Generalized rule antecedent structure for TSK type of dynamic models: Structure identification and parameter estimation

Abstract

Scope and Method of Study: A novel rule antecedent structure is proposed to generalize TSK type of dynamic fuzzy models to deal with the problem of curse of dimensionality in conventional TSK fuzzy models. The proposed antecedent structure uses only nonlinear variables, which directly reduce the number of possible rules by reducing antecedent dimension. Additionally, one more degree of freedom is introduced to design antecedents to cover an antecedent space more efficiently, which further reduces the number of rules. The resultant GTSK model is identified in two stages. A novel recursive estimation based on spatially rearranged data is used to determine the consequent and antecedent variables. Model parameter values are obtained from partitioned antecedent space, which is the result of solving a series of splitting and regression problems.

Findings and Conclusions: The proposed rule antecedent structure is able to substantially reduce the complexity in a TSK type of dynamic model. The proposed dynamic order determination and nonlinear component detection methods are tested to be able to identify model structures and shown to be less sensitive to noise than other methods. Instead of directly estimating model parameters, the proposed approach solves a series of splitting and regression problems to partition the antecedent space as well as compute the antecedent and consequent parameters. The resultant antecedent partition is meaningful. The boundaries divide an antecedent space into regions, within which a linear relation is valid. The resultant GTSK model is tested on several nonlinear dynamic processes and shown to be more interpretable and informative than other modeling methods without loss of accuracy.