A comparison of methods for the statistics of slow-drift oscillations

A probabilistic model for the slowly varying horizontal motion of a moored floating structure, excited by nonlinear, second order wave forces is derived. The model consists of a coupled system of three white-noise excited stochastic differential equations that govern a continuous vector Markov process. Different methods are applied for the investigation of the first passage time probabilities of the displacement of the marine structure. The methods include time history simulation estimation of the first four moments, time history simulation of the first passage problem, and finite element solution of the backward Kolmogorov equation governing the first passage time distribution. The impact of non-Gaussian aspects of the response on extreme value statistics is demonstrated.