A Collaborative Learning Spatiotemporal Three-Dimensional Fuzzy Framework for Modeling Complex Distributed Parameter Systems

Distributed parameter systems (DPSs) are prevalent in various industrial processes. However, spatiotemporal coupling, nonlinearity, and time-varying dynamics lead to complex modeling of DPSs. Traditional approaches often fail to address these challenges effectively. This paper proposes a collaborative three-dimensional (3D) fuzzy modeling framework that integrates automatic clustering based on an adaptive genetic algorithm and support vector regression (SVR) for complex DPS modeling. The proposed method constructs a collaborative 3D fuzzy model by utilizing automatic clustering to extract fuzzy rules and employing SVR to learn spatial basis functions while incorporating spatiotemporal separation and synthesis. Experimental validation of the rapid thermal chemical vapor deposition heating process demonstrates the effectiveness and superiority of the proposed approach.