On the Exceedance Probabilities of Extreme Drift Motions of An Offshore Structure

The response statistics of a compliant offshore structure excited by slowly varying wave drift forces is calculated by use of a numerical path integral solution method.The path integral solution is based on the Gauss-Legendre interpolation scheme,and the values of the response probability density are obtained at the Gauss quadrature points in sub-intervals.It is demonstrated that a distinct advantage of the path integral solution is that the joint probability density of the response displacement and velocity is one of the by products of the calculations.This makes it possible to calculate the mean level up-crossing rates,which provides estimates of the exceedance probabilities of specified response levels for given time periods.