Using the stochastic averaging method, the probability density function (PDF) of roll motion for parametric rolling in irregular waves is obtained. In this paper, the stochastic averaging method using Hamiltonian proposed by Dostal is used, and the PDF of roll amplitude and Hamiltonian are derived from the equations of roll motion. In addition, the asymptotic behavior of PDF is investigated to improve the accuracy of the calculation. Furthermore, to improve the applicability of this method, the simulation-based stochastic method is proposed. Compared to the results of the stochastic averaging method proposed by Roberts and Dostal, the results using this improved method show a good agreement. The results are examined for parametric excitation using white noise as well as colored noise. Moreover, the relationship between the scale parameter and the PDF is theoretically analyzed and formulated.

使用随机平均方法，获得用于不规则波中参数滚动的滚动运动的概率密度函数（PDF）。本文采用了Dostal提出的基于哈密顿量的随机平均方法，并根据横摆运动方程推导了横摆幅值和哈密顿量的PDF。另外，研究了PDF的渐近行为以提高计算的准确性。此外，为了提高该方法的适用性，提出了一种基于仿真的随机方法。与Roberts和Dostal提出的随机平均方法的结果相比，使用这种改进方法的结果显示出良好的一致性。使用白噪声和有色噪声检查结果的参量激励。而且，