基于振动特征指标与Kriging模型的结构损伤识别方法研究
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摘要
结构损伤识别一直是土木工程、航空航天、海洋工程等事业的热门研究课题。近半个世纪以来,损伤识别理论和试验技术得到了空前的发展。人们致力于寻找一种实时的、鲁棒的、无损的、高效的结构损伤识别方法。其中,基于振动测试的损伤识别方法引起了学术界和工程界广泛的关注与研究,其基本思路是通过结构损伤引起的动力学特征和响应的变化,来检测损伤的位置,并预测损伤的程度。结构损伤识别属于系统参数辨识的理论范畴,它不仅仅是单纯意义上的对结构功能和性态的诊断和修复,更积极的意义在于使人们重新认识结构的特征,并指导设计人员对以后的类似结构进行改进设计。
完整意义上的损伤识别问题包括四个部分,即判断结构是否存在损伤,损伤的定位,损伤定量分析,和评估结构损伤后的剩余服役寿命。本文从损伤的定位和定量分析入手,总结了当前的损伤识别研究进展,将以往的损伤识别方法分为损伤定位检测方法,损伤定量识别方法和结构裂纹识别方法。对连续体结构的损伤识别方法进行了系统地基础性研究,具体工作有以下几个方面：
1.概述了当前研究中常用的损伤定位基础指标。针对于不同测量点位置的选取对多损伤区域敏感程度的差异,以频响函数曲率指标为基础,提出了一种多步的检测方法,使用少量的传感器进行多步判定,来提高损伤定位的准确性和可靠性。通过简支梁的有限元数值算例,详细比较了模态曲率方法、柔度曲率方法和基于频响函数曲率的多步判定方法对梁状多损伤结构的识别效果和抗噪能力。最后采用试验建模的技术,对局部减薄的多损伤管道和局部裂纹的单损伤管道进行损伤识别试验研究。
2.研究了仅利用损伤后结构的振动特征指标进行损伤定位的方法。根据频响函数虚部与模态柔度的相关性,建立了一种基于频响函数虚部类的损伤定位指标,通过引入间隙平滑方法(GSM)来定位损伤。数值算例比较了模态阵型指标、均匀载荷面指标和频响函数虚部类指标对于板结构多损伤检测的准确性和抗噪声能力,讨论了该指标的优越性。在此基础上,进一步提出了基于Thompson离群点统计分析与间隙平滑方法相结合的损伤定位方法,对噪声引起的偶然性奇异值进行筛选和剔除,从而达到噪声抑制的目的。
3.针对于损伤定量识别反演问题的多维度、多极值特点,利用SCE(Shuffled Complex Evolution)优化算法作为损伤识别的基础。通过建立振动特征指标的目标函数,将损伤定量识别问题转化为优化问题。为了进一步缩短优化迭代的时间,引入了Kriging代理模型的理论。根据SCE算法中的复合型进化过程与Kriging代理模型更新过程的共同特点,将两者结合起来,提出了一种Kriging-SCE算法。使用满足精度准则的Kriging代理模型,替代有限元分析过程。对于复合型进化中的当前最优点停滞使得代理模型无法更新问题,给出了一种基于多元正态分布抽样的加点方法,数值和试验算例比较了各个损伤指标构成的目标函数在优化过程中的计算效率。
4.提出了基于Kriging代理模型的结构裂纹识别策略。利用初始样本构造Kriging代理模型,建立裂纹模型参数与结构动力响应的关系,来代替原有损伤参数与结构动力响应关系,从而最大程度上减少了在反演优化迭代过程中反复网格剖分和冗繁的有限元计算过程。改进了Kriging代理模型与SCE算法相结合的识别过程,进一步减少了代理模型更新的次数。使用SCE算法提供的全局最优单点加点准则进行代理模型更新,以改进初始代理模型的在最优解附近的预测精度。详细讨论了初始样本数量对裂纹识别效率及识别结果的影响。该理论对解决板结构上任意裂纹的识别问题具有一定价值。
Structural damage identification is always a hot topic in the field of civil engineering, aerospace and ocean engineering. The theory and experimental technology of damage identification have been unprecedentedly developed for the last half-century. People are focusing on finding a real-time, robust, nondestructive and efficient way for structural damage identification, in which methods of damage identification based on vibration measurement attracts attention and a great number of research in the community of academy and engineering extensively. The basic thought is to detect damage location and predict its level by using the changes in structural dynamic characteristics and responses caused by the damage. Structural damage identification can be seated in the theory of system identification, which doesn't simply mean to diagnose and repair the structural function and performance, but also makes people reconsider the original structures and help designers improve similar structures further.
The damage assessment consists of four sections in the full sense, that is, to estimate whether the damage is present or not, to locate the damage, to do quantitative analysis of the damage and to predict the remaining service life of the structure. In this thesis, the author starts with damage location detection and quantitative analysis. The previous literatures summarized and divided into damage localization, damage quantification, and crack identification. The fundamental research on damage identification method of continuum structural is systematically studied, which can be summarized in the following respects.
1. Some kinds of basic index for damage localization in recent research are first summarized. A multi-step decision method for structural damage detection is presented to improve its accuracy and reliability based on the different performance of frequency response curvature obtained at different measurement points on localization results. Numerical example of multi-damaged simply-supported beam is used to illustrate the validity of the presented method. The efficiencies and anti-noise abilities of modal curvature method, flexibility curvature method and the proposed method are analyzed and compared in detail. Finally, experimental examples of a multi-damaged pipeline with local reduction and a single-damaged pipeline with local crack based on experimental model are preformed to verify the correctness and feasibility of the proposed method.
2. A scheme for damage detection in plate which is based upon vibration data only out of damaged structure is studied. According to the tight connection between imaginary part of frequency response function (IFRF) and modal flexibility, a new kind of damage index coupled with gapped smoothing method (GSM) based on uniform load surface formula, namely flexibility of IFRF (FIFRF), is constructed. The effectiveness of model shapes index, uniform load surface index and FIFRF index are analyzed in conditions of different noise levels by the numerical examples. On this basis of FIFRF index, a new damage localization method combined with Thompson outlier analysis and GSM is further presented to filter and eliminate the outlier in detection results caused by measurement noise, so as to achieve success on repressing noise.
3. Due to the multi-dimension and multi-extreme of the optimization problem on damage quantification, SCE algorithm is introduced as the basic. Damage quantification can be translated to an optimization problem by establishing objective function of vibration information. To improve the efficiency of damage identification and decrease time of structural analysis, the Kriging surrogate model (KSM) is firstly introduced and combined with SCE algorithm, namely Kriging-SCE method, according to the commonalities between the process of SCE complex evolvement and KSM updating. The original finite element analysis (FEA) can be then replaced by Kriging surrogate model with satisfying precision. An adding point criteria based upon multivariate normal sampling method is introduced to solve the problem on KSM updating during the stagnation of current optimization in SCE complex evolvement. Finally the calculation efficiency of original SCE and Kriging-SCE algorithm is compared by numerical and experimental examples.
4. An efficient method of crack identification based on a Kriging surrogate model is presented. The initial samples are used to construct the initial Kriging model which characterizes the relationship between the crack parameters and their corresponding structural dynamic responses, instead of the dynamic constitutive relation for reducing re-meshing process at every iterative step of optimization and the time-consuming FE calculation. To improve the accuracy of the surrogate model around the optimal point and reduce the times of FEA, the Kriging-SCE method is improved, which utilizes the current global optimal point to update the initial Kriging model. The effects of initial sampling size on the identification efficiency and the precision of the identified results are also investigated. This proposed method has certain significance for arbitrary crack identification in a plate.
完整意义上的损伤识别问题包括四个部分,即判断结构是否存在损伤,损伤的定位,损伤定量分析,和评估结构损伤后的剩余服役寿命。本文从损伤的定位和定量分析入手,总结了当前的损伤识别研究进展,将以往的损伤识别方法分为损伤定位检测方法,损伤定量识别方法和结构裂纹识别方法。对连续体结构的损伤识别方法进行了系统地基础性研究,具体工作有以下几个方面：
1.概述了当前研究中常用的损伤定位基础指标。针对于不同测量点位置的选取对多损伤区域敏感程度的差异,以频响函数曲率指标为基础,提出了一种多步的检测方法,使用少量的传感器进行多步判定,来提高损伤定位的准确性和可靠性。通过简支梁的有限元数值算例,详细比较了模态曲率方法、柔度曲率方法和基于频响函数曲率的多步判定方法对梁状多损伤结构的识别效果和抗噪能力。最后采用试验建模的技术,对局部减薄的多损伤管道和局部裂纹的单损伤管道进行损伤识别试验研究。
2.研究了仅利用损伤后结构的振动特征指标进行损伤定位的方法。根据频响函数虚部与模态柔度的相关性,建立了一种基于频响函数虚部类的损伤定位指标,通过引入间隙平滑方法(GSM)来定位损伤。数值算例比较了模态阵型指标、均匀载荷面指标和频响函数虚部类指标对于板结构多损伤检测的准确性和抗噪声能力,讨论了该指标的优越性。在此基础上,进一步提出了基于Thompson离群点统计分析与间隙平滑方法相结合的损伤定位方法,对噪声引起的偶然性奇异值进行筛选和剔除,从而达到噪声抑制的目的。
3.针对于损伤定量识别反演问题的多维度、多极值特点,利用SCE(Shuffled Complex Evolution)优化算法作为损伤识别的基础。通过建立振动特征指标的目标函数,将损伤定量识别问题转化为优化问题。为了进一步缩短优化迭代的时间,引入了Kriging代理模型的理论。根据SCE算法中的复合型进化过程与Kriging代理模型更新过程的共同特点,将两者结合起来,提出了一种Kriging-SCE算法。使用满足精度准则的Kriging代理模型,替代有限元分析过程。对于复合型进化中的当前最优点停滞使得代理模型无法更新问题,给出了一种基于多元正态分布抽样的加点方法,数值和试验算例比较了各个损伤指标构成的目标函数在优化过程中的计算效率。
4.提出了基于Kriging代理模型的结构裂纹识别策略。利用初始样本构造Kriging代理模型,建立裂纹模型参数与结构动力响应的关系,来代替原有损伤参数与结构动力响应关系,从而最大程度上减少了在反演优化迭代过程中反复网格剖分和冗繁的有限元计算过程。改进了Kriging代理模型与SCE算法相结合的识别过程,进一步减少了代理模型更新的次数。使用SCE算法提供的全局最优单点加点准则进行代理模型更新,以改进初始代理模型的在最优解附近的预测精度。详细讨论了初始样本数量对裂纹识别效率及识别结果的影响。该理论对解决板结构上任意裂纹的识别问题具有一定价值。
Structural damage identification is always a hot topic in the field of civil engineering, aerospace and ocean engineering. The theory and experimental technology of damage identification have been unprecedentedly developed for the last half-century. People are focusing on finding a real-time, robust, nondestructive and efficient way for structural damage identification, in which methods of damage identification based on vibration measurement attracts attention and a great number of research in the community of academy and engineering extensively. The basic thought is to detect damage location and predict its level by using the changes in structural dynamic characteristics and responses caused by the damage. Structural damage identification can be seated in the theory of system identification, which doesn't simply mean to diagnose and repair the structural function and performance, but also makes people reconsider the original structures and help designers improve similar structures further.
The damage assessment consists of four sections in the full sense, that is, to estimate whether the damage is present or not, to locate the damage, to do quantitative analysis of the damage and to predict the remaining service life of the structure. In this thesis, the author starts with damage location detection and quantitative analysis. The previous literatures summarized and divided into damage localization, damage quantification, and crack identification. The fundamental research on damage identification method of continuum structural is systematically studied, which can be summarized in the following respects.
1. Some kinds of basic index for damage localization in recent research are first summarized. A multi-step decision method for structural damage detection is presented to improve its accuracy and reliability based on the different performance of frequency response curvature obtained at different measurement points on localization results. Numerical example of multi-damaged simply-supported beam is used to illustrate the validity of the presented method. The efficiencies and anti-noise abilities of modal curvature method, flexibility curvature method and the proposed method are analyzed and compared in detail. Finally, experimental examples of a multi-damaged pipeline with local reduction and a single-damaged pipeline with local crack based on experimental model are preformed to verify the correctness and feasibility of the proposed method.
2. A scheme for damage detection in plate which is based upon vibration data only out of damaged structure is studied. According to the tight connection between imaginary part of frequency response function (IFRF) and modal flexibility, a new kind of damage index coupled with gapped smoothing method (GSM) based on uniform load surface formula, namely flexibility of IFRF (FIFRF), is constructed. The effectiveness of model shapes index, uniform load surface index and FIFRF index are analyzed in conditions of different noise levels by the numerical examples. On this basis of FIFRF index, a new damage localization method combined with Thompson outlier analysis and GSM is further presented to filter and eliminate the outlier in detection results caused by measurement noise, so as to achieve success on repressing noise.
3. Due to the multi-dimension and multi-extreme of the optimization problem on damage quantification, SCE algorithm is introduced as the basic. Damage quantification can be translated to an optimization problem by establishing objective function of vibration information. To improve the efficiency of damage identification and decrease time of structural analysis, the Kriging surrogate model (KSM) is firstly introduced and combined with SCE algorithm, namely Kriging-SCE method, according to the commonalities between the process of SCE complex evolvement and KSM updating. The original finite element analysis (FEA) can be then replaced by Kriging surrogate model with satisfying precision. An adding point criteria based upon multivariate normal sampling method is introduced to solve the problem on KSM updating during the stagnation of current optimization in SCE complex evolvement. Finally the calculation efficiency of original SCE and Kriging-SCE algorithm is compared by numerical and experimental examples.
4. An efficient method of crack identification based on a Kriging surrogate model is presented. The initial samples are used to construct the initial Kriging model which characterizes the relationship between the crack parameters and their corresponding structural dynamic responses, instead of the dynamic constitutive relation for reducing re-meshing process at every iterative step of optimization and the time-consuming FE calculation. To improve the accuracy of the surrogate model around the optimal point and reduce the times of FEA, the Kriging-SCE method is improved, which utilizes the current global optimal point to update the initial Kriging model. The effects of initial sampling size on the identification efficiency and the precision of the identified results are also investigated. This proposed method has certain significance for arbitrary crack identification in a plate.
引文
[1]Doebling S W, Farrar C R, Prime M B. A summary review of vibration-based damage identification methods[J]. Shock and Vibration Digest,1998,30(2):91-105.
[2]袁颖.桥梁结构损伤识别方法的相关问题研究[D].大连：大连理工大学,2006.
[3]于繁华.基于计算智能技术的桥梁结构损伤识别研究[D].吉林：吉林大学,2008.
[4]Salawu O S. Detection of structural damage through changes in frequency:a review[J]. Engineering structures,1997,19(9):718-723.
[5]Montalvao D, Maia N M M, Ribeiro A M R.A review of vibration-based structural health monitoring with special emphasis on composite materials[J]. Shock and Vibration Digest,2006,38(4):295-326.
[6]Sohn H, Farrar C R, Hemez F M, et al. A review of structural health monitoring literature: 1996-2001 [M]. Los Alamos,, New Mexico:Los Alamos National Laboratory,2004.
[7]Yan Y J, Cheng L, Wu Z Y, et al. Development in vibration-based structural damage detection technique[J]. Mechanical Systems and Signal Processing,2007,21(5):2198-2211.
[8]Carden E P, Fanning P. Vibration based condition monitoring:a review[J]. Structural Health Monitoring, 2004,3(4):355-377.
[9]闫桂荣,段忠东,欧进萍.基于结构振动信息的损伤识别研究综述[J].地震工程与工程振动,2007,27(3)：95-103.
[10]Dimarogonas A D. Vibration of cracked structures:a state of the art review[J]. Engineering Fracture Mechanics,1996,55(5):831-857.
[11]胡家顺,冯新,李昕,等.裂纹梁振动分析和裂纹识别方法研究进展[J].振动与冲击,2008,26(11)：146-152.
[12]Pandey A K, Biswas M, Samman M M. Damage detection from changes in curvature mode shapes[J]. Journal of sound and vibration,1991,145(2):321-332.
[13]Stubbs N, Kim J T, Topole K.. An efficient and robust algorithm for damage localization in offshore platforms[C]//Proc. ASCE Tenth Structures Congress.1992,546.
[14]Jauregui D V, Farrar C R. Comparison of damage identification algorithms on experimental modal data from a bridge[C]//PROCEEDINGS-SPIE THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING. SPIE INTERNATIONAL SOCIETY FOR OPTICAL,1996:1423-1429.
[15]Salawu O S, Williams C. Damage location using vibration mode shapes[C]//Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series.1994,2251:933.
[16]Abdel Wahab M M, De Roeck G. Damage detection in bridges using modal curvatures:application to a real damage scenario[J]. Journal of Sound and Vibration,1999,226(2):217-235.
[17]Raghavendrachar M, Aktan A E. Flexibility by multireference impact testing for bridge diagnostics[J]. Journal of Structural Engineering,1992,118(8):2186-2203.
[18]Pandey A K, Biswas M. Damage detection in structures using changes in flexibility[J]. Journal of sound and vibration,1994,169(1):3-17.
[19]曹晖,Friswell M I基于模态柔度曲率的损伤检测方法[J].工程力学,2006,23(004)：33-38.
[20]张丽梅,陈务军,杜守军,等.钢桁架结构损伤检测的柔度曲率幅值突变系数法[J].东南大学学 报：自然科学版,2005,35(A01)：133-138.
[21]Petro S H, Chen S E, GangaRao H V S. Damage detection using vibration measurements[C]// Proceedings,15th IMAC, Orlando, FL,1997,pp.113-127.
[22]Carrasco C J, Osegueda R A, Ferregut C M, et al. Damage localization in a space truss model using modal strain energy[C]//PROCEEDINGS-SPIE THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING. SPIE INTERNATIONAL SOCIETY FOR OPTICAL,1997:1786-1792.
[23]Cornwell P, Doebling S W, Farrar C R. Application of the strain energy damage detection method to plate-like structures[J]. Journal of Sound and Vibration,1999,224(2):359-374.
[24]Doebling S W, Hemez F M, Peterson L D, et al. Improved damage location accuracy using strain energy-based mode selection criteria[J]. AIAA journal,1997,35(4):693-699.
[25]Cornwell P J, Kam M, Carlson B, et al. Comparative study of vibration-based damage ID algorithms[C]//PROCEEDINGS-SPIE THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING. SPIE INTERNATIONAL SOCIETY FOR OPTICAL,1998,2:1710-1716.
[26]徐峰,彭海阔,孟光.基于损伤因子的板架结构损伤识别方法研究[J].振动与冲击,2010,29(12)：22-25.
[27]Sampaio R P C, Maia N M M, Silva J M M. Damage detection using the frequency-response-function curvature method[J]. Journal of Sound and Vibration,1999,226(5):1029-1042.
[28]Maia N M M, Silva J M M, Almas E A M, et al. Damage detection in structures:from mode shape to frequency response function methods[J]. Mechanical Systems and Signal Processing,2003,17(3): 489-498.
[29]汪之松,郭惠勇,李正良.基于频率响应的不同结构损伤识别方法研究[J].工程力学,2008,25(006)：6-13.
[30]Huynh D, He J, Tran D. Damage location vector:A non-destructive structural damage detection technique[J]. Computers & structures,2005,83(28):2353-2367.
[31]Quek S T, Tran V A, Hou X Y, et al. Structural damage detection using enhanced damage locating vector method with limited wireless sensors[J]. Journal of sound and vibration,2009,328(4):411-427.
[32]Liu X, Lieven N A J, Escamilla-Ambrosio P J. Frequency response function shape-based methods for structural damage localisation[J]. Mechanical systems and signal processing,2009,23(4):1243-1259.
[33]Fang S E, Perera R, Huerta M C. Damage Localization Based on Power Spectral Density Analysis[J]. Key Engineering Materials,2007,347:589-594.
[34]Fang S E, Perera R. Power mode shapes for early damage detection in linear structures [J]. Journal of Sound and Vibration,2009,324(1):40-56.
[35]Bayissa W L, Haritos N. Structural damage identification in plates using spectral strain energy analysis[J]. Journal of Sound and Vibration,2007,307(1):226-249.
[36]Guo H, Zhang L. A weighted balance evidence theory for structural multiple damage localization[J]. Computer methods in applied mechanics and engineering,2006,195(44):6225-6238.
[37]Guo H Y. Structural damage detection using information fusion technique[J]. Mechanical systems and signal processing,2006,20(5):1173-1188.
[38]郭惠勇,张陵,蒋健.不同信息融合方法在结构损伤识别上的应用和分析[J].工程力学,2006,23(1)：28-32.
[39]Chandrashekhar M, Ganguli R. Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic[J]. Journal of sound and vibration,2009,326(3):939-957.
[40]杨彦芳,宋玉普.基于主元分析和频响函数的网架结构损伤识别方法[J].工程力学,2007,24(9)：105-110.
[41]Da Silva S, Dias Junior M, Lopes Junior V, et al. Structural damage detection by fuzzy clustering[J]. Mechanical Systems and Signal Processing,2008,22(7):1636-1649.
[42]张力,张瑜.基于模糊理论的结构损伤模式识别[J].西安工业大学学报,2009,29(2)：177-183.
[43]冉志红,李乔.基于模糊聚类和支持向量机的损伤识别方法[J].振动工程学报,2007,20(006)：618-622.
[44]Ratcliffe C P. Damage detection using a modified Laplacian operator on mode shape data[J]. Journal of Sound and Vibration,1997,204(3):505-517.
[45]Ratcliffe C P, Bagaria W J. Vibration technique for locating delamination in a composite beam[J]. Aiaa Journal,1998,36(6):1074-1077.
[46]Wu D, Law S S. Damage localization in plate structures from uniform load surface curvature[J]. Journal of Sound and Vibration,2004,276(1):227-244.
[47]Yoon M K, Heider D, Gillespie J W, et al. Local damage detection using the two-dimensional gapped smoothing method[J]. Journal of Sound and Vibration,2005,279(1):119-139.
[48]Baneen U, Kinkaid N M, Guivant J E, et al. Vibration based damage detection of a beam-type structure using noise suppression method[J]. Journal of Sound and Vibration,2012,331(8): 1777-1788.
[49]Liu X, Escamilla-Ambrosio P J, Lieven N A J. Extended Kalman filtering for the detection of damage in linear mechanical structures[J]. Journal of Sound and Vibration,2009,325(4):1023-1046.
[50]吴新亚,周丽.基于有限范围自适应卡尔曼滤波的结构损伤识别方法[J].振动工程学报,2007,20(4)：401-406.
[51]周丽,吴新亚,尹强,等.基于自适应卡尔曼滤波方法的结构损伤识别实验研究[J].振动工程学报,2008,21(2)：197-202.
[52]Rodriguez R, Escobar J A, Gomez R. Damage detection in instrumented structures without baseline modal parameters[J]. Engineering Structures,2010,32(6):1715-1722.
[53]Wang X Q, Wong W O, Cheng L. Modal power flow with application to damage detection[J]. International Journal of Engineering Science,2009,47(4):512-523.
[54]Wong W O, Wang X Q, Cheng L. Modal power flow analysis of a damaged plate[J]. Journal of Sound and Vibration,2009,320(1):84-100.
[55]朱翔.裂纹损伤结构的振动功率流特性与损伤识别[D].华中科技大学,2007.
[56]Zhu D, Yi X, Wang Y, et al. Mobile Sensor Networks:A New Approach for Structural Health Monitoring[C]//Structures Congress 2010@ s19th Analysis and Computation Specialty Conference. ASCE.2010:159-168.
[57]Waldron K, Ghoshal A, Schulz M J, et al. Damage detection using finite element and laser operational deflection shapes[J]. Finite elements in analysis and design,2002,38(3):193-226.
[58]Lu K. Dynamics Based Damage Detection of Plate-Type Structures[D]. The University of Akron, 2005.
[59]Siringoringo D M, Fujino Y. Experimental study of laser Doppler vibrometer and ambient vibration for vibration-based damage detection[J]. Engineering structures,2006,28(13):1803-1815.
[60]Chen J C, Garba J A. On orbit damage assessment for large space structures[C]//Structures, Structural Dynamics and Materials Conference,28 th, Monterey, CA, Technical Papers. Part 1.1987,6(8).
[61]Zimmerman D C, Kaouk M. Structural damage detection using a minimum rank update theory[J]. Journal of Vibration and Acoustics,1994,116(2):222-231.
[62]Kaouk M, Zimmerman D C. Structural damage assessment using a generalized minimum rank perturbation theory[J]. AIAA journal,1994,32(4):836-842.
[63]Doebling S W. Minimum-rank optimal update of elemental stiffness parameters for structural damage identification[J]. AIAA journal,1996,34(12):2615-2621.
[64]Doebling S W. Damage detection and model refinement using elemental stiffness perturbations with constrained connectivity[R]. Los Alamos National Lab., NM (United States),1996.
[65]杨秋伟,刘济科.基于最小秩修正的结构损伤识别方法[J].机械强度,2008,29(6)：891-893.
[66]杨秋伟,刘济科.结构损伤检测的最小秩修正方法[J].振动与冲击,2008,27(004)：7-9.
[67]Yang Q W, Liu J K. Damage identification by the eigenparameter decomposition of structural flexibility change[J]. International journal for numerical methods in engineering,2009,78(4): 444-459.
[68]高维成,刘伟,钱成.基于剩余模态力和模态应变能理论的网架结构损伤识别[J].工程力学,2007,24(5)：93-100.
[69]Hu S L J, Li H, Wang S. Cross-model cross-mode method for model updating[J]. Mechanical Systems and Signal Processing,2007,21(4):1690-1703.
[70]Li H, Wang J, James Hu S L. Using incomplete modal data for damage detection in offshore jacket structures[J]. Ocean Engineering,2008,35(17):1793-1799.
[71]王俊荣.海洋平台结构物损伤检测与模型修正方法研究[D].山东青岛：中国海洋大学,2009.
[72]Hu S L J, Huajun L. Simultaneous mass, damping, and stiffness updating for dynamic systems[J]. AIAA journal,2007,45(10):2529-2537.
[73]Friswell M, Mottershead J E. Finite element model updating in structural dynamics[M]. Springer, 1995.
[74]Messina A, Williams E J, Contursi T. Structural damage detection by a sensitivity and statistical-based method[J]. Journal of Sound and Vibration,1998,216(5):791-808.
[75]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)：66-70.
[76]Shi Z Y, Law S S, Zhang L M. Damage localization by directly using incomplete mode shapes[J]. Journal of Engineering Mechanics,2000,126(6):656-660.
[77]杨永春,杨风艳,詹宇翀.结构损伤识别中灵敏度法的改进[J].振动与冲击,2006,25(5)：126-129.
[78]孙国,张洪武,蔡贤辉,等.基于模态误差函数灵敏度分析的损伤识别方法[J].振动工程学报,2008,20(3)：303-308.
[79]Yang Q W. A Flexibility-Based Method for Structural Damage Identification Using Ambient Modal Data[J]. International Journal of Space Structures,2009,24(3):153-159.
[80]Yang Q W. A mixed sensitivity method for structural damage detection[J]. Communications in Numerical Methods in Engineering,2009,25(4):381-389.
[81]Yan W J, Ren W X, Huang T L. Statistic structural damage detection based on the closed-form of element modal strain energy sensitivity[J]. Mechanical Systems and Signal Processing,2012,28: 183-194.
[82]Lu Z R, Law S S. Features of dynamic response sensitivity and its application in damage detection[J]. Journal of sound and vibration,2007,303(1):305-329.
[83]Lu Z R, Law S S. Features of dynamic response sensitivity and its application in damage detection[J]. Journal of sound and vibration,2007,303(1):305-329.
[84]Law S S, Zhang K., Duan Z D. Structural damage detection from coupling forces between substructures under support excitation[J]. Engineering Structures,2010,32(8):2221-2228.
[85]Schulz M J, Pai P F, Abdelnaser A S. Frequency response function assignment technique for structural damage identification[C]//PROCEEDINGS-SPIE THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING. SPIE INTERNATIONAL SOCIETY FOR OPTICAL,1996:105-111.
[86]Wang Z, Lin R M, Lim M K. Structural damage detection using measured FRF data[J]. Computer Methods in Applied Mechanics and Engineering,1997,147(1):187-197.
[87]Asma F, Bouazzouni A. Finite element model updating using variable separation[J]. European Journal of Mechanics-A/Solids,2007,26(4):728-735.
[88]Mottershead J E, Link M, Friswell M I. The sensitivity method in finite element model updating:A tutorial[J]. Mechanical Systems and Signal Processing,2011,25(7):2275-2296.
[89]Weber B, Paultre P, Proulx J. Structural damage detection using nonlinear parameter identification with Tikhonov regularization[J]. Structural Control and Health Monitoring,2006,14(3):406-427.
[90]Li X Y, Law S S. Adaptive Tikhonov regularization for damage detection based on nonlinear model updating[J]. Mechanical Systems and Signal Processing,2010,24(6):1646-1664.
[91]Li X Y, Law S S. Consistent Regularization for Damage Detection with Noise and Model Errors[J]. AIAA journal,2010,48(4):777-787.
[92]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)：29-33.
[93]Perera R, Ruiz A, Manzano C. An evolutionary multiobjective framework for structural damage localization and quantification[J]. Engineering Structures,2007,29(10):2540-2550.
[94]Rao M A, Srinivas J, Murthy B S N. Damage detection in vibrating bodies using genetic algorithms[J]. Computers & structures,2004,82(11):963-968.
[95]Gomes H M, Silva N R S. Some comparisons for damage detection on structures using genetic algorithms and modal sensitivity method[J]. Applied Mathematical Modelling,2008,32(11): 2216-2232.
[96]Au F T K, Cheng Y S, Tham L G, et al. Structural damage detection based on a micro-genetic algorithm using incomplete and noisy modal test data[J]. Journal of sound and vibration,2003,259(5): 1081-1094.
[97]Li J, Huang M, Zhu H. Study on Different Residual and Weight Coefficient in Model Updating of Bridge Structure[C]//The 9th International Conference of Chinese Transportation Professionals (ICCTP 2009), August.2009:5-8.
[98]Nobahari M, Seyedpoor S M. Structural damage detection using an efficient correlation-based index and a modified genetic algorithm[J]. Mathematical and Computer Modelling,2011,53(9):1798-1809.
[99]Kang F, Li J, Xu Q. Damage detection based on improved particle swarm optimization using vibration data[J]. Applied Soft Computing,2012.
[100]Begambre O, Laier J E. A hybrid Particle Swarm Optimization-Simplex algorithm (PSOS) for structural damage identification[J]. Advances in Engineering Software,2009,40(9):883-891.
[101]Seyedpoor S M. Structural damage detection using a multi-stage particle swarm optimization[J]. Advances in Structural Engineering,2011,14(3):533-549.
[102]Seyedpoor S M. A two stage method for structural damage detection using a modal strain energy based index and particle swarm optimization[J]. International Journal of Non-Linear Mechanics,2012, 47(1):1-8.
[103]Lee J J, Lee J W, Yi J H, et al. Neural networks-based damage detection for bridges considering errors in baseline finite element models[J]. Journal of Sound and Vibration,2005,280(3):555-578.
[104]李忠献,杨晓明,丁阳.基于结构响应统计特征的神经网络损伤识别方法[J].工程力学,2007,24(9)：1-7.
[105]Li Z X, Yang X M. Damage identification for beams using ANN based on statistical property of structural responses[J]. Computers & structures,2008,86(1):64-71.
[106]Mehrjoo M, Khaji N, Moharrami H, et al. Damage detection of truss bridge joints using Artificial Neural Networks[J]. Expert Systems with Applications,2008,35(3):1122-1131.
[107]Rutherford A C, Inman D J, Park G, et al. Use of response surface metamodels for identification of stiffness and damping coefficients in a simple dynamic system[J]. Shock and Vibration,2005,12(5): 317-332.
[108]Fang S E, Perera R. Damage identification by response surface based model updating using D-optimal design[J]. Mechanical Systems and Signal Processing,2011,25(2):717-733.
[109]Nandwana B P, Maiti S K. Detection of the location and size of a crack in stepped cantilever beams based on measurements of natural frequencies[J]. Journal of Sound and Vibration,1997,203(3): 435-446.
[110]Gudmundson P. The dynamic behaviour of slender structures with cross-sectional cracks[J]. Journal of the Mechanics and Physics of Solids,1983,31(4):329-345.
[111]Liang R Y, Choy F K, Hu J. Detection of cracks in beam structures using measurements of natural frequencies[J]. Journal of the Franklin Institute,1991,328(4):505-518.
[112]Ostachowicz W M, Krawczuk M. Analysis of the Effect of Cracks on the Natural Frequencies of a cantilever Beam[J]. Journal of sound and vibration,1991,150(2):191-201.
[113]Lele S P, Maiti S K. Modelling of transverse vibration of short beams for crack detection and measurement of crack extension[J]. Journal of Sound and Vibration,2002,257(3):559-583.
[114]Owolabi G M, Swamidas A S J, Seshadri R. Crack detection in beams using changes in frequencies and amplitudes of frequency response functions[J]. Journal of sound and vibration,2003,265(1): 1-22.
[115]唐天国,刘浩吾,陈春华,等.梁裂缝损伤检测的模态应变能法及试验研究[J].工程力学,2005,22：39-45.
[116]Vakil-Baghmisheh M T, Peimani M, Sadeghi M H, et al. Crack detection in beam-like structures using genetic algorithms[J]. Applied Soft Computing,2008,8(2):1150-1160.
[117]Faverjon B, Sinou J J. Identification of an open crack in a beam using an a posteriori error estimator of the frequency response functions with noisy measurements [J]. European Journal of Mechanics-A/Solids European Journal of Mechanics-A/Solids,2009,28(1):75-85.
[118]Buezas F S, Rosales M B, Filipich C P. Damage detection with genetic algorithms taking into account a crack contact model[J]. Engineering Fracture Mechanics,2011,78(4):695-712.
[119]Hu J, Liang R Y. An integrated approach to detection of cracks using vibration characteristics[J]. Journal of the Franklin Institute,1993,330(5):841-853.
[120]Shifrin E I, Ruotolo R. Natural frequencies of a beam with an arbitrary number of cracks [J]. Journal of Sound and Vibration,1999,222(3):409-423.
[121]Shifrin E I, Ruotolo R. Natural frequencies of a beam with an arbitrary number of cracks[J]. Journal of Sound and Vibration,1999,222(3):409-423.
[122]Lee J. Identification of multiple cracks in a beam using natural frequencies[J]. Journal of sound and vibration,2009,320(3):482-490.
[123]Lee J. Identification of multiple cracks in a beam using vibration amplitudes[J]. Journal of Sound and Vibration,2009,326(1):205-212.
[124]Lam H F, Ng C T. A probabilistic method for the detection of obstructed cracks of beam-type structures using spatial wavelet transform[J]. Probabilistic Engineering Mechanics,2008,23(2): 237-245.
[125]Mazanoglu K, Sabuncu M. A frequency based algorithm for identification of single and double cracked beams via a statistical approach used in experiment[J]. Mechanical Systems and Signal Processing,2012,30:168-185.
[126]范德礼,郑世杰.基于遗传算法和结构优化的多裂纹梁损伤识别[J].江苏航空,2011,S1：50-53.
[127]Krawczuk M, Palacz M, Ostachowicz W. Wave propagation in plate structures for crack detection[J]. Finite elements in analysis and design,2004,40(9):991-1004.
[128]Krawczuk M, Palacz M, Ostachowicz W. Wave propagation in plate structures for crack detection[J]. Finite elements in analysis and design,2004,40(9):991-1004.
[129]Hadjileontiadis L J, Douka E. Crack detection in plates using fractal dimension[J]. Engineering structures,2007,29(7):1612-1625.
[130]Lam H F, Yin T. Statistical detection of multiple cracks on thin plates utilizing dynamic response[J]. Engineering structures,2010,32(10):3145-3152.
[131]Hu H, Wu C, Lu W J. Damage detection of circular hollow cylinder using modal strain energy and scanning damage index methods[J]. Computers & structures,2011,89(1):149-160.
[132]Nichols J M, Moore E Z, Murphy K. D. Bayesian identification of a cracked plate using a population-based Markov Chain Monte Carlo method[J]. Computers & Structures,2011,89(13): 1323-1332.
[133]Moore E Z, Murphy K D, Nichols J M. Crack identification in a freely vibrating plate using Bayesian parameter estimation[J]. Mechanical Systems and Signal Processing,2011,25(6):2125-2134.
[134]方圣恩.基于有限元模型修正的结构损伤识别方法研究[D].长沙：中南大学,2010.
[135]傅志方.振动模态分析与参数辨识[M].机械工业出版社,1990.
[136]李东升,张莹,任亮,等.结构健康监测中的传感器布置方法及评价准则[J].力学进展,2011,41(1)：39-50.
[137]Mao Y M, Guo X L, Zhao Y. A state space force identification method based on Markov parameters precise computation and regularization technique[J]. Journal of Sound and Vibration,2010,329(15): 3008-3019.
[138]曹晖,林秀萍.结构损伤识别中噪声的模拟[J].振动与冲击,2010,29(5)：106-109.
[139]Zhang Z, Aktan A E. Application of modal flexibility and its derivatives in structural identification[J]. Journal of Research in Nondestructive Evaluation,1998,10(1):43-61.
[140]Grubbs F E. Sample criteria for testing outlying observations[J]. The Annals of Mathematical Statistics,1950,21(1):27-58.
[141]Thompson W R. On a criterion for the rejection of observations and the distribution of the ratio of deviation to sample standard deviation[J]. The Annals of Mathematical Statistics,1935,6(4): 214-219.
[142]Duan Q, Sorooshian S, Gupta V. Effective and efficient global optimization for conceptual rainfall-runoff models[J]. Water Resources Research,1992,28(4):1015-1031.
[143]Mariani V C, Justi Luvizotto L G, Guerra F A, et al. A hybrid shuffled complex evolution approach based on differential evolution for unconstrained optimization[J]. Applied Mathematics and Computation,2011,217(12):5822-5829.
[144]Mariani V C, Coelho L S. A hybrid shuffled complex evolution approach with pattern search for unconstrained optimization[J]. Mathematics and Computers in Simulation,2011,81(9):1901-1909.
[145]Mockus J, Tiesis V, Zilinskas A. The application of Bayesian methods for seeking the extremum[J]. Towards Global Optimization,1978,2:117-129.
[146]高月华,基于kriging代理模型的优化设计方法及其在注塑成型中的应用[D],大连：大连理工大学,2008.
[147]Sakata S, Ashida F, Zako M. An efficient algorithm for Kriging approximation and optimization with large-scale sampling data[J]. Computer methods in applied mechanics and engineering,2004,193(3): 385-404.
[148]Song X M, Zhan C S, Xia J, Integration of a statistical emulator approach with the SCE-UA method for parameter optimization of a hydrological model[J], Chinese Science Bulletin,2012,57(26): 3397-3403.
[149]Rencher A C, Christensen W F. Methods of multivariate analysis[M]. Wiley,2012.
[150]Li J, Huang M, Zhu H. Study on Different Residual and Weight Coefficient in Model Updating of Bridge Structure[C]//The 9th International Conference of Chinese Transportation Professionals (ICCTP 2009), August.2009:5-8.
[2]袁颖.桥梁结构损伤识别方法的相关问题研究[D].大连：大连理工大学,2006.
[3]于繁华.基于计算智能技术的桥梁结构损伤识别研究[D].吉林：吉林大学,2008.
[4]Salawu O S. Detection of structural damage through changes in frequency:a review[J]. Engineering structures,1997,19(9):718-723.
[5]Montalvao D, Maia N M M, Ribeiro A M R.A review of vibration-based structural health monitoring with special emphasis on composite materials[J]. Shock and Vibration Digest,2006,38(4):295-326.
[6]Sohn H, Farrar C R, Hemez F M, et al. A review of structural health monitoring literature: 1996-2001 [M]. Los Alamos,, New Mexico:Los Alamos National Laboratory,2004.
[7]Yan Y J, Cheng L, Wu Z Y, et al. Development in vibration-based structural damage detection technique[J]. Mechanical Systems and Signal Processing,2007,21(5):2198-2211.
[8]Carden E P, Fanning P. Vibration based condition monitoring:a review[J]. Structural Health Monitoring, 2004,3(4):355-377.
[9]闫桂荣,段忠东,欧进萍.基于结构振动信息的损伤识别研究综述[J].地震工程与工程振动,2007,27(3)：95-103.
[10]Dimarogonas A D. Vibration of cracked structures:a state of the art review[J]. Engineering Fracture Mechanics,1996,55(5):831-857.
[11]胡家顺,冯新,李昕,等.裂纹梁振动分析和裂纹识别方法研究进展[J].振动与冲击,2008,26(11)：146-152.
[12]Pandey A K, Biswas M, Samman M M. Damage detection from changes in curvature mode shapes[J]. Journal of sound and vibration,1991,145(2):321-332.
[13]Stubbs N, Kim J T, Topole K.. An efficient and robust algorithm for damage localization in offshore platforms[C]//Proc. ASCE Tenth Structures Congress.1992,546.
[14]Jauregui D V, Farrar C R. Comparison of damage identification algorithms on experimental modal data from a bridge[C]//PROCEEDINGS-SPIE THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING. SPIE INTERNATIONAL SOCIETY FOR OPTICAL,1996:1423-1429.
[15]Salawu O S, Williams C. Damage location using vibration mode shapes[C]//Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series.1994,2251:933.
[16]Abdel Wahab M M, De Roeck G. Damage detection in bridges using modal curvatures:application to a real damage scenario[J]. Journal of Sound and Vibration,1999,226(2):217-235.
[17]Raghavendrachar M, Aktan A E. Flexibility by multireference impact testing for bridge diagnostics[J]. Journal of Structural Engineering,1992,118(8):2186-2203.
[18]Pandey A K, Biswas M. Damage detection in structures using changes in flexibility[J]. Journal of sound and vibration,1994,169(1):3-17.
[19]曹晖,Friswell M I基于模态柔度曲率的损伤检测方法[J].工程力学,2006,23(004)：33-38.
[20]张丽梅,陈务军,杜守军,等.钢桁架结构损伤检测的柔度曲率幅值突变系数法[J].东南大学学 报：自然科学版,2005,35(A01)：133-138.
[21]Petro S H, Chen S E, GangaRao H V S. Damage detection using vibration measurements[C]// Proceedings,15th IMAC, Orlando, FL,1997,pp.113-127.
[22]Carrasco C J, Osegueda R A, Ferregut C M, et al. Damage localization in a space truss model using modal strain energy[C]//PROCEEDINGS-SPIE THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING. SPIE INTERNATIONAL SOCIETY FOR OPTICAL,1997:1786-1792.
[23]Cornwell P, Doebling S W, Farrar C R. Application of the strain energy damage detection method to plate-like structures[J]. Journal of Sound and Vibration,1999,224(2):359-374.
[24]Doebling S W, Hemez F M, Peterson L D, et al. Improved damage location accuracy using strain energy-based mode selection criteria[J]. AIAA journal,1997,35(4):693-699.
[25]Cornwell P J, Kam M, Carlson B, et al. Comparative study of vibration-based damage ID algorithms[C]//PROCEEDINGS-SPIE THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING. SPIE INTERNATIONAL SOCIETY FOR OPTICAL,1998,2:1710-1716.
[26]徐峰,彭海阔,孟光.基于损伤因子的板架结构损伤识别方法研究[J].振动与冲击,2010,29(12)：22-25.
[27]Sampaio R P C, Maia N M M, Silva J M M. Damage detection using the frequency-response-function curvature method[J]. Journal of Sound and Vibration,1999,226(5):1029-1042.
[28]Maia N M M, Silva J M M, Almas E A M, et al. Damage detection in structures:from mode shape to frequency response function methods[J]. Mechanical Systems and Signal Processing,2003,17(3): 489-498.
[29]汪之松,郭惠勇,李正良.基于频率响应的不同结构损伤识别方法研究[J].工程力学,2008,25(006)：6-13.
[30]Huynh D, He J, Tran D. Damage location vector:A non-destructive structural damage detection technique[J]. Computers & structures,2005,83(28):2353-2367.
[31]Quek S T, Tran V A, Hou X Y, et al. Structural damage detection using enhanced damage locating vector method with limited wireless sensors[J]. Journal of sound and vibration,2009,328(4):411-427.
[32]Liu X, Lieven N A J, Escamilla-Ambrosio P J. Frequency response function shape-based methods for structural damage localisation[J]. Mechanical systems and signal processing,2009,23(4):1243-1259.
[33]Fang S E, Perera R, Huerta M C. Damage Localization Based on Power Spectral Density Analysis[J]. Key Engineering Materials,2007,347:589-594.
[34]Fang S E, Perera R. Power mode shapes for early damage detection in linear structures [J]. Journal of Sound and Vibration,2009,324(1):40-56.
[35]Bayissa W L, Haritos N. Structural damage identification in plates using spectral strain energy analysis[J]. Journal of Sound and Vibration,2007,307(1):226-249.
[36]Guo H, Zhang L. A weighted balance evidence theory for structural multiple damage localization[J]. Computer methods in applied mechanics and engineering,2006,195(44):6225-6238.
[37]Guo H Y. Structural damage detection using information fusion technique[J]. Mechanical systems and signal processing,2006,20(5):1173-1188.
[38]郭惠勇,张陵,蒋健.不同信息融合方法在结构损伤识别上的应用和分析[J].工程力学,2006,23(1)：28-32.
[39]Chandrashekhar M, Ganguli R. Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic[J]. Journal of sound and vibration,2009,326(3):939-957.
[40]杨彦芳,宋玉普.基于主元分析和频响函数的网架结构损伤识别方法[J].工程力学,2007,24(9)：105-110.
[41]Da Silva S, Dias Junior M, Lopes Junior V, et al. Structural damage detection by fuzzy clustering[J]. Mechanical Systems and Signal Processing,2008,22(7):1636-1649.
[42]张力,张瑜.基于模糊理论的结构损伤模式识别[J].西安工业大学学报,2009,29(2)：177-183.
[43]冉志红,李乔.基于模糊聚类和支持向量机的损伤识别方法[J].振动工程学报,2007,20(006)：618-622.
[44]Ratcliffe C P. Damage detection using a modified Laplacian operator on mode shape data[J]. Journal of Sound and Vibration,1997,204(3):505-517.
[45]Ratcliffe C P, Bagaria W J. Vibration technique for locating delamination in a composite beam[J]. Aiaa Journal,1998,36(6):1074-1077.
[46]Wu D, Law S S. Damage localization in plate structures from uniform load surface curvature[J]. Journal of Sound and Vibration,2004,276(1):227-244.
[47]Yoon M K, Heider D, Gillespie J W, et al. Local damage detection using the two-dimensional gapped smoothing method[J]. Journal of Sound and Vibration,2005,279(1):119-139.
[48]Baneen U, Kinkaid N M, Guivant J E, et al. Vibration based damage detection of a beam-type structure using noise suppression method[J]. Journal of Sound and Vibration,2012,331(8): 1777-1788.
[49]Liu X, Escamilla-Ambrosio P J, Lieven N A J. Extended Kalman filtering for the detection of damage in linear mechanical structures[J]. Journal of Sound and Vibration,2009,325(4):1023-1046.
[50]吴新亚,周丽.基于有限范围自适应卡尔曼滤波的结构损伤识别方法[J].振动工程学报,2007,20(4)：401-406.
[51]周丽,吴新亚,尹强,等.基于自适应卡尔曼滤波方法的结构损伤识别实验研究[J].振动工程学报,2008,21(2)：197-202.
[52]Rodriguez R, Escobar J A, Gomez R. Damage detection in instrumented structures without baseline modal parameters[J]. Engineering Structures,2010,32(6):1715-1722.
[53]Wang X Q, Wong W O, Cheng L. Modal power flow with application to damage detection[J]. International Journal of Engineering Science,2009,47(4):512-523.
[54]Wong W O, Wang X Q, Cheng L. Modal power flow analysis of a damaged plate[J]. Journal of Sound and Vibration,2009,320(1):84-100.
[55]朱翔.裂纹损伤结构的振动功率流特性与损伤识别[D].华中科技大学,2007.
[56]Zhu D, Yi X, Wang Y, et al. Mobile Sensor Networks:A New Approach for Structural Health Monitoring[C]//Structures Congress 2010@ s19th Analysis and Computation Specialty Conference. ASCE.2010:159-168.
[57]Waldron K, Ghoshal A, Schulz M J, et al. Damage detection using finite element and laser operational deflection shapes[J]. Finite elements in analysis and design,2002,38(3):193-226.
[58]Lu K. Dynamics Based Damage Detection of Plate-Type Structures[D]. The University of Akron, 2005.
[59]Siringoringo D M, Fujino Y. Experimental study of laser Doppler vibrometer and ambient vibration for vibration-based damage detection[J]. Engineering structures,2006,28(13):1803-1815.
[60]Chen J C, Garba J A. On orbit damage assessment for large space structures[C]//Structures, Structural Dynamics and Materials Conference,28 th, Monterey, CA, Technical Papers. Part 1.1987,6(8).
[61]Zimmerman D C, Kaouk M. Structural damage detection using a minimum rank update theory[J]. Journal of Vibration and Acoustics,1994,116(2):222-231.
[62]Kaouk M, Zimmerman D C. Structural damage assessment using a generalized minimum rank perturbation theory[J]. AIAA journal,1994,32(4):836-842.
[63]Doebling S W. Minimum-rank optimal update of elemental stiffness parameters for structural damage identification[J]. AIAA journal,1996,34(12):2615-2621.
[64]Doebling S W. Damage detection and model refinement using elemental stiffness perturbations with constrained connectivity[R]. Los Alamos National Lab., NM (United States),1996.
[65]杨秋伟,刘济科.基于最小秩修正的结构损伤识别方法[J].机械强度,2008,29(6)：891-893.
[66]杨秋伟,刘济科.结构损伤检测的最小秩修正方法[J].振动与冲击,2008,27(004)：7-9.
[67]Yang Q W, Liu J K. Damage identification by the eigenparameter decomposition of structural flexibility change[J]. International journal for numerical methods in engineering,2009,78(4): 444-459.
[68]高维成,刘伟,钱成.基于剩余模态力和模态应变能理论的网架结构损伤识别[J].工程力学,2007,24(5)：93-100.
[69]Hu S L J, Li H, Wang S. Cross-model cross-mode method for model updating[J]. Mechanical Systems and Signal Processing,2007,21(4):1690-1703.
[70]Li H, Wang J, James Hu S L. Using incomplete modal data for damage detection in offshore jacket structures[J]. Ocean Engineering,2008,35(17):1793-1799.
[71]王俊荣.海洋平台结构物损伤检测与模型修正方法研究[D].山东青岛：中国海洋大学,2009.
[72]Hu S L J, Huajun L. Simultaneous mass, damping, and stiffness updating for dynamic systems[J]. AIAA journal,2007,45(10):2529-2537.
[73]Friswell M, Mottershead J E. Finite element model updating in structural dynamics[M]. Springer, 1995.
[74]Messina A, Williams E J, Contursi T. Structural damage detection by a sensitivity and statistical-based method[J]. Journal of Sound and Vibration,1998,216(5):791-808.
[75]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)：66-70.
[76]Shi Z Y, Law S S, Zhang L M. Damage localization by directly using incomplete mode shapes[J]. Journal of Engineering Mechanics,2000,126(6):656-660.
[77]杨永春,杨风艳,詹宇翀.结构损伤识别中灵敏度法的改进[J].振动与冲击,2006,25(5)：126-129.
[78]孙国,张洪武,蔡贤辉,等.基于模态误差函数灵敏度分析的损伤识别方法[J].振动工程学报,2008,20(3)：303-308.
[79]Yang Q W. A Flexibility-Based Method for Structural Damage Identification Using Ambient Modal Data[J]. International Journal of Space Structures,2009,24(3):153-159.
[80]Yang Q W. A mixed sensitivity method for structural damage detection[J]. Communications in Numerical Methods in Engineering,2009,25(4):381-389.
[81]Yan W J, Ren W X, Huang T L. Statistic structural damage detection based on the closed-form of element modal strain energy sensitivity[J]. Mechanical Systems and Signal Processing,2012,28: 183-194.
[82]Lu Z R, Law S S. Features of dynamic response sensitivity and its application in damage detection[J]. Journal of sound and vibration,2007,303(1):305-329.
[83]Lu Z R, Law S S. Features of dynamic response sensitivity and its application in damage detection[J]. Journal of sound and vibration,2007,303(1):305-329.
[84]Law S S, Zhang K., Duan Z D. Structural damage detection from coupling forces between substructures under support excitation[J]. Engineering Structures,2010,32(8):2221-2228.
[85]Schulz M J, Pai P F, Abdelnaser A S. Frequency response function assignment technique for structural damage identification[C]//PROCEEDINGS-SPIE THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING. SPIE INTERNATIONAL SOCIETY FOR OPTICAL,1996:105-111.
[86]Wang Z, Lin R M, Lim M K. Structural damage detection using measured FRF data[J]. Computer Methods in Applied Mechanics and Engineering,1997,147(1):187-197.
[87]Asma F, Bouazzouni A. Finite element model updating using variable separation[J]. European Journal of Mechanics-A/Solids,2007,26(4):728-735.
[88]Mottershead J E, Link M, Friswell M I. The sensitivity method in finite element model updating:A tutorial[J]. Mechanical Systems and Signal Processing,2011,25(7):2275-2296.
[89]Weber B, Paultre P, Proulx J. Structural damage detection using nonlinear parameter identification with Tikhonov regularization[J]. Structural Control and Health Monitoring,2006,14(3):406-427.
[90]Li X Y, Law S S. Adaptive Tikhonov regularization for damage detection based on nonlinear model updating[J]. Mechanical Systems and Signal Processing,2010,24(6):1646-1664.
[91]Li X Y, Law S S. Consistent Regularization for Damage Detection with Noise and Model Errors[J]. AIAA journal,2010,48(4):777-787.
[92]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)：29-33.
[93]Perera R, Ruiz A, Manzano C. An evolutionary multiobjective framework for structural damage localization and quantification[J]. Engineering Structures,2007,29(10):2540-2550.
[94]Rao M A, Srinivas J, Murthy B S N. Damage detection in vibrating bodies using genetic algorithms[J]. Computers & structures,2004,82(11):963-968.
[95]Gomes H M, Silva N R S. Some comparisons for damage detection on structures using genetic algorithms and modal sensitivity method[J]. Applied Mathematical Modelling,2008,32(11): 2216-2232.
[96]Au F T K, Cheng Y S, Tham L G, et al. Structural damage detection based on a micro-genetic algorithm using incomplete and noisy modal test data[J]. Journal of sound and vibration,2003,259(5): 1081-1094.
[97]Li J, Huang M, Zhu H. Study on Different Residual and Weight Coefficient in Model Updating of Bridge Structure[C]//The 9th International Conference of Chinese Transportation Professionals (ICCTP 2009), August.2009:5-8.
[98]Nobahari M, Seyedpoor S M. Structural damage detection using an efficient correlation-based index and a modified genetic algorithm[J]. Mathematical and Computer Modelling,2011,53(9):1798-1809.
[99]Kang F, Li J, Xu Q. Damage detection based on improved particle swarm optimization using vibration data[J]. Applied Soft Computing,2012.
[100]Begambre O, Laier J E. A hybrid Particle Swarm Optimization-Simplex algorithm (PSOS) for structural damage identification[J]. Advances in Engineering Software,2009,40(9):883-891.
[101]Seyedpoor S M. Structural damage detection using a multi-stage particle swarm optimization[J]. Advances in Structural Engineering,2011,14(3):533-549.
[102]Seyedpoor S M. A two stage method for structural damage detection using a modal strain energy based index and particle swarm optimization[J]. International Journal of Non-Linear Mechanics,2012, 47(1):1-8.
[103]Lee J J, Lee J W, Yi J H, et al. Neural networks-based damage detection for bridges considering errors in baseline finite element models[J]. Journal of Sound and Vibration,2005,280(3):555-578.
[104]李忠献,杨晓明,丁阳.基于结构响应统计特征的神经网络损伤识别方法[J].工程力学,2007,24(9)：1-7.
[105]Li Z X, Yang X M. Damage identification for beams using ANN based on statistical property of structural responses[J]. Computers & structures,2008,86(1):64-71.
[106]Mehrjoo M, Khaji N, Moharrami H, et al. Damage detection of truss bridge joints using Artificial Neural Networks[J]. Expert Systems with Applications,2008,35(3):1122-1131.
[107]Rutherford A C, Inman D J, Park G, et al. Use of response surface metamodels for identification of stiffness and damping coefficients in a simple dynamic system[J]. Shock and Vibration,2005,12(5): 317-332.
[108]Fang S E, Perera R. Damage identification by response surface based model updating using D-optimal design[J]. Mechanical Systems and Signal Processing,2011,25(2):717-733.
[109]Nandwana B P, Maiti S K. Detection of the location and size of a crack in stepped cantilever beams based on measurements of natural frequencies[J]. Journal of Sound and Vibration,1997,203(3): 435-446.
[110]Gudmundson P. The dynamic behaviour of slender structures with cross-sectional cracks[J]. Journal of the Mechanics and Physics of Solids,1983,31(4):329-345.
[111]Liang R Y, Choy F K, Hu J. Detection of cracks in beam structures using measurements of natural frequencies[J]. Journal of the Franklin Institute,1991,328(4):505-518.
[112]Ostachowicz W M, Krawczuk M. Analysis of the Effect of Cracks on the Natural Frequencies of a cantilever Beam[J]. Journal of sound and vibration,1991,150(2):191-201.
[113]Lele S P, Maiti S K. Modelling of transverse vibration of short beams for crack detection and measurement of crack extension[J]. Journal of Sound and Vibration,2002,257(3):559-583.
[114]Owolabi G M, Swamidas A S J, Seshadri R. Crack detection in beams using changes in frequencies and amplitudes of frequency response functions[J]. Journal of sound and vibration,2003,265(1): 1-22.
[115]唐天国,刘浩吾,陈春华,等.梁裂缝损伤检测的模态应变能法及试验研究[J].工程力学,2005,22：39-45.
[116]Vakil-Baghmisheh M T, Peimani M, Sadeghi M H, et al. Crack detection in beam-like structures using genetic algorithms[J]. Applied Soft Computing,2008,8(2):1150-1160.
[117]Faverjon B, Sinou J J. Identification of an open crack in a beam using an a posteriori error estimator of the frequency response functions with noisy measurements [J]. European Journal of Mechanics-A/Solids European Journal of Mechanics-A/Solids,2009,28(1):75-85.
[118]Buezas F S, Rosales M B, Filipich C P. Damage detection with genetic algorithms taking into account a crack contact model[J]. Engineering Fracture Mechanics,2011,78(4):695-712.
[119]Hu J, Liang R Y. An integrated approach to detection of cracks using vibration characteristics[J]. Journal of the Franklin Institute,1993,330(5):841-853.
[120]Shifrin E I, Ruotolo R. Natural frequencies of a beam with an arbitrary number of cracks [J]. Journal of Sound and Vibration,1999,222(3):409-423.
[121]Shifrin E I, Ruotolo R. Natural frequencies of a beam with an arbitrary number of cracks[J]. Journal of Sound and Vibration,1999,222(3):409-423.
[122]Lee J. Identification of multiple cracks in a beam using natural frequencies[J]. Journal of sound and vibration,2009,320(3):482-490.
[123]Lee J. Identification of multiple cracks in a beam using vibration amplitudes[J]. Journal of Sound and Vibration,2009,326(1):205-212.
[124]Lam H F, Ng C T. A probabilistic method for the detection of obstructed cracks of beam-type structures using spatial wavelet transform[J]. Probabilistic Engineering Mechanics,2008,23(2): 237-245.
[125]Mazanoglu K, Sabuncu M. A frequency based algorithm for identification of single and double cracked beams via a statistical approach used in experiment[J]. Mechanical Systems and Signal Processing,2012,30:168-185.
[126]范德礼,郑世杰.基于遗传算法和结构优化的多裂纹梁损伤识别[J].江苏航空,2011,S1：50-53.
[127]Krawczuk M, Palacz M, Ostachowicz W. Wave propagation in plate structures for crack detection[J]. Finite elements in analysis and design,2004,40(9):991-1004.
[128]Krawczuk M, Palacz M, Ostachowicz W. Wave propagation in plate structures for crack detection[J]. Finite elements in analysis and design,2004,40(9):991-1004.
[129]Hadjileontiadis L J, Douka E. Crack detection in plates using fractal dimension[J]. Engineering structures,2007,29(7):1612-1625.
[130]Lam H F, Yin T. Statistical detection of multiple cracks on thin plates utilizing dynamic response[J]. Engineering structures,2010,32(10):3145-3152.
[131]Hu H, Wu C, Lu W J. Damage detection of circular hollow cylinder using modal strain energy and scanning damage index methods[J]. Computers & structures,2011,89(1):149-160.
[132]Nichols J M, Moore E Z, Murphy K. D. Bayesian identification of a cracked plate using a population-based Markov Chain Monte Carlo method[J]. Computers & Structures,2011,89(13): 1323-1332.
[133]Moore E Z, Murphy K D, Nichols J M. Crack identification in a freely vibrating plate using Bayesian parameter estimation[J]. Mechanical Systems and Signal Processing,2011,25(6):2125-2134.
[134]方圣恩.基于有限元模型修正的结构损伤识别方法研究[D].长沙：中南大学,2010.
[135]傅志方.振动模态分析与参数辨识[M].机械工业出版社,1990.
[136]李东升,张莹,任亮,等.结构健康监测中的传感器布置方法及评价准则[J].力学进展,2011,41(1)：39-50.
[137]Mao Y M, Guo X L, Zhao Y. A state space force identification method based on Markov parameters precise computation and regularization technique[J]. Journal of Sound and Vibration,2010,329(15): 3008-3019.
[138]曹晖,林秀萍.结构损伤识别中噪声的模拟[J].振动与冲击,2010,29(5)：106-109.
[139]Zhang Z, Aktan A E. Application of modal flexibility and its derivatives in structural identification[J]. Journal of Research in Nondestructive Evaluation,1998,10(1):43-61.
[140]Grubbs F E. Sample criteria for testing outlying observations[J]. The Annals of Mathematical Statistics,1950,21(1):27-58.
[141]Thompson W R. On a criterion for the rejection of observations and the distribution of the ratio of deviation to sample standard deviation[J]. The Annals of Mathematical Statistics,1935,6(4): 214-219.
[142]Duan Q, Sorooshian S, Gupta V. Effective and efficient global optimization for conceptual rainfall-runoff models[J]. Water Resources Research,1992,28(4):1015-1031.
[143]Mariani V C, Justi Luvizotto L G, Guerra F A, et al. A hybrid shuffled complex evolution approach based on differential evolution for unconstrained optimization[J]. Applied Mathematics and Computation,2011,217(12):5822-5829.
[144]Mariani V C, Coelho L S. A hybrid shuffled complex evolution approach with pattern search for unconstrained optimization[J]. Mathematics and Computers in Simulation,2011,81(9):1901-1909.
[145]Mockus J, Tiesis V, Zilinskas A. The application of Bayesian methods for seeking the extremum[J]. Towards Global Optimization,1978,2:117-129.
[146]高月华,基于kriging代理模型的优化设计方法及其在注塑成型中的应用[D],大连：大连理工大学,2008.
[147]Sakata S, Ashida F, Zako M. An efficient algorithm for Kriging approximation and optimization with large-scale sampling data[J]. Computer methods in applied mechanics and engineering,2004,193(3): 385-404.
[148]Song X M, Zhan C S, Xia J, Integration of a statistical emulator approach with the SCE-UA method for parameter optimization of a hydrological model[J], Chinese Science Bulletin,2012,57(26): 3397-3403.
[149]Rencher A C, Christensen W F. Methods of multivariate analysis[M]. Wiley,2012.
[150]Li J, Huang M, Zhu H. Study on Different Residual and Weight Coefficient in Model Updating of Bridge Structure[C]//The 9th International Conference of Chinese Transportation Professionals (ICCTP 2009), August.2009:5-8.