A Spatiotemporal Fuzzy Modeling Approach Combining Automatic Clustering and Hierarchical Extreme Learning Machines for Distributed Parameter Systems

Gang Zhou, Xianxia Zhang (), Tangchen Wang and Bing Wang
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Gang Zhou: School of Mechatronics and Automation, Shanghai University, Shanghai 200444, China
Xianxia Zhang: School of Mechatronics and Automation, Shanghai University, Shanghai 200444, China
Tangchen Wang: School of Mechatronics and Automation, Shanghai University, Shanghai 200444, China
Bing Wang: School of Mechatronics and Automation, Shanghai University, Shanghai 200444, China

Mathematics, 2025, vol. 13, issue 3, 1-19

Abstract: Modeling distributed parameter systems (DPSs) is challenging due to their strong nonlinearity and spatiotemporal coupling. In this study, a three-dimensional fuzzy modeling method combining genetic algorithm (GA)-based automatic clustering and hierarchical extreme learning machine (HELM) is proposed for DPS modeling. The method utilizes GA-based automatic clustering to learn the premise part of 3D fuzzy rules, while HELM is employed to learn spatial basis functions and construct a complete fuzzy rule base. This approach effectively captures the spatiotemporal coupling characteristics of the system and mitigates the information loss commonly observed in dimensionality reduction in traditional fuzzy modeling methods. Through experimental verification, the proposed method is successfully applied to a rapid thermal chemical vapor deposition system. The experimental results demonstrate that the method can accurately predict temperature distribution and maintain good robustness under noise and disturbances.

Keywords: distributed parameter system; genetic algorithm; automatic clustering; hierarchical extreme learning machine; fuzzy model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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