A Novel Three-Dimensional Fuzzy Modeling Method for Nonlinear Distributed Parameter Systems

Abstract

Data-based spatio-temporal modeling has rapidly developed over the past ten years. However, traditional spatio-temporal modeling methods will encounter some uncertainty caused by model reduction. In addition, the established model is complicated and short of linguistic interpretability. In this study, a novel three-dimensional (3-D) fuzzy modeling framework without model reduction is proposed and a new 3-D fuzzy modeling method based on clustering and support vector regression is developed. This method is based on a 3-D fuzzy system that naturally fuses time/space separation and time/space synthesis into a unified framework. Utilizing the machine learning algorithms (clustering and support vector regression), a 3-D fuzzy system is constructed for modeling an unknown nonlinear distributed parameter system. The advantages of the proposed modeling method over the traditional spatio-temporal modeling method are linguistic interpretability and no reliance on model reduction. The proposed modeling method consists of three steps. First, the nearest neighborhood clustering algorithm is used to learn initial structure model of antecedent sets of 3-D fuzzy rules. Then, similarity measure is used to simplify the initial structure via combining similar fuzzy sets and similar fuzzy rules. Finally, a support vector regression algorithm is applied to calculate spatial functions in the consequent sets of 3-D fuzzy rules. The simulation results demonstrate the effectiveness of the proposed modeling method.