Split-time method for estimation of probability of capsizing caused by pure loss of stability

• Multi-years development of split-time method for capsizing probability is reviewed.
• Capsizing is upcrossing of intermediate level and transition to capsized equilibrium.
• Upcrossing relates probability and time of exposure.
• Motion perturbation at upcrossing instant yields metric of likelihood of capsizing.
• Generalized Pareto distribution is used to extrapolate the metric.

The paper reviews a multi-year research effort for using the split-time method to calculate the probability of ship capsizing due to pure loss of stability in irregular waves. The idea of the split-time method is to separate the complex problem into two less complex problems: a non-rare problem that involves the upcrossing of an intermediate level of roll and a rare problem that focuses on capsizing after an upcrossing. An initial implementation using a dynamic model with piecewise linear stiffness, which can be considered to be the simplest model of capsizing in beam seas, led to the concept of critical roll rate as the smallest roll rate at the instant of upcrossing that inevitably leads to capsizing. The extension of the split-time method to pure loss of stability required the consideration of the change of roll stiffness in waves and led to calculating the critical roll rate at each upcrossing. A metric of the likelihood of capsizing has been defined as the difference between the observed and critical roll rate at the instances of upcrossing. The probability of capsizing after upcrossing is found by approximating the tail with the Generalized Pareto Distribution.