Uncertainty Quantification and Error Propagation Principle of Structural Flexibility with Time-Varying Dynamic Properties

The investigation of the time-varying properties of vehicle-bridge interaction (VBI) systems has gained much attention in recent years. Use the moving vehicle-induced time-varying dynamic properties for rapid flexibility identification of bridges without the requirement for input force measurement is a promising strategy. However, there exist various uncertainties in the process of data measurement and parameter identification, resulting in a large bias in the results. To address this problem, this paper proposes to investigate the uncertainty quantification and error propagation principle of structural flexibility identified from moving vehicle-induced dynamic responses. First, uncertainties associated with the basic modal parameters (e.g., natural frequencies, damping ratios, and unscaled mode shapes) were quantified by the fast Bayesian method. Second, the uncertainties associated with the scaling factor identified using the time-varying dynamic properties of the VBI system were quantified by the Gaussian mixture model (GMM) and expectation maximum (EM) algorithm. Finally, the error propagation principle was thoroughly investigated by perturbation analysis, from which the confidential interval of mass-normalized mode shapes, modal flexibility, and predicted static deflection were quantified. The effectiveness and robustness of the proposed method were then successfully verified by an experimental model. Results show that the predicted deflections with confidence intervals contain directly measured deflections by displacement transducers, verifying the correctness of the proposed method. The obtained results are beneficial for rapid reliability assessment and long-term performance deterioration investigation of numerous bridges in road networks.