A Copula Framework for Joint Probability Density of Wind Speed, Wind Direction, and Wind Attack Angle Based on Dirichlet Process Mixture Model

The structural safety and performance of long-span bridges in coastal areas are significantly influenced by the wind field. Traditional univariate or simplified multivariate probabilistic models often fail to capture the multimodal and nonlinear dependencies among wind parameters, leading to inaccuracies in wind-induced risk assessment. This study proposes a novel joint probability density function framework for wind speed, wind direction, and wind attack angle, integrating a Dirichlet process mixture model (DPMM) for marginal distributions and a Regular Vine (R-Vine) copula for dependency modeling. The DPMM adaptively identifies the number of mixture components without presetting, effectively capturing multimodal and periodic characteristics of the wind field. The R-Vine copula flexibly models complex nonlinear dependencies among the three variables. A case study using field data from the Beikou Bridge demonstrates the capability to reveal seasonal wind patterns of the proposed model. By explicitly parametrizing the underlying wind regimes, the DPMM-based framework enables physically interpretable wind field decomposition. This provides direct support for probabilistic wind field modeling, supporting enhanced wind-resistant design and operational management of coastal long-span bridges.