Non-linear Parameter Estimation Using Volterra Series with Multi-tone Excitation

The functional form representation of input-output relationship through Volterra series provides a structured mathematical platform for the study of nonlinear systems. It employs multi-dimensional kernels, which upon convolution with the applied excitation forces, express system response in the form of a power series. Frequency domain transforms of these multi-dimensional kernels provide higher order frequency response functions, which are related to first order kernel transfroms through the set of nonlinear parameters of the system. This relationship has been employed in this paper to develop a nonlinear parameter estimation procedure. Multi-tone excitation is used here and response harmonic amplitudes at fundamental as well as higher order combination tones are measured. Volterra series expression for these response amplitudes provides a set of nonlinear equations involving the first order kernel transforms and the nonlinear parameters. Linear and nonlinear parameters are estimated by solving the set of nonlinear equations and by standard curve fitting procedures.