Abstract
This paper describes recent progress and issues in the development of the split-time method for predicting the probability of a roll motion stability failure – capsize or extreme roll motion event – for a ship operating in irregular ocean waves. The split-time method attempts to address the challenge presented by the rarity and physical complexity of such events by separating the problem into a sequence of non-rare and rare problems that can be practically characterized with advanced numerical methods. In the broadest terms, the non-rare problem can be described as determining the rate of occurrence of an intermediate event such as the upcrossing of a threshold roll angle, while the rare problem can be described as determining the probability of capsizing when this intermediate event is realized. The current development of the method focuses on two areas related to the application of this method for nonlinear ship motion in quartering seas.
The first area of development is the variation of the ship's roll restoring curve in following or quartering seas, which is a key element in a pure loss of stability event. To incorporate this phenomenon, the split-time method has been reformulated with the intermediate roll threshold and the critical roll rate leading to capsizing after upcrossing described by stochastic processes. The implementation of this method with the results of numerical simulation data has led to several important results, including the understanding that roll and roll rates may be dependent processes in quartering seas and the development of a novel procedure for characterizing distribution of the dependent process at the instant of upcrossing.
The second area of development is the probabilistic model of surf-riding, which is a necessary step toward evaluating the probability of capsizing or large roll motion due to broaching-to following surf-riding. Recent results include the evaluation of a suitable wave celerity in irregular seas and the use of the existence or non-existence of surf-riding equilibria to describe a ship's transition into and out of surf-riding.