Application of a new copmact optimized T-S fuzzy model to nonlinear system identification

Abstract

A new encoding scheme is presented for learning the Takagi-Sugeno (T-S) fuzzy model from data by non-dominated sorting genetic algorithm (NSGAII). The proposed encoding scheme consists of two parts. First part is related to input selection and the second one is related to antecedent structure of T-S fuzzy model (selection of rules, number of rules and parameters of MFs). The main aim of proposed scheme is to reduce both model’s complexity and error. The subtractive clustering method with least square estimator has been used for determining the initial structure of fuzzy model. So the center’s range of influence for each of the data dimensions is considered as an adjustable parameter in order to obtain better clusters. The input structure and center’s ranges of influence are all represented in one chromosome and evolved together through a well-known multi objective optimization method namely NSGAII, such that the optimization of rule structure, input structure, and MF parameters can be achieved simultaneously. The performance of the developed evolving T-S fuzzy model is first validated by studying the benchmark Box-Jenkins nonlinear system identification problem. Then, it is applied to approximate the forward and inverse dynamic behaviors of a magneto-rheological (MR) damper of which identification problem is significantly difficult due to its inherently hysteretic and highly nonlinear dynamics. It is shown by the validation applications that the developed evolving T-S fuzzy model can identify the nonlinear system satisfactorily with acceptable number of rules and inputs.