Probability density function for wave elevation based on Gaussian mixture models

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.