环境激励下斜拉索阻尼识别的贝叶斯方法研究  

Bayesian Approach Study for Identifying Damping of Stay Cables Using Ambient Vibration Measurements

作　　者：封周权[1,2] 张吉仁 王亚飞[1] 刘志文[1] 华旭刚[1] 陈政清[1] FENG Zhou-quan;ZHANG Ji-ren;WANG Ya-fei;LIU Zhi-wen;HUA Xu-gang;CHEN Zheng-qing(Key Laboratory for Wind and Bridge Engineering of Hunan Province,Changsha 410082,Hunan,China;Research Institute of Hunan University in Chongqing,Chongqing 401133,China)

机构地区：[1]湖南大学风工程与桥梁工程湖南省重点实验室,湖南长沙410082 [2]湖南大学重庆研究院,重庆401133

出　　处：《中国公路学报》2023年第7期114-124,共11页China Journal of Highway and Transport

基　　金：国家自然科学基金项目(52178284,51708203);湖南省自然科学基金项目(2021JJ30106);重庆市自然科学基金项目(2022NSCQ-MSX5727);智慧城市物联网国家重点实验室(澳门大学)开放课题项目(SKL-IoTSC(UM)-2021-2023/ORP/GA09/2022)。

摘　　要：斜拉索是大跨度斜拉桥中最关键的结构构件之一,其动力特性(频率和阻尼等)在大跨度斜拉桥的设计、施工、监测和振动控制中发挥着重要作用,斜拉索阻尼识别对于斜拉索的振动分析和减振设计至关重要。为了实现在环境激励状态下斜拉索阻尼比的高精度识别,并同步对识别结果不确定性进行量化分析,首先通过建立斜拉索模态参数的后验概率密度函数(Probability Density Function,PDF)将模态参数识别转化为求最大后验概率点的约束优化问题,从而得到模态参数的最佳估计(Most Probable Values,MPV);其次推导了负对数似然函数的Hessian矩阵解析表达式,并进一步得到后验协方差矩阵,从中提取和计算变异系数(Coefficient of Variation,COV)以量化模态参数最佳估计的不确定性;最后将所提方法应用于某大跨度斜拉桥斜拉索阻尼比的识别,使用加速度计采集了该桥7根斜拉索的环境振动数据,利用所提方法得到了模态阻尼比的MPV值及其变异系数。研究结果表明:所提方法可以得到目标模态参数的最佳估计,并能够有效量化最佳估计的不确定性,由Hessian矩阵解析方法得到的后验协方差矩阵具有良好的计算精度;环境激励下由加速度响应数据识别所得多根斜拉索模态阻尼比变化规律基本一致,均随模态阶数呈现“先增后减”趋势,计算所得模态阻尼比COV值均小于0.005%,表明识别结果具有较高的可靠性。Stay cables are among the most important structural components of long-span cable-stayed bridges.Their dynamic characteristics(frequency and damping)play important roles in the design,construction,monitoring,and vibration control of long-span cable-stayed bridges.Identifying cable damping is essential for the vibration analysis and vibration reduction design of stay cables.This study simultaneously realizes the high-precision identification of the cable damping ratio under ambient excitation and quantifies the uncertainty of the identified results.First,modal parameter identification was transformed into a constrained optimization problem to determine the maximum a posteriori probability(MAP)estimate by establishing the posterior probability density function(PDF)of the modal parameters of the stay cable,and the most probable values(MPVs)of the modal parameters were obtained.Second,the analytic expression of the Hessian matrix of the negative log-likelihood function was derived,and the posterior covariance matrix was obtained,from which the coefficient of variation(COV)was extracted and calculated to quantify the uncertainty of the identified modal parameters.Finally,the proposed method was used to identify the cable damping ratios of a long-span cable-stayed bridge.The ambient vibration data of the seven stay cables were collected using accelerometers,and the MPVs and COVs of the modal damping ratios were obtained using the proposed method.The results show that the proposed method can determine the optimal estimate of the target modal parameters and effectively quantify the uncertainty of the optimal estimate.The posterior covariance matrix obtained by the analytic expression of the Hessian matrix has good computational accuracy.The variation rules of the modal damping ratios of the multiple cables identified from the acceleration response data under ambient excitation are the same and increase and then decrease with the modal order.The COVs of the estimated modal damping ratios are less than 0.005%,indicating th

关 键 词：桥梁工程 贝叶斯推理 解析方法 斜拉索 阻尼比 环境激励 不确定性 

分 类 号：U441.3[建筑科学—桥梁与隧道工程]