Joint values of temperature and wind actions on long–span bridges based on mixed copula with Bayesian selection approach

Wind and temperature, as key environmental loads, significantly affect the performance of long–span bridges, and the correlation of wind and temperature actions is important for reliability and safety evaluation of long–span bridges. This study aims to describe the joint probability distribution and spatiotemporal correlation of wind and temperature actions, and propose a rational load pattern for structural design. A Bayesian selection method is proposed to determine components of a mixed copula model. The Expectation Maximization method (EM) with the Broyden–Fletcher–Goldfarb–Shanno algorithm (BFGS), is employed to derive the weight and dependence parameters of the mixed copula model. This model accurately captures the dependence between wind and temperature monitoring data. The joint values of temperature and wind actions (JVTWA) are obtained via Kendall return period. Results show that the Bayesian selection method effectively identifies the mixed copula components, enabling a more precise evaluation of joint actions reduction. The mixed copula model improves flexibility and accuracy, offering a better representation of dependence. The JVTWA values, derived from the mixed copula model, demonstrate reduced attenuation compared to extreme value superposition. Therefore, JVTWA should be used in the design of long–span bridges instead of univariate values, enhancing accuracy of wind and temperature effects, optimizing structural design, and supporting energy conservation and emissions reduction.