基于自由度缩聚的最小秩修正损伤诊断  

Minimum Rank Correction Damage Identification Based on Modal Reduction

作　　者：李国庆 罗帅 张丽[2] LI Guoqing;LUO Shuai;ZHANG Li(School of Civil Engineering,Shaoxing University,Shaoxing,Zhejiang 312000,P.R.China;Department of Civil Engineering,Gongqing College of Nanchang University,Jiujiang,Jiangxi 332020,P.R.China)

机构地区：[1]绍兴文理学院土木工程学院,浙江绍兴312000 [2]南昌大学共青学院土木工程系,江西九江332020

出　　处：《应用数学和力学》2020年第10期1103-1109,共7页Applied Mathematics and Mechanics

基　　金：广东省自然科学基金(2015A030310168)。

摘　　要：为了解决实测模态参数与有限元分析模态参数不匹配对损伤诊断精度影响的问题,推导了基于自由度缩聚法的残余力向量公式及最小秩修正公式.通过对结构自由度缩聚后的损伤前、后残余力向量的运算,可以得出相较于损伤前的残余力变化率向量,将残余力变化率向量元素的绝对值作为改进的残余力向量,通过运用推导出的改进残余力向量,能够较好地解决采用最小秩修正法时所选取模态个数必须等于待修正刚度矩阵秩这一矛盾,并由缩聚后最小秩修正公式计算出损伤程度.研究表明:在考虑噪音干扰下,改进的残余力向量法对自由度缩聚后的受损结构依然具有较高地识别精度.利用推导的最小秩修正公式进行损伤程度识别其结果是可靠的.本文所提方法既可以实现对实测自由度不完备结构的损伤定位,又可进行损伤程度的识别,具有较高的鲁棒性和损伤诊断性能.To solve the problem that the measured modal parameters and the finite element a⁃nalysis modal parameters do not match in damage identification,the residual force vector for⁃mula and the minimum rank update formula based on the modal reduction method were de⁃rived.Through the calculation of the residual force vectors of damaged and undamaged struc⁃tures,the change rate of the residual force vector was obtained,and the absolute values of the residual force change rate vector elements were defined as the improved residual force vector.With the improved residual force vector,the correct number of modes used in the minimum rank update method was determined,and the minimum rank update formula based on modal reduction was used to calculate the damage extent.The results show that,under noise interfer⁃ence,the presented method could well locate the damage with incomplete modal data.The damage extent identification based on the derived minimum rank update formula is reliable.The method is robust and accurate in structural damage identification for measured incomplete⁃DOF structures.

关 键 词：最小秩修正 模态缩聚 残余力向量 抗噪分析 损伤诊断 

分 类 号：TU317[建筑科学—结构工程]