Probability analysis and parameter estimation for nonlinear relative wave motions on a semi-submersible using the method of LH-moments

Nonlinear relative wave motions and air gap performance greatly affect the operation and security of semi-submersibles in harsh environments. An appropriate air gap is essential to preventing potential impact loads, and accurate prediction for long-return-period events is of great concern. Given the random and nonlinear nature of relative wave motions, a reliable approach for their prediction is a challenging task that warrants further research. In this study, a modified three-parameter Rayleigh distribution model for nonlinear relative wave crests was derived utilising a quadratic transformation of incident waves. The method of LH-moments was used to estimate the unknown parameters from sample data, and the relationship between the parameters and LH-moments was derived. The sample data used for the probability analysis were obtained from a model test programme for a semi-submersible. The first-order parameter of the model was found to decrease with increasing η, whereas the second-order parameter was found to increase. A larger second-order parameter indicates higher nonlinearity of the relative wave motions for a 100-year-return sea state than for a 1-year-return sea state. In general, using LH-moments to estimate the parameters of the probability distribution results in better prediction of large relative wave crests with low probabilities of exceedance, because the estimation of the three parameters in the nonlinear Rayleigh model using LH-moments released the constraint on the linear term.

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