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In computing ship motion statistics (e.g., exceeding probability) in anirregular wave field, it is a common practice to represent the irregular wavesby a large number of wave groups and compute the motion statistics from thedistribution of these wave groups. While this procedure significantly reducesthe computational cost, the uncertainties introduced in this reduced-ordercomputation have not been quantified. In general, the representation of acontinuous wave field by separated groups loses information about wave phases,frequency modulation and initial conditions of ship when encountering the wavegroups, among which the last one is arguably the most influential factor forthe ship motion statistics. In this paper, we test three methods to incorporatethe ship initial conditions into the computation of roll motion exceedingprobability, namely the methods of natural initial condition, pre-computedinitial condition and constant initial condition. For different input wavespectra and ship motion dynamics (in terms of the parametric excitation levelmodeled by a nonlinear roll equation), the performances of the three methodsare carefully benchmarked and the superiority of the natural initial conditionmethod is demonstrated. We finally show that the computation using the naturalinitial condition method can be greatly accelerated through a sequentialsampling algorithm making use of the variational heteroscedastic Gaussianprocess regression.

Effects of varying initial conditions of ship encountering wave groups in computing extreme motion statistics