Statistics of extreme ship motions in broad-band wave field

We consider the evaluation of extreme ship motion probability in a broad-band irregular wave field. For this problem, the previous techniques developed for the parameterization of the narrow-band wave field, i.e., methods based on the wave group structures, cannot be directly applied. The group-based statistics that are widely used in existing works also become ambiguous. In this work, we develop a new framework to directly resolve the temporal exceeding probability, defined as the fraction of time that ship motions exceed a given threshold. The parameterization of the wave field will be based on structures with elevations exceeding some threshold that are well suited to broad-band waves. The effectiveness of the proposed approach will be demonstrated in multiple broad-band wave fields with ship motion simulated by nonlinear roll equations.