基于希尔伯特—黄变换的结构模态参数识别研究
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摘要
模态参数识别对土木工程结构健康监测、损伤评估等的理论研究及工程应用具有重要意义。近年来,基于结构振动信号的时频分析方法得到了广泛研究和应用。希尔伯特一黄变换(Hilbert Huang Transform,简称HHT)是一种优于传统方法的信号处理新技术,具有完全自适应性,不受Heisenberg测不准原理制约等优点,能处理非线性、非平稳数据。HHT已广泛应用于很多学科领域,包括结构模态参数识别,并且取得了良好的效果。基于上述考虑,本文主要进行了如下几方面的研究工作:
1.通过数值仿真算例,对HHT方法的信号处理特性进行了研究。采用HHT方法对谐波叠加信号、经典的线性调频(Chirp)信号、自由衰减信号等进行了计算和分析,指出HHT方法能有效处理非线性、非平稳数据,但模态混叠和端点效应问题还有待于进一步研究。
2.对基于HHT变换的结构模态参数识别理论进行了深入研究,提出了基于峰频带通信号HHT的结构模态参数识别方法,并在MATLAB平台上编制了相应的计算分析程序。首先利用傅里叶变换得到信号的自功率谱,以确定结构固有频率的大致分布区间;然后采用带通滤波器对信号进行滤波处理,得到包含各峰值频率在内的带通响应信号;最后对带通信号进行HHT以识别结构模态参数。研究表明,该方法有效的解决了EMD分解过程中的模态混叠问题。同时,本文采用去端点的办法,剔除了端点效应对结构模态参数识别的影响。
3.对一钢筋混凝土框架结构模型进行了试验模态分析。根据试验室条件下采集的脉冲激励响应信号,运用本文提出的基于峰频带通信号HHT的模态参数识别方法,识别了框架结构模型的固有频率、模态阻尼和振型等模态参数。固有频率与理论计算值吻合良好,验证了本文方法的有效性。
Modal Parameter identification of civil engineering struetures play an important role in research and application fields such as structural health monitoring, structural damage assessment. In recent years, extensive research and application has been done to develop the methods of time-frequency analysis based on vibration signal. Compared with traditional methods of signal analysis, HHT is a new technology for the analysis of signal. Being totally adaptive, and not subjcet to Heisenberg uncertainty principle, HHT has been proved to be ideal method for non-linear and non-stationary data. HHT has been widely used in many disciplines,including modal parameter identification,and produced good results. According to the consideration mentioned above,this thesis forcuses on the following aspcets of researeh:
1.Value simulation and computation example were taken to study the characteristic of HHT method.Classical signals such as superposed signal, linear frequency-modulation (Chirp) signal, freedom weaken signal was computed and analyzed,which has shown that HHT method is effective to analysis non-linear and non-stationary data,and also there were some questions such as endpoint problems and modal mixing and so on.
2.Theory of modal parameter identification based on HHT transformation was studied. A new method of modal parameter identification was proposed in the paper, which was based on HHT method to peak-frequency bandpass signal.And needed analysing and computing programs were generated based on MATLAB. At first, power spectrum obtained from Fourier transformation lay out the distribution of modal frequency of the pulse excitation response signal. And then, bandpass response signal containing peak frequency was obtained by bandpass filter. Finally, modal parameters was identificated through HHT method based on the bandpass response signal.The result demonstrated that the method proposed in this article successfully soluted the modal mixing problem.And the endpoint effection on modal parameters identification was rejected in HHT by means of removing endpoints of analyzed signal.
3.Experiment modal analysis was studied on the reinforced concrete frame. Modal parameters of the structure,including natural frequency, damping ratio, and modal shape,was identifecated using the method provided in the paper based on palse excitation response signal,which can be gathered in experimental condition. identification results of natural frequency being identical with the calculated values,testify that method of the paper was reliable.
1.通过数值仿真算例,对HHT方法的信号处理特性进行了研究。采用HHT方法对谐波叠加信号、经典的线性调频(Chirp)信号、自由衰减信号等进行了计算和分析,指出HHT方法能有效处理非线性、非平稳数据,但模态混叠和端点效应问题还有待于进一步研究。
2.对基于HHT变换的结构模态参数识别理论进行了深入研究,提出了基于峰频带通信号HHT的结构模态参数识别方法,并在MATLAB平台上编制了相应的计算分析程序。首先利用傅里叶变换得到信号的自功率谱,以确定结构固有频率的大致分布区间;然后采用带通滤波器对信号进行滤波处理,得到包含各峰值频率在内的带通响应信号;最后对带通信号进行HHT以识别结构模态参数。研究表明,该方法有效的解决了EMD分解过程中的模态混叠问题。同时,本文采用去端点的办法,剔除了端点效应对结构模态参数识别的影响。
3.对一钢筋混凝土框架结构模型进行了试验模态分析。根据试验室条件下采集的脉冲激励响应信号,运用本文提出的基于峰频带通信号HHT的模态参数识别方法,识别了框架结构模型的固有频率、模态阻尼和振型等模态参数。固有频率与理论计算值吻合良好,验证了本文方法的有效性。
Modal Parameter identification of civil engineering struetures play an important role in research and application fields such as structural health monitoring, structural damage assessment. In recent years, extensive research and application has been done to develop the methods of time-frequency analysis based on vibration signal. Compared with traditional methods of signal analysis, HHT is a new technology for the analysis of signal. Being totally adaptive, and not subjcet to Heisenberg uncertainty principle, HHT has been proved to be ideal method for non-linear and non-stationary data. HHT has been widely used in many disciplines,including modal parameter identification,and produced good results. According to the consideration mentioned above,this thesis forcuses on the following aspcets of researeh:
1.Value simulation and computation example were taken to study the characteristic of HHT method.Classical signals such as superposed signal, linear frequency-modulation (Chirp) signal, freedom weaken signal was computed and analyzed,which has shown that HHT method is effective to analysis non-linear and non-stationary data,and also there were some questions such as endpoint problems and modal mixing and so on.
2.Theory of modal parameter identification based on HHT transformation was studied. A new method of modal parameter identification was proposed in the paper, which was based on HHT method to peak-frequency bandpass signal.And needed analysing and computing programs were generated based on MATLAB. At first, power spectrum obtained from Fourier transformation lay out the distribution of modal frequency of the pulse excitation response signal. And then, bandpass response signal containing peak frequency was obtained by bandpass filter. Finally, modal parameters was identificated through HHT method based on the bandpass response signal.The result demonstrated that the method proposed in this article successfully soluted the modal mixing problem.And the endpoint effection on modal parameters identification was rejected in HHT by means of removing endpoints of analyzed signal.
3.Experiment modal analysis was studied on the reinforced concrete frame. Modal parameters of the structure,including natural frequency, damping ratio, and modal shape,was identifecated using the method provided in the paper based on palse excitation response signal,which can be gathered in experimental condition. identification results of natural frequency being identical with the calculated values,testify that method of the paper was reliable.
引文
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[2]曹树谦,张文德,萧龙翔.振动结构模态分析理论、试验与应用.(第一版)天津:天津大学出版社.2001,104-139.
[3]禹丹江.土木工程结构模态参数识别理论、实现与应用[D].福州:福州大学,2006,1-60.
[4]海伦,斯帝芬拉门滋,萨斯著,白通化,郭继忠译.模态分析理论与试验[M].北京:北京理工大学出版社.2001,53-73.
[5]姚志远.大型工程结构模态识别的理论和方法研究[D].南京:东南学,2004,1-4.
[6]傅志方,华宏星.模态分析理论与应用[M].上海:上海交通大学出版社,2000.
[7]IBRAHIM,S.R.,Mikulcik E.C..A method for the direct identification of vibration parameters from the free responses,Shock and Vibration Bulletin.1997(4):183-198.
[8]IBRAHIM S.R..modal parameter identification from responses of general unknown random inputs.Proceedings of the 14th IMAC.1996,2204-2219.
[9]赵淑红.时频分析方法及其在地震数据处理中的应用[D].西安:长安大学,2006.
[10]于德介,程军圣,杨宁.机械故障诊断的Hilbert-Huang变换方法[M].北京:科学出版社,2006:14-22.
[11]Kim H,Melhem H.Damage detection of structures by wavelet analysis.Engineerin EngineeringStructures,2004,26:347-362
[12]于开平,邹经湘,史梓香.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
[13]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
[14]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
[15]N.E.Huang,Z.Shen.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis.Proc R soc Lond.A 1998(454):903-995.
[16]N.E.Huang,Zheng Shen,and Steven R.Long.A New View of Nonlinear Water Waves the Hilbert Spectrum.Annual Review Fluid Mechanics. 1999.31:417-457.
[17]杜寿昌,梁虹.基于Hilbert-Huang变换的第一心音信号时频分析[J].云南民族大学学报(自然科学版),2004,13(2):95-98.
[18]B.Liu,S.Riemenschneider,Y.Xu.Gearboxfault diagnosis using empirical mode decomposition and Hilbert spectrum.Mechanical Systems and Signal Processing 20(2006):718-734.
[19]Z.K.Peng,W.Peter.Tse and F.L.Chu.An improved Hilbert-Huang transform and its application in vibration signal analysis.Journal of Sound and Vibration 286(2005):187-205.
[20]Y.K.Wen and Ping Gu.Description and Simulation of Non-stationary Processes Based on Hilbert Spectra Journal of Engineering Mechanics,ASCE130(2004):942-951.
[21]Norden E.Huang,Man-Li Wu,Wendong Qu,Steven R.Long and Samuel S.P.Shen.Applications of Hilbert-Huang transform to non-stationary financial time series analysis Applied Stochastic Models Bus.Ind.,2003(19):245-268.
[22]J N.Yang,Y.Lei,S W.Pan,et al System identification of linear structures based on Hilbert-Huang spectral analysis.Partl:Normal modes.Earthquake Engineering and Structural Dynamics,2003,32:1443-1467.
[23]J.N.Yang,Y.Lei,S W.Pan,et al System identification of linear structures based on Hilbert-Huang spectral analysis.Part 2:Complex modes.Earthquake 77 Engineering and Structural Dynamics,2003,32:1533-1554.
[24]J.N.Yang,Y.Lei,S.Lin,and N.Huang.Hilbert-Huang based approach for structural damage detection Journal of Engineering Mechanics(ASCE).2004,130(1):85-95.
[25]H.T.Vincent,S.L.J.Hu,Z.Hou.Damage Detection Using Empirical Mode Decomposition Method and a Comparison with Wavelet Analysis.Signal Processing and Diagnostic Methods.1999:891-900.
[26]Chih-Chen Chang and Chun-Wing Poon Dynamic Characterization of a DamageBeam using Empirical Mode Decomposition and Hilbert Spectrum method Health Monitoring and Smart Nondestructive Evaluation of Structural and Biological SystemⅢ.2004,399-410.
[27]Liming W.Salvino.Empirical Mode Analysis of Structural Response and Damping,Conference on Structural Dynamic,2002(1):503-509.
[28]Chin-Hsiung Loh,Tsu-Chiu Wu,and Norden E.Huang.Application of the Empirical Node Decomposition-Hilbert Spectrum Method to Identify Near-Fault Ground-Notion Characteristics and Structural Responses.Bulletin of the Seismological Society of America,2001,91(5):1339-1357.
[29]Ray RuiChong Zhang.Applications of Non-stationary,Nonlinear Data Processing and Analysis in Earthquake Engineering,the Fourth International Conference on Nonlinear Mechanics,2002,Shanghai,721-727.
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