HHT方法在结构模态参数识别中的改进
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摘要
在Hilbert-Huang变换(HHT)的基础上,采用ChebyshevⅠ类带通滤波器对测量响应进行滤波,使得经EMD分解得到的固有模态函数(IMF)包含所有需要的模态,解决了模态混淆问题;采用去端点法预处理模态响应的相位和幅值,进行线性最小二乘法拟合,解决了端点效应问题;并推导了如何利用HHT识别比例阻尼结构体系的振型,获得了结构的各阶模态参数.分别通过4自由度数值试验和4自由度实验室框架结构试验说明了本文算法的有效性.
Based on the HHT(Hilbert-Huang Transform),the ChebyshevⅠtype filter was adopted to process the measured free vibration signal to solve the mode-mixing problem,so that all the structural modes could be acquired from IMFs.Meanwhile,removing endpoints were used during the linear least-square fit procedure to avoid the endpoint effect.Besides obtaining the modal frequencies and damping ratios,the formulation of mode shapes of proportional-damping structure was also derived.The simulation results of 4-NDOF numerical case and 4-NDOF frame structure in the laboratory have demonstrated that the proposed approach is accurate and effective.
Based on the HHT(Hilbert-Huang Transform),the ChebyshevⅠtype filter was adopted to process the measured free vibration signal to solve the mode-mixing problem,so that all the structural modes could be acquired from IMFs.Meanwhile,removing endpoints were used during the linear least-square fit procedure to avoid the endpoint effect.Besides obtaining the modal frequencies and damping ratios,the formulation of mode shapes of proportional-damping structure was also derived.The simulation results of 4-NDOF numerical case and 4-NDOF frame structure in the laboratory have demonstrated that the proposed approach is accurate and effective.
引文
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[9]张永利.HHT结合NExT法识别结构参数[J].工程抗震与加固,2009.31(5):8-13.ZHANG Yong-li.Identification of structural parameters based onHHT and NExT[J].Earthquake Resistant Engineering and Retrofit-ting,2009,31(5):8-13.(In Chinese)
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[11]汪家慰,刘正士,王慧.HHT法识别结构模态频率和阻尼比的改进[J].合肥工业大学学报:自然科学版,2010,33(5):647-651.WANG Jia-wei,LIU Zheng-shi,WANG Hui.Improvement onHHT method for identifying modal frequency and damping ratio ofstructure[J].Journal of Heifei University of Technology,2010,33(5):647-651.(In Chinese)
[12]陈文新.基于希尔伯特—黄变换的结构模态参数识别研究[D].湘潭:湖南科技大学,2009.CHEN Wen-xin.Study on modal parameters identification of struc-tures based on Hilbert-Huang transform[D]Xiangtan:Hunan Uni-versity of Science and Technology,2009.(In Chinese)
[13]杨宇,于德介,程军圣,等.经验模态分解(EMD)在滚动轴承故障诊断中的应用[J].湖南大学学报:自然科学版,2003,30(5):25-28.YANG Yu,YU De-jie,CHENG Jun-shen,et al.Application of em-prical mode decomposition(EMD)in roller bearing fault diagnosis[J].Journal of Hunan University:Natural Sciences,2003,30(5):25-28.(In Chinese)
[14]刘泉,阙大顺,郭志强.数字信号处理原理与实现[M].2版.北京:电子工业出版社.2009.LIU Quan,QUE Da-shun,GUO Zhi-qiang.Digital signal processingand realization[M].2nd ed.Beijing:Electrical Industry Press,2009.(In Chinese)
[2]汪璇,曹万强.Hilbert变换及其基本性质分析[J].湖北大学学报:自然科学版,2008,30(1):53-55.WANG Xuan,CAO Wan-qiang.The Hilbert transform and its char-acters[J].Journal of Hubei University:Natural Science,2008,30(1):53-55.(In Chinese)
[3]YANG J N,LEI Y.Identification of natural frequencies and dampingratios of linear structures via Hilbert transform and empirical modedecomposition[C]//Proceeding of the IASTED International Confer-ence on Intelligent System and Control,1999:310-335.
[4]YANG J N,LEI Ying,PAN S,et al.System identification of linearstructures based on Hilbert-Huang spectral analysis.Part 1:normalmodes[J].Earthquake Engineering&Structural Dynamics,2003,32(9):1443-1467.
[5]YANG J N,LEI Y,PAN S,et al.System identification of linearstructures based on Hilbert-Huang spectral analysis.Part 2:Com-plex modes[J].Earthquake Engineering and Structural Dynamics,2003,32(10):1533-1554.
[6]陈隽,徐幼麟.HHT方法在结构模态参数识别中的应用[J].振动工程学报,2003,16(3):383-388.CHEN Jun,XU You-lin.Application of HHT for modal parameteridentification to civil structures[J].Journal of Vibration Engineering,2003,16(03):383-388.(In Chinese)
[7]PENG Z K,TSE P W,CHU F L.An improved Hilbert-Huangtransform and its application in vibration signal analysis[J].Journalof Sound and Vibration,2005,286(1/2):187-205.
[8]韩建平,李文达,王飞行.基于Hilbert-Huang变换和随机子空间识别的模态参数识别[J].地震工程与工程振动,2010,30(1):53-59.HAN Jian-ping,LI Wen-da,WANG Fei-xing.Modal parameter i-dentification based on Hilbert-Huang transform and stochastic sub-space identification[J].Journal of Earthquake Engneering and Engi-neering Vibration,2010,30(1):53-59.(In Chinese)
[9]张永利.HHT结合NExT法识别结构参数[J].工程抗震与加固,2009.31(5):8-13.ZHANG Yong-li.Identification of structural parameters based onHHT and NExT[J].Earthquake Resistant Engineering and Retrofit-ting,2009,31(5):8-13.(In Chinese)
[10]YANG J N,LEI Y,LIN S,et al.Hilbert-Huang based approach forstructural damage detection[J].Journal of Engineering Mechanics,2004.130(1):85-95.
[11]汪家慰,刘正士,王慧.HHT法识别结构模态频率和阻尼比的改进[J].合肥工业大学学报:自然科学版,2010,33(5):647-651.WANG Jia-wei,LIU Zheng-shi,WANG Hui.Improvement onHHT method for identifying modal frequency and damping ratio ofstructure[J].Journal of Heifei University of Technology,2010,33(5):647-651.(In Chinese)
[12]陈文新.基于希尔伯特—黄变换的结构模态参数识别研究[D].湘潭:湖南科技大学,2009.CHEN Wen-xin.Study on modal parameters identification of struc-tures based on Hilbert-Huang transform[D]Xiangtan:Hunan Uni-versity of Science and Technology,2009.(In Chinese)
[13]杨宇,于德介,程军圣,等.经验模态分解(EMD)在滚动轴承故障诊断中的应用[J].湖南大学学报:自然科学版,2003,30(5):25-28.YANG Yu,YU De-jie,CHENG Jun-shen,et al.Application of em-prical mode decomposition(EMD)in roller bearing fault diagnosis[J].Journal of Hunan University:Natural Sciences,2003,30(5):25-28.(In Chinese)
[14]刘泉,阙大顺,郭志强.数字信号处理原理与实现[M].2版.北京:电子工业出版社.2009.LIU Quan,QUE Da-shun,GUO Zhi-qiang.Digital signal processingand realization[M].2nd ed.Beijing:Electrical Industry Press,2009.(In Chinese)
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