基于小波分析的连续梁损伤识别研究
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摘要
连续梁结构是桥梁的一种常见形式,在工程中应用广泛。在风、地震荷载作用及自然环境侵蚀下,结构某些部位将产生损伤,结构的刚度、强度等力学性能随之降低,这种力学性能的降低直接影响到结构动力特性的变化。小波变换是一种时频域分析方法,具有多分辨率分析的特点,是奇异性信号分析的合适工具。本文基于国内外学者对结构损伤识别方法的研究,采用位移均方差作为损伤指标,并利用小波变换来实现结构损伤位置和损伤程度的识别。
无论是现场测试还是数值分析,所采集到的动力响应信息是有限的。当对其进行小波变换时,各个分解量在其边界处一般都会出现Gibbs现象。通过比较处理有限区间信号边界问题的典型方法,文中提出了基于曲线拟合技术的信息拓展方法,并通过算例验证了该方法。
针对无刚度变化的连续梁,利用信息拓展的方法,抑制Gibbs振荡现象影响,对连续梁结构进行损伤识别,将小波变换识别结构损伤信息的范围拓展到结构整体,特别是结构边界区域;对于多损伤的连续梁结构,由于受损伤之间以及自身支座的影响,结构损伤位置难以识别。为此,引入信息截断的方法,从而消除这些影响,并结合信息拓展方法对响应信息进行处理,完成损伤位置的准确识别。
最后利用小波系数模极大值点处对应的Lipschitz指数来判断结构损伤的程度。对移动荷载作用下连续梁结构的位移均方差曲线进行连续小波变换,研究Lipschitz指数随损伤程度、损伤位置、损伤发生的数量、损伤之间的影响、荷载的大小、荷载速度的变化规律。
The multisupported beam structure is a common form of bridge,and widely applied in engineering. Under the wind or earthquake loads, and natural environment erosion, some local structural damage appear and its mechanics character degradation of stiffness and strength. This degradation has the directly effect on the structure dynamic character. Wavelet transform is a analysis method both for time and frequency domain, and it adapted well to singularity analysis for its multi-resolution. Based on study of civil and abroad scholars to structural damage identification methods in this paper, standard deviation of acceleration used as damage index, and wavelet transform is used for identification of the site and degree of damage.
Dynamic response information of collectting is limited, whether field test or numerical analysis. Each decomposition amount could generally appeared Gibbs phenomenon at its boundary while wavelet transform. After compared the typical methods by treating edge problem of the signal with limited time zone, method of information expansion based on curve fitting is proposed in the paper, and validated this method by numerical example.
For the multisupported beam with uniform stiffness,the method of expanding the use of information and inhibit the effects of Gibbs oscillations, the multisupported beam structures for damage detection, wavelet transform to identify structural damage information of the range extends Dao whole structure, particularly the border region is a structure; for more multisupported beam damage, due to injury as well as between the impact of their bearing, structural damage location is difficult to identify. To this end, the introduction of information truncated methods to eliminate these effects and to develop methods of combining information on the response information to process, complete and accurate identification of damage location.
Finally, the wavelet coefficients modulus maxima points corresponding Lipschitz index to determine the extent of structural damage. On the multisupported beam under moving load displacement of the structure of the continuous wavelet transform variance curve, with the damage of Lipschitz index of the degree of damage location, damage occurred in the number of injuries between the effects of load size, load speed variation.
无论是现场测试还是数值分析,所采集到的动力响应信息是有限的。当对其进行小波变换时,各个分解量在其边界处一般都会出现Gibbs现象。通过比较处理有限区间信号边界问题的典型方法,文中提出了基于曲线拟合技术的信息拓展方法,并通过算例验证了该方法。
针对无刚度变化的连续梁,利用信息拓展的方法,抑制Gibbs振荡现象影响,对连续梁结构进行损伤识别,将小波变换识别结构损伤信息的范围拓展到结构整体,特别是结构边界区域;对于多损伤的连续梁结构,由于受损伤之间以及自身支座的影响,结构损伤位置难以识别。为此,引入信息截断的方法,从而消除这些影响,并结合信息拓展方法对响应信息进行处理,完成损伤位置的准确识别。
最后利用小波系数模极大值点处对应的Lipschitz指数来判断结构损伤的程度。对移动荷载作用下连续梁结构的位移均方差曲线进行连续小波变换,研究Lipschitz指数随损伤程度、损伤位置、损伤发生的数量、损伤之间的影响、荷载的大小、荷载速度的变化规律。
The multisupported beam structure is a common form of bridge,and widely applied in engineering. Under the wind or earthquake loads, and natural environment erosion, some local structural damage appear and its mechanics character degradation of stiffness and strength. This degradation has the directly effect on the structure dynamic character. Wavelet transform is a analysis method both for time and frequency domain, and it adapted well to singularity analysis for its multi-resolution. Based on study of civil and abroad scholars to structural damage identification methods in this paper, standard deviation of acceleration used as damage index, and wavelet transform is used for identification of the site and degree of damage.
Dynamic response information of collectting is limited, whether field test or numerical analysis. Each decomposition amount could generally appeared Gibbs phenomenon at its boundary while wavelet transform. After compared the typical methods by treating edge problem of the signal with limited time zone, method of information expansion based on curve fitting is proposed in the paper, and validated this method by numerical example.
For the multisupported beam with uniform stiffness,the method of expanding the use of information and inhibit the effects of Gibbs oscillations, the multisupported beam structures for damage detection, wavelet transform to identify structural damage information of the range extends Dao whole structure, particularly the border region is a structure; for more multisupported beam damage, due to injury as well as between the impact of their bearing, structural damage location is difficult to identify. To this end, the introduction of information truncated methods to eliminate these effects and to develop methods of combining information on the response information to process, complete and accurate identification of damage location.
Finally, the wavelet coefficients modulus maxima points corresponding Lipschitz index to determine the extent of structural damage. On the multisupported beam under moving load displacement of the structure of the continuous wavelet transform variance curve, with the damage of Lipschitz index of the degree of damage location, damage occurred in the number of injuries between the effects of load size, load speed variation.
引文
1郭健.基于小波分析的结构损伤识别方法研究. [浙江大学博士学位论文]. 2004
2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.地震工程与工程振动, 2007, 27(3): 95-103
3杨秋伟.基于振动的结构损伤识别方法研究进展.振动与冲击, 2007, 26(10): 86-91
4郭惠勇,李正良,彭川.结构损伤动力识别技术的研究与进展.重庆建筑大学学报, 2008, 30(1): 140-145
5郭惠勇,李正良,罗乐.基于频率响应和统计理论的结构损伤识别研究.振动与冲击, 2007, 26(11): 25-28
6任宜春.基于小波分析的结构损伤诊断方法研究. [湖南大学硕士学位论文]. 2004
7孙宗光.大跨度斜拉桥结构的动力损伤检测. [浙江大学博士学位论文]. 2001
8陈长征,罗跃纲,白秉三等.结构损伤检测与智能诊断.北京:科学出版社, 2001
9 O.S. Salawu. Detection of structural damage through changes in frequencies: a review. Engineering Structures, 1997, 19(9): 718-723
10 J.H. Kim, H.S. Jeon and C.W. Lee. Application of the modal assurance criteria for detecting and locating structural faults. Proceedings of the 10th international Modal Analysis Conference, San Diego, CA, USA: 536-540
11 Z.Y. Shi, S.S. Law and L.M. Zhang. Damage localization by directly using incomplete mode shapes. Journal of Engineering Mechanics, 2000, 126(5): 656-660
12 A.K. Pandey, M. Biswas and M.M. Samman. Damage detection from changes in curvature mode shapes. Journal of Sound and Vibration, 1991, 145(2): 321-332
13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
14 C.R. Farrar, D.A. Jauregui. Comparative study of damage identification algorithms applied to a bridge:Ⅰ.experiment. Smart Material Structure, 1998, 7(5): 704-719
15 A. Alvandi, C. Cremona. Assessment of vibration-based damage identificationtechniques. Journal of Sound and Vibration, 2006, 292(1/2): 179-202
16 M. Schulz, A.S. Naser. Locating structural damage using frequency response functions. Journal of Intelligent Material Systems and Structures, 1998, 9: 899-905
17 G. Park, H.H. Cudney, D.J. Inman. An integrated health monitoring technique using structural impedance sensors. Journal of Intelligent Material Systems and Structures, 2000, 11: 448-455
18 N.G. Park, Y.S. Park. Damage detection using spatially incomplete frequency response functions. Mechanical Systems and Signal Processing, 2003, 17(3): 519-532
19杨彦芳,宋玉普,纪卫红.基于实测频响函数主成分的在役网架损伤识别方法.振动与冲击, 2007, 26(9): 128-132
20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.工程力学, 2007, 24(9): 105-110
21 A.K. Pandey, M. Biswas. Damage detection in structures using changes in flexibility. Journal of Sound and Vibration, 1994, 169(1): 3-17
22 D. Bernal. Load vectors for damage localization. Journal of Engineering Mechanics, 2002, 128(1): 7-14
23 Z.D. Duan, G.R. Yan, J.P. Ou, B.F. Spencer. Damage localization in ambient vibration by constructing proportional flexibility matrix. Journal of Sound and Vibration, 2005, (284): 455-466
24孙国,顾元宪.连续梁结构损伤识别的改进柔度阵方法.工程力学, 2003, 20(4): 50-54
25 S.W. Doebling, C.R. Farrar, M.B. Prime. A summary review of vibration-based damage identification methods. The Shock and Vibration Digest, 1998, 30(2): 91-105
26张立涛,李兆霞,费庆国.基于加速度时域信息的结构损伤识别方法研究.振动与冲击, 2007, 26(9): 138-141
27孙增寿.基于小波的土木工程结构损伤识别方法研究. [福州大学博士学位论文]. 2006
28任伟新,韩建刚,孙增寿.小波分析在土木工程结构中的应用.北京:中国铁道出版社, 2006
29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
30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
31 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
32 Wong L A, Chen J C. Nonlinear and Chaotic Behavior of Structural System Investigated by wavelet Transform Techniques. International Joumal of Nonlinear Mechanics, 2001, 36: 221-235
33 Kijewski T, Kareem A. Wavelet Transform for System Identification in Civil Engineering. Computer-Aided Civil and Infrastructure Engineering, 2003, 18: 339-355
34 Z. Hou, M. Noori, R.S. Amand. Wavelet-based approach for structural damage detection. Journal of Engineering Mechanics, 2000, 126(7): 677-683
35郭建,孙炳南.基于小波变换的桥梁健康监测多尺度分析.浙江大学学报(工学版), 2005, 39(1): 114-118
36 K.M. Liew, Q. Wang. Application of wavelet theory of for crack identification in structure. Journal of Engineering Mechanics, 1998, 124(2): 152-157
37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
38李洪泉,董亮,吕西林.基于小波变换的结构损伤识别与实验分析.土木工程学报, 2003, 36(5): 69-75
39 J.C. Hong, Y.Y. Kim, H.C. Lee, Y.W. Lee. Damage detection using the Lipschitz exponent estimated by the wavelet transform: applications to vibration modes of a beam. Solids and Structures, 2002, 39: 1803-1816
40任宜春,马石城,林琳.移动荷载作用下梁裂缝识别的小波方法研究.振动与冲击, 2004, 23(2): 81-83
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42 S. Mallat, W.L. Hwang. Singularity Detection and Processing with Wavelets. IEEE Transactions on Information Theory, 1992, 38(2): 617-643
43周春华,龙源,晏俊伟,蔡立艮.基于WTMM的爆破振动信号奇异性分析.振动与冲击, 2007, 26(1): 108-111
44张波,李健君.一种基于小波变换与奇异值分解对振动系统模态频率进行识别的新方法.振动与冲击, 2006, 25(6): 88-91
45胡广书.现代信号处理教程.北京:清华大学出版社, 2004
46 M. Farge. Wavelet transforms and their applications to turbulence. Annual, Rev Fluid Mech, 1992, 24: 523-531
47欧进萍,王光远.结构随机振动.北京:高等教育出版社, 1998
48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.工程力学, 2007, 24(9): 1-7
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2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.地震工程与工程振动, 2007, 27(3): 95-103
3杨秋伟.基于振动的结构损伤识别方法研究进展.振动与冲击, 2007, 26(10): 86-91
4郭惠勇,李正良,彭川.结构损伤动力识别技术的研究与进展.重庆建筑大学学报, 2008, 30(1): 140-145
5郭惠勇,李正良,罗乐.基于频率响应和统计理论的结构损伤识别研究.振动与冲击, 2007, 26(11): 25-28
6任宜春.基于小波分析的结构损伤诊断方法研究. [湖南大学硕士学位论文]. 2004
7孙宗光.大跨度斜拉桥结构的动力损伤检测. [浙江大学博士学位论文]. 2001
8陈长征,罗跃纲,白秉三等.结构损伤检测与智能诊断.北京:科学出版社, 2001
9 O.S. Salawu. Detection of structural damage through changes in frequencies: a review. Engineering Structures, 1997, 19(9): 718-723
10 J.H. Kim, H.S. Jeon and C.W. Lee. Application of the modal assurance criteria for detecting and locating structural faults. Proceedings of the 10th international Modal Analysis Conference, San Diego, CA, USA: 536-540
11 Z.Y. Shi, S.S. Law and L.M. Zhang. Damage localization by directly using incomplete mode shapes. Journal of Engineering Mechanics, 2000, 126(5): 656-660
12 A.K. Pandey, M. Biswas and M.M. Samman. Damage detection from changes in curvature mode shapes. Journal of Sound and Vibration, 1991, 145(2): 321-332
13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
14 C.R. Farrar, D.A. Jauregui. Comparative study of damage identification algorithms applied to a bridge:Ⅰ.experiment. Smart Material Structure, 1998, 7(5): 704-719
15 A. Alvandi, C. Cremona. Assessment of vibration-based damage identificationtechniques. Journal of Sound and Vibration, 2006, 292(1/2): 179-202
16 M. Schulz, A.S. Naser. Locating structural damage using frequency response functions. Journal of Intelligent Material Systems and Structures, 1998, 9: 899-905
17 G. Park, H.H. Cudney, D.J. Inman. An integrated health monitoring technique using structural impedance sensors. Journal of Intelligent Material Systems and Structures, 2000, 11: 448-455
18 N.G. Park, Y.S. Park. Damage detection using spatially incomplete frequency response functions. Mechanical Systems and Signal Processing, 2003, 17(3): 519-532
19杨彦芳,宋玉普,纪卫红.基于实测频响函数主成分的在役网架损伤识别方法.振动与冲击, 2007, 26(9): 128-132
20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.工程力学, 2007, 24(9): 105-110
21 A.K. Pandey, M. Biswas. Damage detection in structures using changes in flexibility. Journal of Sound and Vibration, 1994, 169(1): 3-17
22 D. Bernal. Load vectors for damage localization. Journal of Engineering Mechanics, 2002, 128(1): 7-14
23 Z.D. Duan, G.R. Yan, J.P. Ou, B.F. Spencer. Damage localization in ambient vibration by constructing proportional flexibility matrix. Journal of Sound and Vibration, 2005, (284): 455-466
24孙国,顾元宪.连续梁结构损伤识别的改进柔度阵方法.工程力学, 2003, 20(4): 50-54
25 S.W. Doebling, C.R. Farrar, M.B. Prime. A summary review of vibration-based damage identification methods. The Shock and Vibration Digest, 1998, 30(2): 91-105
26张立涛,李兆霞,费庆国.基于加速度时域信息的结构损伤识别方法研究.振动与冲击, 2007, 26(9): 138-141
27孙增寿.基于小波的土木工程结构损伤识别方法研究. [福州大学博士学位论文]. 2006
28任伟新,韩建刚,孙增寿.小波分析在土木工程结构中的应用.北京:中国铁道出版社, 2006
29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
30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
31 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
32 Wong L A, Chen J C. Nonlinear and Chaotic Behavior of Structural System Investigated by wavelet Transform Techniques. International Joumal of Nonlinear Mechanics, 2001, 36: 221-235
33 Kijewski T, Kareem A. Wavelet Transform for System Identification in Civil Engineering. Computer-Aided Civil and Infrastructure Engineering, 2003, 18: 339-355
34 Z. Hou, M. Noori, R.S. Amand. Wavelet-based approach for structural damage detection. Journal of Engineering Mechanics, 2000, 126(7): 677-683
35郭建,孙炳南.基于小波变换的桥梁健康监测多尺度分析.浙江大学学报(工学版), 2005, 39(1): 114-118
36 K.M. Liew, Q. Wang. Application of wavelet theory of for crack identification in structure. Journal of Engineering Mechanics, 1998, 124(2): 152-157
37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
38李洪泉,董亮,吕西林.基于小波变换的结构损伤识别与实验分析.土木工程学报, 2003, 36(5): 69-75
39 J.C. Hong, Y.Y. Kim, H.C. Lee, Y.W. Lee. Damage detection using the Lipschitz exponent estimated by the wavelet transform: applications to vibration modes of a beam. Solids and Structures, 2002, 39: 1803-1816
40任宜春,马石城,林琳.移动荷载作用下梁裂缝识别的小波方法研究.振动与冲击, 2004, 23(2): 81-83
41林宝龙.小波变换在结构损伤识别中的应用研究. [浙江大学硕士学位论文]. 2006
42 S. Mallat, W.L. Hwang. Singularity Detection and Processing with Wavelets. IEEE Transactions on Information Theory, 1992, 38(2): 617-643
43周春华,龙源,晏俊伟,蔡立艮.基于WTMM的爆破振动信号奇异性分析.振动与冲击, 2007, 26(1): 108-111
44张波,李健君.一种基于小波变换与奇异值分解对振动系统模态频率进行识别的新方法.振动与冲击, 2006, 25(6): 88-91
45胡广书.现代信号处理教程.北京:清华大学出版社, 2004
46 M. Farge. Wavelet transforms and their applications to turbulence. Annual, Rev Fluid Mech, 1992, 24: 523-531
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