基于小波分析和神经网络的结构损伤识别研究
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摘要
论文基于石油钻井平台从一四层钢框架结构模型出发,围绕该模型发生不同程度的损伤展开识别和诊断工作,提出了基于小波分析和神经网络识别损伤的两步法。在求解结构的动力响应时,引入了计算精度高、无条件稳定且无超越现象的高阶单步-β算法,对得到的相应结点加速度响应进行一层离散小波变换,对所得到的细节信号尖峰高度的变化规律进行分析,考虑了小波函数选取、荷载强度、噪声标准及损伤程度等因素对小波识别损伤能力的影响,提出了适用于工程应用的加速度响应小波变换细节信号的尖峰高度确定损伤位置的方法。
为了更真实模拟环境激励,在求解动力响应过程中加入了一定量的噪音干扰,因此论文在对相关数据进行小波变换前需要对所测得的数据进行小波降噪预处理。论文阐述了小波阈值法降噪原理,考虑了小波函数的选取、分解的尺度及阈值选取对信号降噪的影响,以信噪比和均方根误差两个指标作为评价降噪效果的优劣,提出了适用于环境激励的结构动力响应降噪流程。
论文将传统的单一损伤识别方法发展为损伤识别两步法。在利用小波分析确定了损伤发生的位置后,引入BP神经网络,采用与损伤程度相关的指标固有频率平方变化比作为特征参数输入网络,从结构发生不同程度的损伤建立了一个三层BP网络,并利用训练好的网络对结构的损伤程度做出判断。
During the exploration and development of the oilfield,the large rise rig derrick structure is the essential component that bears the loads.For the environment that it works is far more abominable than the general steel structure thing,especially with the development of marine petroleum industry, oil rig derrick structure will suffer from the influence of earthquake, window storm, fire, flood and such natural disasters in it's complex working environment. The various kind of negative influence will also made the building structure damaged in different level. All this influence and damage will threaten the Structural Security.
This paper carryed out analysis and research on a four floor steel structure health monitoring based on oil rig derrick structure. On the basis of drawing into high degree of accuracy and unconditional stable high ordered single-stepβ-method to count structural dynamic response, this paper pointed out two steps for analysis of structural damage. That is, to use wavelet analysis to supervise the damage on-line and to locate the damage position. Then to use BP neural net-work to define the degree of damage further. The concrete works are as follow：
(1) Based on the widely reading, the paper made a summary about the method of large-scale structural's damage's detection at the moment, introduced the basis of wavelet theory, and the employment of wavelet analysis and neural network in the field of civil engineering.
(2) Since damage of structural will lead to the weakness of natural frequency while calculating the structural's response. Under the stimulation of environment, the shape of viberation is quite sensitive for partial rigidity, so the paper used high order single-stepβmethod to calculate nonlinear structure dynamic response, because this method is more accuracy in ccounting, unconditional stable and unexceed phenomenon over other methods.
(3) Because there are all kinds of noise disturbing during the real surveying, the paper added different standard noise when imitating the stimulation of environment, before the wavelet transform of the acceleration response the date should have been treated of noise reduction. For using wavelet to reduce noise, the paper made a detailed contrast-ing and analysis on the selection of wavelet function, decomposition of scale, the method of noise reduction and so on. using two index, that is, the ratio of signal and noise and the roof mean square error to judge the effection of noise reduction. Finally, put forward the technological process for reducing the noise:using the bior6.8 wavelet 2-scale rigrsure rules to estimate the threshold to pretreat the noise reduction, and have get satisfactive results.
(4) In the supervision of the structural damage online and locating of the damage position, the selection of wavelet function is very important, it may influence the result of the damage detection directly, so this paper has made detailed contracting and analysis, through the acceleration response's discrete decomposition to obtain the detail signal spike height to judge the ability of the wavelet's function in damage detection by a lot of analysis, and decided to adopt Doubechies wavelet to monitor the structure and judge the damage position.
(5) This paper considered the different structural condition and damage condition did a discrete wavelet transform to the interrelated node acceleration response, considing the wavelet functiln, load intensity, noise standard and damage degree etc. factors, put forward the method of using the signal spike heigh to define the position of damaget to decide.
(6) In order to analyze the influence to the distinguishing ability of wavelet analysis in a whole, the paper made much analysis and contracting in different sides such as the standard of noise, load intensity and damage degree, and gained a conclusion that increasing of load intensity and damage degree will increase the distinguishing ability of wavelet, on the contrary, the increasing of the noise standard will make the useful signal covered by noise and decrease the distinguishing ability of wavelet, even made it undistinctive.
(7) Paper put forward two step method for identifying the damage based on wavelet analysis and the BP neural net-work. Since the neural frequency of structural will decrease while the structure being damaged. Only by the change of natural frequency the damage can not be found obviously, the paper used an index related to the damage degrees, that is, the change rate of squared natural frequency, as the feature parameter inputing the BP net. Bulit BP neural net-work from different sides such as the happening of different damage situation in single supporter and different damage degree at the same time, then using the well trained net-work to judge the damage degree, the error of the result is small. This proved the feasibility of the usage of neural net-work in judging the damage degree.
为了更真实模拟环境激励,在求解动力响应过程中加入了一定量的噪音干扰,因此论文在对相关数据进行小波变换前需要对所测得的数据进行小波降噪预处理。论文阐述了小波阈值法降噪原理,考虑了小波函数的选取、分解的尺度及阈值选取对信号降噪的影响,以信噪比和均方根误差两个指标作为评价降噪效果的优劣,提出了适用于环境激励的结构动力响应降噪流程。
论文将传统的单一损伤识别方法发展为损伤识别两步法。在利用小波分析确定了损伤发生的位置后,引入BP神经网络,采用与损伤程度相关的指标固有频率平方变化比作为特征参数输入网络,从结构发生不同程度的损伤建立了一个三层BP网络,并利用训练好的网络对结构的损伤程度做出判断。
During the exploration and development of the oilfield,the large rise rig derrick structure is the essential component that bears the loads.For the environment that it works is far more abominable than the general steel structure thing,especially with the development of marine petroleum industry, oil rig derrick structure will suffer from the influence of earthquake, window storm, fire, flood and such natural disasters in it's complex working environment. The various kind of negative influence will also made the building structure damaged in different level. All this influence and damage will threaten the Structural Security.
This paper carryed out analysis and research on a four floor steel structure health monitoring based on oil rig derrick structure. On the basis of drawing into high degree of accuracy and unconditional stable high ordered single-stepβ-method to count structural dynamic response, this paper pointed out two steps for analysis of structural damage. That is, to use wavelet analysis to supervise the damage on-line and to locate the damage position. Then to use BP neural net-work to define the degree of damage further. The concrete works are as follow：
(1) Based on the widely reading, the paper made a summary about the method of large-scale structural's damage's detection at the moment, introduced the basis of wavelet theory, and the employment of wavelet analysis and neural network in the field of civil engineering.
(2) Since damage of structural will lead to the weakness of natural frequency while calculating the structural's response. Under the stimulation of environment, the shape of viberation is quite sensitive for partial rigidity, so the paper used high order single-stepβmethod to calculate nonlinear structure dynamic response, because this method is more accuracy in ccounting, unconditional stable and unexceed phenomenon over other methods.
(3) Because there are all kinds of noise disturbing during the real surveying, the paper added different standard noise when imitating the stimulation of environment, before the wavelet transform of the acceleration response the date should have been treated of noise reduction. For using wavelet to reduce noise, the paper made a detailed contrast-ing and analysis on the selection of wavelet function, decomposition of scale, the method of noise reduction and so on. using two index, that is, the ratio of signal and noise and the roof mean square error to judge the effection of noise reduction. Finally, put forward the technological process for reducing the noise:using the bior6.8 wavelet 2-scale rigrsure rules to estimate the threshold to pretreat the noise reduction, and have get satisfactive results.
(4) In the supervision of the structural damage online and locating of the damage position, the selection of wavelet function is very important, it may influence the result of the damage detection directly, so this paper has made detailed contracting and analysis, through the acceleration response's discrete decomposition to obtain the detail signal spike height to judge the ability of the wavelet's function in damage detection by a lot of analysis, and decided to adopt Doubechies wavelet to monitor the structure and judge the damage position.
(5) This paper considered the different structural condition and damage condition did a discrete wavelet transform to the interrelated node acceleration response, considing the wavelet functiln, load intensity, noise standard and damage degree etc. factors, put forward the method of using the signal spike heigh to define the position of damaget to decide.
(6) In order to analyze the influence to the distinguishing ability of wavelet analysis in a whole, the paper made much analysis and contracting in different sides such as the standard of noise, load intensity and damage degree, and gained a conclusion that increasing of load intensity and damage degree will increase the distinguishing ability of wavelet, on the contrary, the increasing of the noise standard will make the useful signal covered by noise and decrease the distinguishing ability of wavelet, even made it undistinctive.
(7) Paper put forward two step method for identifying the damage based on wavelet analysis and the BP neural net-work. Since the neural frequency of structural will decrease while the structure being damaged. Only by the change of natural frequency the damage can not be found obviously, the paper used an index related to the damage degrees, that is, the change rate of squared natural frequency, as the feature parameter inputing the BP net. Bulit BP neural net-work from different sides such as the happening of different damage situation in single supporter and different damage degree at the same time, then using the well trained net-work to judge the damage degree, the error of the result is small. This proved the feasibility of the usage of neural net-work in judging the damage degree.
引文
[1]邹青龙,付海龙等.基于小波和神经网络的石油井架损伤定位研究[J].科学技术与工程,2009(4).870-874
[2]苗同臣,陈淮等.石油钻井塔架结构的动力响应分析.工程力学,1995(增).
[3]段梦兰,吴永宁.海冰环境中海洋石油钢结构的破坏分析[J].石油学报,1999,20(3)：71-77.
[4]任国友.石油钻机井架结构风振响应分析[D].黑龙江：大庆石油学院,2004.
[5]张爱林,田汝珉.考虑初始缺陷的服役井架承载力分析[J].石油矿场机械,1994,23(6)：9-12.
[6]欧进萍.重大工程的智能监测与健康诊断[J].工程力学,2002(增).
[7]孙鸿敏,李宏男.土木工程结构健康监测研究进展[J].防灾减灾工程学报.2003,23(3)：92-98.
[8]叶蔚,声发射源安全检测系统[J].江汉大学学报.1999,16(3)：67-69.
[9]朱宏平.结构损伤检测的智能方法[M].北京：人民交通出版社,2009.
[10]Sanayei Masoud,Onipede Oladipo.Damage assessment of structures using static text data. AIAA Journal,1991,29(7):1174-1179.
[11]Yam L H,Li Y Y,Wong W O.Sensitivity studies of parameters for damage detection of plate-like structures using static and dynamic approaches.Engineering structures,2002,24(11): 1465-1475.
[12]Wang X, Hu N,Fukunaga H, et al. Structural damage identification using static test data and changes in frequencies. Engineering Structures,2001,23(6):610-621.
[13]Banan M R,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.
[14]Banan M R,Banan M R,Hjelamstad K D.Parameter estimation of structures from static response.Ⅱ:Numerical simulation studies. Journal of Structural Engineering,1994,120(11): 3259-3283.
[15]崔飞,袁万城.等.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,2000,28(1)：5-8.
[16]崔飞,袁家城,等.基于静载试验进行桥梁结构损伤识别.桥梁建设,2003(2)：4-7.
[17]张启伟,范立础.利用动静态测量数据的桥梁结构损伤识别.同济大学学报,1998,26(5)：528-532.
[18]蔡晶,吴智深,等.静力荷载作用下结构参数识别及状态评估的统计分析.工程力学,2004,21(6)：76-83.
[19]Lifshitz J M,Rotem A.Determination of reinforcement unbonding of composites by a vibration technique. Journal Of Composite Materials,1969(3):412-423.
[20]Tracy J J,Pardoen G G.Effect of delamination on the natural frequencies of composite laminates. Journal of Composite Materials,1989,23(12):1200-1215.
[21]Cawley P,Adams R D.The location of defects in structures from measurements of natural frequencies. Journal of Strain Analysis,1979,14(2):49-57.
[22]Morassi A,Rovere N.Localizing a notch in a steel frame from frequency measurements. Journal of Engineering Mechanics-Asce,1997,123(5):422-432.
[23]Stubbs N,Osegueda R.Global damage detection in solids-experimental verification.Modal Analysis:the International Journal of Analytical and Experimental Modal Analysis,1990.5(2): 81-97.
[24]Stubbs N,Osegueda R.Global non-destructive damage evaluation in solids. Modal Analysis: the International Journal of Analytical and Experimental Modal Analysis,1990,5(2):67-79.
[25]Hearn G.,Testa R.B.Modal Analysis for Damage Detection in Structures. Journal of Structural Engineering, ASCE,1991,117:3042-3063.
[26]高芳清,金建明,高淑英.基于模态分析的结构损伤检测方法研究.西南交通大学学报,1998,33(1)：108-113
[27]C.R. Farrar,P.J. Cornwell,S.W Doebling et al. Structural Health Monitoring Studies of the Alamosa Canyon and 1-40 Bridge. Los Alamos,NU,USA:Los Alamos National Laboratory, 2000.
[28]Pandey A.K., Biswas M. Damage Detection in Structures Using Changes in Flexibility.
[29]李功宇,郑华文.损伤结构的曲率模态分析[J].振动、测试与诊断.2002,22(2)：136-141.
[30]Allemang R J,Brown D L.A correlation coefficient for modal vector analysis. Proceedings of the First International Modal Analysis Conference,1982:110-116.
[31]Levine N A J, Ewins D J. Spatial correlation of mode shapes, the coordinate modal assurance criterion(COMAC).Proceedings of the 6th International Modal Analysis Conference,1988:690-695.
[32]West W M. Illustration of the use of modal assurance criterion to detect structural changes in an orbiter test specimen. Proceedings of Air Force Conference on Aircraft Structural Integrity, 1984:1-6.
[33]Yuen M M F.A numerical study of the eigenparameters of a damaged cantilever. Journal of Sound and Vibration,1985,103(3):301-310.
[34]Topole K G,Stubbs N.Nondestructive damage evaluation of a structure from limited modal parameters.Earthquake Engineering and Structural Dynamics,1995,24(11):1427-1436.
[35]郭国会,易伟建.基于模态参数进行连续梁损伤诊断的数值研究.振动与冲击,2001,20(1)：72-75.
[36]Pandey A K,Biswas M,Samman M M.Damage detection from changes in curvature mode shapes.Journal of Sound and Vibration,1991,145(2):321-332.
[37]Pandey A.K,Biswas M.Damage Detection in Structures Using Changes in Flexibility. Journal of Sound and Vibration,1994(169):3-17.
[38]Shi Z Y,Law S S,Zhang L M.Structural damage detection from modal strain energy change. Journal of Engineering Mechanics-Asce,2000,126(12):1216-1223.
[39]Shi Z Y,Law S S,Zhang L M.Structural damage localization from elemental modal strain energy change. Journal of Engineering Mechanics-Asce,2002,128(5):521-529.
[40]袁明,贺国京.基于模态应变能的结构损伤检测方法研究[J].铁道学报.2002,24(2)：92-94.
[41]高成,董长虹,等.小波分析与应用[M].北京：国防工业出版社,2007.
[42]李建平,杨万年(译)Ingrid Daubechies(著).小波十讲(Ten Lectures on wavelets) [M].国防工业出版社,2004.
[43]宋廷苏.小波分析在结构损伤识别中的应用[D].哈尔滨：中国地震局工程力学研究所,2006.
[44]杨福生.小波变换的工程分析与应用[M].北京：科学出版社,1999.
[45]施养杭.小波分析在土木工程中的应用[J].工程力学,2003(增刊)：529-532
[46]唐和生,薛松涛,等.基于小波变换在线结构损伤检侧分析研究[J].固体力学学报,2004,(1)：47-52.
[47]蒋欣.基于小波分析的梁损伤识别方法研究[D].湖南：长沙理工大学,2007.
[48]张伟伟.基于小波理论的结构损伤识别方法研究[D].山西：太原理工大学,2006.
[49]Surace C,Ruotolo R.Crack detection of a beam using the wavelet transform [C].Honolulu Hawaii:Proceedings the 12th International Modal Analysis Conference.1994,1141-1147.
[50]Wang W J,McFadden P D.Application of orthogonal wavelets to early gear damage detection [J].Mechanical Systems and Signal Processing,995,9(5):497-507.
[51]Liew K M,Wang Q.Application of wavelet theory for crack identification in structure. Journal of Engineering Mechanics,1998,124(2):152-157.
[52]Hou,Z. K.,and Noori,M.Application of wavelet analysis forstructural health monitoring. Proc., 2nd Int. Workshop on Structural Health Monitoring, Stanford Univ., Stanford,Calif.,1999, 946-955.
[53]Hou,Z.K.,Noori,M.,and St. Amand, R.Wavelet-based approach for structural damage detection. Journal of Engineering Mechanics,2000,126(7):677-683.
[54]Hou,Z.K., and Hera, A. A system identification technique using pseudo-wavelets [J]. Intell. Mater. Syst. Struct.2001,12-10:681-688.
[55]Hou,Z.K.,and Hera, A.Progress of phase Ⅱ study of the ASCE health monitoring benchmark data using wavelet approach[C]. Columbia Univ. New York:Proc.,15th ASCE Engineering Mechanics Conf.,2002.Control, Como, Italy, in press.
[56]Hou,Z.K.,Yoshiyuli Suzuli, Y., Shimizu,H.,and Hera,A. "Damage detection of a wooden house during shaking table testing using wavelet-based approach." Proc.,3rd World Conf. on Structural.
[57]YJ Wu and R. Du.Feature Extraction And Assessment Using Wavelet Packets for Monitoring Machining Processes. Mechanical System and Signal Processing[J].1996,10(1):29-53
[58]Gary G Yen,Kuo-Chang lin. Wavelet Packet Feature Extraction for Vibration Monitoring[J]. IEEE Transactions on Industrial Electronics.2000,47(3):650-667.
[59]Han J G,Sun Z S,Ren W X.Wavelet based damage identification of beams [A]. In:Proceedings of the eighth international symposium on structural engineering for young experts[C].Beijing:sp, 2004:56-363.
[60]闫桂荣,基于广义柔度矩阵和小波分析的结构损伤识别方法[D].黑龙江,哈尔滨工业大学,2006
[61]Amaravadi, Proceedings V., Rao, V., Kovai, L.R. Structural health monitoring using wavelet transforms.of SPIE,2001.
[62]高宝成,时良平,史铁林,杨叔子.基于小波分析的简支梁裂缝识别方法研究[J].振动工程学报,1993,10(1)：81-85.
[63]丁幼亮,李爱群,韩晓林.基于小波包分析的结构实时损伤报警数值研究[J].东南大学学报,2003.33(5)：643-646
[64]郭健.基于小波分析的结构损伤识别方法研究[D].浙江：浙江大学,2004.
[65]任宜春.基于小波分析的结构损伤诊断方法研究[D].湖南：湖南大学,2004.
[66]Wang Q, Deng X M, Damage detection with spatial wavelets. Internationnal Journalof Solids and Structures,1999(36):3443-3468.
[67]Hong, J. C., Kim, Y.Y., Lee, H.C., Lee, Y.W. Damage detection using the Lipschitz exponent estimated by the wavelet transform:applications to vibration modes of a beam. International Journal of Solids and structures,2002,39(7):1803-1816.
[68]Hagan Martin T,Demuth Howard B,Beale Mark.Neural network design.Boston:PWS Publishing,1996.
[69]庄镇泉,王熙法,等.神经网络与神经计算机[M].北京：科学出版社,1992.
[70]Venkatasubramanian V and Chan K.A neural network methodology for process fault diagnosis[J].Journal of AIChE,1989,35(12):1993-2002.
[71]Wu X J,Ghaboussi and Garrett.Use of neural networks in detection of structural damage[J]. Computes and Structures,1992,42(4):649-659.
[72]Elkordy et al. Neural network trained by analytically simulated damage states[J].Journal of Computing in Civil Engineering,1993,7(2):130-145.
[73]Elkordy et al.A structural damage neural network monitoring system[J].Microcomputers in Civil Engineering.1994(9):83-96.
[74]Lim,t.w.,Povich,C.R., Geometric approach to strain-displacement mapping for space truss structures, Structural Dynamicsand Materials Conference.1997, April 7,Part 4 (of 4)
[75]郭国会,易伟建.基于神经网络的结构边界条件识别和损伤诊断.湖南大学学报,1998,25(1)：71-76.
[76]郭杏林,陈建林.基于神经网络技术的结构损伤探测.大连理工大学学报,2002(3)：269-273.
[77]周仙通,王柏生,等.用神经网络和优化方法进行结构参数识别.计算力学学报,2001(2)：235-238.
[78]瞿伟廉,陈伟.多层及高层框架结构地震损伤诊断的神经网络方法[J].地震工程与工程振动学报.2002,22(1)：43-48.
[79]黄东梅,瞿伟廉.高耸塔架结构节点损伤的指标分析与反分析两步诊断法[J].华中科技大学学报.2003,20(2)：61-64.
[80]王柏生,刘承斌,何国波.用统计神经网络进行结构损伤存在检测[J].土木工程学报.2004,37(8)：24-49.
[81]罗跃纲,彭永恒,文邦椿.工程结构损伤的集成神经网络识别研究[J].振动与冲击.2006,25(1)：15-17.
[82]李宏男,孙鸿敏.基于小波分析和神经网络的框架结构损伤诊断方法[J].地震工程与工程振动,2003(5)：139-148.
[83]鞠彦忠,阎贵平,等.用小波神经网络检测结构损伤[J].工程力学,2003(6)：176-181.
[84]邱颖,任青文.小波变换与神经网络的结构损伤检测[J].河海大学学报,2004(3)：295-299.
[85]闵志华.基于小波分析和神经网络的结构损伤识别研究[D].武汉理工大学,2006.
[86]刁延松.基于神经网络和小波分析的海洋平台结构损伤检测研究[D].中国海洋大学2006.
[87]张悦华,程开东.结构缺损位置识别[J].吉林大学自然科学学报,1997,10(4)：22-24
[88]刘涛,曾祥利,等.实用小波分析入门[M].北京：国防工业出版社,2006.
[89]张国华,张文娟,等.小波分析与应用基础[M].西安：西安工业大学出版社,2006.
[90]崔锦泰(著),程正兴(译)小波分析导论[M].西安：西安交通大学出版社,1995.
[91]刘明才.小波分析及其应用[M].北京：清华大学出版社,2005.
[92]周伟,桂林,等.小波分析高级技术[M].西安：西安电子科技大学出版社,2006.
[93]刘贵忠,邸双亮.小波分析及其应用[M].西安：西安电子科技大学出版社,2001.
[94]魏明果.实用小波分析[M].北京：北京理工大学出版社,2005.
[95]E.A.Johnson,A.M.ASCE;H.F.Lam;L.S.Katafygiotis,A.M.ASCE;and J L.Beck, M.ASCEPhase IIASC-ASCEStructural Health Monitoring Benchmark Problem Using Simulated Data，JOURNAL OF ENGINEERING MECHANICS (C) ASCE/JANUARY 2004/3.
[96]Johnson E A,Lam H F,Katafygiotis L S and ET A L.A benchmark problem for structural health monitoring and damage detection[A]. Proceedings of the Engineering Mechanics Specialty Conference[C],Austin,Texas,May,2000.
[97]Bernal D and Gunes B.Observe/Kalman and subspace identification of the UBC Benchmark structural mode[A].Proceedings of the Engineering Mechanics Specialty Conference[C], Austin,Texas,May,2000.
[98]Dyke S J,Caicedo J M and Johnson E A.Monitoring of a Benchmark structure for damage identification [A].Proceedings of the Engineering Mechanic Specialty Conference[C],Austin, Texas,May,2000.
[99]Katafygiotis L S,Lam H F et al.Application of a statistical approach on Benchmark damage detection problem[A]. Proceedings of the Engineering Mechanic Specialty Conference[C], Austin, Texas, May,2000.
[100]Hera A and Hou Z K.Wavelet-based approach for ASCE structural health monitoring Benchmark studies[A]. Proceedings of the 3rdInternational Workshop on Structural Health Monitoring[C], Stanford, September,2001.
[101]Ni Y Q,Wang B S,Ko J M,Jiang S F.The artificial neural network methods for damage datectiion of a benchmark structure[A]. The Third International Workshop on Structural Health Monitoring[C],Stanford, CA,Sep.,2001.
[102]Black C J and Ventura C E.Blind test on damage Detection of a steel Frame structure[A].16th International Modal Analysis Conference(IMAC XVI) [C],Santa Barbara,California,February, 1998:623-629.
[103]Adriana Hera,Zhikun Hou.Application of wavelet analysis for structural health monitoring[J]. ASCE, Journal of Engineering Mechanics,2004(1):96-104.
[104]Au S K,Yuen K V and Beck J L.Two-stage system identification results for Benchmark structure[A]. Proceedings of the Engineering Mechanics Specialty Conference[C], Austin, Texas, May,2000.
[105]包世华.结构动力学[M].武汉：武汉理工大学出版社,2005.
[106]邹经湘,王本利,等.结构动力学[M].哈尔滨：哈尔滨工业大学出版社,1996.
[107]王焕定,张英,等.用高阶单步法作结构非线性地震响应及瞬时振动控制[J].工程力学,1996,(增)：511-515.
[108]Wang Huanding,Zhang Yongshan and Wang Wei.A high order single step-pmethod for nonlinear structural dynamic analysis[J]. Journal of Harbin Institute of Technology(New Series), Vol.10,No.2,2003:113-119.
[109]王焕定,张永山,等.非线性结构时程分析的高阶单步法[J].地震工程与工程振动,1996(3)：48-54.
[110]MallatS.Theoryformulti-resolution signal decomposition:The wavelet representation[J].IEEE Trnasactionson Pattern Analysi and Machine Intelligence,1989,11(7):674-693.
[111]韩震宇,申旭娟,石章林.信号的多分辨分析及其在消噪中的应用[J].四川联合大学学报,1999,3(1)：52-58.
[112]Mallat S,H Wang W L.Singularity detection and processing with wavelets[J]. IEEE Transaction on Information Theory,1992,38(2):617-643.
[113]彭玉华,汪文秉.小波用于估测散射波波达时间及去噪[J].电子学报,1996,24(4)：113-116.
[114]杜芳,卢文胜,曹文清.振动台试验测试信号去噪的小波变换方法[J].振动与冲击,1999,18(2)：26-29.
[115]刘曙光,殷明.子波消噪技术及其应用[J].西北纺织工学院学报,1999,13(1)：16-20.
[116]Donoho D L,Johnstone I M.Ideal spatial adaptation by wavelet shrinkage[J]. Biometrika, 1994,81(3):425-455.
[117]Donoho D L.De-noising by soft thresholding[J].IEEE Transcations on Information Theory, 1995,41 (3):613-627.
[118]Donoho DL,Johnstone M.Adaptation to unknown Smoothness via wavelet shrinkage[J]. Journal of the American Statistical Association,1995,90(12):1200-1224.
[119]李爱萍,段利国.小波分析在信号降噪处理中的应用[J].太原理工大学学报,2001,(1)：69-71.
[120]朱华.小波分析及其在信号降噪中的应用研究[D].湖北：武汉理工大学,2007.
[121]张茁生,蔡元龙.小波分析在信号处理中的应用[J].无线电工程,1994(8)：11-18.
[122]文莉,刘正士,等.小波去噪的几种方法[J].合肥工业大学学报,2002(2)：167-172.
[123]文莉.小波变换在去噪及结构动态特性分析中的应用研究[D].安徽：合肥工业大学,2002.104-106.
[124]张鹏.基于小波理论的白鹤隧道围岩稳定性非线性研究[D].吉林：吉林大学,2009.
[125]文鸿雁,张正禄.非线性小波变换阈值法去噪改进[J].测绘通报,2006(3)：18-21
[126]叶裕雷,戴文战.一种基于新阈值函数的小波信号去噪方法[J].计算机应用,2006(7)：1617-1619.
[127]崔华,宋国乡.二基于小波阈值去噪方法的一种改进方案[J].现代电子技术,2005,(1)：8-9.
[128]戴朝华,朱云芳,等.一种新的小波消噪阐值选取方法[J].设计与研究,2005(6)：33-35.
[129]李杏梅,陈亮.小波阐值去噪在图像去噪中的应用[J].现代计算机,2006(10)：78-80.
[130]兰芸,樊可清.基于小波阈值去噪方法的研究[J].科技信息,2008,(2)：209-210.
[131]林京.基于最大似然估计的小波阐值消噪技术及信号特征提取[J].仪器仪表学报.2005,26(9)：924-925
[132]楼顺天,刘小东,等.基于MATLAB 7.X的系统分析与设计--信号处理[M].西安：西安电子科技大学出版社,2005.
[133]胡昌华,李国华.基于MATLAB 7.X的系统分析与设计--小波分析[M].西安：西安电子科技大学出版社,2008.
[134]张鹄志.基于小波分析的框架损伤诊断与在线监控[D].湖南：湖南大学,2008.
[135]林宝龙.小波变换在结构损伤识别中的应用研究[D].浙江：浙江大学建筑工程学院,2006.
[136]杜秀丽,汪风泉.结构损伤识别的周期小波方法[J].东南大学学报(自然科学版),2006,(4)：609-612.
[137]张伟伟,王志华,等.多分辨率分析在悬臂梁裂纹检测中的应用[J].太原理工大学学报,2005(6)：666-668.
[138]张兆德,王德禹.基于动力特性与小波变换的损伤检测方法在海洋平台中的应用[J].上海造船,2005(1)：27-30.
[139]孙增寿,韩建刚,等.基于曲率模态和小波变换的结构损伤位置识别[J].地震工程与工程振动,2005(4)：44-49.
[140]曾凡锋,蔡自兴,等.基于小波变换的系统辨识方法[J].南昌大学学报(工科版),1998(2)：15-19.
[141]张华智,冯毅芳.利用小波分析方法识别结构模态参数[J].四川建筑科学研究,2007(6)：24-29.
[142]林京,屈梁生.基于连续小波变换的奇异性检测与故障诊断[J].振动工程学报,2000(4)：523-530.
[143]孙增寿,韩建刚,等.基于小波分析的结构损伤检测研究进展[J].地震工程与工程振动,2005(2)：93-99.
[144]Surace C, Ruotolo R. Crack detection of a beam using the wavelet transform[C].Honolulu Hawaii:Proceedings the 12th International Modal Analysis Conference.1994,1141-1147.
[145]Wang W.J, McFadden P D. Application of orthogonal wavelets to early gear damage detection[J]. Mechanical Systems and Signal Processing,1995,(5):497-507.
[146]Al-khalidy A, Noori M, Hou Z, et al. Health monitoring systems of linear structures using wavelet analysis[A]. Stanford:International Workshop on Structural Health Monitoring [C].1997: 164-175.
[147]Al-khalidy A, Noori M, Hou Z, Carmona R, Yamamoto S, Masuda A, et al.A study of health monitoring systems of linear structures using wavelet analysis[J].A SMEP VP,1997,(347):49-58.
[148]Me Culloch W W and Pitts W.A logic calculus of the ideas imment in neurons activity[J]. Bulletin of Mathematical Biophysics,1943(5):115-133
[149]Rosenblatt F.The peiceptron:A perceiving and recognizing automation (project PARA)[R]. Cornell Aeronautical Laboratory Report,86-406-1,1959
[150]
[151]Hopfield J. J. Neural networks and physical systems with emergent collective computing abilities[A].Proc.Acad.SCI[C].U.S.A.,1982,79:2554-2558
[152]Rumelhart D.E.Parallel distributed processing:Exploration in the microstructure of Cognition[M].Cambridge,MA:MIT Press,1986
[153]Kudvs J N,Munir N and Tan P W.Damage detection in smart structures using neural networks and finite-elemnt analysis[J]. Smart Mater. Struct.,1992,1:108-112.
[154]Bishop C M.Neural networks and their applications[J].Review of scientific Instrumentation, 1994,65(6):1803-1832.
[155]Adeli H.Neural networks in civil engineering:1989-2000[J].Computer-Aided Civil and InfrastructureEngineering,2001,16:126-142.
[156]虞和济,等.基于神经网络的智能诊断[M].北京：冶金工业出版社,2000.
[157]戴兴华.基于小波神经网络的振动结构损伤诊断[D].福建：福州大学,2006.
[158]欧进萍.结构振动控制—主动、半主动和智能控制[M].北京：科技出版社,2003.
[159]王柏生.结构损伤检测与识别技术[M].杭州：浙江大学出版社,2000.
[160]姜绍飞.基于神经网络的结构优化与损伤检测[M].北京：科学出版社,2002.
[161]陈长征等.结构损伤检测与智能诊断[M].北京：科学出版社,2001.
[162]李斌.基于改进的BP神经网络的结构损伤检测研究[D].湖北：华中科技大学,2002
[163]邓薇.函数速查手册[M].北京：人民邮电出版社,2008.
[164]阙金声三峡工程涪陵区水库塌岸非线性预测研究[D].吉林：吉林大学,2007.
[165]Kaminski P C.The approximation location of damage through the analysis of natural frequencies with artificial neural networks[J] Journal of Process Mechanical Engineering,1995, 209(E2):117-124.
[166]Worden K A et al. Neural networks for fault location[C].11thInternatonal Modal Analysis Conference.1993,USA:47-54.
[167]Tsou P and Shen M H H.Structural damage detection and identification using neural network[J]. AIAA Journal,1994,32(1):176-183.
[168]冯立芳.小波和神经网络相结合的结构损伤识别方法[D].浙江大学.2006
[169]姜绍飞,钟善桐.神经网络在结构工程中的应用[J].哈尔滨建筑大学学报,1998,(6)：129-133.
[170]张跃强.基于神经网络的结构损伤检测方法研究[D].北京：北京工业大学,2004.
[2]苗同臣,陈淮等.石油钻井塔架结构的动力响应分析.工程力学,1995(增).
[3]段梦兰,吴永宁.海冰环境中海洋石油钢结构的破坏分析[J].石油学报,1999,20(3)：71-77.
[4]任国友.石油钻机井架结构风振响应分析[D].黑龙江：大庆石油学院,2004.
[5]张爱林,田汝珉.考虑初始缺陷的服役井架承载力分析[J].石油矿场机械,1994,23(6)：9-12.
[6]欧进萍.重大工程的智能监测与健康诊断[J].工程力学,2002(增).
[7]孙鸿敏,李宏男.土木工程结构健康监测研究进展[J].防灾减灾工程学报.2003,23(3)：92-98.
[8]叶蔚,声发射源安全检测系统[J].江汉大学学报.1999,16(3)：67-69.
[9]朱宏平.结构损伤检测的智能方法[M].北京：人民交通出版社,2009.
[10]Sanayei Masoud,Onipede Oladipo.Damage assessment of structures using static text data. AIAA Journal,1991,29(7):1174-1179.
[11]Yam L H,Li Y Y,Wong W O.Sensitivity studies of parameters for damage detection of plate-like structures using static and dynamic approaches.Engineering structures,2002,24(11): 1465-1475.
[12]Wang X, Hu N,Fukunaga H, et al. Structural damage identification using static test data and changes in frequencies. Engineering Structures,2001,23(6):610-621.
[13]Banan M R,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.
[14]Banan M R,Banan M R,Hjelamstad K D.Parameter estimation of structures from static response.Ⅱ:Numerical simulation studies. Journal of Structural Engineering,1994,120(11): 3259-3283.
[15]崔飞,袁万城.等.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,2000,28(1)：5-8.
[16]崔飞,袁家城,等.基于静载试验进行桥梁结构损伤识别.桥梁建设,2003(2)：4-7.
[17]张启伟,范立础.利用动静态测量数据的桥梁结构损伤识别.同济大学学报,1998,26(5)：528-532.
[18]蔡晶,吴智深,等.静力荷载作用下结构参数识别及状态评估的统计分析.工程力学,2004,21(6)：76-83.
[19]Lifshitz J M,Rotem A.Determination of reinforcement unbonding of composites by a vibration technique. Journal Of Composite Materials,1969(3):412-423.
[20]Tracy J J,Pardoen G G.Effect of delamination on the natural frequencies of composite laminates. Journal of Composite Materials,1989,23(12):1200-1215.
[21]Cawley P,Adams R D.The location of defects in structures from measurements of natural frequencies. Journal of Strain Analysis,1979,14(2):49-57.
[22]Morassi A,Rovere N.Localizing a notch in a steel frame from frequency measurements. Journal of Engineering Mechanics-Asce,1997,123(5):422-432.
[23]Stubbs N,Osegueda R.Global damage detection in solids-experimental verification.Modal Analysis:the International Journal of Analytical and Experimental Modal Analysis,1990.5(2): 81-97.
[24]Stubbs N,Osegueda R.Global non-destructive damage evaluation in solids. Modal Analysis: the International Journal of Analytical and Experimental Modal Analysis,1990,5(2):67-79.
[25]Hearn G.,Testa R.B.Modal Analysis for Damage Detection in Structures. Journal of Structural Engineering, ASCE,1991,117:3042-3063.
[26]高芳清,金建明,高淑英.基于模态分析的结构损伤检测方法研究.西南交通大学学报,1998,33(1)：108-113
[27]C.R. Farrar,P.J. Cornwell,S.W Doebling et al. Structural Health Monitoring Studies of the Alamosa Canyon and 1-40 Bridge. Los Alamos,NU,USA:Los Alamos National Laboratory, 2000.
[28]Pandey A.K., Biswas M. Damage Detection in Structures Using Changes in Flexibility.
[29]李功宇,郑华文.损伤结构的曲率模态分析[J].振动、测试与诊断.2002,22(2)：136-141.
[30]Allemang R J,Brown D L.A correlation coefficient for modal vector analysis. Proceedings of the First International Modal Analysis Conference,1982:110-116.
[31]Levine N A J, Ewins D J. Spatial correlation of mode shapes, the coordinate modal assurance criterion(COMAC).Proceedings of the 6th International Modal Analysis Conference,1988:690-695.
[32]West W M. Illustration of the use of modal assurance criterion to detect structural changes in an orbiter test specimen. Proceedings of Air Force Conference on Aircraft Structural Integrity, 1984:1-6.
[33]Yuen M M F.A numerical study of the eigenparameters of a damaged cantilever. Journal of Sound and Vibration,1985,103(3):301-310.
[34]Topole K G,Stubbs N.Nondestructive damage evaluation of a structure from limited modal parameters.Earthquake Engineering and Structural Dynamics,1995,24(11):1427-1436.
[35]郭国会,易伟建.基于模态参数进行连续梁损伤诊断的数值研究.振动与冲击,2001,20(1)：72-75.
[36]Pandey A K,Biswas M,Samman M M.Damage detection from changes in curvature mode shapes.Journal of Sound and Vibration,1991,145(2):321-332.
[37]Pandey A.K,Biswas M.Damage Detection in Structures Using Changes in Flexibility. Journal of Sound and Vibration,1994(169):3-17.
[38]Shi Z Y,Law S S,Zhang L M.Structural damage detection from modal strain energy change. Journal of Engineering Mechanics-Asce,2000,126(12):1216-1223.
[39]Shi Z Y,Law S S,Zhang L M.Structural damage localization from elemental modal strain energy change. Journal of Engineering Mechanics-Asce,2002,128(5):521-529.
[40]袁明,贺国京.基于模态应变能的结构损伤检测方法研究[J].铁道学报.2002,24(2)：92-94.
[41]高成,董长虹,等.小波分析与应用[M].北京：国防工业出版社,2007.
[42]李建平,杨万年(译)Ingrid Daubechies(著).小波十讲(Ten Lectures on wavelets) [M].国防工业出版社,2004.
[43]宋廷苏.小波分析在结构损伤识别中的应用[D].哈尔滨：中国地震局工程力学研究所,2006.
[44]杨福生.小波变换的工程分析与应用[M].北京：科学出版社,1999.
[45]施养杭.小波分析在土木工程中的应用[J].工程力学,2003(增刊)：529-532
[46]唐和生,薛松涛,等.基于小波变换在线结构损伤检侧分析研究[J].固体力学学报,2004,(1)：47-52.
[47]蒋欣.基于小波分析的梁损伤识别方法研究[D].湖南：长沙理工大学,2007.
[48]张伟伟.基于小波理论的结构损伤识别方法研究[D].山西：太原理工大学,2006.
[49]Surace C,Ruotolo R.Crack detection of a beam using the wavelet transform [C].Honolulu Hawaii:Proceedings the 12th International Modal Analysis Conference.1994,1141-1147.
[50]Wang W J,McFadden P D.Application of orthogonal wavelets to early gear damage detection [J].Mechanical Systems and Signal Processing,995,9(5):497-507.
[51]Liew K M,Wang Q.Application of wavelet theory for crack identification in structure. Journal of Engineering Mechanics,1998,124(2):152-157.
[52]Hou,Z. K.,and Noori,M.Application of wavelet analysis forstructural health monitoring. Proc., 2nd Int. Workshop on Structural Health Monitoring, Stanford Univ., Stanford,Calif.,1999, 946-955.
[53]Hou,Z.K.,Noori,M.,and St. Amand, R.Wavelet-based approach for structural damage detection. Journal of Engineering Mechanics,2000,126(7):677-683.
[54]Hou,Z.K., and Hera, A. A system identification technique using pseudo-wavelets [J]. Intell. Mater. Syst. Struct.2001,12-10:681-688.
[55]Hou,Z.K.,and Hera, A.Progress of phase Ⅱ study of the ASCE health monitoring benchmark data using wavelet approach[C]. Columbia Univ. New York:Proc.,15th ASCE Engineering Mechanics Conf.,2002.Control, Como, Italy, in press.
[56]Hou,Z.K.,Yoshiyuli Suzuli, Y., Shimizu,H.,and Hera,A. "Damage detection of a wooden house during shaking table testing using wavelet-based approach." Proc.,3rd World Conf. on Structural.
[57]YJ Wu and R. Du.Feature Extraction And Assessment Using Wavelet Packets for Monitoring Machining Processes. Mechanical System and Signal Processing[J].1996,10(1):29-53
[58]Gary G Yen,Kuo-Chang lin. Wavelet Packet Feature Extraction for Vibration Monitoring[J]. IEEE Transactions on Industrial Electronics.2000,47(3):650-667.
[59]Han J G,Sun Z S,Ren W X.Wavelet based damage identification of beams [A]. In:Proceedings of the eighth international symposium on structural engineering for young experts[C].Beijing:sp, 2004:56-363.
[60]闫桂荣,基于广义柔度矩阵和小波分析的结构损伤识别方法[D].黑龙江,哈尔滨工业大学,2006
[61]Amaravadi, Proceedings V., Rao, V., Kovai, L.R. Structural health monitoring using wavelet transforms.of SPIE,2001.
[62]高宝成,时良平,史铁林,杨叔子.基于小波分析的简支梁裂缝识别方法研究[J].振动工程学报,1993,10(1)：81-85.
[63]丁幼亮,李爱群,韩晓林.基于小波包分析的结构实时损伤报警数值研究[J].东南大学学报,2003.33(5)：643-646
[64]郭健.基于小波分析的结构损伤识别方法研究[D].浙江：浙江大学,2004.
[65]任宜春.基于小波分析的结构损伤诊断方法研究[D].湖南：湖南大学,2004.
[66]Wang Q, Deng X M, Damage detection with spatial wavelets. Internationnal Journalof Solids and Structures,1999(36):3443-3468.
[67]Hong, J. C., Kim, Y.Y., Lee, H.C., Lee, Y.W. Damage detection using the Lipschitz exponent estimated by the wavelet transform:applications to vibration modes of a beam. International Journal of Solids and structures,2002,39(7):1803-1816.
[68]Hagan Martin T,Demuth Howard B,Beale Mark.Neural network design.Boston:PWS Publishing,1996.
[69]庄镇泉,王熙法,等.神经网络与神经计算机[M].北京：科学出版社,1992.
[70]Venkatasubramanian V and Chan K.A neural network methodology for process fault diagnosis[J].Journal of AIChE,1989,35(12):1993-2002.
[71]Wu X J,Ghaboussi and Garrett.Use of neural networks in detection of structural damage[J]. Computes and Structures,1992,42(4):649-659.
[72]Elkordy et al. Neural network trained by analytically simulated damage states[J].Journal of Computing in Civil Engineering,1993,7(2):130-145.
[73]Elkordy et al.A structural damage neural network monitoring system[J].Microcomputers in Civil Engineering.1994(9):83-96.
[74]Lim,t.w.,Povich,C.R., Geometric approach to strain-displacement mapping for space truss structures, Structural Dynamicsand Materials Conference.1997, April 7,Part 4 (of 4)
[75]郭国会,易伟建.基于神经网络的结构边界条件识别和损伤诊断.湖南大学学报,1998,25(1)：71-76.
[76]郭杏林,陈建林.基于神经网络技术的结构损伤探测.大连理工大学学报,2002(3)：269-273.
[77]周仙通,王柏生,等.用神经网络和优化方法进行结构参数识别.计算力学学报,2001(2)：235-238.
[78]瞿伟廉,陈伟.多层及高层框架结构地震损伤诊断的神经网络方法[J].地震工程与工程振动学报.2002,22(1)：43-48.
[79]黄东梅,瞿伟廉.高耸塔架结构节点损伤的指标分析与反分析两步诊断法[J].华中科技大学学报.2003,20(2)：61-64.
[80]王柏生,刘承斌,何国波.用统计神经网络进行结构损伤存在检测[J].土木工程学报.2004,37(8)：24-49.
[81]罗跃纲,彭永恒,文邦椿.工程结构损伤的集成神经网络识别研究[J].振动与冲击.2006,25(1)：15-17.
[82]李宏男,孙鸿敏.基于小波分析和神经网络的框架结构损伤诊断方法[J].地震工程与工程振动,2003(5)：139-148.
[83]鞠彦忠,阎贵平,等.用小波神经网络检测结构损伤[J].工程力学,2003(6)：176-181.
[84]邱颖,任青文.小波变换与神经网络的结构损伤检测[J].河海大学学报,2004(3)：295-299.
[85]闵志华.基于小波分析和神经网络的结构损伤识别研究[D].武汉理工大学,2006.
[86]刁延松.基于神经网络和小波分析的海洋平台结构损伤检测研究[D].中国海洋大学2006.
[87]张悦华,程开东.结构缺损位置识别[J].吉林大学自然科学学报,1997,10(4)：22-24
[88]刘涛,曾祥利,等.实用小波分析入门[M].北京：国防工业出版社,2006.
[89]张国华,张文娟,等.小波分析与应用基础[M].西安：西安工业大学出版社,2006.
[90]崔锦泰(著),程正兴(译)小波分析导论[M].西安：西安交通大学出版社,1995.
[91]刘明才.小波分析及其应用[M].北京：清华大学出版社,2005.
[92]周伟,桂林,等.小波分析高级技术[M].西安：西安电子科技大学出版社,2006.
[93]刘贵忠,邸双亮.小波分析及其应用[M].西安：西安电子科技大学出版社,2001.
[94]魏明果.实用小波分析[M].北京：北京理工大学出版社,2005.
[95]E.A.Johnson,A.M.ASCE;H.F.Lam;L.S.Katafygiotis,A.M.ASCE;and J L.Beck, M.ASCEPhase IIASC-ASCEStructural Health Monitoring Benchmark Problem Using Simulated Data，JOURNAL OF ENGINEERING MECHANICS (C) ASCE/JANUARY 2004/3.
[96]Johnson E A,Lam H F,Katafygiotis L S and ET A L.A benchmark problem for structural health monitoring and damage detection[A]. Proceedings of the Engineering Mechanics Specialty Conference[C],Austin,Texas,May,2000.
[97]Bernal D and Gunes B.Observe/Kalman and subspace identification of the UBC Benchmark structural mode[A].Proceedings of the Engineering Mechanics Specialty Conference[C], Austin,Texas,May,2000.
[98]Dyke S J,Caicedo J M and Johnson E A.Monitoring of a Benchmark structure for damage identification [A].Proceedings of the Engineering Mechanic Specialty Conference[C],Austin, Texas,May,2000.
[99]Katafygiotis L S,Lam H F et al.Application of a statistical approach on Benchmark damage detection problem[A]. Proceedings of the Engineering Mechanic Specialty Conference[C], Austin, Texas, May,2000.
[100]Hera A and Hou Z K.Wavelet-based approach for ASCE structural health monitoring Benchmark studies[A]. Proceedings of the 3rdInternational Workshop on Structural Health Monitoring[C], Stanford, September,2001.
[101]Ni Y Q,Wang B S,Ko J M,Jiang S F.The artificial neural network methods for damage datectiion of a benchmark structure[A]. The Third International Workshop on Structural Health Monitoring[C],Stanford, CA,Sep.,2001.
[102]Black C J and Ventura C E.Blind test on damage Detection of a steel Frame structure[A].16th International Modal Analysis Conference(IMAC XVI) [C],Santa Barbara,California,February, 1998:623-629.
[103]Adriana Hera,Zhikun Hou.Application of wavelet analysis for structural health monitoring[J]. ASCE, Journal of Engineering Mechanics,2004(1):96-104.
[104]Au S K,Yuen K V and Beck J L.Two-stage system identification results for Benchmark structure[A]. Proceedings of the Engineering Mechanics Specialty Conference[C], Austin, Texas, May,2000.
[105]包世华.结构动力学[M].武汉：武汉理工大学出版社,2005.
[106]邹经湘,王本利,等.结构动力学[M].哈尔滨：哈尔滨工业大学出版社,1996.
[107]王焕定,张英,等.用高阶单步法作结构非线性地震响应及瞬时振动控制[J].工程力学,1996,(增)：511-515.
[108]Wang Huanding,Zhang Yongshan and Wang Wei.A high order single step-pmethod for nonlinear structural dynamic analysis[J]. Journal of Harbin Institute of Technology(New Series), Vol.10,No.2,2003:113-119.
[109]王焕定,张永山,等.非线性结构时程分析的高阶单步法[J].地震工程与工程振动,1996(3)：48-54.
[110]MallatS.Theoryformulti-resolution signal decomposition:The wavelet representation[J].IEEE Trnasactionson Pattern Analysi and Machine Intelligence,1989,11(7):674-693.
[111]韩震宇,申旭娟,石章林.信号的多分辨分析及其在消噪中的应用[J].四川联合大学学报,1999,3(1)：52-58.
[112]Mallat S,H Wang W L.Singularity detection and processing with wavelets[J]. IEEE Transaction on Information Theory,1992,38(2):617-643.
[113]彭玉华,汪文秉.小波用于估测散射波波达时间及去噪[J].电子学报,1996,24(4)：113-116.
[114]杜芳,卢文胜,曹文清.振动台试验测试信号去噪的小波变换方法[J].振动与冲击,1999,18(2)：26-29.
[115]刘曙光,殷明.子波消噪技术及其应用[J].西北纺织工学院学报,1999,13(1)：16-20.
[116]Donoho D L,Johnstone I M.Ideal spatial adaptation by wavelet shrinkage[J]. Biometrika, 1994,81(3):425-455.
[117]Donoho D L.De-noising by soft thresholding[J].IEEE Transcations on Information Theory, 1995,41 (3):613-627.
[118]Donoho DL,Johnstone M.Adaptation to unknown Smoothness via wavelet shrinkage[J]. Journal of the American Statistical Association,1995,90(12):1200-1224.
[119]李爱萍,段利国.小波分析在信号降噪处理中的应用[J].太原理工大学学报,2001,(1)：69-71.
[120]朱华.小波分析及其在信号降噪中的应用研究[D].湖北：武汉理工大学,2007.
[121]张茁生,蔡元龙.小波分析在信号处理中的应用[J].无线电工程,1994(8)：11-18.
[122]文莉,刘正士,等.小波去噪的几种方法[J].合肥工业大学学报,2002(2)：167-172.
[123]文莉.小波变换在去噪及结构动态特性分析中的应用研究[D].安徽：合肥工业大学,2002.104-106.
[124]张鹏.基于小波理论的白鹤隧道围岩稳定性非线性研究[D].吉林：吉林大学,2009.
[125]文鸿雁,张正禄.非线性小波变换阈值法去噪改进[J].测绘通报,2006(3)：18-21
[126]叶裕雷,戴文战.一种基于新阈值函数的小波信号去噪方法[J].计算机应用,2006(7)：1617-1619.
[127]崔华,宋国乡.二基于小波阈值去噪方法的一种改进方案[J].现代电子技术,2005,(1)：8-9.
[128]戴朝华,朱云芳,等.一种新的小波消噪阐值选取方法[J].设计与研究,2005(6)：33-35.
[129]李杏梅,陈亮.小波阐值去噪在图像去噪中的应用[J].现代计算机,2006(10)：78-80.
[130]兰芸,樊可清.基于小波阈值去噪方法的研究[J].科技信息,2008,(2)：209-210.
[131]林京.基于最大似然估计的小波阐值消噪技术及信号特征提取[J].仪器仪表学报.2005,26(9)：924-925
[132]楼顺天,刘小东,等.基于MATLAB 7.X的系统分析与设计--信号处理[M].西安：西安电子科技大学出版社,2005.
[133]胡昌华,李国华.基于MATLAB 7.X的系统分析与设计--小波分析[M].西安：西安电子科技大学出版社,2008.
[134]张鹄志.基于小波分析的框架损伤诊断与在线监控[D].湖南：湖南大学,2008.
[135]林宝龙.小波变换在结构损伤识别中的应用研究[D].浙江：浙江大学建筑工程学院,2006.
[136]杜秀丽,汪风泉.结构损伤识别的周期小波方法[J].东南大学学报(自然科学版),2006,(4)：609-612.
[137]张伟伟,王志华,等.多分辨率分析在悬臂梁裂纹检测中的应用[J].太原理工大学学报,2005(6)：666-668.
[138]张兆德,王德禹.基于动力特性与小波变换的损伤检测方法在海洋平台中的应用[J].上海造船,2005(1)：27-30.
[139]孙增寿,韩建刚,等.基于曲率模态和小波变换的结构损伤位置识别[J].地震工程与工程振动,2005(4)：44-49.
[140]曾凡锋,蔡自兴,等.基于小波变换的系统辨识方法[J].南昌大学学报(工科版),1998(2)：15-19.
[141]张华智,冯毅芳.利用小波分析方法识别结构模态参数[J].四川建筑科学研究,2007(6)：24-29.
[142]林京,屈梁生.基于连续小波变换的奇异性检测与故障诊断[J].振动工程学报,2000(4)：523-530.
[143]孙增寿,韩建刚,等.基于小波分析的结构损伤检测研究进展[J].地震工程与工程振动,2005(2)：93-99.
[144]Surace C, Ruotolo R. Crack detection of a beam using the wavelet transform[C].Honolulu Hawaii:Proceedings the 12th International Modal Analysis Conference.1994,1141-1147.
[145]Wang W.J, McFadden P D. Application of orthogonal wavelets to early gear damage detection[J]. Mechanical Systems and Signal Processing,1995,(5):497-507.
[146]Al-khalidy A, Noori M, Hou Z, et al. Health monitoring systems of linear structures using wavelet analysis[A]. Stanford:International Workshop on Structural Health Monitoring [C].1997: 164-175.
[147]Al-khalidy A, Noori M, Hou Z, Carmona R, Yamamoto S, Masuda A, et al.A study of health monitoring systems of linear structures using wavelet analysis[J].A SMEP VP,1997,(347):49-58.
[148]Me Culloch W W and Pitts W.A logic calculus of the ideas imment in neurons activity[J]. Bulletin of Mathematical Biophysics,1943(5):115-133
[149]Rosenblatt F.The peiceptron:A perceiving and recognizing automation (project PARA)[R]. Cornell Aeronautical Laboratory Report,86-406-1,1959
[150]
[151]Hopfield J. J. Neural networks and physical systems with emergent collective computing abilities[A].Proc.Acad.SCI[C].U.S.A.,1982,79:2554-2558
[152]Rumelhart D.E.Parallel distributed processing:Exploration in the microstructure of Cognition[M].Cambridge,MA:MIT Press,1986
[153]Kudvs J N,Munir N and Tan P W.Damage detection in smart structures using neural networks and finite-elemnt analysis[J]. Smart Mater. Struct.,1992,1:108-112.
[154]Bishop C M.Neural networks and their applications[J].Review of scientific Instrumentation, 1994,65(6):1803-1832.
[155]Adeli H.Neural networks in civil engineering:1989-2000[J].Computer-Aided Civil and InfrastructureEngineering,2001,16:126-142.
[156]虞和济,等.基于神经网络的智能诊断[M].北京：冶金工业出版社,2000.
[157]戴兴华.基于小波神经网络的振动结构损伤诊断[D].福建：福州大学,2006.
[158]欧进萍.结构振动控制—主动、半主动和智能控制[M].北京：科技出版社,2003.
[159]王柏生.结构损伤检测与识别技术[M].杭州：浙江大学出版社,2000.
[160]姜绍飞.基于神经网络的结构优化与损伤检测[M].北京：科学出版社,2002.
[161]陈长征等.结构损伤检测与智能诊断[M].北京：科学出版社,2001.
[162]李斌.基于改进的BP神经网络的结构损伤检测研究[D].湖北：华中科技大学,2002
[163]邓薇.函数速查手册[M].北京：人民邮电出版社,2008.
[164]阙金声三峡工程涪陵区水库塌岸非线性预测研究[D].吉林：吉林大学,2007.
[165]Kaminski P C.The approximation location of damage through the analysis of natural frequencies with artificial neural networks[J] Journal of Process Mechanical Engineering,1995, 209(E2):117-124.
[166]Worden K A et al. Neural networks for fault location[C].11thInternatonal Modal Analysis Conference.1993,USA:47-54.
[167]Tsou P and Shen M H H.Structural damage detection and identification using neural network[J]. AIAA Journal,1994,32(1):176-183.
[168]冯立芳.小波和神经网络相结合的结构损伤识别方法[D].浙江大学.2006
[169]姜绍飞,钟善桐.神经网络在结构工程中的应用[J].哈尔滨建筑大学学报,1998,(6)：129-133.
[170]张跃强.基于神经网络的结构损伤检测方法研究[D].北京：北京工业大学,2004.