive population analysis for near-infrared spectroscopy in chemical modeling. IEEE Access, 2019, 7, 167195- 167209. doi: 10.1109/ACCESS.2019.2954115
5	KIM G H, KIM S H Variable selection for artificial neural networks with applications for stock price prediction. Applied Artificial Intelligence, 2019, 33 (1): 54- 67. doi: 10.1080/08839514.2018.1525850
6	TAKAGI T, SUGENO M Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. on Systems, Man, and Cybernetics, 1985, 15 (1): 116- 132.
7	SUGENO M, YASUKAWA T A fuzzy-logic-based approach to qualitative modeling. IEEE Trans. on Fuzzy Systems, 1993, 122 (1): 7- 31.
8	LI C S, ZHOU J Z, XIANG X Q, et al T-S fuzzy model identification based on a novel fuzzy c-regression model clustering algorithm. Engineering Applications of Artificial Intelligence, 2009, 22 (4/5): 646- 653. doi: 10.1016/j.engappai.2009.02.003
9	CHANG C W, TAO C W A novel approach to implement Takagi–Sugeno fuzzy models representation. IEEE Trans. on Cybernetics, 2017, 47 (9): 2353- 2361. doi: 10.1109/TCYB.2017.2701900
10	LUO M N, SUN F C, LIU H P Hierarchical sparse representation for T-S fuzzy systems identification. IEEE Trans. on Fuzzy Systems, 2013, 21 (6): 1032- 1043. doi: 10.1109/TFUZZ.2013.2240690
11	GUO F, LIN L, XIE X, et al Novel hybrid rule network based on TS fuzzy rules. Neural Network World, 2015, 25 (1): 93- 116. doi: 10.14311/NNW.2015.25.005
12	ZHAO K, LI S R, KANG Z J. Takagi-Sugeno fuzzy modeling and control of nonlinear system with adaptive clustering algorithms. Proc. of the 10th International Conference on Modelling, Identification and Control, 2018: 1−6.
13	ZOU W, LI C S, ZHANG N A T-S fuzzy model identification approach based on a modified inter Type-2 FRCM algorithm. IEEE Trans. on Fuzzy Systems, 2018, 26 (3): 1104- 1113. doi: 10.1109/TFUZZ.2017.2704542
14	LI C S, ZOU W, ZHANG N, et al An evolving T-S fuzzy model identification approach based on a special membership function and its application on pump-turbine governing system. Engineering Application of Artificial Intelligence, 2018, 69, 93- 103. doi: 10.1016/j.engappai.2017.12.005
15	YAN S Q, ZHOU J Z, ZHENG Y, et al An improved hybrid backtracking search algorithm based T-S fuzzy model and its implementation to hydroelectric generating units. Neurocomputing, 2018, 275, 2066- 2079. doi: 10.1016/j.neucom.2017.10.036
16	CHROUTA J, FARHANI J, ZAAFOURI A, et al. A methodology for modelling of Takagi-Sugeno fuzzy model based on multi-particle swarm optimization: application to gas furnace system. Proc. of the 6th International Conference on Control, Decision and Information Technologies, 2019: 23−26.
17	LI R C, GUO Y Q, NGUANG S K, et al Takagi-Sugeno fuzzy model identification for turbofan aero-engines with guaranteed stability. Chinese Journal of Aeronautics, 2018, 31 (6): 1206- 1214. doi: 10.1016/j.cja.2018.04.010
18	JOHANSEN S V, BENDTSEN J D, JENSEN M R, et al Broiler weight forecasting using dynamic neural network models with input variable selection. Computers and Electronics in Agriculture, 2019, 159, 97- 109. doi: 10.1016/j.compag.2018.12.014
19	CHANG F, HEINEMANN P H Optimizing prediction of human assessments of dairy odors using input variable selection. Computers and Electronics in Agriculture, 2018, 150, 402- 410. doi: 10.1016/j.compag.2018.05.017
20	WANG Q, FAN C H, BAI J Y, et al SO₂ emission characteristic modeling based on variable selection and SVM . Thermal Power Generation, 2018, 47 (3): 68- 75.
21	LOVATTI B P O, NASCIMENTO M H C, NETO A C, et al Use of random forest in the identification of important variables. Microchemical Journal, 2019, 145, 1129- 1134. doi: 10.1016/j.microc.2018.12.028
22	BANAKAR A, AZEEM M F. Input selection for TSK fuzzy model based on modified mountain clustering. Proc. of the 3rd International IEEE Conference on Intelligent Systems, 2006: 295–299.
23	LIN Y H, CUNNINGHAM G A, COGGESHALL S V, et al Nonlinear system input structure identification: two stage fuzzy curves and surfaces. IEEE Trans. on System, Man, and Cybernetics—Part A: Systems and Humans, 1998, 28 (5): 678- 684. doi: 10.1109/3468.709615
24	GUSTAFSON D E, KESSEL W C. Fuzzy clustering with a fuzzy covariance matrix. Proc. of the 17th IEEE Conference on Decision Control, 1979: 761−766.
25	GATH I, GEVA A B Unsupervised optimal fuzzy clustering. IEEE Trans. on Pattern Analysis and Machine Intelligence, 1989, 11 (7): 773- 781. doi: 10.1109/34.192473
26	TSAI S H, CHEN Y W A novel identification method for Takagi-Sugeno fuzzy model. Fuzzy Sets and Systems, 2018, 338, 117- 135. doi: 10.1016/j.fss.2017.10.012
27	ZHU L F, WANG J S, WANG H Y A novel clustering validity function of FCM clustering algorithm. IEEE Access, 2019, 7, 152289- 152315. doi: 10.1109/ACCESS.2019.2946599
28	TSEKOURAS G E On the use of the weighted fuzzy C-means in fuzzy modeling. Advance Engineering Software, 2005, 36 (5): 287- 300. doi: 10.1016/j.advengsoft.2004.12.001
29	KIM E, PARK M, JI S, et al A new approach to fuzzy modeling. IEEE Trans. on Fuzzy Systems, 1997, 5 (3): 328- 337. doi: 10.1109/91.618271
30	JIANG W, YANG T, SHOU Y H, et al Improved evidential fuzzy c-means method. Journal of Systems Engineering and Electronics, 2018, 29 (1): 187- 195. doi: 10.21629/JSEE.2018.01.19
31	LIU Z, CHEN X H, LIU J, et al Source number estimation method based on fuzzy C-means clustering. Systems Engineering and Electronics, 2019, 41 (2): 244- 247.
32	LO J C, YANG C H A heuristic error-feedback learning algorithm for fuzzy modeling. IEEE Trans. on Systems, Man, and Cybernetics—Part A: Systems and Humans, 1999, 29 (6): 686- 691. doi: 10.1109/3468.798075
33	MASOUMI M S, KHANJANI M, QADERI K Uplift capacity prediction of suction caisson in clay using a hybrid intelligence method (GMDH-HS). Applied Ocean Research, 2016, 59, 408- 416. doi: 10.1016/j.apor.2016.07.005
34	LIU F C. Fuzzy model identification of nonlinear system and its application. Beijing: National Defense Industry Press, 2006. (in Chinese)
35	BOX G E, JENKINS G M. Time series analysis: forecasting and control. San Fransisco: Holden-Day Inc., 1976.
36	LI C S, ZHOU J Z, FU B, et al T-S fuzzy model identification with a gravitational search-based hyper-plane clustering algorithm. IEEE Trans. on Fuzzy Systems, 2012, 20 (2): 305- 317. doi: 10.1109/TFUZZ.2011.2173693
37	LI C S, ZHOU J Z, LI Q Q, et al A new T-S fuzzy-modeling approach to identify a boiler-turbine system. Expert Systems with Applications, 2010, 37 (3): 2214- 2221. doi: 10.1016/j.eswa.2009.07.052
38	LIU F C, WANG L X, JIA X J, et al The application of linear/nonlinear active disturbance rejection switching control in variable load pneumatic loading system. Journal of Mechanical Engineering, 2018, 54 (12): 225- 232.

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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References 38

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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