基于残余能量灵敏度分析的结构损伤识别研究
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摘要
土木工程结构在长期运营过程中受各种因素影响,不可避免地会遭受不同程度的损伤。结构损伤识别作为健康监测的核心内容之一,是近年来的研究热点。工程结构的动态特征灵敏度分析对工程结构的损伤识别、动态设计、优化设计、控制理论和动力修改等方面的研究有着十分重要的意义。近年来,由基本模态参数衍生出来的基于能量的指标如应变能、残余能量等对损伤的敏感性得到了广泛关注,其灵敏度分析也成为一个重要内容。本文对残余能量和单元残余能量进行了灵敏度分析,并将其用于结构损伤识别,得到了一些有益的结论。主要工作和研究内容如下：
1.回顾了损伤识别的发展,综述了结构动态特性灵敏度分析和损伤识别的研究现状,指出了当前损伤识别研究存在的不足。
2.提出了基于残余能量灵敏度的损伤识别方法,建立了相应的损伤识别方程组,通过求解损伤方程组,能同时识别损伤位置和损伤程度的。仿真算例分析结果表明了该方法的有效性。
3.定义单元残余能量,推导了无阻尼线性系统单元残余能量的一阶灵敏度和二阶灵敏度解析表达式,分析了单元残余能量对损伤参数的灵敏度,进一步建立了基于单元残余能量灵敏度分析的结构损伤方程组。为解决方程组的病态问题,引入了增广方程组法,该方法只需第一阶模态参数便能同时识别结构损伤位置和损伤程度。
4.为研究基于单元残余能量灵敏度分析的损伤识别方法对不同结构的适用性,采用一简支梁和一平面桁架结构进行了仿真分析,结果表明,该方法能很好识别损伤位置和损伤程度。
5.引入蒙特卡罗方法对基于单元残余能量的灵敏度分析方法进行了抗噪性能研究,并研究了损伤识别精度与损伤程度、噪声水平、结构类型的关系。
Affected by various factors,civil engineering structures inevitably suffer different extent damage in the course of a long-term operation. As one of important contents in health monitoring,structural damage identification is a hot research topic in recent years. The dynamic characteristic sensitivity analysis of engineering structures plays an important role in many fields of structural engineering such as damage identification,dynamic design,structural optimization design,control theory and dynamic modification. Due to the sensitivity to damage,the energy-based indicators like strain energy and residual energy derived from basic modal parameters draw worldwide attention in recent years. This paper analyzes the sensitivity of the residual energy and the element residual energy,and their applications to structural damage identification. Some useful conclusions are made.The main contents are detailed as following:
1.Review the development of damage identification. Research situation of the structural dynamic sensitivity analysis and damage identification are summarized and the shortcomings in damage identification are pointed out.
2.Propose the damage identification method based on residual energy sensitivity,The corresponding damage identification equations are established. Damage location and severity can be simultaneously determinated by solving the equations.Numerical simulation studies show that the proposed method is effective.
3.Propose the new indicator-element residual energy. Based on this,the first order and the second order sensitivity formula for linear system without damping are derived,and the sensitivity of element residual energy of the damage parameter is analyzed. Furthermore,the damage identification equations based on sensitivity analysis of element residual energy are also established. To solve the ill-conditioned problem of the equations,a new solution technique-augmented system method is introduced. The method can simultaneously identify the damage location and severity by only using the first order mode parameters.
4.The applicability of the residual energy sensitivity analysis-based damage identification method for different structures is studied by numerical simulation for a simply supported beam and a plane truss structure.The results indicate that the presented method is able to identify the location and severity of damaged element.
5.The Monte-Carlo method is used to research anti-noise performance of the damage identification method based on element residual energy sensitivity analysis.Damage identification accuracy related with damage severity,noise level and structure type is also investigated.
1.回顾了损伤识别的发展,综述了结构动态特性灵敏度分析和损伤识别的研究现状,指出了当前损伤识别研究存在的不足。
2.提出了基于残余能量灵敏度的损伤识别方法,建立了相应的损伤识别方程组,通过求解损伤方程组,能同时识别损伤位置和损伤程度的。仿真算例分析结果表明了该方法的有效性。
3.定义单元残余能量,推导了无阻尼线性系统单元残余能量的一阶灵敏度和二阶灵敏度解析表达式,分析了单元残余能量对损伤参数的灵敏度,进一步建立了基于单元残余能量灵敏度分析的结构损伤方程组。为解决方程组的病态问题,引入了增广方程组法,该方法只需第一阶模态参数便能同时识别结构损伤位置和损伤程度。
4.为研究基于单元残余能量灵敏度分析的损伤识别方法对不同结构的适用性,采用一简支梁和一平面桁架结构进行了仿真分析,结果表明,该方法能很好识别损伤位置和损伤程度。
5.引入蒙特卡罗方法对基于单元残余能量的灵敏度分析方法进行了抗噪性能研究,并研究了损伤识别精度与损伤程度、噪声水平、结构类型的关系。
Affected by various factors,civil engineering structures inevitably suffer different extent damage in the course of a long-term operation. As one of important contents in health monitoring,structural damage identification is a hot research topic in recent years. The dynamic characteristic sensitivity analysis of engineering structures plays an important role in many fields of structural engineering such as damage identification,dynamic design,structural optimization design,control theory and dynamic modification. Due to the sensitivity to damage,the energy-based indicators like strain energy and residual energy derived from basic modal parameters draw worldwide attention in recent years. This paper analyzes the sensitivity of the residual energy and the element residual energy,and their applications to structural damage identification. Some useful conclusions are made.The main contents are detailed as following:
1.Review the development of damage identification. Research situation of the structural dynamic sensitivity analysis and damage identification are summarized and the shortcomings in damage identification are pointed out.
2.Propose the damage identification method based on residual energy sensitivity,The corresponding damage identification equations are established. Damage location and severity can be simultaneously determinated by solving the equations.Numerical simulation studies show that the proposed method is effective.
3.Propose the new indicator-element residual energy. Based on this,the first order and the second order sensitivity formula for linear system without damping are derived,and the sensitivity of element residual energy of the damage parameter is analyzed. Furthermore,the damage identification equations based on sensitivity analysis of element residual energy are also established. To solve the ill-conditioned problem of the equations,a new solution technique-augmented system method is introduced. The method can simultaneously identify the damage location and severity by only using the first order mode parameters.
4.The applicability of the residual energy sensitivity analysis-based damage identification method for different structures is studied by numerical simulation for a simply supported beam and a plane truss structure.The results indicate that the presented method is able to identify the location and severity of damaged element.
5.The Monte-Carlo method is used to research anti-noise performance of the damage identification method based on element residual energy sensitivity analysis.Damage identification accuracy related with damage severity,noise level and structure type is also investigated.
引文
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[2]Saltelli A,Chan K,Scott E M. Sensitivity Analysis. NewYork:John WilY&Sons,Ltd,2000
[3]傅志方,华宏星.模态分析理论与应用.上海：上海交通大学出版社,2000
[4]Fox R L,Kapoor M P. Rates of change of eigenvalues and eigenvectors. AIAA Journal,1968,6(12):2426～2429
[5]Neson R B.Simplified calculation of eigenvector derivatives. AIAA Journal, 1988,26:361～366
[6]Ojalvo I U. Efficient calculation of modal sensitivity for systems with repeated frequencise. AIAA Journal,1988,26:361～366
[7]Lee I W,Jung G H. An efficient algebraic method for computation of natural frequency and mode shape sensitivities:Part I:distinct natural frequencies. Computers and Structures,1997,62(3):429～435
[8]Lee I W,Jung G H. An efficient algebraic method for computation of natural frequeney and mode shape sensitivities:Part II:multiple natural frequencies. Computers and Structures,1997,62(3):437～443
[9]Zhao J,Dewolf J T. Sensitivity study for vibrational parameters used in damage detection. Journal of Structural Engineering,1999,125(4):410～416
[10]程远胜,吕磊,王真.基于结构柔度灵敏度的损伤定位.华中科技大学学报(自然科学版),2007,35(9)：5～7
[11]瞿祖清,华宏星,傅志方.一种频响函数灵敏度分析方法.机械强度,1999,21(2)：95～97
[12]颜王吉.单元模态应变能灵敏度及其在结构损伤识别中的应用：[硕士学位论文].长沙：中南大学,2008
[13]Doebling S W,Farrar C R,Prime M B. A summary review of vibration-based damage identification methods. Shock Vib Digest,1998,30(2):91～105
[14]Rytter A. Vibration-based inspection of civil engineering structures:[Ph. D. Dissertation].Aalborg(Dnemark):Department of Building Technology and Structural Engineering,Aalborg University,1993
[15]董聪.现代结构系统可靠性理论及其应用.北京：科学出版社,2001
[16]冯新.木工程结构识别方法的研究：[博士学位论文].大连：大连理工大学,2002
[17]管迪华.模态分析技术.北京：清华大学出版社,1996
[18]Sanayei M,Onipede O.Damage assessment of structures using static test data. AIAA Journal,1991,29(7):1174～1179
[19]Banan M R, Hjelmstad K D. Parameter estimation of structures from static response,I:Computational Aspects. Journal of Structural Engineering,1994, 120(11):3243～3258
[20]Banan M R,Hjelmstad K D. Parameter estimation of structures from static response,Ⅱ:Numerical Simulation Studies. Journal of Structural Engineering, 1994,120 (11):3259～3283
[21]张启伟.桥梁结构模型修正与损伤识别：[博士学位论文].上海：同济大学,1999
[22]崔飞,袁万城,史家钧.基于静态应变及位移测量的结构损伤识别法.同济大学学报(自然科学版),2000,28(1)：5～8
[23]Lifshitz J M,Rotem A. Determination of reinforcement unbonding of composites by a vibration technique.Journal of Composite Materials,1969,3: 412～423
[24]Adams R D,Cawley P,Pye C J,Stone B J. A vibration technique for non-destructively assessing the integrity of structures. Journal of Mechanical Engineering Science,1978,20:93～100
[25]Zhang W W.A sensitivity analysis in fault vibration diagnosis of structures. Proceeding of 5th IMAC,1987,496～501
[26]West W M. Illustration of the use of modal assurance criterion to detect structural changes in an orbiter test specimen. Proceedings of the Air Force Conference on Aircraft Structural Integrity,USA,1984,1～6
[27]Yuen M M F. A numerical study of the eigenparameters of a damaged cantilever. Journal of Sound and Vibration,1985,103:301～310
[28]Srinivasan M G,Kot C A. Effects of damage on the modal parameters of a cylindrical shell. Proceeding of 10th IMAC,1992,529～535
[29]Chen Y, Swamidas A S J. Dynamic characteristics and modal parameters of a plate with a small growing surface crack. Proceeding of 12th IMAC,1994, 1155～1161
[30]Dong C,Zhang P Q,Feng W Q,Huang T C. The sensitivity study of the modal parameters of a cracked beam. Proceeding of 12th IMAC,1994,98～104
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