Abstract In this work, the C11 container ship is taken as an example to analyze its rolling performances in random longitudinal or oblique waves. Firstly, a dynamic model of C11 roll in random waves is improved, and it is verified by the model test and numerical simulation. Mathematically, this dynamic model is a one-dimensional stochastic differential equation with random parametric (and external) excitation. Secondly, an enhanced stochastic averaging method is proposed to solve this stochastic differential equation. The validity of the solutions was verified by Monte Carlo simulation. At last, the probabilistic characteristics of the extreme rolling response were investigated based on the calculated results using enhanced stochastic averaging method. According to the analysis, some advices for ship's manoeuvring can be put forward when ships are navigating in random waves.

中文翻译：

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用于估计随机纵波或斜波中船舶横摇的随机平均

摘要 本文以C11型集装箱船为例，分析其在随机纵波或斜波下的横摇性能。首先，对随机波浪中C11横摇的动力学模型进行了改进，并通过模型试验和数值模拟进行了验证。在数学上，这个动态模型是一个具有随机参数（和外部）激励的一维随机微分方程。其次，提出了一种增强随机平均法来求解该随机微分方程。蒙特卡罗模拟验证了解的有效性。最后，在计算结果的基础上，采用增强随机平均法研究了极端滚动响应的概率特性。根据分析，对船舶'的一些建议