Bayesian structural model updating using ambient vibration data collected by multiple setups

Structural model updating aims at calculating the in-situ structural properties (e.g., stiffness and mass) based on measured responses. One common approach is to first identify the modal parameters (i.e., natural frequencies and mode shapes) and then use them to update the structural parameters. In reality, the degrees of freedom that can be measured are usually limited by number of available sensors and accessibility of targeted measurement locations. Then, multiple setups are designed to cover all the degrees of freedom of interest and performed sequentially. Conventional methods do not account for identification uncertainty, which becomes critical when excitation information is not available. This is the situation in model updating utilizing ambient vibration data, in which the excitations, such as wind, traffic, and human activities, are random in nature and difficult to be measured. This paper develops a Bayesian model updating method incorporating modal identification information in multiple setups. Based on a recent fundamental two-stage Bayesian formulation, the posterior uncertainty of modal parameters is incorporated into the updating process without heuristics that are commonly applied in formulating the likelihood function. Synthetic and experimental data are used to illustrate the proposed method.