Extracting compact fuzzy rules for nonlinear system modeling using subtractive clustering, GA and unscented filter

This paper presents a two stage procedure for building optimal fuzzy model from data for nonlinear dynamical systems. Both stages are embedded into Genetic Algorithm (GA) and in the first stage emphasis is placed on structural optimization by assigning a suitable fitness to each individual member of population in a canonical GA. These individuals represent coded information about the structure of the model (number of antecedents and rules). This information is consequently utilized by subtractive clustering to partition the input space and construct a compact fuzzy rule base. In the second stage, Unscented Filter (UF) is employed for optimization of model parameters, that is, parameters of the input-output Membership Functions (MFs). The proposed hybrid approach exploits the advantages and utilizes the desirable characteristics of all three algorithms for extracting accurate and compact fuzzy models. Case studies are given to illustrate the efficiency of the modeling procedure. Benchmark examples are analyzed and the results are compared with those obtained by Adaptive Nero-fuzzy Inference System (ANFIS). In all cases enhanced performance and superior results are obtained from the proposed procedure. (C) 2007 Elsevier Inc. All rights reserved.