Orthogonalised frequency domain volterra model for non-gaussian inputs

Abstract

An orthogonalised Volterra system model, valid for both non-Gaussian and Gaussian inputs, is presented. The approach is based on ordered sets of conditioned orthogonal higherorder input vectors in the frequency domain, and utilises co-ordinate transformation to relate the orthogonal and nonorthogonal system models. The orthogonal model exhibits no interference effects, thus facilitating physical interpretation of the nonlinear system model. The importance of non-Gaussian excitation in the nonlinear system identification procedure is discussed. The performance of the orthogonalised Volterra model is measured in terms of a generalised nonlinear system coherence function, and compared with the results of the Wiener (for Gaussian input) and Volterra models. The advantages of the orthogonalised Volterra model are illustrated by using it to model the linear and quadratic responses of a tension leg platform subject to random seas, given experimental input-output time series data.