A hierarchical Bayesian model updating method for bridge structures by fusing multi-source information

The expanding structural health monitoring (SHM) systems on bridge structures have provided an abundance of multi-source data for finite element model updating (FEMU). The SHM systems on bridges usually include surveillance cameras, vibration sensors (e.g., accelerometers, strain gauges, and displacement sensors), and sometimes a weight-in-motion (WIM) system. Currently, the majority of FEMU studies focus on identified modal parameters derived from vibration data, neglecting the incorporation of video and WIM data in the updating process, which impedes a thorough quantification of uncertainty associated with the structural parameters of interest. Therefore, this paper proposes a hierarchical Bayesian FEMU framework to comprehensively integrate a variety of information sources, including videos, WIM, and vibration data. The data features comprise the static deflections of the bridge under traffic load and modal parameters identified from acceleration measurements. The measured static deflections are extracted from raw displacement data using the locally weighted regression and smoothing scatterplots method. Computer vision-based technology is employed to pinpoint the location of vehicle load on the bridge, which is then integrated into a FEM to predict vehicle-load-induced static deflection. A two-stage Markov Chain Monte Carlo sampling approach is proposed to evaluate the high-dimensional posterior distribution efficiently. The effectiveness of the proposed method is demonstrated on a laboratory three-span bridge model. The results show that the hierarchical Bayesian FEMU can provide accurate estimation and uncertainty quantification on structural stiffness and mass parameters. The updated model accurately predicts both static deflection and modal parameters, exhibiting model-predicted variability in close alignment with the identified values for observed and unobserved responses. Remarkably, this holds true even for unseen loading conditions which are not included in the updating process. These observations validate the capability of the proposed method for multi-source data fusion and uncertainty quantification of real-world bridge structures under operational conditions.