Abstract In this article, Gaussian mixture models are used to estimate the probability density function of wave elevation in the context of the second-order random wave theory. Two approaches are used to construct the Gaussian mixture probability distribution. One is the moment estimate in which the unknown parameters are determined by matching the moments of Gaussian mixture model with those of the real wave process. The other is the maximum likelihood estimation in which the expectation–maximization (EM) algorithm is used to determine the parameters in statistical models. The proposed Gaussian mixture distribution is favorably validated by using Monte Carlo simulations in comparison with other theoretical distribution models. Numerical results reveal a clear dependence of the probability distribution structure on the wave steepness and the spectral shape. Finally, three sets of observation data are applied to further confirm the accuracy and efficiency of Gaussian mixture model.

中文翻译：

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基于高斯混合模型的波浪高程概率密度函数

摘要 本文在二阶随机波浪理论的背景下，使用高斯混合模型来估计波浪高程的概率密度函数。两种方法用于构建高斯混合概率分布。一种是通过将高斯混合模型的矩与真实波浪过程的矩相匹配来确定未知参数的矩估计。另一种是最大似然估计，其中使用期望最大化（EM）算法来确定统计模型中的参数。与其他理论分布模型相比，所提出的高斯混合分布通过使用蒙特卡罗模拟得到了有利的验证。数值结果揭示了概率分布结构对波陡度和光谱形状的明显依赖性。最后应用三组观测数据进一步验证高斯混合模型的准确性和效率。