Dynamic reliability prediction for the steel box girder based on multivariate Bayesian dynamic Gaussian copula model and SHM extreme stress data

This article presents the dynamic reliability prediction method of the existing steel box girder considering the time-variant nonlinear correlations among the performance functions for the failure modes at the multiple control monitoring points. Firstly, the multivariate Bayesian dynamic linear model (MBDLM) considering the nonlinear correlations among the multiple variables is built to predict the extreme stresses at the different control monitoring points; secondly, based on the predicted covariance matrix of MBDLM, the dynamic correlation coefficients between any two performance functions can be accurately predicted; and finally, multivariate Bayesian dynamic Gaussian copula model through combining MBDLM with Gaussian copula technique is proposed to predict the dynamic reliability of the steel box girder, and the monitoring extreme stress data of an actual bridge are provided to illustrate the feasibility and application of the proposed method. The results show that predicted dynamic reliability of the bridge girder with considering the time-variant nonlinear correlation of failure modes at the multiple control monitoring points is bigger than that without considering the time-dependent nonlinear correlation. It is illustrated that the predicted results without considering the dynamic nonlinear correlation of failure modes at the multiple control monitoring points are more conservative.