基于位移响应协方差参数的数值仿真和实测损伤识别研究

本文使用结构位移响应协方差参数进行结构损伤识别，首先推导和建立位移响应协方差参数的解析公式，它是结构频率、振型和阻尼等模态参数的函数，结构物理参数的改变会导致该协方差参数的改变；对一个七层框架结构进行数值模拟分析来演示该方法的有效性，通过比较结构不同状态下各单元位移响应协方差参数CoD的分布曲线，研究各单元CoD与损伤程度的关系曲线，发现损伤位置处的CoD改变最大，其次是对称和附近单元，通过单损伤和多损伤工况研究分析，表明基于结构损伤前后CoD的改变，能成功判定损伤发生和识别出损伤位置，最后把该方法应用于一个实验室简支钢梁的损伤识别，通过对锤击振动下的加速度响应进行二次积分得到位移响应，并比较钢梁损伤前后的CoD，得到损伤概率向量，成功识别出损伤位置。该方法具有较好的噪声鲁棒性，无需结构分析模型，计算简便，具有较好的工程应用性。

Numerical and experimental study of damage identification based on covariance of displacement response

Covariance of displacement response is used for damage detection in the article.The analytical formula of the covariance of displacement response (CoD) is derived and established.It is the function of structural frequency,mode shape and damping ratio and so on.The change of the structural physical parameters will lead to the change of CoD.A seven-floor steel frame structure is numerically studied to demonstrate the feasibility of the proposed method.From the CoD distribution of different damage states and the curve of CoD of every element versus the damage extent,it can be seen that the damaged elements have the biggest changes of CoD and the neighboring and symmetric elements have the second biggest changes.The analysis of a single-damage case and a multiple-damage cases,shows that the damage occurrence and damage location can be identified successfully based on the changes of CoDs between the intact state and the damage state.Finally the proposed method is applied to damage detection of a simply supported steel beam tested in a lab.The displacement responses are obtained by twice integrating the measured acceleration responses of the beam excited by a hammer.Then the CoDs are computed and their changes are obtained due to the cut on the beam.The damage probability vector is obtained from the normalization of the CoD change vector.The sensor nearest the damage location has the biggest damage probability.So the damage location is found satisfactorily.The proposed method has good noise robustness,does not need the analytical structural model and is easily computed.So it has good performance in engineering applications.