Tail Structure of Roll and Metric of Capsizing in Irregular Waves

Extreme values of ship motions and loads in irregular waves are of considerable interest for both the analysis of prospective designs and the development of operational guidance. However, the direct evaluation of these extremes via Monte-Carlo methods is cost-prohibitive, as they are too rare to be predicted by a model test or numerical simulation of sufficient fidelity in realistic sea conditions. This paper describes recent developments in extreme value assessment procedures that are based on characterizing the extreme response from a finite set of numerical simulations. The specific focus of the present work is to use physical considerations to determine the type of tail of a distribution for a random variable that characterizes the extreme motion. This essentially adds physical information into the statistical model and may decrease the statistical uncertainty associated with extreme value prediction. The paper considers tails of two random variables: peaks of roll motions and values of the capsizing metric from the split-time method. A theoretical a certain closed-form solutions the large roll angles the metric. linear system with triangular stiffness is a qualitative model of a dynamical system softening stiffness (reduced at larger roll angles), closed-form reveal the principle form of the tails of the must have heavy