An Improved Generalized Fuzzy Model Based on Epanechnikov Quadratic Kernel and Its Application to Nonlinear System Identification

Abstract

Fuzzy models have excellent capability of describing nonlinear system, so that a wide variety of models is proposed. However, these models are difficult to train and interpret with a hypothesis of data independence. Base on the above problems, an improved generalized fuzzy model is proposed by rules centralization, a new mixture model is built by substituting Epanechnikov quadratic kernel for Gaussian kernel of Gaussian mixture model, and the mutual transformation between the two models is proved. The proposed fuzzy model can not only provide good interpretability, but also easily estimate the parameters of the fuzzy model using the proposed mixture model. In addition, this proposed fuzzy model has higher segmentation efficiency for the input space with consideration of data correlation. The experimental results of a well-known nonlinear system identification show that the proposed fuzzy model has the best performance with fewer fuzzy rules and better generalization ability than some popular models.