基于全量补偿算法的结构损伤识别
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摘要
频率和振型是反应结构动力特性的主要模态参数,文中对损伤结构的频率和振型进行了研究。通过实测损伤结构的频率和振型,利用矩阵理论修正理论有限元模型,使之与实测损伤结构的频率和振型一致;将修正的理论有限元模型表达成单元刚度矩阵与损伤因子的线性组合,把损伤识别问题转化为组合系数的识别问题。给定损伤因子的合理取值范围,用优化方法求解损伤因子。通过对十跨桁架结构的数值仿真,仅用结构的前5阶频率和振型就能很好的识别结构的损伤,且该方法不需要对实测振型进行归一化处理,具有较强的实用性。
The frequency and vibration mode were the main modal parameters representing dynamic characteristics of structure,and the frequency and vibration mode of the damaged structure were studied in this paper. First,through measuring the frequency and vibration modes of the damaged structure,a correction theory of matrix was used was used to modify the finite element model,which was consistent with the frequency and vibration modes measured from the damaged structure. Secondly,the finite element model( FEM) of the revision theory can be expressed by a linear combination of the element stiffness matrix and the damage factor. The damage identification problem transformed into the solution of the combination coefficients. Next,the range of reasonable values of damage factors was given and the damage factors could be solved by the optimization method. Through the numerical simulation of a ten-span truss structure,the structural damage could be identified significantly by merely using frequencies and vibration modes of the first five orders. Furthermore,the method does not need to normalize the measured vibration modes,but has strong applicability.
The frequency and vibration mode were the main modal parameters representing dynamic characteristics of structure,and the frequency and vibration mode of the damaged structure were studied in this paper. First,through measuring the frequency and vibration modes of the damaged structure,a correction theory of matrix was used was used to modify the finite element model,which was consistent with the frequency and vibration modes measured from the damaged structure. Secondly,the finite element model( FEM) of the revision theory can be expressed by a linear combination of the element stiffness matrix and the damage factor. The damage identification problem transformed into the solution of the combination coefficients. Next,the range of reasonable values of damage factors was given and the damage factors could be solved by the optimization method. Through the numerical simulation of a ten-span truss structure,the structural damage could be identified significantly by merely using frequencies and vibration modes of the first five orders. Furthermore,the method does not need to normalize the measured vibration modes,but has strong applicability.
引文
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[8]杨栋,任伟新.基于递归矩阵奇异熵的损伤识别方法[J].振动与冲击,2012,31(3):60-63.YANG Dong,REN Weixin.Structure damage detecting using singular entropy of recurrence matrix[J].Journal of Vibration and Shock,2012,31(3):60-63.
[9]杜思义,殷学纲,陈淮.基于矩阵摄动理论识别结构损伤的筛选法[J].应用力学学报,2008,25(1):75-78.DU Siyi,YIN Xuegang,CHEN Huai.Sieve method for identifying damage based on matrix perturbation theory[J].Chinese Journal of Applied Mechanics,2008,25(1):75-78.
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[14]安永辉,欧进萍.大跨度钢桁桥模型的精细化损伤定位模拟和实验研究[J].计算力学学报,2011,28(5):730-736.AN Yonghui,OU Jinping.Experimental and numerical studied on precise damage localization of a long-span steel truss bridge model[J].Chinese Journal of Computational Mechanics,2011,28(5):730-736.
[15]王秋萍,郭迅.基于损伤部位向量法的钢框架损伤识别研究[J].世界地震工程,2012,28(1):50-55.WANG Qiuping,GUO Xun.DLV-based research on damage identification of steel frame[J].World Earthquake Engineering,2012,28(1):50-55.
[16]邓昌,顾培英,汤雷.基于移动附加质量的损伤诊断技术[J].振动与冲击,2010,29(7):135-138.DENG Chang,GU Peiying,Tang Lei.Damage diagnosis based on natural frequencies of a structure by adding known masses[J].Journal of vibration and Shock,2010,29(7):153-138.
[17]侯吉林,欧进萍,JANKOWSKI L.基于局部主频率的子结构损伤识别研究与实验[J].工程力学,2012,29(9):99-105.HOU Jilin,OU Jinping,JANKOWSKI L.The study and experiment of substructure damage identification based on local primary frequency[J].Engineering Mechanics,2012,29(9):99-105.
[18]张纯,宋固全,吴光宇.改进的正则化模型修正方法在结构损伤识别中的应用[J].工程力学,2012,29(2):29-43.ZHANG Chun,SONG Guquan,WU Guangyu.Structure damage identification by finite element model updated with improved tikhonov regularization[J].Engineering Mechanics,2012,29(2):29-43.
[19]孙晓丹,欧进萍,侯钢领,等.基于Bayesian估计的整体和局部信息融合的损伤识别[J].工程力学,2012,29(6):234-239.SUN Xiaodan,OU Jinping,HOU Gangling,et al.Damage Identification based on Baysian fusion of global and local information[J].Engineering Mechanics,2012,29(6):234-239.
[20]张笑华,任伟新,禹丹江.结构模态参数识别的随机子空间法[J].福州大学学报,2005,33(10):46-49.ZHANG Xiaohua,REN Weixin,YU Danjiang.Structural modal parameter identification appling stochastic subspace identification[J].Journal of Fuzhou University,2005,33(10):46-49.
[2]KIM H,MELHEM H.Damage detection of structures by wavelet analysis[J].Journal of Engineering Structures,2004,26(3):7-14.
[3]SALAWU O S.Detection of structural damage through changes in frequency:a review[J].Engineering Structures,1997,19(9):718-723.
[4]VESTRONI F,CAPECCHI D.Damage detection in beam structures based on frequency measurements[J].Journal of Engineering Mechanics,2000,126(7):761-768.
[5]李范春,李成.结构损伤识别的数值模拟[J].船舶力学,2006,10(5):119-126.LI Fanchun,LI Cheng.Numerical simulation of the structural damage identification[J].Journal of Ship Mechanics.2006,10(5):119-126.
[6]刘春城,刘佼,李宏男.基于支持向量机的大型输电铁塔损伤识别方法研究[J].应用基础与工程科学学报,2010,18(4):616-625.LIU Chuncheng,LIU Jiao,LI Hongnan.Damage identification for transmission tower based on support vector machines[J].Journal of Basic Science and Engineering,2010,18(4):616-625.
[7]宗周红,褚福鹏,牛杰.基于响应面模型修正的桥梁结构损伤识别方法[J].土木工程学报,2013,46(2):115-122.ZONG Zhouhong,CHU Fupeng,NIU Jie.Damage identication methods of bridge structures using reponse surface based on finite element model updating[J].China Civil Engineering Journal,2013,46(2):115-122.
[8]杨栋,任伟新.基于递归矩阵奇异熵的损伤识别方法[J].振动与冲击,2012,31(3):60-63.YANG Dong,REN Weixin.Structure damage detecting using singular entropy of recurrence matrix[J].Journal of Vibration and Shock,2012,31(3):60-63.
[9]杜思义,殷学纲,陈淮.基于矩阵摄动理论识别结构损伤的筛选法[J].应用力学学报,2008,25(1):75-78.DU Siyi,YIN Xuegang,CHEN Huai.Sieve method for identifying damage based on matrix perturbation theory[J].Chinese Journal of Applied Mechanics,2008,25(1):75-78.
[10]REN W X,ROECK G.Structural damage identification using modal data.1:simulation verification[J].Journal of Structural Engineering,2002,128(1):87-95.
[11]ELKORDY M F,CHANG K C,LEE G C.Application of neural networks in vibrational signature analysis[J].Journal of Engineering Mechanics,1998,120(2):251-264.
[12]唐和生,薛松涛,陈镕,等.序贯最小二乘支持向量机的结构系统识别[J].振动工程学报,2006,19(3):382-387.TANG Hesheng,XUE Songtao,CHEN Rong,et al.Sequential LS-SVM for structural systems identification[J].Journal of Vibration Engineering,2006,19(3):382-387.
[13]孙继广.一类反特征值问题的最小二乘解[J].计算数学,1987,9(2):206-216.SUN Jiguang.Least-squares solutions of a class of inverse eigenvalue problems[J].Mathematica Numerical Sinica,1987,9(2):206-216.
[14]安永辉,欧进萍.大跨度钢桁桥模型的精细化损伤定位模拟和实验研究[J].计算力学学报,2011,28(5):730-736.AN Yonghui,OU Jinping.Experimental and numerical studied on precise damage localization of a long-span steel truss bridge model[J].Chinese Journal of Computational Mechanics,2011,28(5):730-736.
[15]王秋萍,郭迅.基于损伤部位向量法的钢框架损伤识别研究[J].世界地震工程,2012,28(1):50-55.WANG Qiuping,GUO Xun.DLV-based research on damage identification of steel frame[J].World Earthquake Engineering,2012,28(1):50-55.
[16]邓昌,顾培英,汤雷.基于移动附加质量的损伤诊断技术[J].振动与冲击,2010,29(7):135-138.DENG Chang,GU Peiying,Tang Lei.Damage diagnosis based on natural frequencies of a structure by adding known masses[J].Journal of vibration and Shock,2010,29(7):153-138.
[17]侯吉林,欧进萍,JANKOWSKI L.基于局部主频率的子结构损伤识别研究与实验[J].工程力学,2012,29(9):99-105.HOU Jilin,OU Jinping,JANKOWSKI L.The study and experiment of substructure damage identification based on local primary frequency[J].Engineering Mechanics,2012,29(9):99-105.
[18]张纯,宋固全,吴光宇.改进的正则化模型修正方法在结构损伤识别中的应用[J].工程力学,2012,29(2):29-43.ZHANG Chun,SONG Guquan,WU Guangyu.Structure damage identification by finite element model updated with improved tikhonov regularization[J].Engineering Mechanics,2012,29(2):29-43.
[19]孙晓丹,欧进萍,侯钢领,等.基于Bayesian估计的整体和局部信息融合的损伤识别[J].工程力学,2012,29(6):234-239.SUN Xiaodan,OU Jinping,HOU Gangling,et al.Damage Identification based on Baysian fusion of global and local information[J].Engineering Mechanics,2012,29(6):234-239.
[20]张笑华,任伟新,禹丹江.结构模态参数识别的随机子空间法[J].福州大学学报,2005,33(10):46-49.ZHANG Xiaohua,REN Weixin,YU Danjiang.Structural modal parameter identification appling stochastic subspace identification[J].Journal of Fuzhou University,2005,33(10):46-49.
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