A multi-objective subtractive FCM based TSK fuzzy system with input selection, and its application to dynamic inverse modelling of MR dampers

A new encoding scheme is presented for a fuzzy-based nonlinear system identification methodology, using the subtractive Fuzzy C-Mean clustering and a modified version of non-dominated sorting genetic algorithm. This method is able to automatically select the best inputs as well as the structure of the fuzzy model such as rules and membership functions. Moreover, three objective functions are considered to satisfy both accuracy and compactness of the model. The proposed method is then employed to identify the inverse model of a highly nonlinear structural control device, namely Magnetorheological (MR) damper. It is shown that the developed evolving Takagi–Sugeno-Kang (TSK) fuzzy model can identify and grasp the nonlinear dynamics of inverse systems very well, while a small number of inputs and fuzzy rules are required for this purpose.