A methodology for predicting the probability density function of roll motion for irregular beam seas is developed in the author’s previous research. In this paper, two methods for the prediction of the probability density function (PDF) of the rolling amplitude are examined. One of these methods is an approach based on a non-Gaussian PDF with the use of the equivalent linearization and the moment method, which has been used by Maki in the field of naval architecture. In the framework of this method, the instantaneous joint PDF of the roll and roll rate can be calculated. Thereby, the transformation from the joint PDF to the PDF of the total energy H is necessary. In this paper, the transformation from the joint PDF of instantaneous roll and rate to the PDF of H was conducted. The other method is the energy-based stochastic averaging method, whereby the PDF of the total energy H is determined from which the roll amplitude is calculated. It is noteworthy that the proposed theory aims to predict the PDF of the amplitude of the vessel due to wind or flooding. For such conditions, the restoring curve (GZ curve) has asymmetricity. To take into account this asymmetricity, a new theory for the transform of the PDF of the total energy H to the PDFof amplitude is proposed. The obtained theoretical results show almost complete agreement, and both of the two theoretical methods i.e., the energy-based stochastic averaging method and the non-Gaussian PDF method with the use of the equivalent linearization and moment method, show equivalent prediction performance even in the asymmetric condition.

作者先前的研究开发了一种预测不规则海浪横摇运动概率密度函数的方法。本文研究了两种预测滚动幅度的概率密度函数（PDF）的方法。这些方法中的一种是基于非高斯PDF的方法，其中使用了等效线性化和矩量方法，Maki已在海军建筑领域中使用了该方法。在此方法的框架中，可以计算出侧倾和侧倾速率的瞬时联合PDF。因此，有必要将总能量H从联合PDF转换为PDF 。本文将瞬时滚动和速率的联合PDF转换为H的PDF进行了。另一种方法是基于能量的随机平均方法，由此确定总能量H的PDF，从该PDF可以计算出横滚幅度。值得注意的是，提出的理论旨在预测由于风或洪水引起的船舶振幅的PDF。对于这种情况，恢复曲线（GZ曲线）具有不对称性。考虑到这种不对称性，提出了一种新的理论，用于转换总能量H的PDF提出了幅度的PDF。所获得的理论结果表明几乎完全吻合，并且使用等效线性化和矩量法的基于能量的随机平均方法和非高斯PDF方法这两种理论方法甚至都在等效条件下表现出了等效的预测性能。不对称条件。