结构损伤识别中的广义残余力向量差法研究
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摘要
采用矩阵摄动有限元方法,给出了结构损伤识别方程。为减小模型误差和测试误差对损伤识别结果的影响,利用残余力向量对损伤单元的敏感性,提出了广义残余力向量差的概念。为提高损伤识别结果精度和计算效率,联合采用广义残余力向量差定位与频率变化定量的结构损伤识别方法,先运用广义残余力向量差来初步确定损伤位置,再根据频率摄动运用测试精度较高的频率筛选计算损伤程度并确认损伤位置。实例证明,即使考虑测试误差,该方法仍然可以实现对损伤位置和程度的快速准确识别,具有较强的噪声鲁棒性。
According to matrix perturbation finite element method,a structural damage identification equation is derived.Using the sensitive properties of residual force vector to damage element,a concept of generalized residual force vector is proposed to reduce the effect of errors in modeling and measurements on identification results.To improve the accuracy of identification results and raise calculating efficiency,a combined method is used to identify structural damage based on the perturbation of frequency and generalized residual force vector.Firstly generalized residual force vector difference is used to locate possible damage elements,then damage elements and damage extent are determined by the perturbation of frequency which had high test precision.The example show that considering test errors,the method still could identify the damage quickly and accurately and has strong noise robusticity.
According to matrix perturbation finite element method,a structural damage identification equation is derived.Using the sensitive properties of residual force vector to damage element,a concept of generalized residual force vector is proposed to reduce the effect of errors in modeling and measurements on identification results.To improve the accuracy of identification results and raise calculating efficiency,a combined method is used to identify structural damage based on the perturbation of frequency and generalized residual force vector.Firstly generalized residual force vector difference is used to locate possible damage elements,then damage elements and damage extent are determined by the perturbation of frequency which had high test precision.The example show that considering test errors,the method still could identify the damage quickly and accurately and has strong noise robusticity.
引文
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[15]宋玉普,张亮,刘志鑫.测量模态不完整情况下空间网架结构的损伤识别[J].土木工程学报,2009,42(1):10～15Song Yu-pu,Zhang Liang,Liu Zhi-xin.Damage Identification of Space Truss with Incomplete Measured Data[J].China Civil Engineering Journal,2009,42(1):10～15(in Chinese)
[16]徐国萍,刘洪兵,艾磊.基于Park-Ang模型的框架结构地震损伤性能评估[J].工程抗震与加固改造,2011,33(4):7～10Xu Guo-ping,Liu Hong-bing,Ai Lei.Seismic Performance Evaluation for Frame Structure Based on Park-Ang Damage Model[J].Earthquake Resistant Engineering and Retrofitting,2011,33(4):7～10(in Chinese)
[2]Stubbs N,Osegueda R.Global Nondestructive Damage Evaluation in Solid[J].International Journal of Analytical and Experimental Modal Analysis,1990,(2):67～79
[3]杜思义,殷学纲,陈淮.基于频率变化识别结构损伤的摄动有限元方法[J].工程力学,2007,24(4):66～70Du Si-yi,Yin Xue-gang,Chen Huai.The Perturbation FEM to Identify Damages Based on Frequency Changes[J].Engineering Mechanics,2007,24(4):66～70(in Chinese)
[4]殷学纲,雷跃明.摄动有限元法在结构动力模型修改中的应用[J].应用力学学报,1992,9(2):38～45Yin Xue-gang,Lei Yue-ming.Application of Perturbation Finite Element Method in Structure Dynamic Model Modification[J].Chinese Journal of Applied Mechanics,1992,9(2):38～45(in Chinese)
[5]陈塑寰.结构动态设计的矩阵摄动理论[M].北京:科学出版社,1999Chen Su-huan.Matrix Perturbation Theory in Structure Dynamic Design[M].Beijing:Science Press,1999(in Chinese)
[6]Fabrizio V,Danilo C.Damage Detection in Beam Structures Based on Frequency Measurements[J].Journal of Engineering Mechanics,2000,126(7):761～768
[7]Norris S,Tafe H B,Roberto O.Nondestructive Const Ruction Error Detection in Large Space Structures[J].AIAA,1990,28(11):146～152
[8]Hassiotis S,Jeong G D.Assessment of Structural Damage from Natural Frequency Measurement[J].Computers and Structures,1993,49(4):679～691
[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):75～78Du Si-yi,Yin Xue-gang,Chen Huai.Screening Method for Identifying Damage Based on Matrix Perturbation Theory[J].Chinese Journal of Applied Mechanics,2008,25(1):75～78(in Chinese)
[10]He Wei,He Rong,Li Ya-wei.Research and Implementation of Damage Orientation by General Residual Force Vector[A].ICMET’09[C],Beijing,August8,2009
[11]何伟.中、下承式钢管混凝土拱桥损伤识别关键问题研究[D].郑州:郑州大学博士学位论文,2010He Wei.Research on the Key Problem of Damage Identification Method for Half Through or Through Concrete Filled Steel Tubular Arch Bridge[D].Zhengzhou:Zhengzhou University,2010(in Chinese)
[12]Ricles J M,Kosmatka J B.Damage Detection in Elastic Structures using Vibratory Residual Forces and Weighted Sensitivity[J].AIAA,1992,30(9):2310～2316
[13]杨秋伟,刘济科.损伤识别一种改进的残余力向量法[J].固体力学学报,2006,27(1):83～85Yang Qiu-wei,Liu Ji-ke.An Improved Method for Structural Damage Identification Based on Residual Forces Vector[J].Acta Mechanica Solida Sinica,2006,27(1):83～85(in Chinese)
[14]Wang Bo,He Wei.A New Method Based on Matrix Perturbation and Improved Residual Force Vector for Structural Damage Detection[A].IEEE ICCSIT2009[C],Beijing,August11,2009
[15]宋玉普,张亮,刘志鑫.测量模态不完整情况下空间网架结构的损伤识别[J].土木工程学报,2009,42(1):10～15Song Yu-pu,Zhang Liang,Liu Zhi-xin.Damage Identification of Space Truss with Incomplete Measured Data[J].China Civil Engineering Journal,2009,42(1):10～15(in Chinese)
[16]徐国萍,刘洪兵,艾磊.基于Park-Ang模型的框架结构地震损伤性能评估[J].工程抗震与加固改造,2011,33(4):7～10Xu Guo-ping,Liu Hong-bing,Ai Lei.Seismic Performance Evaluation for Frame Structure Based on Park-Ang Damage Model[J].Earthquake Resistant Engineering and Retrofitting,2011,33(4):7～10(in Chinese)
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