基于附加质量优化与特征值灵敏度的结构损伤识别  

Structural damage detection based on optimized added masses and eigenvalue sensitivity

作　　者：黄铧 马俊[1,2] 伍晓顺 HUANG Hua;MA Jun;WU Xiaoshun(Jiangxi University of Science and Technology,School of Civil and Surveying&Mapping Engineering(Nanchang),Nanchang 330013,China;Jiangxi University of Science and Technology,Nanchang Key Laboratory of Virtual Digital Factory and Cultural Communications,Nanchang 330013,China)

机构地区：[1]江西理工大学土木与测绘工程学院(南昌),南昌330013 [2]江西理工大学南昌市虚拟数字工程与文化传播重点实验室,南昌330013

出　　处：《江西冶金》2023年第4期331-341,共11页Jiangxi Metallurgy

基　　金：国家自然科学基金资助项目(51868026);江西省自然科学基金资助项目(20202BAB204028)。

摘　　要：建立一种附加质量优化与特征值灵敏度相结合的结构损伤识别方法。通过在原结构上附加多组经优化的集中质量获得多个具有相同刚度的新结构,再利用原结构和新结构的实测特征值建立灵敏度方程组,求解损伤参数。以灵敏度矩阵的条件数最小作为目标函数,建立附加质量优化的数学模型,并使用粒子群算法进行寻优;采用二次奇异值截断法求解灵敏度方程组。为克服灵敏度矩阵的病态性和数据噪声的干扰,提出奇异值贡献指标,以合理确定奇异值截断阈值。某悬臂梁的数值分析表明,持续增加新结构的数量难以得到足够小的灵敏度矩阵条件数,但可以增加高质量奇异值分量的数量或改善奇异值分量的质量;利用奇异值贡献指标可以合理确定奇异值截断阈值;采用二次奇异值截断法和增加新结构数量均有利于提高结构损伤的识别精度。A method was proposed to detect structural damage by combining optimized added masses and eigenvalue sensitivity.By adding several sets of optimized masses to the original structure,some new structures with unchanged structural stiffness were obtained.Eigenvalue sensitivity equations were then constructed to obtain damage parameters by utilizing the measured eigenvalues of both the original and new structures.First,the mathematical model with the optimization of additional masses was established by setting the minimum condition number of the sensitivity matrix as the objective function.The particle swarm optimization algorithm was employed to find the best value.Second,a quadratic singular value truncation method was adopted to solve the best sensitivity equations.To overcome the morbidity of sensitivity matrix and the jamming of data noise,the singular value contribution index is suggested to determine the singular value truncation threshold reasonably.The numerical analysis of a cantilever beam shows that it is difficult to achieve a small enough condition number of the sensitivity matrix by continuously increasing the number of new structures,but it can increase the amount of high-quality singular value components or improve the quality of the singular value components.The singular value contribution indicator can determine a reasonable truncation threshold of singular values.Both utilizing the quadratic singular value truncation method and increasing new structures are beneficial to improving structural damage identification accuracy.

关 键 词：损伤识别 模态测试 附加质量 优化算法 灵敏度 

分 类 号：TU311[建筑科学—结构工程]