Fuzzy functions based ARX model and new fuzzy basis function models for nonlinear system identification

  • Authors:
  • Selami Beyhan;Musa Alci

  • Affiliations:
  • Electrical and Electronics Engineering Department, Ege University, Izmir, Turkey;Electrical and Electronics Engineering Department, Ege University, Izmir, Turkey

  • Venue:
  • Applied Soft Computing
  • Year:
  • 2010

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Abstract

In this study, auto regressive with exogenous input (ARX) modeling is improved with fuzzy functions concept (FF-ARX). Fuzzy function with least squares estimation (FF-LSE) method has been recently developed and widely used with a small improvement with respect to least squares estimation method (LSE). FF-LSE is structured with only inputs and their membership values. This proposed model aims to increase the capability of the FF-LSE by widening the regression matrix with lagged input-output values. In addition, by using same idea, we proposed also two new fuzzy basis function models. In the first, basis of the fuzzy system and lagged input-output values are structured together in the regression matrix and named as ''L-FBF''. Secondly, instead of using basis function, the membership values of the lagged input-output values are used in the regression matrix by using Gaussian membership functions, called ''M-FBF''. Therefore, the power of the fuzzy basis function is also enhanced. For the corresponding models, antecedent part parameters for the input vectors are determined with fuzzy c-means (FCM) clustering algorithm. The consequent parameters of the all models are estimated with the LSE. The proposed models are utilized and compared for the identification of nonlinear benchmark problems.