Nonlinear system identification using Takagi-Sugeno type neuro-fuzzy model

Neuro-fuzzy (NF) modeling can be regarded as a gray-box technique on the boundary between neural networks and qualitative fuzzy models. The main motivation for this investigation is to develop an identification procedure for nonlinear systems and processes without having their complete information. The main problem in developing the Takagi-Sugeno (TS) type of neuro-fuzzy models is to identify the number of membership functions partitioning each input variable or the number of rules. Moreover, the neuro-fuzzy model of particular interest of type TS also has problem of poor initialization. In this paper, an algorithm for neuro-fuzzy modeling of nonlinear system identification is given, with an emphasis on the trade-off between accuracy and interpretability. The proposed algorithm not only solves the problem of poor initialization but also automatically identifies the optimal structure of the model and still gives the more accurate results in comparison to the standard neuro-fuzzy models. A two-step procedure of Takagi-Sugeno type neuro-fuzzy model is proposed here for nonlinear system modeling. In first step, a method of generation of optimal rule base is proposed and in the next step, based on the generated rule base, the structure of the neuro-fuzzy network is decided and thereafter, the constructed NF model is trained by improved Levenberg-Marquardt algorithm (LIMA). The proposed scheme not only eliminates the usual "trial-and-error" mechanism of structure identification but also accelerates the learning process by good initialization of fuzzy membership functions and rules consequents. The proposed method is tested on various benchmark problems. The corresponding results show that a good modeling capability is achieved without employing any complicated optimization procedure for structure identification of neuro-fuzzy model.