应用路径积分法解船舶倾覆概率问题

Calculation of Ship Capsize Probability by Using Path Integration Method

横浪情况下的倾覆 ,只在严重海浪下才会发生。因此是一个强非线性问题。可以采用首次通过的概念来研究。为此 ,必须求出随时间演变的概率密度分布函数。通常可应用在时间域内解相应的Fokker-Planck方程的方法求取。由于这一方程求解比较困难。一个较有效的办法是应用路径积分法。但这一方法原理上是一个近似方法。是否可用于解首次通过尚待考核。本文主要讨论求解船舶横对随机波的倾覆概率时 ,用路径积分法解一次通过问题的可用性。文中对假想的船舶在白噪声波上的倾覆 ,用路径积分法和有限差分法两种方法求解。两种方法得出的倾覆前时间(一次通过时间)的概率分布基本相同。

The first passage was applied to the problem of ship capsize in random beam sea. The solution of correspond Fokker-Planck equation under the correspond boundary conditions was obtained by the method of path integration. The applicability of such approximate method in first passage problem was discussed and validate by comparison with other numerical solution. Some examples were presented in this paper together with the concluding remarks.