一种新的路径积分法在船舶横摇概率计算中的应用

基于Gauss-Legendre积分规则提出了一种新的路径积分法来计算随机横浪中船舶非线性横摇运动的概率密度分布,新的路径积分法能够得出精确的瞬态概率密度分布,包括系统响应尾部区域的概率分布,其对系统的可靠性分析是十分重要的.船舶随机横摇运动微分方程考虑到阻尼力与恢复力的非线性.数值模拟了联合概率密度函数随时间的演变,分析了外部激励强度对船舶稳态概率密度分布的影响.数值模拟的结果表明新的路径积分法对研究船舶非线性横摇运动概率密度分布是十分有效的.

Calculation of Ship Rolling Probability Using a New Path Integration Method

A new path integration method (PIM) based on the Gauss-Legendre quadrature integration rule is proposed for calculating the probability density of the nonlinear roll motion of ships in stochastic beam seas.The new path integration method is capable of producing accurate results of probability density distribution as it evolves with time,including the tail region where the probability value is very important for the system reliability analysis.The ship roll motion is described by a nonlinear rendom differential equation that includes a nonlinear damping moment and restoring moment. The evolution of the joint probability density distribution and the stationary probability distribution is simulated by the new path integration scheme and the stationary probability distribution with respect to the strength of the external excitation is analyzed.The results indicate that the new path integration method is efficient in the studying the probability distribution of ship nonlinear roll motion from the numerical simulation results.