基于 Copula 函数的箱梁桥波浪砰击力多峰值联合概率模型研究

The strong nonlinearity of wave forces in the suspended state of offshore bridges makes it difficult to predict wave forces. Existing wave force predictions mainly focus on single-peak predictions, with insufficient characterization of the correlation between different peaks, limiting their applicability. Based on water tank model experiments, this paper explores the probability distribution characteristics of multiple peaks of vertical wave forces, and constructs and verifies the joint probability model between two peak forces using the Copula function. The analysis results show that: there is a strong nonlinear positive correlation between different peak wave forces within one wave period; The comparison results of three different evaluation methods indicate that the bivariate Weibull and Lognormal distributions are respectively most suitable for describing the second and third peak wave forces. Based on the Expectation-Maximization (EM) algorithm, BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm and K-fold cross-validation, a mixed Copula joint distribution model for multiple peak vertical wave forces of box girder bridges is established and compared with the single Copula joint distribution model, the study shows that the single Copula model cannot fully capture the joint distribution characteristics, especially the multi-peak characteristics of wave forces on the superstructure of offshore bridges, but the mixed Copula model shows better fitting performance in the multi-peak area, data dense area, and tail sparse area.