Surge response statistics of tension leg platforms under wind and wave loads: a statistical quadratization approach

Commonly, in offshore applications, frequency domain analyses of nonlinear systems have been approximately carried out using the method of equivalent statistical linearization. This method, however, fails to capture 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. Herein, a method of equivalent statistical quadratization is proposed, whereby a statistically asymmetric nonlinearity in the forcing of a tension leg platform (TLP) is cast in a quadratic form. The present quadratization method takes advantage of the Gaussianity of the first order response to simplify the recasting of the nonlinearity in its approximate polynomial form. A Volterra series approach leads to the development of transfer functions from which the response spectrum as well as statistics 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 by linearization and, when used in the framework of some available non-Gaussian probability density function models, indicate acceptable agreement with time-domain simulations of the original nonlinear differential equations. In addition, the response power spectral density contains an additional peak near the resonant frequency of the TLP, where input energy at difference frequencies of the input spectrum lies, corroborating information gleaned from the time-domain simulation.