A novel self-constructing Radial Basis Function Neural-Fuzzy System

Abstract

This paper proposes a novel self-constructing least-Wilcoxon generalized Radial Basis Function Neural-Fuzzy System (LW-GRBFNFS) and its applications to non-linear function approximation and chaos time sequence prediction. In general, the hidden layer parameters of the antecedent part of most traditional RBFNFS are decided in advance and the output weights of the consequent part are evaluated by least square estimation. The hidden layer structure of the RBFNFS is lack of flexibility because the structure is fixed and cannot be adjusted effectively according to the dynamic behavior of the system. Furthermore, the resultant performance of using least square estimation for output weights is often weakened by the noise and outliers.This paper creates a self-constructing scenario for generating antecedent part of RBFNFS with particle swarm optimizer (PSO). For training the consequent part of RBFNFS, instead of traditional least square (LS) estimation, least-Wilcoxon (LW) norm is employed in the proposed approach to do the estimation. As is well known in statistics, the resulting linear function by using the rank-based LW norm approximation to linear function problems is usually robust against (or insensitive to) noises and outliers and therefore increases the accuracy of the output weights of RBFNFS. Several nonlinear functions approximation and chaotic time series prediction problems are used to verify the efficiency of self-constructing LW-GRBFNIS proposed in this paper. The experimental results show that the proposed method not only creates optimal hidden nodes but also effectively mitigates the noise and outliers problems.