Approaches to rare events in stochastic dynamics of ships

The paper reviews problems and solutions related to extreme ship motions in random waves. In its general form, the dynamical system is described by integro-differential equations. The bandwidth of excitation is medium; stiffness is extremely nonlinear and random. In standard ship design, the main tools for the engineering evaluation are model experiments and numerical simulations using potential flow hydrodynamics with empirical models for non-potential flow forces. However, a direct Monte Carlo approach is impractical because of the high cost of running these tools and the rarity of extreme motion events. To obtain a practical solution, the principle of separation can be used to effectively consider the nonlinear phenomena resulting in an extreme response and the conditions that lead to the occurrence of such phenomena. This paper discusses fundamental aspects of three methods that use the principle of separation: the peaks-over-threshold/envelope peaks-over-threshold method, the split-time method, and the critical wave group method.

► Extreme responses of a ship in waves are rare, making direct Monte-Carlo impractical.
► The principle of separation subdivides the problem into non-rare and rare elements.
► Non-rare problem targets the probability to reach intermediate level of response.
► Rare problem is to solve for a large response after the intermediate level was exceeded.
► Methods discussed: envelope peaks-over-threshold, split-time and critical wave groups.