Stable ANFIS2 for Nonlinear System Identification

This paper presents a novel adaptive neuro fuzzy inference system that uses interval Gaussian type-2 fuzzy sets in the antecedent part and Gaussian type-1 fuzzy sets as coefficients of linear combination of input variables in the consequent part. The capability of the proposed ANFIS2 for function approximation and dynamical system identification is remarkable. Furthermore, knowing the fact that fast learning algorithms are so vital for real time systems identification, another simplified ANFIS2 with crisp coefficients of linear combination of input variables in the consequent part is presented. Although the structure of the proposed ANFIS2 are very similar to that of the traditional ANFIS, in ANFIS2 a layer is added for the purpose of type reduction. An adaptive learning rate based backpropagation algorithm with convergence guaranteed is used for parameter learning. Finally, the proposed ANFIS2s are used to identify three nonlinear systems as case studies. A comparison between ANFIS2 with Gaussian type-1 fuzzy, interval value and crisp value as coefficients of linear combination of input variables in the consequent part and ANFIS is presented. Simulation results show that the proposed ANFIS2 with Gaussian type-1 fuzzy sets as coefficients of linear combination of input variables in the consequent part has a better performance as well as a high accuracy though it requirs more training time. (C) 2016 Elsevier B.V. All rights reserved.