Abstract The bivariate distribution of zero-up-crossing wave heights and associated periods is important in the stochastic modelling of ocean waves and is of theoretical and practical interest among scientists and engineers. Recently, joint descriptions in mixed sea states have garnered attention. The present study proposes a mixture bivariate lognormal model to characterise the joint distribution in sea states with two-peaked spectra. A parametric distribution based on conditional modelling is compared with the presented model. To verify the fitted models, secondary waves, which can be formed when waves propagate over marine obstacles, were generated in laboratory conditions and simulated data were obtained by the Ochi–Hubble model. The joint distributions of wave heights and periods, as well as the marginal distributions of these two wave parameters in three types of combined sea states are studied and discussed. Results show that the conditional model is not suitable for fitting the bivariate distribution, which may be primarily owing to its inaccurate description of the wave period distribution. Joint probability density functions of wave heights and periods created using a finite mixture model provide improved performance and can describe the bimodal nature of the distribution relatively well.

中文翻译：

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使用有限混合模型的混合海况下单个波高和周期的联合分布

摘要 过零波高和相关周期的双变量分布在海浪的随机建模中很重要，并且在理论和实践中引起了科学家和工程师的兴趣。最近，混合海况的联合描述引起了关注。本研究提出了一种混合双变量对数正态模型来表征具有双峰光谱的海况的联合分布。将基于条件建模的参数分布与所呈现的模型进行比较。为了验证拟合模型，在实验室条件下生成了波浪在海洋障碍物上传播时可以形成的二次波，并通过 Ochi-Hubble 模型获得了模拟数据。波高和周期的联合分布，以及这两种波浪参数在三种组合海况下的边际分布进行了研究和讨论。结果表明，条件模型不适合拟合二元分布，这可能主要是由于其对波浪周期分布的描述不准确。使用有限混合模型创建的波高和周期的联合概率密度函数提供了改进的性能，并且可以相对较好地描述分布的双峰性质。