Analytical method of capsizing probability in the time domain for ships in the random beam seas

Abstract

The methods for constructing safe basins of ships and predicting their survival probability in random waves were studied. The nonlinear differential equation of the rolling motion of ships in random beam seas was established considering nonlinear damping, nonlinear restoring moment, and random waves. The random rolling differential equation was solved in the time domain by applying the harmonic acceleration method and by synthetically considering the instantaneous state of ships and the narrowband wave energy spectrum. The numerical simulation of random capsizing course was brought forward, the safe basins were constructed for safe navigation, and the survival probabilities of ships were calculated. As an example, the safe basins on the rolling initial value plane were constructed for a 30.27-meter-long fishing vessel according to different initial conditions and random wave parameters. The survival probabilities of the fishing vessel under different significant wave heights were predicted. Thus, the survival probabilities of ships in random seas can be predicted quantitatively by the proposed method.

Keywords

random bean waves, ships capsizing, safe basin, survival probability