Efficient identification of third order Volterra models using interpolation techniques

Abstract

The paper presents an efficient method for the identification of third-order Volterra models in the frequency domain. The main difficulty of such modeling is that it requires an excessive amount of measurements. When an arbitrary, band-limited periodic signal with N harmonics is applied as excitation to a plant, its third-order kernel is to be determined at N/sup 3/ frequency points. This leads to an estimation problem with O {N/sup 3/} linear unknown vs. O {N} equations. In order to get as many linear equations as unknowns, the experiment must be repeated O {N/sup 2/} times, each time with different exciting Fourier amplitudes. The new approach presented in the paper reduces model complexity. The quadratic and cubic kernel surfaces are approximated by smooth functions, the parameters of which become the new linear unknowns. Since the number of parameters does not grow with N, the size of the experiments can be brought down. As the modified model is a projection, the solution can, of course, be only approximate. The underlying assumptions that allow this approximation are explained and experimental case studies illustrate the workability of the ideas. A signal filtering technique is also described as an additional resort when identifying characteristics with narrow resonance peaks. This latter problem arises e.g. during the identification of a nonlinear resonator device.