Probabilistic Baseline of Finite Element Model of Bridges under Environmental Temperature Changes

The material properties and structural stiffness of actual bridges fluctuate with variations in environmental temperature; therefore, it is not appropriate to use a determined finite element model (FEM) as the baseline model for localizing the structural damage of bridges. To address this issue, we proposed the concept of the probabilistic baseline of FEM of bridges under variable environmental temperature, that is, we established reasonable probability distributions of the physical parameters of bridges that are suitable for damage localization with varying environmental temperature. First, a method is presented to obtain the probabilistic baseline of FEM of bridges, which imports cluster analysis into stochastic FEM updating. Unlike the conventional methods, the measured natural frequencies first are classified into different clusters using the Gaussian mixture method (GMM), with each cluster consisting of measured data that satisfy the same Gaussian distribution. Then, the conventional methods of stochastic FEM updating can be conveniently implemented to obtain the probabilistic baseline of FEM for each cluster. Second, for each cluster, the mean values and covariance of the updating parameters are updated in two sequential steps, and a new approach is proposed for determining the initial covariance of the updating parameters. The results of an actual example show that predetermining a reasonable initial covariance for the updating parameters can accurately and efficiently obtain the updated results. Finally, the effectiveness of the presented method is verified through the monitoring data of an actual bridge.