Optimization of Extreme Design Parameters for Swell-Dominated Waves Using a Gaussian Mixture Model

Environmental condition assessment is essential for the design of floating wind turbines, particularly when determining design sea states that balance safety and economy. The environmental contour method, typically constructed through the Inverse First Order Reliability Method combined with parametric joint distributions, is widely adopted for this purpose. However, conventional models often struggle to adequately characterize complex sea states involving mixed wind and swell systems, which exhibit multimodality and irregular dependence structures. To address this limitation, this study applies the use of Gaussian mixture models (GMM) to construct environmental contours. The GMM-based approach models the joint distribution of environmental variables in a flexible and data-adaptive manner, with the number of mixture components determined by the Bayesian Information Criterion and model parameters estimated via the expectation-maximization algorithm. Compared with the conventional conditional Weibull–Lognormal model, the GMM significantly improves fitting accuracy: the RMSE decreases from approximately 0.06 to below 0.0013, and the R2 increases to nearly 1.000 across all three datasets. The KS and χ2 tests confirm that the GMM adequately fits the observed data at the 0.05 significance level, whereas the baseline model is rejected in several cases. For the 100-year return period, the GMM yields maximum significant wave heights of 4.19–4.55 m with associated peak periods of 18.8–20.3 s, while the baseline model gives 4.02–4.18 m and 14.3–14.6 s, respectively. These quantitative improvements demonstrate that the mixture-based contours capture the intricate characteristics of wind–swell coexisting sea conditions more accurately, leading to enhanced representativeness of extreme sea states. Consequently, the adopted method enables more refined and reliable design sea state assessments for tested datasets, contributing to the optimization of environmental parameter selection for floating wind turbines.