Stochastic Response of Offshore Platforms by Statistical Cubicization

Abstract

In this study, a method of statistical cubicization is proposed to predict stochastic response of offshore platform to a Morison-type nonlinear random wave loading. The nonlinearity is replaced by an equivalent polynomial expansion up to cubic order. The Volterra series method is used to solve the resulting nonlinear equivalent system in the frequency domain. Complete expressions to evaluate response central moments up to the fourth order are obtained for a three-term Volterra system driven by a stationary Gaussian input. To make the developed method efficient and practical, an efficient solution scheme is proposed to implement the Volterra series method. Results (i.e., response mean, variance, skewness, and kurtosis) are presented for the cases of fixed offshore structures and compared with those obtained by simulation, equivalent linearization, and quadratization methods. The statistical cubicization method is superior to both the statistical linearization and quadratization method.