Comparison of fuzzy and Volterra series nonlinear system modeling approaches

Abstract

In this study, we investigated modeling performances of two popular nonlinear system identification methods, namely fuzzy modeling and Volterra series. In literature a general approach to nonlinear structure modeling does not exist, therefore both fuzzy models and Volterra series are interesting and widely used as they can approximate a large class of nonlinear functions. In fuzzy modeling, a dynamic system is modeled using a set of fuzzy membership functions and rules. The fuzzy model parameters are trained using optimization techniques. In Volterra series approach, the dynamic system is modeled using a set of kernel functions that represent the first and higher order convolutions. The kernel functions are typically estimated using an orthogonal expansion technique using a set of suitable basis functions such as Laguerre. We compared the modeling performance of these approaches on a hypothetical test system whose kernels or structure is known priori and observed that the Volterra modeling based on Laguerre basis expansion of kernels offers better performance.