Spatiotemporal online fuzzy modeling with knowledge-driven differential evolution automatic clustering for distributed parameter systems

Distributed parameter systems are prevalent in various industrial processes and attract significant attention. However, these systems exhibit complex spatiotemporal coupling characteristics, and effectively determining the fuzzy rules of the antecedent set is crucial for improving modeling performance. Traditional clustering methods typically rely on empirical heuristics and are unable to adapt to dynamic system characteristics under changing environments. In high-dimensional and nonlinear scenarios, the number of fuzzy rule combinations grows exponentially, significantly increasing computational complexity. Therefore, an online spatiotemporal three-dimensional fuzzy modeling method based on knowledge-driven differential evolution automatic clustering and extreme learning machine (3D-OSADE-ELM) is proposed for the complex nonlinear distributed parameter system. First, an automatic clustering mechanism based on differential evolution and extreme learning machine initializes the fuzzy rules within the three-dimensional fuzzy system. Subsequently, a knowledge-driven archiving mechanism dynamically updates the fuzzy rules of the antecedent set during the online incremental learning phase. Finally, the spatial basis function is obtained by learning the output weight of the online extreme learning machine. The validation experiments conducted on the rapid thermal chemical vapor deposition reactor system and the nonisothermal packed-bed system demonstrate the effectiveness and superiority of the proposed method.