Evaluation of the critical wave groups method in calculating the probability of ship capsize in beam seas

Abstract

The paper proposes certain improvements in the setup of the “critical wave groups” method which has been introduced in the past for calculating the probability of extreme roll responses. Moreover, a precise mathematical formulation of the “critical wave groups” concept is presented and the selection of key parameters for its computational setting is discussed. The most significant development concerns the hitherto assumption of zero initial conditions of the vessel at the instant of a wave group encounter, which is now removed through probabilistic treatment of ship's initial state. The improved method is evaluated for its potential to produce accurate estimates in the various regions of roll response distribution including the tail, where the efficiency of direct Monte Carlo simulations is very low. In the range of intermediate responses, it is demonstrated that the method becomes more effective when employing the expected wave sequences given a sea state, instead of regular waveforms, for determining “critical” (for ship stability) wave episodes. Lastly, two alternative implementations of the “critical wave groups” concept are assessed; one empirical, where the distributions of main parameters, such as the wave period and height, are deduced from simulations of the wave field; and one where they are calculated directly from the spectrum.