基于小波分析的桥梁损伤识别研究
|
摘要
桥梁是交通运输系统的重要组成部分,随着现代交通事业的飞速发展,对桥梁结构的安全性和使用要求越来越高。如果桥梁结构发生破坏,对国民经济、社会稳定和人民的生命财产产生重大影响。需要快速有效地识别出桥梁结构可能发生损伤部位和损伤程度,因此,对桥梁结构进行实时的健康检测、损伤识别是十分必要。
本文首先介绍了小波分析的理论基础,小波分析是近十几年发展起来的数学理论,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。接着介绍了小波奇异性检测的原理,运用连续小波变换可以很好的对简支梁桥的损伤位置进行精确定位,通过小波系数模极大值和变换尺度得到的Lipschitz指数对损伤程度进行识别。
利用Ansys软件建模模拟一简支梁桥结构发生不同损伤的情况,提取桥梁的振型模态,利用小波函数对基本振型进行多尺度变换,由小波系数模极大值识别出桥梁结构发生损伤的位置,根据小波系数模极大值的相对大小判断损伤的相对程度。通过模极大值的小波系数得到Lipschitz指数,用来描述损伤的程度。讨论了损伤程度大小、损伤位置、尺度大小、小波基的选择、振型阶数对识别损伤位置和程度的影响。讨论了轻微损伤时,以应变模态和曲率模态作为小波变换参数比以振型为参数的识别效果更好。建立实体桥梁模型,利用小波变换可以明显的发现桥梁损伤的位置。
Bridge is one of the vital parts of the traffic and transportation system. With rapid development of the modern transportation, more and more requirements are taken out due to safety and utility of bridges. If a bridge loses its function, national economics, social stability, people's lives will be affected. The bridge structure damaged position and extent need be identified quickly and efficiently, therefore, it is very necessary to set up a system to carry out real-time healthy detection, damage identification for a bridge.
The paper is related to the basic theories. Wavelet analysis is a new mathematic method which has developed rapidly. It is regarded as a breakthrough of Fourier Analysis. It has strong analytical skills with time-frequency. then wavelet singularity theory is described, continuous wavelet transform can be used to detect exactly the damaged location in a damaged bean-bridge. And meanwhile continuous wavelet transform can be used to estimate the Lipschitz exponent, the magnitude of which can be used as an indicator of the damage extent.
Finite element model is built by Ansys to simulate different damage situation of a simply supported bridge. The vibration mode shape is analyzed using continuous wavelet transform by wavelet on multiple scales. And the damage position and damage degree can be identified by the maximum of modulus of the wavelet coefficients and the Lipschitz exponent. In addition, some influencing factors are analyzed, such as the location of damage, damage degree,the size of scale, the type of mother wavelet and wavelet transform, the step of vibration mode shape. The Strain mode and the curvature mode are analyzed using continuous wavelet transform by wavelet, they have better results when we discuss minor damages. Established entity bridge model, location of damage can be found using wavelet transform.
本文首先介绍了小波分析的理论基础,小波分析是近十几年发展起来的数学理论,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。接着介绍了小波奇异性检测的原理,运用连续小波变换可以很好的对简支梁桥的损伤位置进行精确定位,通过小波系数模极大值和变换尺度得到的Lipschitz指数对损伤程度进行识别。
利用Ansys软件建模模拟一简支梁桥结构发生不同损伤的情况,提取桥梁的振型模态,利用小波函数对基本振型进行多尺度变换,由小波系数模极大值识别出桥梁结构发生损伤的位置,根据小波系数模极大值的相对大小判断损伤的相对程度。通过模极大值的小波系数得到Lipschitz指数,用来描述损伤的程度。讨论了损伤程度大小、损伤位置、尺度大小、小波基的选择、振型阶数对识别损伤位置和程度的影响。讨论了轻微损伤时,以应变模态和曲率模态作为小波变换参数比以振型为参数的识别效果更好。建立实体桥梁模型,利用小波变换可以明显的发现桥梁损伤的位置。
Bridge is one of the vital parts of the traffic and transportation system. With rapid development of the modern transportation, more and more requirements are taken out due to safety and utility of bridges. If a bridge loses its function, national economics, social stability, people's lives will be affected. The bridge structure damaged position and extent need be identified quickly and efficiently, therefore, it is very necessary to set up a system to carry out real-time healthy detection, damage identification for a bridge.
The paper is related to the basic theories. Wavelet analysis is a new mathematic method which has developed rapidly. It is regarded as a breakthrough of Fourier Analysis. It has strong analytical skills with time-frequency. then wavelet singularity theory is described, continuous wavelet transform can be used to detect exactly the damaged location in a damaged bean-bridge. And meanwhile continuous wavelet transform can be used to estimate the Lipschitz exponent, the magnitude of which can be used as an indicator of the damage extent.
Finite element model is built by Ansys to simulate different damage situation of a simply supported bridge. The vibration mode shape is analyzed using continuous wavelet transform by wavelet on multiple scales. And the damage position and damage degree can be identified by the maximum of modulus of the wavelet coefficients and the Lipschitz exponent. In addition, some influencing factors are analyzed, such as the location of damage, damage degree,the size of scale, the type of mother wavelet and wavelet transform, the step of vibration mode shape. The Strain mode and the curvature mode are analyzed using continuous wavelet transform by wavelet, they have better results when we discuss minor damages. Established entity bridge model, location of damage can be found using wavelet transform.
引文
1.欧进萍.重大工程结构的累积损伤与安全度评定[C]//走向21世纪的中国力学,中国科协第9次“青年科学家论坛”报告文集[M].北京:清华大学出版社,1996:12-13.
2 姜增国.小波方法在桥梁结构损伤识别中的应用研究[D].武汉:武汉理工大学,2007:1-2
3.秦权.桥梁结构的健康监测[J].中国公路学报,2000,15(1):34-35.
4.高怀涛,王君杰.桥梁检测和状态评估研究与应用[J].世界地震工程,2000,15(1):34-35
5.Rytter.A Vibration Based Inspection of Civil Engineering Structures[J].Building Technology and Structural Engineering,1993,12(1):78-79
6.Cawley P,Admas R D.The locations of defects in Structures form measurements of natural frequencies[J].Journal of strain Analysis,1979,14(2):49-57.
7.Sutbbs N,Broome T H,Osegueda R.Nondestructive construction error detection in lager space structures[J].AIAA Journal,1990,28(1):146-152.
8.Geogre Hearn,Rene B Testa.Modal Analysis for Damage Detection in Structures Journal of Structural Engineering[J].ASCE,1991,117(10):3042-3061
9.Salawu O S.Detection of structural damage through changes in frequency[J].a review Engineering Structures,1997,9(9):718-723.
10.刘济科,汤凯.基于振动特性的损伤识别方法的研究进展[J].中山大学学报,2004,23(1):45-46.
11.Yuen,MMEA Numerical Study of the Eigen parameters of a Damaged Cantilever[J].Journal of Sound and Vibration,1985,103(1):301-310.
12.Pandey A.K.,Biswas M.,Samman M.M.Damage Detection from Changes Incurvature Mode Shapes[J].Journal of Sound and Vibration,1991,145(2):321-332.
13.师本强.基于动柔度变化的结构损伤检测[J].工程力学增刊,2001,20(1):112-116.
14.王术新,姜哲.基于结构振动损伤识别技术的研究现状及进展[J].振动与冲击,2004,23(4):99-102
15.Pandey AK,Biswas M.Damage detection from changes in flexibility[J].Journal of Sound and Vibration,1994,168(2):126-128.
16.李国强,郝坤超,陆烨.弯剪型悬臂结构损伤识别的柔度法[J].地震工程与工程振 动,1999,10(2):56-58.
17.綦宝晖,邬瑞锋,李桂华,李志国.基于柔度阵的悬臂弯剪型建筑结构损伤识别方法[J].工业建筑,2000,26(1):91-95.
18.李德葆,诸葛鸿程,王波.验应变模态分析原理和方法[J].清华大学学报,1990,24(2):83-86.
19.董聪.基于动力特性的结构损伤定位力法[J].力学与实践,1999,21(1):1-6.
20.徐丽.基于模态参数的混凝土框架结构损伤诊断研究[D].长沙:湖南大学,2004:8-9.
21.杜思义.桥梁结构损伤识别的应变模态方法研究[D].郑州:郑州大学,2002:9-10.
22.何敏.基于概率神经网络的桥梁损伤定位研究[D].成都:西南交通大学,2008:8-10.
23.DENewland.avelet Analysis of Vibration,Part 1:Theory[M].Journal of Vibration and Acoustics,1994,26(2):69-72.
24.W.J.Wang,Application of orthogonal wavelets to early gear damage detection[J].Mechanical Systems and Signal processing,1995,21(1):47-51.
25.AI-Khalidy A,et.study of health monitoring systems of linear structures using wavelet analysis[J].ASME PVP,1997,33(5):179-184.
26.AI-Khalidy A,Noori M,HouZ,YamamotoS,Masuda A,Sone,A.Health Monitoring systems of Linear structures using wavelet analysis,roceedings,nternational Workshop in Structural health Monitoring[J].urrent Status and Perspectives,1997,13(1):59-65.
27.Kasi Amaravadi,Vittal Rao,Mark Derriso.Structural integrity monitoring of bonded Composite patch repairs of aging airframes using wavelet transforms[J].Structural health monitoring,1997,16(1):129-134.
28.HouZ,Noori h,Amand R S.Wavelet-based approach for structural damage detection[J].Journal of Engineering Mechanics,2000,19(2):253-257.
29.Liew K M,Wang Q.Application of wavelet theory for crack identification Structure[J].Journal of Engineering Mechanics,1998,45(3):456-462.
30.Wang Q,Wang D,Sun X.Crack detection of structure for plane problem with spatial wavelets SPIE[J].Newport beach,2001,32(1):125-130.
31.Pitter.S,Kamarthi,S,V.Feature extraction form wavelet coefficients for pattern recognition tasks[J].IEEF Transactions on Pattern Analysis and Machine Intelligence,1999,56(1):267-271.
32.Wang.P,VachtsevanosG.Fault prognosis using dynamic wavelet neural networks[J].Maintenance and Reliability ConferenceMARCON99,1999,23(2):156-162.
33.VachtsevanosG,WangP,Khiripet,N.Prognostication algorithms and performance assessment methodologies[J].ATP Fall National Meeting Condition-Based Maintenance Workshop.San Jose California,1999,36(1):92-198.
34.L.H.Yam,Y JYin,JS Jiang.Vibration-based damage detection for composite structures Using wavelet transform and neural network identification[J].Composite Structures,2003,32(1):456-461.
35.Sun Zhi,Chang Chi-Chen.Wavelet packer signature:A novel structural condition index[J].China-Japan Workshop in Vibration Control and Monitoring of Structures and Third Chinese Symposium on Structural Vibration Control,2002,12(1):356-362.
36.Z.Sun,CC,hang.StrueturaldamageassessmentbasedonwaveletPackettransform[J].Journal of Structural Engineering,2002,11(2):135-139.
37.Han J G.,Ren W X,Sun Z S.Wavelet packet based damage identification of beam structures International[J].Journal of Solids and Structures,2005,16(4):259-264.
38.LiZ,XiaSM,WangJ.SuXY.Damage detection of cracked beams based on wavelet transforms[J].Imitational Journal of Impact Engineering,2006,19(3):346-350.
39.杨福生.波变换的工程分析与应用[M].北京:科学出版社,2001:236-239.
40.彭玉华.波变换与工程应用[M].北京:科学出版社,2001:298-296.
41.程正兴.波分析算法与应用[M].西安:西安交通大学出版社,2001:216-229.
42.Mallta,H wang S,W L.Singularity Detection and Processing with wavelets[J].IEEE Transaction Theory,1992,17(1):26-32.
43.Kuris Gurley,Ahsan Kareem.Application of wavelet transform in earthquake[J].wind andocean Engineering Structures,1999,15(2):523-530.
44.Farge M.Wavelet transforms and their applications to turbulence Annual[J].Rev Fluid Mech,1992,12(2):412-420.
45.康耀红.数据融合理论与应用[M].西安:电子科技大学出版社,1997:126-130.
46.谭善文,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[J].重庆学学报,2001,11(1):153-159.
47.李围.ANSYS土木工程应用实例[M].北京:中国水利水电出版社,2007:7-8.
48.姜雪峰.基于应变模态的城市桥梁损伤识别的定量化研究[D].北京:北京工业大学,2006:45-46.
49.张俊海.基于模态参数在损伤检测中的应用[D].西安:西安理工大学,2007:51-53.
50.任宜春.基于小波分析的结构损伤诊断方法研究[D].长沙:湖南大学,2004:46-47.
51.黄燕.基于模态参数小波变换的结构损伤识别方法研究[D].长沙:长沙理工大学,2008:53-55.
52.陈建荣.基于小波分析的梁结构裂缝检测[D].汕头:汕头大学,2008:55-56.
53.李德葆,陆秋海,秦权.承弯结构的曲率模态分析[J].清华大学学报,2002,56(1):6-10.
2 姜增国.小波方法在桥梁结构损伤识别中的应用研究[D].武汉:武汉理工大学,2007:1-2
3.秦权.桥梁结构的健康监测[J].中国公路学报,2000,15(1):34-35.
4.高怀涛,王君杰.桥梁检测和状态评估研究与应用[J].世界地震工程,2000,15(1):34-35
5.Rytter.A Vibration Based Inspection of Civil Engineering Structures[J].Building Technology and Structural Engineering,1993,12(1):78-79
6.Cawley P,Admas R D.The locations of defects in Structures form measurements of natural frequencies[J].Journal of strain Analysis,1979,14(2):49-57.
7.Sutbbs N,Broome T H,Osegueda R.Nondestructive construction error detection in lager space structures[J].AIAA Journal,1990,28(1):146-152.
8.Geogre Hearn,Rene B Testa.Modal Analysis for Damage Detection in Structures Journal of Structural Engineering[J].ASCE,1991,117(10):3042-3061
9.Salawu O S.Detection of structural damage through changes in frequency[J].a review Engineering Structures,1997,9(9):718-723.
10.刘济科,汤凯.基于振动特性的损伤识别方法的研究进展[J].中山大学学报,2004,23(1):45-46.
11.Yuen,MMEA Numerical Study of the Eigen parameters of a Damaged Cantilever[J].Journal of Sound and Vibration,1985,103(1):301-310.
12.Pandey A.K.,Biswas M.,Samman M.M.Damage Detection from Changes Incurvature Mode Shapes[J].Journal of Sound and Vibration,1991,145(2):321-332.
13.师本强.基于动柔度变化的结构损伤检测[J].工程力学增刊,2001,20(1):112-116.
14.王术新,姜哲.基于结构振动损伤识别技术的研究现状及进展[J].振动与冲击,2004,23(4):99-102
15.Pandey AK,Biswas M.Damage detection from changes in flexibility[J].Journal of Sound and Vibration,1994,168(2):126-128.
16.李国强,郝坤超,陆烨.弯剪型悬臂结构损伤识别的柔度法[J].地震工程与工程振 动,1999,10(2):56-58.
17.綦宝晖,邬瑞锋,李桂华,李志国.基于柔度阵的悬臂弯剪型建筑结构损伤识别方法[J].工业建筑,2000,26(1):91-95.
18.李德葆,诸葛鸿程,王波.验应变模态分析原理和方法[J].清华大学学报,1990,24(2):83-86.
19.董聪.基于动力特性的结构损伤定位力法[J].力学与实践,1999,21(1):1-6.
20.徐丽.基于模态参数的混凝土框架结构损伤诊断研究[D].长沙:湖南大学,2004:8-9.
21.杜思义.桥梁结构损伤识别的应变模态方法研究[D].郑州:郑州大学,2002:9-10.
22.何敏.基于概率神经网络的桥梁损伤定位研究[D].成都:西南交通大学,2008:8-10.
23.DENewland.avelet Analysis of Vibration,Part 1:Theory[M].Journal of Vibration and Acoustics,1994,26(2):69-72.
24.W.J.Wang,Application of orthogonal wavelets to early gear damage detection[J].Mechanical Systems and Signal processing,1995,21(1):47-51.
25.AI-Khalidy A,et.study of health monitoring systems of linear structures using wavelet analysis[J].ASME PVP,1997,33(5):179-184.
26.AI-Khalidy A,Noori M,HouZ,YamamotoS,Masuda A,Sone,A.Health Monitoring systems of Linear structures using wavelet analysis,roceedings,nternational Workshop in Structural health Monitoring[J].urrent Status and Perspectives,1997,13(1):59-65.
27.Kasi Amaravadi,Vittal Rao,Mark Derriso.Structural integrity monitoring of bonded Composite patch repairs of aging airframes using wavelet transforms[J].Structural health monitoring,1997,16(1):129-134.
28.HouZ,Noori h,Amand R S.Wavelet-based approach for structural damage detection[J].Journal of Engineering Mechanics,2000,19(2):253-257.
29.Liew K M,Wang Q.Application of wavelet theory for crack identification Structure[J].Journal of Engineering Mechanics,1998,45(3):456-462.
30.Wang Q,Wang D,Sun X.Crack detection of structure for plane problem with spatial wavelets SPIE[J].Newport beach,2001,32(1):125-130.
31.Pitter.S,Kamarthi,S,V.Feature extraction form wavelet coefficients for pattern recognition tasks[J].IEEF Transactions on Pattern Analysis and Machine Intelligence,1999,56(1):267-271.
32.Wang.P,VachtsevanosG.Fault prognosis using dynamic wavelet neural networks[J].Maintenance and Reliability ConferenceMARCON99,1999,23(2):156-162.
33.VachtsevanosG,WangP,Khiripet,N.Prognostication algorithms and performance assessment methodologies[J].ATP Fall National Meeting Condition-Based Maintenance Workshop.San Jose California,1999,36(1):92-198.
34.L.H.Yam,Y JYin,JS Jiang.Vibration-based damage detection for composite structures Using wavelet transform and neural network identification[J].Composite Structures,2003,32(1):456-461.
35.Sun Zhi,Chang Chi-Chen.Wavelet packer signature:A novel structural condition index[J].China-Japan Workshop in Vibration Control and Monitoring of Structures and Third Chinese Symposium on Structural Vibration Control,2002,12(1):356-362.
36.Z.Sun,CC,hang.StrueturaldamageassessmentbasedonwaveletPackettransform[J].Journal of Structural Engineering,2002,11(2):135-139.
37.Han J G.,Ren W X,Sun Z S.Wavelet packet based damage identification of beam structures International[J].Journal of Solids and Structures,2005,16(4):259-264.
38.LiZ,XiaSM,WangJ.SuXY.Damage detection of cracked beams based on wavelet transforms[J].Imitational Journal of Impact Engineering,2006,19(3):346-350.
39.杨福生.波变换的工程分析与应用[M].北京:科学出版社,2001:236-239.
40.彭玉华.波变换与工程应用[M].北京:科学出版社,2001:298-296.
41.程正兴.波分析算法与应用[M].西安:西安交通大学出版社,2001:216-229.
42.Mallta,H wang S,W L.Singularity Detection and Processing with wavelets[J].IEEE Transaction Theory,1992,17(1):26-32.
43.Kuris Gurley,Ahsan Kareem.Application of wavelet transform in earthquake[J].wind andocean Engineering Structures,1999,15(2):523-530.
44.Farge M.Wavelet transforms and their applications to turbulence Annual[J].Rev Fluid Mech,1992,12(2):412-420.
45.康耀红.数据融合理论与应用[M].西安:电子科技大学出版社,1997:126-130.
46.谭善文,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[J].重庆学学报,2001,11(1):153-159.
47.李围.ANSYS土木工程应用实例[M].北京:中国水利水电出版社,2007:7-8.
48.姜雪峰.基于应变模态的城市桥梁损伤识别的定量化研究[D].北京:北京工业大学,2006:45-46.
49.张俊海.基于模态参数在损伤检测中的应用[D].西安:西安理工大学,2007:51-53.
50.任宜春.基于小波分析的结构损伤诊断方法研究[D].长沙:湖南大学,2004:46-47.
51.黄燕.基于模态参数小波变换的结构损伤识别方法研究[D].长沙:长沙理工大学,2008:53-55.
52.陈建荣.基于小波分析的梁结构裂缝检测[D].汕头:汕头大学,2008:55-56.
53.李德葆,陆秋海,秦权.承弯结构的曲率模态分析[J].清华大学学报,2002,56(1):6-10.