桥梁颤振导数识别及颤振分析的不确定性研究

Uncertainty Quantification on Flutter Derivative Identification and Flutter Analysis of Bridges

由于风洞试验和理论模型的各种不确定性,通过风洞试验获得的颤振导数及相应的颤振临界风速存在不确定性。为了量化这些不确定性,提出了一种创新的近似贝叶斯方法。该方法通过抽样和模拟来近似表达似然函数,从而实现颤振导数的准确识别和不确定性量化。同时,还研究了颤振导数不确定性在颤振分析中的传播情况。采用子集模拟技术与近似贝叶斯方法相结合,以提高参数后验样本的抽样效率。该方法不仅能够获得颤振导数和颤振临界风速的最优估计,还能获得其后验概率分布。通过理想平板数值模拟和实桥主梁断面风洞试验,验证了该方法的有效性,并将其与传统最小二乘法进行了比较。研究结果显示:该方法得到的颤振导数最优估计与最小二乘法结果非常接近;在低风速下,所有导数的不确定性都较小,而在中高风速情况下,大多数导数都具有较大的不确定性,尤其是接近颤振临界风速时,所有导数的不确定性均较大;颤振导数的不确定性会在颤振分析中传播,导致颤振临界风速也存在较大的不确定性。所提出的近似贝叶斯方法能够准确识别颤振导数,并量化其不确定性,从而实现桥梁颤振性能的概率性评价;为桥梁颤振分析提供了新的思路,为确保桥梁的抗风安全提供了有力支持。

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.