A time/space separation based 3D fuzzy modeling approach for nonlinear spatially distributed systems

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...

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Bibliographic Details
Published in:International journal of automation and computing 2018-02, Vol.15 (1), p.52-65
Main Authors: Zhang, Xian-Xia, Fu, Zhi-Qiang, Li, Shao-Yuan, Zou, Tao, Wang, Bing
Format: Article
Language:English
Subjects:
Basis functions
CAE) and Design
Computer Applications
Computer networks
Computer simulation
Computer-Aided Engineering (CAD
Control
Engineering
Fuzzy sets
Fuzzy systems
Mechatronics
Modelling
Nonlinear systems
Parameter identification
Particle swarm optimization
Research Article
Robotics
Separation
Three dimensional models
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Summary: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.
ISSN:1476-8186
1751-8520
DOI:10.1007/s11633-017-1080-0