Uncertainty Quantification on Flutter Derivative Identification and Flutter Analysis of Bridges

Inherent uncertainties in wind tunnel testing and theoretical models are associated with flutter derivatives and critical flutter wind speeds obtained through wind tunnel testing. To quantify these uncertainties, we propose an innovative approximate Bayesian computational method. This method approximates the likelihood function through sampling and simulation, thereby achieving accurate identification and uncertainty quantification of flutter derivatives. In addition, we investigated the propagation of uncertainties in the flutter derivatives during flutter analysis. Subset simulation was combined with approximate Bayesian computation to improve the sampling efficiency of the posterior samples. This method provides optimal estimates for flutter derivatives and critical wind speeds and yields their posterior probability distributions. We validated the effectiveness of our approach through numerical simulations of flat plates and wind tunnel tests on an actual bridge girder sectional model, and compared it with the traditional least squares method. The results demonstrate a high degree of consistency between the optimal estimates obtained using the proposed method and those obtained using the least-squares method. At low wind speeds, the uncertainties in all derivatives were relatively small; whereas, at medium to high wind speeds, most derivatives exhibited larger uncertainties, particularly near the critical wind speed of the flutter, where all derivatives became highly uncertain. The uncertainty of the flutter derivatives propagates in the flutter analysis, resulting in substantial uncertainty in the critical wind speed of the flutter. The proposed approximate Bayesian method accurately identifies flutter derivatives and quantifies their uncertainties, thereby enabling a probabilistic assessment of bridge flutter performance. This study provides new insights for bridge flutter studies and offers robust support for ensuring the wind-resistant safety of bridges. © 2023 Xi'an Highway University. All rights reserved.