基于振动信号的结构模态参数识别与损伤分析
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摘要
振动模态参数是决定结构动力特性的主要参数,在结构建模、振动控制、损伤识别和结构优化等方面起着很重要的作用。本文以小波变换和Hilbert-Huang变换(HHT)为主要工具,对结构模态参数识别问题和结构损伤问题进行了研究。
1.研究了基于复Morlet小波变换的结构模态参数识别方法。利用复Morlet小波变换对结构的自由振动响应信号进行分析,通过小波脊线对应的尺度和脊线上的小波系数识别其瞬时频率和瞬时振幅。利用复Morlet小波因子与中心频率之间的关系,在小波因子为(N=2-20)范围内对自由振动信号进行了结构模态参数的辨识。当N增大时,振动信号的频域分辨率就得到了提高,此时对模态参数识别有较好的效果,但相应的时域分辨率会降低,故N的取值并非越大越好。参数N的作用是协调频域和时域的分辨率使之达到最佳的折衷状态。对白噪声激励下振动信号的结构模态参数识别是依据相关函数理论,利用复Morlet进行模态参数的识别,并取得了不错的识别效果。利用高频噪声信号的小波变换系数小、振动有效信号主要表现为低频的特点,对含有白噪声的振动信号进行结构模态参数的识别。以上方法均能使模态参数的辨识误差控制在允许范围内。
2.利用EMD分解对振动信号进行结构模态参数的识别,识别误差在5%以内。对于三自由度及以上结构,应用HHT方法识别模态参数就不理想。故采用对振动信号先添加带通滤波器、再利用HHT进行模态参数识别的方法,识别误差也较小。提出了基于EMD的小波变换法进行结构模态参数识别的方法：对振动信号进行EMD分解,将分解得到的本征模函数(IMF)利用小波变换法进行结构模态参数识别,并且识别误差控制在8%以内。利用HHT方法对含有白噪声的振动信号进行结构模态参数的识别,由于EMD对此信号分解的效果不好,故识别的误差较大。
3.利用基于小波变换的模态参数识别法和基于小波包的能量法进行结构损伤的分析。前者是利用损伤前后结构的模态参数发生变化的特点判断结构损伤。其间利用相乘最小逆指数法来解决信号提前衰减的问题,有利于损伤的分析。后者通过将振动信号用小波包分解为若干个频段,利用损伤前后各个频率成份能量变化的特点进行损伤分析。两方法都能较好的进行结构损伤的分析。
Modal parameter identification of vibration is required by structural vibration characteristics analysis, damage diagnosis, and optimization design of structural dynamics characteristics. This paper is based on the application of wavelet analysis and Hilbert-Huang transform in structural modal parameter identification, and the structural damage is also analyzed.
1. The modal parameter identification of structural vibration by Morlet wavelet transform is studied. The free vibration response signal is analyzed by Morlet wavelet transform. The instantaneous frequency and amplitude are recognized by the scale and the wavelet coefficient of the ridge, so the inherence frequency and damping ratios are estimated. The signal of free vibration response is analyzed between 2 and 20 of wavelet factor N by the relation of wavelet factor and wavelet center frequency. If wavelet factor N is larger, it will be better in Modal parameter identification. But it is instead of reducing the resolution in time. The parameter of N is applied to solve the contradiction of resolution between in time and in frequency making both of them better. Modal parameter identification of vibration in noisy environment based on correlation function is researched. For identification the vibration signal which is added white noise signal, the method is proposed, which is based on the theory that the wavelet transform coefficient of noise signal is very small and the main vibration signal is low-frequency signal. The identification error is controlled in permitted range.
2. Modal parameter identification of vibration based on EMD is researched. And the identification error is less in five percent. For three degree of freedom structure, the method of HHT is bad. The signal based on band pass filter before it is processed by HHT. And the identification error is also small using this method. The method based on the combing of Morlet wavelet and EMD is proposed for parameter identification. The vibration signal which is decomposed by EMD is transformed by wavelet. The identification error is controlled in eight percent. The noised signal of structural vibration is analyzed. For identification the vibration signal which is added white noise signal, the method of HHT is proposed. The identification error is bigger for the bad decomposed by EMD.
3. Structural damage is studied by the methods of Modal parameter identification and wavelet energy. The former is based on the change of Modal parameter in the damaged structure. For the ratio of attenuation factor may be large in the structural, multiplied by the smallest inverse index method is proposed in the damaged modal. The latter is based on change of the signal energy in each band frequency in damaged modal, which is decomposed by the wavelet packet.
1.研究了基于复Morlet小波变换的结构模态参数识别方法。利用复Morlet小波变换对结构的自由振动响应信号进行分析,通过小波脊线对应的尺度和脊线上的小波系数识别其瞬时频率和瞬时振幅。利用复Morlet小波因子与中心频率之间的关系,在小波因子为(N=2-20)范围内对自由振动信号进行了结构模态参数的辨识。当N增大时,振动信号的频域分辨率就得到了提高,此时对模态参数识别有较好的效果,但相应的时域分辨率会降低,故N的取值并非越大越好。参数N的作用是协调频域和时域的分辨率使之达到最佳的折衷状态。对白噪声激励下振动信号的结构模态参数识别是依据相关函数理论,利用复Morlet进行模态参数的识别,并取得了不错的识别效果。利用高频噪声信号的小波变换系数小、振动有效信号主要表现为低频的特点,对含有白噪声的振动信号进行结构模态参数的识别。以上方法均能使模态参数的辨识误差控制在允许范围内。
2.利用EMD分解对振动信号进行结构模态参数的识别,识别误差在5%以内。对于三自由度及以上结构,应用HHT方法识别模态参数就不理想。故采用对振动信号先添加带通滤波器、再利用HHT进行模态参数识别的方法,识别误差也较小。提出了基于EMD的小波变换法进行结构模态参数识别的方法：对振动信号进行EMD分解,将分解得到的本征模函数(IMF)利用小波变换法进行结构模态参数识别,并且识别误差控制在8%以内。利用HHT方法对含有白噪声的振动信号进行结构模态参数的识别,由于EMD对此信号分解的效果不好,故识别的误差较大。
3.利用基于小波变换的模态参数识别法和基于小波包的能量法进行结构损伤的分析。前者是利用损伤前后结构的模态参数发生变化的特点判断结构损伤。其间利用相乘最小逆指数法来解决信号提前衰减的问题,有利于损伤的分析。后者通过将振动信号用小波包分解为若干个频段,利用损伤前后各个频率成份能量变化的特点进行损伤分析。两方法都能较好的进行结构损伤的分析。
Modal parameter identification of vibration is required by structural vibration characteristics analysis, damage diagnosis, and optimization design of structural dynamics characteristics. This paper is based on the application of wavelet analysis and Hilbert-Huang transform in structural modal parameter identification, and the structural damage is also analyzed.
1. The modal parameter identification of structural vibration by Morlet wavelet transform is studied. The free vibration response signal is analyzed by Morlet wavelet transform. The instantaneous frequency and amplitude are recognized by the scale and the wavelet coefficient of the ridge, so the inherence frequency and damping ratios are estimated. The signal of free vibration response is analyzed between 2 and 20 of wavelet factor N by the relation of wavelet factor and wavelet center frequency. If wavelet factor N is larger, it will be better in Modal parameter identification. But it is instead of reducing the resolution in time. The parameter of N is applied to solve the contradiction of resolution between in time and in frequency making both of them better. Modal parameter identification of vibration in noisy environment based on correlation function is researched. For identification the vibration signal which is added white noise signal, the method is proposed, which is based on the theory that the wavelet transform coefficient of noise signal is very small and the main vibration signal is low-frequency signal. The identification error is controlled in permitted range.
2. Modal parameter identification of vibration based on EMD is researched. And the identification error is less in five percent. For three degree of freedom structure, the method of HHT is bad. The signal based on band pass filter before it is processed by HHT. And the identification error is also small using this method. The method based on the combing of Morlet wavelet and EMD is proposed for parameter identification. The vibration signal which is decomposed by EMD is transformed by wavelet. The identification error is controlled in eight percent. The noised signal of structural vibration is analyzed. For identification the vibration signal which is added white noise signal, the method of HHT is proposed. The identification error is bigger for the bad decomposed by EMD.
3. Structural damage is studied by the methods of Modal parameter identification and wavelet energy. The former is based on the change of Modal parameter in the damaged structure. For the ratio of attenuation factor may be large in the structural, multiplied by the smallest inverse index method is proposed in the damaged modal. The latter is based on change of the signal energy in each band frequency in damaged modal, which is decomposed by the wavelet packet.
引文
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[2]续秀忠,华宏星,陈兆能.基于环境激励的模态参数识别方法综述.振动与冲击.2002,21(3)： 1-5.
[3]James G H, Carne T G, Lauffer J P. The natural excitation technique (NExT) for modal parameter extraction from operating structures [J]. The International Journal of Analytical and Experimental Modal Analysis.1995,10(4):260-277.
[4]李中付.环境激励下的线性结构模态参数辨识.[博士学位论文].上海交通大学,2001.
[5]吴亚峰,姜节胜.结构模态参数识别的子空间辨识方法.应用力学学报.2001,18,增刊：331-334.
[6]丁康,陈健林,苏向荣.平稳和非平稳振动信号的若干处理方法及发展.振动工程学报.2003,16(1)：1-10.
[7]Kim H, Melhem H. Damage detection of structures by wavelet analysis. Engineering Structures.2004,26:347-362.
[8]于开平,邹经湘,史桂香.小波分析在结构系统辨识中的应用.力学与实践.1998,20(5)： 42-44.
[9]李宏男,孙鸿敏.小波分析在土木工程领域中的应用.世界地震工程.2003,19(2)：16-22.
[10]孙增寿,韩建刚,任伟新.基于小波分析的结构损伤检测研究进展.地震工程与工程振动.2005,25(2)：93-99.
[11]伊廷华,李宏男,王国新.基于小波变换的结构模态参数识别.振动工程学报.2006,19(1)： 51-56.
[12]王国兴,李华军,潘新颖.小波包分析在结构损伤时间识别及结构模态参数识别中的应用.工程力学.2003,增刊：608-612.
[13]Huang N E, Shen Z, Long S R, etc. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary times series analysis. Proceedings of Royal Society of London Series A.1998,454:903-995.
[14]Kijewski T, Kareem A. Nonlinear signal analysis:time-frequency perspective. Journal of Engineering Mechanics.2007,133(2):238-245.
[15]Kijewski T, Kareem A. Efficacy of Hilbert and wavelet transforms for time frequency analysis.Journal of Engineering Mechanics.2006,132(10):1037-1049.
[16]Yang JN, Lei Y, Pan S, etc. System identification of linear structures based on Hilbert-Huang spectral analysis. Part I:normal modes. Earthquake Engineering and Structural Dynamics.2003,32:1443-1467.
[17]Yang, Lei Y, Pan S, etc. System identification of linear structures based on Hilbert-Huang spectral analysis. PartⅡ:complex modes. Earthquake Engineering and Structural Dynamics.2003,32:1533-1554.
[18]Yang, Lei Y, Lin S, etc. Hilbert-Huang based approach for structural damage detection. Journal of Engineering Mechanics.2004,130(1):85-95.
[19]陈隽,徐幼麟.HHT方法在结构模态参数识别中的应用.振动工程学报.2003,16(3)：382-387.
[20]寇立夯,金峰.基于HHT方法的结构模态参数识别.水利水电科技进展.2008,28(3)：45-49.
[21]程远胜,熊飞,刘均.基于HHT方法的时变多自由度系统的参数识别.华中科技大学学报(自然科学版).2007,35(5)：41-43.
[22]武安绪,宋治平,吴培稚.Hilbert-Huang变换与华北地区历史地震活动分析.中国地球物理学会第二十一届年会论文.2005,8：456.
[23]罗奇峰,石春.HHT变换在地震波谱分析中的应用.第六届全国地震工程学会会议论文集.2002,11：373-376.
[24]常帅,谢剑英.802.11无线网络安全性研究及其工程应用.2005全国仿真技术学术会议论文集.2005,08：296-299.
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