应用路径积分法求解船舶横摇倾覆概率

通过对船舶非线性横摇运动进行分析，建立了船舶横摇运动的非线性微分方程.以路径积分法(PIS)为基础，在时间域内求解相应的二维Fokker-Planck方程，得到随时间演变的船舶横摇运动的转移概率密度.运用首次通过理论，求得船舶倾覆前时间的概率分布.研究了外部激励、横摇阻尼和非线性复原力矩对船舶横摇运动转移概率密度与首次通过时间的影响.研究结果表明，PIS能用于预测船舶首次通过时间概率分布，从而为船舶设计和稳性衡准提供相关的参考.

Calculation of Ship Rolling Capsizing Probability by Path Integral Solution

By analyzing nonlinear rolling motion of the ship, a nonlinear differential equation of ship rolling motion was established. The two-dimensional Fokker Planck equation in time domain was solved by using the path integral solution (PIS) and the transition probability density of the ship rolling was obtained. The distribution of the first passage time was achieved by first passage theory. Some examples were presented and the influences of the magnitude of external excitation, the rolling damping and the nonlinear restoring moment on the transition probability density of the ship rolling and the first passage time were analyzed. The results show that the method is available to predict the distribution of the first passage time and provides valuable reference to the ship design and the safe standards.