The prevention of excessive roll acceleration is one of the fundamental requirements of an oceangoing vessel at sea. In this paper, aiming at this requirement, we propose a new theoretical method for calculating roll angular acceleration, called “PDF line integral method.”. This paper presents the derivation of this method and a numerical comparison with Monte Carlo simulation (MCS) results; also, its validity is shown. Although the utilized GZ curve (restoring curve) exhibits strong asymmetricity, the proposed method can provide for such a condition. With only the information of roll and roll rate joint probability density function (PDF), this method can approximately calculate the roll angular acceleration, which is a high-order differential property. In addition, a relatively good agreement is achieved between the theory and MCS results.

中文翻译：

---

基于PDF线积分法的横摇横摇加速度理论估计

防止过度横摇加速度是海上远洋船舶的基本要求之一。在本文中，针对这一要求，我们提出了一种新的计算滚转角加速度的理论方法，称为“PDF 线积分法”。本文介绍了该方法的推导以及与蒙特卡罗模拟 (MCS) 结果的数值比较；此外，它的有效性被显示出来。尽管利用的 GZ 曲线（恢复曲线）表现出很强的不对称性，但所提出的方法可以提供这样的条件。该方法仅利用侧倾和侧倾率联合概率密度函数（PDF）信息，可以近似计算出侧倾角加速度，这是一种高阶微分性质。此外，理论与MCS结果之间取得了较好的一致性。