A Time/Space Separation Based 3D Fuzzy Modeling Approach for Nonlinear Spatially Distributed Systems

作     者：Xian-Xia Zhang Zhi-Qiang Fu Shao-Yuan Li Tao Zou Bing Wang 

作者机构：Shanghai Key Laboratory of Power Station Automation Technology School of Mechatronics and AutomationShanghai University Institute of Automation Shanghai Jiao Tong University Shenyang Institute of Automation Chinese Academy of Sciences 

出 版 物：《International Journal of Automation and computing》 (国际自动化与计算杂志（英文版）)

年 卷 期：2018年第15卷第1期

页      面：52-65页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Science Foundation of China(Nos.61273182 31570998 51375293 and 61374112) 

主　　题：Spatially distributed system (SDS) system identification 3D fuzzy system Karhunen-Love decomposition particleswarm optimization (PSO). 

摘      要：Spatially distributed systems （SDSs） are usually infinite-dimensional spatio-temporal systems with unknown nonlinearities. Therefore, to model such systems is difficult. In real applications, a low-dimensional model is required. In this paper, a time/space separation based 3D fuzzy modeling approach is proposed for unknown nonlinear SDSs using input-output data measurement. The main characteristics of this approach is that time/space separation and time/space reconstruction are fused into a novel 3D fuzzy system. The modeling methodology includes two stages. The first stage is 3D fuzzy structure modeling which is based on Mamdani fuzzy rules. The consequent sets of 3D fuzzy rules consist of spatial basis functions estimated by Karhunen-Love decomposition. The antecedent sets of 3D fuzzy rules are used to construct temporal coefficients. Going through 3D fuzzy rule inference, each rule realizes time/space synthesis. The second stage is parameter identification of 3D fuzzy system using particle swarm optimization algorithm. After an operation of defuzzification, the output of the 3D fuzzy system can reconstruct the spatio-temporal dynamics of the system. The model is suitable for the prediction and control design of the SDS since it is of low-dimension and simple nonlinear structure. The simulation and experiment are presented to show the effectiveness of the proposed modeling approach.