A new evolving compact optimised Takagi–Sugeno fuzzy model and its application to nonlinear system identification

Abstract

A new encoding scheme is presented for a fuzzy-based nonlinear system identification methodology, using the subtractive clustering and non-dominated sorting genetic algorithm. The proposed method consists of two parts. The first part is related to the selection of most relevant or influencing inputs to the system and the second one is related to the tuning of fuzzy rules and parameters of the membership functions. The main purpose of the proposed scheme is to reduce the complexity and increase the accuracy of the model. In particular, three objectives are considered in the process of optimisation, namely, the number of inputs, number of rules and the root mean square of the modelling error. The performance of the developed method is validated by identifying the Box–Jenkins nonlinear benchmark system, and to the modelling of the forward and inverse dynamic behaviours of a magneto-rheological (MR) damper. The latter is also a challenging problem due to the inherent hysteretic and highly nonlinear dynamics of the MR damper. It is shown that the developed evolving Takagi–Sugeno (T–S) fuzzy model can identify and grasp the nonlinear dynamics of both systems very well, while a small number of inputs and fuzzy rules are required for this purpose.

Keywords:

• Takagi–Sugeno fuzzy model
• subtractive clustering
• NSGA-II
• ANFIS
• nonlinear system identification