The capsizing of a ship is a complex phenomenon with strong nonlinearity and rarity. This work describes the numerical implementation of estimating capsizing probability by the Split-Time method. The common roll motion of the ship is simulated by a 1-DOF model and the roll motion in pure loss of stability is by a new 1.5-DOF model. According to time course of movement, the capsizing probability is calculated by Split-Time method and verified by MonteCarlo method. The advantage and reliability of the Split-Time method is proved.


The large annual number of ship losses and the associated economic and environmental costs occur in world's oceans, which necessitate the development of researching ship capsizing. Because of the complex ship dynamics resulting from fluid–structure interaction in random seas, the current criteria for the evaluation of intact stability of ships developed by the International Maritime Organization (IMO) are based on ship restoring capabilities in still water (IMO2009).

Dynamic stability failures of ship, which is difficult to analyze, may occur through a variety of scenarios. Therefore the necessity of improved intact stability criteria is noted and researchers worldwide are working on the improvement of knowledge on the intact stability.

Spyrou (2011) studied some kinds of dynamic instability in following and quartering seas. Bulian (2005) described the variety of stability with general procedure for the analytical approximation of the GZ curve and its use in time domain simulations. Belenky (2010) simulated the ship motion in irregular waves and computed the instantaneous GZ curve at each time step of the simulations, which make it clear that pure loss of stability is a complex dynamical phenomenon.

The capsizing of ship in the actual sea conditions is necessarily researched by probabilistic method in statistics because it is a random events of complex systems. There is not a reliable method for capsizing probability determination because of the rarity and nonlinearity.

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