Nonlinear System Modeling Using Multiwavelet Expansion Based Volterra Series

Volterra series is powerful for nonlinear system modeling and has gained great interest of scientists across many disciplines for its theory foundation, brief formulation, and precise physics. The main difficulty of engineering application of Volterra series is the identification of Volterra kernels because the number of parameters need to identify increases exponentially with the order of the kernel. To reduce the number of estimated parameters, this paper expands the first kernel and the second kernel with piecewise quadratic multiwavelet basis function and turns the problem into the solution of a few expansion coefficients. The result of the demonstration on a prototypical nonlinear oscillator is shown that the identified kernels match with the analytical kernels very well and they can accurately predict the responses of the system to different inputs. Besides, for the common input cannot include the nonlinear effect of the interaction of different frequency in a nonlinear system, the paper designs input called two dimension chirp suited for identification of the second order Volterra kernel. Compared with the commonly used chirp inputs, numerical experiment verifies that this input can excite the nonlinear characteristics of the system better.