Three-Dimensional Fuzzy Modeling for Nonlinear Distributed Parameter Systems Using Simultaneous Perturbation Stochastic Approximation

Abstract

Many systems in the manufacturing industry have spatial distribution characteristics, which correlate with both time and space. Such systems are known as distributed parameter systems (DPSs). Due to the spatiotemporal coupling characteristics, the modeling of such systems is quite complex. The paper presents a new approach for three-dimensional fuzzy modeling using Simultaneous Perturbation Stochastic Approximation (SPSA) for nonlinear DPSs. The Affinity Propagation clustering approach is utilized to determine the optimal number of fuzzy rules and construct a collection of preceding components for three-dimensional fuzzy models. Fourier space base functions are used in the resulting components of three-dimensional fuzzy models, and their parameters are learned by the SPSA algorithm. The proposed three-dimensional fuzzy modeling technique was utilized on a conventional DPS within the semiconductor manufacturing industry, with the simulation experiments confirming its efficacy.