四维路径积分法解随机海浪下船舶横摇倾覆概率

Calculation of ship rolling capsizing probability based on 4-dimension path integral solution

该文利用二阶自回归模型制作的滤波器,将输入的白噪声转化为有色噪声以模拟真实海况的海浪谱。通过分析船舶大幅横摇运动,建立船舶非线性微分运动方程。将上述两个方程相结合,并转化为伊藤微分方程,通过路径积分法,求解相应的四维Fokker-Planck方程,得到随时间变化的船舶大幅非线性横摇运动的转移概率密度,将其与有限差分法计算得到的结果进行比较。研究结果表明,四维路径积分法具有较高的计算精度可以很好地预测船舶横摇概率分布情况,为船舶稳性衡准提供了相关参考。

By using a filter based on second-order autoregressive model,the input white noise can be transferred into regarding real waves.By analyzing nonlinear rolling motion of the ship in big amplitude,the nonlinear differential equation of ship rolling motion was established.All the equations were combined and transferred them into Ito stochastic differential equation.The Four-dimensional Fokker-Planck equation can be solved by using the path integral solution and the time-dependent transition probability density of the ship rolling was obtained.The result obtained by PIS was compared with the result got by finite difference method.It shows that the 4-dimension PIS with high calculation precision can predict the probability density of the ship rolling correctly and provides reference to the ship design and the safe standards.