^{a}, Ioannis A. Kontolefas

^{b}and Kostas J. Spyrou

^{c}

^{a}panasto@central.ntua.gr

^{b}ikon@central.ntua.gr

^{c}k.spyrou@central.ntua.gr

The paper investigates the structure of the distribution of ship rolling motions in random beam seas using an improved formulation of the so called “critical wave groups” method. The method identifies “critical” wave sequences, which cause slight exceedance of a given roll angle threshold, in terms of the expected wave groups of a sea state. The probability that a ship exceeds that threshold is then calculated through the probability of encountering any wave sequence higher than the determined critical, conditioning on the state of the vessel at the instant of the group encounter. In this study, the “critical wave groups” scheme is utilized for quantifying the contribution of threshold exceedances that lead to capsize (“escapes”) to the total probability of extreme responses. Meanwhile, we build understanding about the distribution of escapes by analyzing the nonlinear phenomena that take place in the phase-space of the dynamical system during critical wave group encounters. The results reveal that the distribution of the roll process can be divided into sub-regions with qualitatively different probabilistic characteristics that are related to the form of the restoring term.