随机风浪中舰船横摇倾覆概率分析

Analysis of rolling capsizing probability of warship under random wind and beam seas

以路径积分法为基础,采用Gauss-Legendre公式探讨了随机风浪作用下舰船的运动及其倾覆概率计算。考虑阻尼力矩、复原力矩的非线性及风浪的随机性,建立了随机风浪中舰船运动的非线性微分方程,应用路径积分法给出白噪声随机扰动和定常风倾力矩作用时横摇角概率密度函数随时间的演变,按照现有的倾覆准则给出舰船倾覆概率的表达式。通过算例,验证了路径积分法的准确性,分析了各个参数对横摇角概率密度的影响,计算得出了不同风速、不同航速下的倾覆概率,以及倾覆概率随时间的变化。研究表明,此方法简便可行,并能在数量上预报舰船在随机风浪下的倾覆概率。

The path integration method based on Gauss-Legendre integration scheme was applied to the motion of ship subjected to random wind and beam seas. Considering the nonlinear damping moment, restoring moment and random wind and seas, the nonlinear differential equation for ship’s rolling motion was established. The rolling angle probability density was analyzed using the path integration method, when the ship was subjected to white noise disturbance and a stationary wind moment, then capsizing probability was also calculated according to the presented rules. The presented method was capable of producing accurate results, which could be proved through the example. At the same time, the influence of each parameter on the probability density was analyzed. Furthermore, the capsizing probability at different velocity of wind and sailing was calculated, and the probability with time was also computed. The study shows that this method is easy to achieve. Thus the rolling capsizing probability of warship in random wind and beam seas could be predicted quantitatively by the proposed method.