中文摘要：

为了研究随机海浪中船舶航行安全域的构造及生存概率的预报方法，考虑阻尼和复原力矩的非线性及海浪的随机性，建立随机横浪中船舶运动的随机非线性微分方程．综合考虑船舶运动的瞬时状态和窄带海浪谱，采用简谐加速度方法在时域内求解横摇随机微分方程，进行随机倾覆过程的数值模拟，构造船舶航行的安全域，计算船舶安全航行的生存概率．选取不同的初始蒂件及随机波浪参数，在横摇初值平面上构造了一手长30．27m渔船航行的安全域，预报了不同有义渡高作用下渔船安全航行的生存概率．采用本文方法，可以从数量上预报船舶在随机海浪中的生存概率．

英文摘要：

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