SURGE RESPONSE STATISTICS OF TENSION LEG PLATFORMS UNDER WIND AND WAVE LOADS - A STATISTICAL QUADRATIZATION APPROACH

Commonly, in offshore applications, frequency domain analyses of nonli near systems have been approximately carried out using the method of e quivalent statistical linearization. This method, however, fails to ca pture the non-Gaussianity of the response in terms of its higher-order statistics. In addition, response energy in frequency ranges outside that of the input spectrum is not observed using this technique. Herei n, a method of equivalent statistical quadratization is proposed, wher eby a statistically asymmetric nonlinearity in the forcing of a tensio n leg platform (TLP) is cast in a quadratic form. The present quadrati zation method takes advantage of the Gaussianity of the first order re sponse to simplify the recasting of the nonlinearity in its approximat e polynomial form. A Volterra series approach leads to the development of transfer functions from which the response spectrum as well as sta tistics of the response may be obtained. Response cumulants, computed up to fourth order via direct integration or the Kac-Siegert technique , reveal the non-Gaussian character of the response which was hidden b y linearization and, when used in the framework of some available non- Gaussian probability density function models, indicate acceptable agre ement with time-domain simulations of the original nonlinear different ial equations. In addition, the response power spectral density contai ns an additional peak near the resonant frequency of the TLP, where in put energy at difference frequencies of the input spectrum lies, corro borating information gleaned from the time-domain simulation.