Joint Probability Distribution of Wind–Wave Actions Based on Vine Copula Function

During its service life, a deep-sea floating structure is likely to encounter extreme marine disasters. The combined action of wind and wave loads poses a threat to its structural safety. In this study, elliptical copula, Archimedean copula, and vine copula models are employed to depict the intricate dependence structure between wind and waves in a specific sea area of the Shandong Peninsula. Moreover, hourly significant wave height, spectral peak period, and 10 m average wind speed hindcast data from 2004 to 2023 are utilized to explore the joint distribution of multidimensional parameters and environmental design values. The results indicate the following: (1) There exists a significant correlation between wind speed and wave parameters. Among them, the C-vine copula model represents the optimal trivariate joint distribution, followed by the Gaussian copula, while the Frank copula exhibits the poorest fit. (2) Compared with the high-dimensional symmetric copula models, the vine copula model has distinct advantages in describing the dependence structure among several variables. The wave height and period demonstrate upper tail dependence characteristics and follow the Gumbel copula distribution. The optimal joint distribution of wave height and wind speed is the t copula distribution. (3) The identification of extreme environmental parameters based on the joint probability distribution derived from environmental contour lines is more in line with the actual sea conditions. Compared with the design values of independent variables with target return periods, it can significantly reduce engineering costs. In conclusion, the vine copula model can accurately identify the complex dependency characteristics among marine variables, offering scientific support for the reliability-based design of floating structures.