基于小波分析的结构损伤诊断方法研究
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摘要
小波分析是近十几年国际上掀起热潮的一个前沿领域，它被认为是傅立叶分析方法的突破性发展，是一种新的时—频两维分析方法。结构的损伤诊断技术是当前结构工程学科十分活跃的研究领域并有广阔的工程应用前景，相关的理论和技术正在不断发展。本文着重对小波分析方法在结构损伤诊断中的应用进行了研究。主要研究内容有：
利用小波奇异性检测原理识别梁结构的损伤位置与损伤程度；对带裂缝梁结构的振型函数和移动荷载作用下梁跨中的位移响应用Mexican Hat小波进行连续小波变换，通过小波系数出现模极大值来判别裂缝的位置，通过模极大值处的小波系数计算Lipschitz指数，由Lipschitz指数的大小来识别裂缝的深度；研究了裂缝位置、振型的测点距离、荷载的移动速度、噪声等因素对识别的影响；对损伤引起的某一区段刚度下降，采用Gauss3小波对梁结构的振型函数和移动荷载作用下跨中的位移响应进行连续小波变换，通过小波系数出现一正一负成对的极大值来识别损伤的位置；数值算例证实了该方法的有效性。
基于小波包分解，得到对损伤敏感频段的能量值构成的特征向量，并采用该特征向量作为损伤因子进行损伤诊断。完成了一根钢筋混凝土简支梁在不同损伤情况下的振动测试。并基于梁在脉冲荷载作用下的响应信号测试数据，用小波包分解技术识别了梁的损伤程度。
对基于复小波变换的振动信号瞬态参数提取原理进行了研究。对粘滞阻尼线性系统和立方非线性系统的自由振动响应进行Morlet复小波变换，从脊线上的小波系数提取瞬态参数从而识别固有频率、模态阻尼和非线性系数。通过三个数值算例，对单自由度线性系统、多自由度线性系统以及立方非线性系统进行了参数识别。
Wavelet analysis is a new time-frequency analysis method which has raised a research upsurge internationally in recent years. It is regarded as a breakthrough of Fourier Analysis. Damage diagnosis technique is an active research domain in cunent structure engineering and has strong engineering background. The correlative theory and technology are developing continuously. This thesis is concentrated on the research of the damage detection method by wavelet transform. The main subjects are summarized as follows:
A wavelet-based approach is proposed for crack identification in beam structure by the singularity's detection. The fundamental vibration mode of a cracked simple-supported beam and the displacement of the middle of the beam under mobile force are analyzed using continuous wavelet transform by Mexican Hat wavelet. The position of the crack is located by the maximum modulus of the wavelet coefficients. The Lipschitzs exponent estimated by the wavelet coefficients is used as a useful indicator of the crack depth, which decays with the increase of crack depth. The influence of the crack location, the sampling distance of the vibration mode and the velocity of moving load to lipschitzs exponent are discussed. It is testified that this method is also in effect to noisy data. The position of the stiffness decline caused by the damage is also detected by this method. The validity of the proposed method is investigated both by analysis and simulations.
The component energy in different frequency bands gained by wavelet packet decomposing which is sensitive to damage is used as damage index. A series of vibration test on a reinforced concrete beam under different damage degree are finished. The damage degree is recognized by the wavelet packet decomposing of the response signal collected in vibration test.
The transient parameters are distilled by the compound wavelet transform of the vibration signal. The impulse response of the linear and non-linear viscous damping system is analysed by Morlet wavelet. The transient frequencies and amplitude are obtained from the ridges of the wavelet transform. So the parameters of the system are identified. The method is illustrated by three simulated example.
利用小波奇异性检测原理识别梁结构的损伤位置与损伤程度；对带裂缝梁结构的振型函数和移动荷载作用下梁跨中的位移响应用Mexican Hat小波进行连续小波变换，通过小波系数出现模极大值来判别裂缝的位置，通过模极大值处的小波系数计算Lipschitz指数，由Lipschitz指数的大小来识别裂缝的深度；研究了裂缝位置、振型的测点距离、荷载的移动速度、噪声等因素对识别的影响；对损伤引起的某一区段刚度下降，采用Gauss3小波对梁结构的振型函数和移动荷载作用下跨中的位移响应进行连续小波变换，通过小波系数出现一正一负成对的极大值来识别损伤的位置；数值算例证实了该方法的有效性。
基于小波包分解，得到对损伤敏感频段的能量值构成的特征向量，并采用该特征向量作为损伤因子进行损伤诊断。完成了一根钢筋混凝土简支梁在不同损伤情况下的振动测试。并基于梁在脉冲荷载作用下的响应信号测试数据，用小波包分解技术识别了梁的损伤程度。
对基于复小波变换的振动信号瞬态参数提取原理进行了研究。对粘滞阻尼线性系统和立方非线性系统的自由振动响应进行Morlet复小波变换，从脊线上的小波系数提取瞬态参数从而识别固有频率、模态阻尼和非线性系数。通过三个数值算例，对单自由度线性系统、多自由度线性系统以及立方非线性系统进行了参数识别。
Wavelet analysis is a new time-frequency analysis method which has raised a research upsurge internationally in recent years. It is regarded as a breakthrough of Fourier Analysis. Damage diagnosis technique is an active research domain in cunent structure engineering and has strong engineering background. The correlative theory and technology are developing continuously. This thesis is concentrated on the research of the damage detection method by wavelet transform. The main subjects are summarized as follows:
A wavelet-based approach is proposed for crack identification in beam structure by the singularity's detection. The fundamental vibration mode of a cracked simple-supported beam and the displacement of the middle of the beam under mobile force are analyzed using continuous wavelet transform by Mexican Hat wavelet. The position of the crack is located by the maximum modulus of the wavelet coefficients. The Lipschitzs exponent estimated by the wavelet coefficients is used as a useful indicator of the crack depth, which decays with the increase of crack depth. The influence of the crack location, the sampling distance of the vibration mode and the velocity of moving load to lipschitzs exponent are discussed. It is testified that this method is also in effect to noisy data. The position of the stiffness decline caused by the damage is also detected by this method. The validity of the proposed method is investigated both by analysis and simulations.
The component energy in different frequency bands gained by wavelet packet decomposing which is sensitive to damage is used as damage index. A series of vibration test on a reinforced concrete beam under different damage degree are finished. The damage degree is recognized by the wavelet packet decomposing of the response signal collected in vibration test.
The transient parameters are distilled by the compound wavelet transform of the vibration signal. The impulse response of the linear and non-linear viscous damping system is analysed by Morlet wavelet. The transient frequencies and amplitude are obtained from the ridges of the wavelet transform. So the parameters of the system are identified. The method is illustrated by three simulated example.
引文
[1] Doebling S w, Farrar C R, Prime M B. A Summary Review of Vibration-based Damage Identification Methods. The Shock and Vibration Digest, 1998,30(2):9 1-105
[2] 宗周红，任伟新，阮毅．土木工程结构损伤诊断研究进展．土木工程学报，2003，36(5)：105-110
[3] 张景绘．动力学系统建模．北京：国防工业出版社，2002
[4] Tso-Chien P, Lee C H. Application of Wavelet Theory to Identify Yielding in Seismic Response of Bi-linear Structures. Earthquake Engineering and Structural Dynamics,2002,31:379-398
[5] Yoshihiro K. Identification of Nonlinear Structural Dynamic Systems Using Wavelet. Journal of Engineering Mechanics, 1998, 124(10): 1059-1066
[6] Iyama H, Kuwamura J. Application of Wavelets to Analysis and Simulation of Earthquake Motions. Earthquake Engineering and Structural Dynamics, 1999, 28: 255～272
[7] 曹晖，赖明，白绍良．基于小波分析的线性结构随机响应求解．重庆大学学报，2000，22(增刊)：47～52
[8] 杨红，曹晖，白绍良．地震波局部时频特性对结构非线性响应的的影响．土木工程学报，2001,34(2)：78-82
[9] 段雪平，朱宏平．地震作用下结构动力响应的小波分析．华中理工大学学报，2000．28(11)：75～78
[10] Ruzzene M, Fasana A, Garibaldi L, Piombo B. Natural Frequencies And Damping Identification Using Wavelet Transform: Application to Real Data. Mechanical Systems and Signal Processing, 1997,11(2):207-218
[11] Wong L A, Chen J C. Nonlinear and Chaotic Behavior of Structural System Investigated by Wavelet Transform Techniques. International Journal of Nonlinear Mechanics, 2001,36:221-235
[12] Kijewski T, Kareem A. Wavelet Transform for System Identification in Civil Engineering. Computer-Aided Civil and Infrastructure Engineering, 2003,18: 339-355
[13] Hou Z, Noori M, Amand R S. Wavelet-based approach for structural damage detection. Journal of Engineering Mechanics,2000,126(7):677～683
[14] Hani M, Hansang K. Damage detection in concrete by fourier and wavelet analysis.
Journal of Engineering Mechanics,2003,129(5):571-577;
[15] Liew K M, Wang Q. Application of wavelet theory for crack identification in structure. Journal of Engineering Mechanics,1998,124(2):152～157
[16] Sun Z, Chang C C.. Structural damage assessment based on wavelet packet transform. Journal of Structural Engineering, 2002,10:1354～1361
[17] 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．地震工程与工程振动，2003，23(5)：141～148
[18] Wang Q, Deng X M, Damage detection with spatial wavelets. Internationnal Journal of Solids and Structures, 1999(36):3443～3468
[19] 李洪泉，董亮，吕西林．基于小波变换的结构损伤识别与试验分析．土木工程学报，2003，36(5)：69-75
[20] 韩晓林，彭岳星，唐新鸣．基桩检测反射波的非线性小波降噪重建方法．土木工程学报，2001，34(6)：105～107
[21] 骆英，柳祖亭，潘宠平．小波滤波在基桩完整性测试系统中的应用研究．实验力学，2000，15(4)：460～465
[22] 向阳，史习智．混凝土结构缺陷的融合识别研究．振动工程学报，2001,14(1)：36～41
[23] 郭国会，桥梁结构动力损伤诊断方法研究．长沙：湖南大学博士学位论文，2001
[24] 谢强，薛松涛．土木工程结构健康监测的研究状况与进展．中国科学基金，2001，(5)：285～287
[25] 赵松年，熊小芸．子波变换与子波分析．北京：电子工业出版社，1996
[26] 陈逢时．子波变换理论及其在信号处理中的应用．北京：国防工业出版社，1998
[27] 徐长发，李国宽．实用小波方法．武汉：华中科技大学出版社，2004
[28] 李水根，吴纪桃．分形与小波．北京：科学出版社，2002
[29] 崔景泰．小波分析导论．西安：西安交通大学出版社，1995
[30] 程正兴．小波分析算法与应用西安：西安交通大学出版社，1998
[31] 胡昌华，张军波，夏军，张伟．基于matlab的系统分析与设计—小波分析．西安：西安电子科技大学出版社，1999
[32] 杨福生．小波变换的工程分析与应用．北京：科学出版社，1999
[33] 刘言柱，陈文良，陈立群．振动力学．北京：高等教育出版社，1998
[34] Liang R y, Fredchoy J H. Theoretical Study of Cracked induced Eigenfrequency Changes on Beam Structures. Journal of Engineering Mechanics, 1992, 118(2):384-397
[35] Haase M, Widjajakuduma J. Damage identification based on ridges and maxima lines of the wavelet transform. International Journal of Engineering Science, 2003, 41:1423-1443
[36] Arata M, Mohammad N, Akira S, Yuito H. Wavelet-based health monitoring of randomly excited structures. 15th ASCE Engineering Mechanics Conference, June, 25,2002, Columbia Univercity, New York
[37] Slavic J, Simonovski I, Boltezar M. Damping identification using a continouse wavelet transform.:application to real data. Journal of Sound and Vibration, 2003, 262:291-307
[38] Nalan O, Savaci F A. Evaluation of instantaneous frequencies by singular value decomposition and determination of degree of chaoticity. IJCI Proceedings of International Conference on signal Processing, 2003,1(2):370-375
[39] Nicola P, Cecilia S. Evaluation of the Nonlinear Dynamic Response to Harmonic Excitation of a Beam with Several Breathing Cracks. Journal of Sound and Vibration, 2000, 235(5):749-762
[40] Carmona R A, Hwang W L, Torresani B. Characterization of Signals by the Ridges of Their Wavelet Transforn. IEEE Transaction on Signal Processing, 1997,45,2586
[41] Neild S A, Williams M S, Mcfadden P D. Nonlinear Characteristics of damaged concrete beams. Journal of Structural Engineering, 2003, 29(2):260-268
[42] Neild S A, Williams M S, Mcfadden P D. Non-linear behavior of reinforced concrete beams under low-amplitude cyclic and vibration loads. Engineering Structure, 2002,24:707-718
[43] Neild S A, Williams M S, Mcfadden P D. A Review of Time-frequency Methods for Structural Vibration Analysis. Engineering Structure, 2003, 25:713-728
[44] Yen G G, Lin K C. Wavelet Packet Feature Extraction for Vibration Monitoring. IEEE Trans. Industrial Electronics, 2000, 47(3):650～667
[45] 易伟建，刘霞．混凝土板的裂缝诊断．振动工程学报，2002，15(2)：224-227
[46] 周先雁．框架结构破损评估．长沙：湖南大学博士学位论文，1996
[47] 陈长征，罗跃刚，白秉三，唐忠．结构损伤检测与智能诊断．北京：科学出版社，2001
[48] 李德葆，陆秋海．试验模态分析及其应用．北京：科学出版社，2001
[49] 沃德．海伦，斯蒂芬．拉门兹，波尔．萨斯．模态分析理论与试验．北京：北京理工大学出版社，2001
[50] 续秀忠，张志谊 华宏星，陈兆能．应用时频分析方法辩识时变系统的模态参数．
振动工程学报，2003，16(3)：358～362
[51] 李国强，李杰．工程结构动力检测理论与应用．北京：科学出版社，2002
[52] 赵学智．广义自适应小波及其在机械测试信号处理中的应用．广州：华南理工大学博士学位论文，2001
[53] 王长军．基于小波分析的结构模态识别和破损诊断方法研究．武汉：武汉理工大学硕士学位论文，2002
[54] 成琼．基于小波分析的齿轮故障诊断研究．长沙：湖南大学硕士学位论文，2001
[55] 肖新标，沈火明．移动荷载速度对简支梁动态响应的影响．西南交通大学学报， 2002，37(增刊)：35—38
[56] 潭善文，秦树人，汤宝平．小波基时频特性及其在分析突变信号中的应用．重庆大学学报，2001，24(2)：12～17
[57] 王俊，汪凤泉，韩晓林，周星德．基于小波分析的框架结构缺陷识别方法．振动、测试与诊断，2002，22(4)
[58] 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．振动工程学报，1997，10(1)：81～85
[59] 黄丁发，陈咏奇 丁晓利等．GPS高层建筑物常荷载振动测试的小波分析．振动与冲击，2001，20(1)：12～15
[60] 高永毅，焦群英，唐果，郎悦．等截面梁纯弯曲振动的几何非线性分析．振动与冲击，2003，22(1)72-74
[61] Sun Q. Singularity Analysis using continous wavelet transform for bearing fault diagnosis. Mechanical Systems and Signal Processing,2002,16(6),1025-1041
[62] Gentile A, Messina A. On the continuous wavelet transform applied to discrete vibration data for detecting open cracks in damage beams. International Journal of Solids and Structures, 2003, 40:295～315
[63] Cheng S M, Wu X J, Wallace W. Vibration response of a beam with breathing crack. Journal of Sound and Vibration, 1999,225(1):201-208
[64] Liang R Y, Hu J L, Choy E Quantitative NDE technique for assessing damages in beam structures. Journal of Engineering Mechanics, 1992,118(7):1468～1487
[65] Mazurek D F, Dewolf J T. Experimental study of bridge monitoring technique. Journal of Structural Engineering, 1990,116(9):2532～2549
[66] Lind R, Snyder K, Brenner M. Wavelet analysis to characterise non-linearities and predict limit cycles of an aeroelastic system. Mechanical Systems and Signal Processing, 2001, 15(2):337～356
[67] Ghobarah A, Abou-elfath H, Biddah A. Response-based damage assessment of
structures. Earthquake Engineering and Structural Dynamics, 1999,28:79～104
[68] Grossmann A. Wavelet transform and edge detection. Stochastics Processes in Physics and Engineering, Hazewinkel M.eds Dodrecht Reidel ,1986
[69] Mallat S. Zero_crossings of wavelet transform. IEEE Trans. on Information Theory, 1991,37(4): 1019～1033
[70] Mallat S, Zhong S. Characterization of signal from multiscale edges. IEEE Trans. on Pattern Analysis and Machine Intelligence, 1992,14(9):710～732
[71] Mallat S, Hwang W L. Sigularity detection and processing with wavelets. IEEE Trans. on Information Theory, 1992,38(2):617～643
[72] 李天云，胡屏，马景兰．小波奇异性检测理论在电力系统负荷特性分析中的应用．东北电力学院学报，1998，18(4)：14～18
[73] 易伟建，徐丽．钢筋混凝土损伤诊断的动测法研究．振动与冲击，2003，22(2)：23～25
[74] 周先雁，沈蒲生，程翔云．用振动参数识别技术对混凝土框架进行破损评估．土木工程学报，1998，31(2)：39～45
[75] 李庆扬，王能超，易大义．数值分析．武汉：华中科技大学出版社，1986
[76] 郑栋梁，李中付，华宏星．结构早期损伤诊断识别技术的现状和发展趋势．振动与冲击，2002，221(2)1～6
[76] 彭志科，何永勇，褚福磊．小波尺度谱在振动信号分析中的应用研究．机械工程学报，2002，38(3)：122～126
[2] 宗周红，任伟新，阮毅．土木工程结构损伤诊断研究进展．土木工程学报，2003，36(5)：105-110
[3] 张景绘．动力学系统建模．北京：国防工业出版社，2002
[4] Tso-Chien P, Lee C H. Application of Wavelet Theory to Identify Yielding in Seismic Response of Bi-linear Structures. Earthquake Engineering and Structural Dynamics,2002,31:379-398
[5] Yoshihiro K. Identification of Nonlinear Structural Dynamic Systems Using Wavelet. Journal of Engineering Mechanics, 1998, 124(10): 1059-1066
[6] Iyama H, Kuwamura J. Application of Wavelets to Analysis and Simulation of Earthquake Motions. Earthquake Engineering and Structural Dynamics, 1999, 28: 255～272
[7] 曹晖，赖明，白绍良．基于小波分析的线性结构随机响应求解．重庆大学学报，2000，22(增刊)：47～52
[8] 杨红，曹晖，白绍良．地震波局部时频特性对结构非线性响应的的影响．土木工程学报，2001,34(2)：78-82
[9] 段雪平，朱宏平．地震作用下结构动力响应的小波分析．华中理工大学学报，2000．28(11)：75～78
[10] Ruzzene M, Fasana A, Garibaldi L, Piombo B. Natural Frequencies And Damping Identification Using Wavelet Transform: Application to Real Data. Mechanical Systems and Signal Processing, 1997,11(2):207-218
[11] Wong L A, Chen J C. Nonlinear and Chaotic Behavior of Structural System Investigated by Wavelet Transform Techniques. International Journal of Nonlinear Mechanics, 2001,36:221-235
[12] Kijewski T, Kareem A. Wavelet Transform for System Identification in Civil Engineering. Computer-Aided Civil and Infrastructure Engineering, 2003,18: 339-355
[13] Hou Z, Noori M, Amand R S. Wavelet-based approach for structural damage detection. Journal of Engineering Mechanics,2000,126(7):677～683
[14] Hani M, Hansang K. Damage detection in concrete by fourier and wavelet analysis.
Journal of Engineering Mechanics,2003,129(5):571-577;
[15] Liew K M, Wang Q. Application of wavelet theory for crack identification in structure. Journal of Engineering Mechanics,1998,124(2):152～157
[16] Sun Z, Chang C C.. Structural damage assessment based on wavelet packet transform. Journal of Structural Engineering, 2002,10:1354～1361
[17] 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．地震工程与工程振动，2003，23(5)：141～148
[18] Wang Q, Deng X M, Damage detection with spatial wavelets. Internationnal Journal of Solids and Structures, 1999(36):3443～3468
[19] 李洪泉，董亮，吕西林．基于小波变换的结构损伤识别与试验分析．土木工程学报，2003，36(5)：69-75
[20] 韩晓林，彭岳星，唐新鸣．基桩检测反射波的非线性小波降噪重建方法．土木工程学报，2001，34(6)：105～107
[21] 骆英，柳祖亭，潘宠平．小波滤波在基桩完整性测试系统中的应用研究．实验力学，2000，15(4)：460～465
[22] 向阳，史习智．混凝土结构缺陷的融合识别研究．振动工程学报，2001,14(1)：36～41
[23] 郭国会，桥梁结构动力损伤诊断方法研究．长沙：湖南大学博士学位论文，2001
[24] 谢强，薛松涛．土木工程结构健康监测的研究状况与进展．中国科学基金，2001，(5)：285～287
[25] 赵松年，熊小芸．子波变换与子波分析．北京：电子工业出版社，1996
[26] 陈逢时．子波变换理论及其在信号处理中的应用．北京：国防工业出版社，1998
[27] 徐长发，李国宽．实用小波方法．武汉：华中科技大学出版社，2004
[28] 李水根，吴纪桃．分形与小波．北京：科学出版社，2002
[29] 崔景泰．小波分析导论．西安：西安交通大学出版社，1995
[30] 程正兴．小波分析算法与应用西安：西安交通大学出版社，1998
[31] 胡昌华，张军波，夏军，张伟．基于matlab的系统分析与设计—小波分析．西安：西安电子科技大学出版社，1999
[32] 杨福生．小波变换的工程分析与应用．北京：科学出版社，1999
[33] 刘言柱，陈文良，陈立群．振动力学．北京：高等教育出版社，1998
[34] Liang R y, Fredchoy J H. Theoretical Study of Cracked induced Eigenfrequency Changes on Beam Structures. Journal of Engineering Mechanics, 1992, 118(2):384-397
[35] Haase M, Widjajakuduma J. Damage identification based on ridges and maxima lines of the wavelet transform. International Journal of Engineering Science, 2003, 41:1423-1443
[36] Arata M, Mohammad N, Akira S, Yuito H. Wavelet-based health monitoring of randomly excited structures. 15th ASCE Engineering Mechanics Conference, June, 25,2002, Columbia Univercity, New York
[37] Slavic J, Simonovski I, Boltezar M. Damping identification using a continouse wavelet transform.:application to real data. Journal of Sound and Vibration, 2003, 262:291-307
[38] Nalan O, Savaci F A. Evaluation of instantaneous frequencies by singular value decomposition and determination of degree of chaoticity. IJCI Proceedings of International Conference on signal Processing, 2003,1(2):370-375
[39] Nicola P, Cecilia S. Evaluation of the Nonlinear Dynamic Response to Harmonic Excitation of a Beam with Several Breathing Cracks. Journal of Sound and Vibration, 2000, 235(5):749-762
[40] Carmona R A, Hwang W L, Torresani B. Characterization of Signals by the Ridges of Their Wavelet Transforn. IEEE Transaction on Signal Processing, 1997,45,2586
[41] Neild S A, Williams M S, Mcfadden P D. Nonlinear Characteristics of damaged concrete beams. Journal of Structural Engineering, 2003, 29(2):260-268
[42] Neild S A, Williams M S, Mcfadden P D. Non-linear behavior of reinforced concrete beams under low-amplitude cyclic and vibration loads. Engineering Structure, 2002,24:707-718
[43] Neild S A, Williams M S, Mcfadden P D. A Review of Time-frequency Methods for Structural Vibration Analysis. Engineering Structure, 2003, 25:713-728
[44] Yen G G, Lin K C. Wavelet Packet Feature Extraction for Vibration Monitoring. IEEE Trans. Industrial Electronics, 2000, 47(3):650～667
[45] 易伟建，刘霞．混凝土板的裂缝诊断．振动工程学报，2002，15(2)：224-227
[46] 周先雁．框架结构破损评估．长沙：湖南大学博士学位论文，1996
[47] 陈长征，罗跃刚，白秉三，唐忠．结构损伤检测与智能诊断．北京：科学出版社，2001
[48] 李德葆，陆秋海．试验模态分析及其应用．北京：科学出版社，2001
[49] 沃德．海伦，斯蒂芬．拉门兹，波尔．萨斯．模态分析理论与试验．北京：北京理工大学出版社，2001
[50] 续秀忠，张志谊 华宏星，陈兆能．应用时频分析方法辩识时变系统的模态参数．
振动工程学报，2003，16(3)：358～362
[51] 李国强，李杰．工程结构动力检测理论与应用．北京：科学出版社，2002
[52] 赵学智．广义自适应小波及其在机械测试信号处理中的应用．广州：华南理工大学博士学位论文，2001
[53] 王长军．基于小波分析的结构模态识别和破损诊断方法研究．武汉：武汉理工大学硕士学位论文，2002
[54] 成琼．基于小波分析的齿轮故障诊断研究．长沙：湖南大学硕士学位论文，2001
[55] 肖新标，沈火明．移动荷载速度对简支梁动态响应的影响．西南交通大学学报， 2002，37(增刊)：35—38
[56] 潭善文，秦树人，汤宝平．小波基时频特性及其在分析突变信号中的应用．重庆大学学报，2001，24(2)：12～17
[57] 王俊，汪凤泉，韩晓林，周星德．基于小波分析的框架结构缺陷识别方法．振动、测试与诊断，2002，22(4)
[58] 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．振动工程学报，1997，10(1)：81～85
[59] 黄丁发，陈咏奇 丁晓利等．GPS高层建筑物常荷载振动测试的小波分析．振动与冲击，2001，20(1)：12～15
[60] 高永毅，焦群英，唐果，郎悦．等截面梁纯弯曲振动的几何非线性分析．振动与冲击，2003，22(1)72-74
[61] Sun Q. Singularity Analysis using continous wavelet transform for bearing fault diagnosis. Mechanical Systems and Signal Processing,2002,16(6),1025-1041
[62] Gentile A, Messina A. On the continuous wavelet transform applied to discrete vibration data for detecting open cracks in damage beams. International Journal of Solids and Structures, 2003, 40:295～315
[63] Cheng S M, Wu X J, Wallace W. Vibration response of a beam with breathing crack. Journal of Sound and Vibration, 1999,225(1):201-208
[64] Liang R Y, Hu J L, Choy E Quantitative NDE technique for assessing damages in beam structures. Journal of Engineering Mechanics, 1992,118(7):1468～1487
[65] Mazurek D F, Dewolf J T. Experimental study of bridge monitoring technique. Journal of Structural Engineering, 1990,116(9):2532～2549
[66] Lind R, Snyder K, Brenner M. Wavelet analysis to characterise non-linearities and predict limit cycles of an aeroelastic system. Mechanical Systems and Signal Processing, 2001, 15(2):337～356
[67] Ghobarah A, Abou-elfath H, Biddah A. Response-based damage assessment of
structures. Earthquake Engineering and Structural Dynamics, 1999,28:79～104
[68] Grossmann A. Wavelet transform and edge detection. Stochastics Processes in Physics and Engineering, Hazewinkel M.eds Dodrecht Reidel ,1986
[69] Mallat S. Zero_crossings of wavelet transform. IEEE Trans. on Information Theory, 1991,37(4): 1019～1033
[70] Mallat S, Zhong S. Characterization of signal from multiscale edges. IEEE Trans. on Pattern Analysis and Machine Intelligence, 1992,14(9):710～732
[71] Mallat S, Hwang W L. Sigularity detection and processing with wavelets. IEEE Trans. on Information Theory, 1992,38(2):617～643
[72] 李天云，胡屏，马景兰．小波奇异性检测理论在电力系统负荷特性分析中的应用．东北电力学院学报，1998，18(4)：14～18
[73] 易伟建，徐丽．钢筋混凝土损伤诊断的动测法研究．振动与冲击，2003，22(2)：23～25
[74] 周先雁，沈蒲生，程翔云．用振动参数识别技术对混凝土框架进行破损评估．土木工程学报，1998，31(2)：39～45
[75] 李庆扬，王能超，易大义．数值分析．武汉：华中科技大学出版社，1986
[76] 郑栋梁，李中付，华宏星．结构早期损伤诊断识别技术的现状和发展趋势．振动与冲击，2002，221(2)1～6
[76] 彭志科，何永勇，褚福磊．小波尺度谱在振动信号分析中的应用研究．机械工程学报，2002，38(3)：122～126
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