基于混合监测理论的桥梁全局响应重构方法  

Bridge full-field response reconstruction method based on hybrid monitoring theory

作　　者：孙海彬 李轶贤 孙利民[1] SUN Haibin;LI Yixian;SUN Limin(College of Civil Engineering,Tongji University,Shanghai 200092,China;Department of Civil and Environmental Engineering,The Hong Kong Polytechnic University,Hong Kong 999077,China)

机构地区：[1]同济大学土木工程学院,上海200092 [2]香港理工大学环境与土木工程系,中国香港999077

出　　处：《振动与冲击》2025年第3期107-114,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金(52378187)。

摘　　要：卡尔曼滤波(Kalman filter,KF)和最大化后验概率法(maximum a posteriori,MAP)是结构荷载识别中常见的两类广义贝叶斯滤波算法,KF法计算效率高但数值稳定性较差,MAP法适用性强却需要复杂的矩阵求逆运算,加之这两类方法对荷载形式和测点布置的苛刻要求,目前仅适用于简单荷载的识别。为此,该研究提出了针对任意分布式荷载的贝叶斯全局响应重构方法,从在线和离线两个角度改进了现有方法。针对在线KF方法,该研究从结构动力特性中导出等效荷载向量来降低未知荷载的维度,得到满足可控性条件的等效系统模型,并采用输入状态联合估计方法同时识别等效荷载和全局响应。针对离线MAP方法,引入考虑了空间相关性的荷载先验分布,采用MAP策略同时对等效荷载和观测噪声进行迭代估计,随后根据识别得到的等效荷载重构全局响应。改进后的在线和离线方法均不需要提前获取荷载位置或分布形式。通过青州大桥在风荷载和交通荷载下采集的响应数据对所提方法的精度和适用性进行了验证。Kalman filter(KF)and maximum a posteriori(MAP)are two common generalized Bayesian filtering algorithms in structural load identification.KF method has high computational efficiency but poor numerical stability,while MAP method has strong applicability but requires complex matrix inversion operations.In addition,these two methods have strict requirements for load form and measurement point arrangement,and are currently only suitable for identifying simple loads.Here,a Bayesian full-field response reconstruction method was proposed for arbitrary distributed loads,it could improve existing methods from both online and offline perspectives.For the online KF method,equivalent load vectors were derived from structural dynamic characteristics to reduce the dimension number of unknown loads,obtain an equivalent system model to satisfy controllability conditions,and use input state joint estimation method for simultaneously identifying equivalent loads and global responses.For the offline MAP method,a load prior distribution considering spatial correlation was introduced,and MAP strategy was used to simultaneously iteratively estimate equivalent load and observed noise.Then,the global response was reconstructed according to the identified equivalent load.The improved online and offline methods could not require prior acquisition of load positions or distribution forms.Finally,the accuracy and applicability of the proposed method were verified with collected response data of Qingzhou Bridge under wind and traffic loads.

关 键 词：卡尔曼滤波(KF) 最大化后验概率(MAP) 混合监测 全局响应重构 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3