ABSTRACT

We present a new orthogonal approach for the estimation of nonlinear FRF's which is valid for general random waves (i.e., non Gaussian as well as Gaussian) while at the same time removing the presence of the interference terms associated with non-Gaussian waves. The approach of this paper is illustrated by using it to quantify the linear and quadratically nonlinear dynamical response of TLP's to random non Gaussian sea wave excitation, and by comparing the performance of the conventional non-orthogonal Volterra model with that of the new conditioned orthogonal model.

INTRODUCTION

This paper is concerned with the application of digital bispectral analysis techniques (Powers and Miksad, 1987) to experimentally detect arid quantify nonlinear wave interaction phenomena associated with quadratic response of marine structures such as tension leg platforms (TLP) in non Gaussian random seas, without "interference" of linear wave force and quadratic wave drift force due to the nonGaussian nature of the wave excitation (S. B. Kim et aI., 1989). The presence of the "interference" terms greatly hinder a physical interpretation of the model. For example, the "interference" terms may result in a positive or negative contribution to the power spectrum of the response predicted by the model, depending on the relative phases of the linear and quadratic components of the model (K. I. Kim et aI., 1987). Thus, the objective of this paper is to present a new approach for the estimation of nonlinear FRF's which is valid for general random waves (i.e., nonGaussian as well as Gaussian) while at the same time removing the presence of the interference associated with non-Gaussian wave. In this paper, we derive conditioned orthogonal polyspectral moment matrices of the wave excitation in terms of conventional polyspectral moment matrices utilizing the Gram-Schmidt orthogonalization procedure which do not depend on the wave statistics.

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