Efficient vector outcrossing analysis of the excursion of a moored vessel

Extreme value prediction of combined first- and second-order motions of a moored floating structure has remained topical for years. Many researchers have applied the Kac–Siegert technique to derive the statistical distribution of the non-Gaussian responses. Almost exclusively, the previous studies have focused on a single-degree-of-freedom system, with the understanding that for any linear dynamical system, one may decouple a specific mode of interest from other degrees-of-freedom. The design philosophy is to assess the allowable limit of each individual motion separately. This paper presents an efficient method for predicting the extreme lateral excursion based on the vector sum of the surge and sway offsets. To this end, the vector outcrossing rate from a prescribed watch-circle is calculated. The joint probability density of the surge and sway responses is approximated using the Nataf transformation. The outcrossing rates thus estimated are found to agree well with those directly extracted from Monte Carlo simulation.