Identification of non-linear dynamic systems using fuzzy system with constrained membership functions

Abstract

This study deals with the use of the rule-based fuzzy system for the identification of non-linear dynamic systems. Main research directions in this field include the complexity reduction of fuzzy models models, structure identification of fuzzy system, and application of new or improved training algorithms. In this study, a constrained fuzzy system (CFS), which is a simplified form of the standard fuzzy system (SFS), was proposed as an alternative identifier of non-linear dynamic systems in order to indirectly reduce the rule explosion problems inherent in fuzzy systems. In addition, the use of two alternative training algorithms, namely the recursive prediction error (WE) and Levenberg-Marquardt (LM) algorithms, were proposed. In this study, the identification performance of the SFS trained by the back-propagation (BP) algorithm forms the basis of comparison when evaluations were made on the performance of the newly proposed CFS models. It was found that, in most cases, the CFS performs better than the SFS with similar number of adjustable parameters. It was also found that the convergence properties of the RPE algorithm are better than those of the BP algorithm, and the performance of the LM algorithm is comparable to that of the RPE algorithm. Furthermore, this study has shown that the CFS is capable of producing adequate models that can satisfy the 95% confidence requirement of the correlation tests. In addition, in a case study, it has been shown that the CFS has some potential to be an alternative tool for aircraft parameter estimation from flight data. It was also found that the CFS could be used as substitutes for the rainfall-runoff models in cases where the autoregressive with exogenous inputs (ARX) and the autoregressive moving average with exogenous inputs (ARMAX) models need further improvements