Extrapolation of ship capsize probability over significant wave height: Foundation on wave groups theory

Abstract

The paper lays formal foundation for the “extrapolation over significant wave height” technique which has recently been incorporated into the Second Generation Intact Stability Criteria of the International Maritime Organization (IMO) for assessing the dynamic stability of ships in waves. The technique aims at estimating efficiently a ship's tendency to capsize in relatively mild sea conditions through parsimonious simulations of ship motion. To address the rarity of capsizes in such conditions, extrapolation is employed for the probability value obtained from severer sea states differing only in their significant wave heights. In its current version, the approach extrapolates as if capsize was caused solely by exceptionally large wave encounters, thus ignoring phenomena such as resonance or wave grouping. Herein, the concept is revisited from the perspective of the “critical wave groups” method which is demonstrated as a general framework enabling rigorous “extrapolation over significant wave height” formulations. In this setting, two new extrapolation models are developed from basic principles as improvements to the one suggested by the IMO. The first model accounts for the joint effect of wave heights and periods, while the second additionally integrates the temporal dependence between consecutive wave heights into the extrapolation scheme. The accuracy of the theoretical predictions as well as their sensitivity to the amount of available data are evaluated for the case of beam-sea rolling assuming two different spectrum types as possible characterizations of the prevailing wave conditions. Justification about the extrapolation capabilities of the derived models is provided in view of the advances in extreme wave stochastics accommodated by the theory of Quasi-Determinism.