An Efficient Formulation of the Critical Wave Groups Method for the Assessment of Ship Stability in Beam Seas

Abstract

The paper presents a simplified setup of the “critical wave groups” method, suitable for swift probabilistic evaluations of ship capsize tendency due to beam-sea resonance. The simplifications proposed herein are twofold and aim at reducing the computational cost associated with the identification of the critical, for ship stability, wave episodes when these are represented by the “expected” wave groups for the ambient sea state. The first simplification concerns the initial conditions of the vessel at the moment of a wave group encounter which, according to the exact “critical wave groups” formulation, should be probabilistically treated. Instead, the simplified approach pursues reliable estimates by examining only the upright equilibrium state. Moreover, by focusing on sea states being highly probable to provoke resonance, fewer simulations need to be performed since, among all critical wave group candidates, the main probability contribution essentially comes from those having periods close to the natural period of the vessel in question. Considering these wave groups only constitutes the second simplification. Within this framework, regular wave trains are also tried to investigate the possibility of eliminating the computational burden due to the generation of the “expected” wave groups. The accuracy of both schemes in calculating the probability of extreme responses is assessed through comparisons with Monte Carlo simulations of roll motion.