Nonlinear system identification using Kautz basis expansion-based Volterra-PARAFAC model

Volterra series is a powerful mathematical tool for nonlinear system analysis, which extends the convolution integral for linear systems to nonlinear systems. There is a wide range of nonlinear engineering systems and structures which can be modeled as Volterra series. The usefulness of Volterra models is mainly because of their ability to approximate any fading memory nonlinear systems to an arbitrary accuracy. One question involved in modeling a functional relationship between the input and output of a system using Volterra series is to identify the Volterra kernel functions, the number of which increases rapidly with the system nonlinearity order and the kernels memory. In this paper, a Kautz basis expansion-based Volterra-PARAFAC model is proposed to identify the Volterra nonlinear system from observations of the in- and outgoing signals. In addition, based on the best linear approximation, an effective method for the choice of initial values of pole parameters is presented, and based on the back propagation through-time technique and the Levenberg-Marquardt algorithm, an optimization algorithm for pole and nonlinear parameters is presented in this paper. The simulation studies verify the effectiveness of the proposed novel Kautz basis expansion-based Volterra-PARAFAC modeling method.