希尔伯特—黄变换（HHT）及其在结构动态性能分析中的应用研究
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摘要
本文围绕着新型信号处理方法Hilbert-Huang变换(HHT),对HHT变换理论及其在结构动态性能分析中的应用进行了较为全面系统的研究。
首先,文章介绍了HHT变换的基本理论,对经验模态分解(EMD)理论和Hilbert变换进行了详细的阐述。由于HHT变换理论自身没有建立严格的数学理论基础,在实际应用中存在多种问题。本文对其中的模态混淆现象、固有模态判据问题、包络拟合方法和端点效应问题等问题进行了相关研究,提出了相应的改进方法,通过数值仿真说明了改进方法是有效的。
其次,在对HHT变换理论详细研究的基础上,针对应用HHT变换理论识别结构的振动模态参数进行了主要研究。包括应用HHT变换从结构的动力响应中识别结构的模态频率、模态阻尼比、模态振型以及如何分离出密集模态等方面进行了研究,得出了一些有益的结论。
最后,通过对悬臂梁结构进行模态试验分析测得悬臂梁结构的动力响应数据,然后应用HHT变换识别出悬臂梁结构的结构振动模态参数,验证HHT方法识别模态参数的有效性。
The theory of Hilbert-Huang Transform and its application in the analysis of the structural dynamic performance are comprehensively and systematically studied in this article.
Firstly, the theory of the empirical mode decomposition and Hilbert transform are illustrated in detail. Because the strict mathematical theoretical basis hasn’t been developed in HHT, many of problems may be encountered in its practical application such as the intrinsic mode function stop criterion,end effects,mode confusion and envelope fitting method. Some studies of these problems are made, and some improvements are presented to heighten the performance of the EMD. Numerical simulations demonstrate the validity of these improvements.
Secondly, based on the HHT which is well-studied, the theory of HHT is applied to identify the vibration modal parameters such as modal frequency, modal damping ratio and modal shape from the dynamic response data of the structures. Some promising conclusions are achieved.
Finally, modal testing is carried out to cantilever beam to collect structural dynamic corresponding data, then applying HHT to identify the modal parameters of the cantilever beam. The results show the effectiveness and validity of the HHT method
首先,文章介绍了HHT变换的基本理论,对经验模态分解(EMD)理论和Hilbert变换进行了详细的阐述。由于HHT变换理论自身没有建立严格的数学理论基础,在实际应用中存在多种问题。本文对其中的模态混淆现象、固有模态判据问题、包络拟合方法和端点效应问题等问题进行了相关研究,提出了相应的改进方法,通过数值仿真说明了改进方法是有效的。
其次,在对HHT变换理论详细研究的基础上,针对应用HHT变换理论识别结构的振动模态参数进行了主要研究。包括应用HHT变换从结构的动力响应中识别结构的模态频率、模态阻尼比、模态振型以及如何分离出密集模态等方面进行了研究,得出了一些有益的结论。
最后,通过对悬臂梁结构进行模态试验分析测得悬臂梁结构的动力响应数据,然后应用HHT变换识别出悬臂梁结构的结构振动模态参数,验证HHT方法识别模态参数的有效性。
The theory of Hilbert-Huang Transform and its application in the analysis of the structural dynamic performance are comprehensively and systematically studied in this article.
Firstly, the theory of the empirical mode decomposition and Hilbert transform are illustrated in detail. Because the strict mathematical theoretical basis hasn’t been developed in HHT, many of problems may be encountered in its practical application such as the intrinsic mode function stop criterion,end effects,mode confusion and envelope fitting method. Some studies of these problems are made, and some improvements are presented to heighten the performance of the EMD. Numerical simulations demonstrate the validity of these improvements.
Secondly, based on the HHT which is well-studied, the theory of HHT is applied to identify the vibration modal parameters such as modal frequency, modal damping ratio and modal shape from the dynamic response data of the structures. Some promising conclusions are achieved.
Finally, modal testing is carried out to cantilever beam to collect structural dynamic corresponding data, then applying HHT to identify the modal parameters of the cantilever beam. The results show the effectiveness and validity of the HHT method
引文
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[13]段全生,贺振华,黄得济. HHT方法及其在地震信号处理中的应用[J].成都理工大学学报(自然科学版),2005,32(4):396-400.
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[18]胡劲松,杨世锡.基于HHT的转子横向裂纹故障诊断[J].动力工程,2004,24(2):218-221.
[19]Z. Chen,S. X. Zheng,Y. M. Sun. Gearbox vibration recognition using empirical mode decomposition method[J]. Journal of south China university of technology(Natural Science Edition),2002,30(9):61-64.
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[21]王敏学,黄方林,陈政清,Hilbert-Huang变换在桥梁振动分析中的应用[J].铁道学报,2005,27(2):80-84.
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[24]P. Flandrin,G. Rilling,P. Goncalves. Empirical mode decomposition as a filter bank[J]. IEEE Signal Processing Letters,2004,11(2):112-114.
[25]韩春明,郭华东,王长林等.基于EMD方法的多尺度边缘提取[J].高技术通讯,2003,6:13-17.
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[30]钱勇,黄成军,陈陈等.基于经验模态分解的局部放电去噪方法[J].电力系统自动化,2005,29(12):53-56.
[31]谭善文,秦树人,汤宝平. Hilbert-Huang变换的滤波特性及其应用[J].重庆大学学报,2004,27(2):9-12.
[32]王世一.数字信号处理(修订版)[M].北京:北京理工大学出版社,2006.
[33]马耀庭,邵毅全.傅里叶变换在应用中的局限性及克服方法[J].内江师范学院学报. 2008,23(12):42-43.
[34]吴剑,代冀阳,孙秀霞.非平稳振动信号的角度域重采样小波解调分析方法[J].振动与冲击. 2009, 28(5):137-138
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[38]S. Q. Rice. Mathematical analysis of random noiseⅢ: statistical properties of random noise currents[J]. Bell Sys. Tech.,1945,24: 46-108.
[39]S. Q. Rice. Mathematical analysis of random noiseⅣ: noise through nonlinear devices[J]. Bell Sys. Tech.,1945,24:109-156
[40]N. E. Huang,Z. Shen,S. R. Long,et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and no-stationary time series analysis[J]. Proc. R. Soc. Lond. A, 1998, 454:903-995.
[41]N. E. Huang,Z. Shen,S. R. Long,et al. A new view of nonlinear water waves: the Hilbert Spectrum [J]. Annual Review of Fluid Mechanics, 1999, 31:417-457.
[42]胡广书.数字信号处理[M],北京:清华大学出版社,2003.
[43]刘俊斐.基于希尔伯特-黄(HHT)的海洋平台结构模态参数识别方法的研究[D],中国海洋大学硕士论文,2007.
[44]钟佑明,金涛,秦树人.希尔伯特-黄变换中的一种新包络线算法[J].数据采集与处理,2005,20(1):13-17.
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[46]盖强,马孝江,张海勇等.一种消除局域波法中边界效应的新方法[J].大连理工大学学报,2002,42(1):115-117.
[47]陈忠,郑时雄. EMD信号分析方法边缘效应的分析[J].数据采集与处理,2003, 13(10):1054-1059.
[48]张郁山,梁建文,胡聿贤.应用自回归模型处理EMD方法中的边界问题[J].自然科学进展,2003,13(10):1054-1059.
[49]傅志方.振动模态分析与参数辨识[M].北京:机械工业出版社,1990.
[50]W. P. Huang,J. T. Jang,H. J. Li. Measurement of excessive vibration of a jacket platform[J]. Proceedings of International Symposium on Safety Science and Technology, ISSST, Tai’an China, 2002, 3:502-506.
[51]J. N. Yang,Y. Lei. Identification of natural frequencies and damping ratios of linear structures via Hilbert transform and empirical mode decomposition[J]. Proceedings of International Conference on Intelligent Systems and Control, IASTED/Acta press, Anaheim, CA, 1999:310-315.
[52]J. N. Yang,Y. Lei. Identification of tall building using noisy wind vibration data[J]. Proceedings of International Conference on Advances in Structural Dynamics, Hong Kong,2000:1093-1100.
[53]段希波,张计光,颜勇.基于Hilbert-Huang变换的多自由度参数辨识[J].上海大学学报(自然科学版),2006,12(4):403-407.
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[2]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.
[3]石春香. HHT变换及其在结构分析中的应用[M].同济大学博士论文,2004.
[4]李黎明.有限元使用教程[M].北京:清华大学出版社,2005.
[5]管迪华.模态分析技术[M].北京:清华大学出版社,1996.
[6]刘宁,王太勇,赵坚.系统模态参数辨识的小波方法[J].天津大学学报. 2006,39(7):788-792.
[7]邓拥军,王伟,钱成春等. EMD方法及Hilbert变换中边界问题的处理[J].科学通报,2001,46(3):257-263.
[8]宋立新,王祁,王玉静等.具有间断事件检测和分离的经验模态分解方法[J].哈尔滨工程大学学报,2007,28:179-182.
[9] R. Deering,J. F. Kaiser. The use of a masking signal to improve empirical mode decomposition[J]. Acoustics, Speech, and Signal Processing, 2005, Proceedings, (ICASSP’05), IEEE International Conference, 18-23 March 2005, Vol.4:485- 488.
[10]G. Rilling,P. Flandrin,P. Goncalves. On empirical mode decomposition ant its algorithm[J]. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03, Grado(I), June, 2003.
[11]黄大吉,赵进平.希尔伯特-黄变换的端点延拓[J].海洋学报,2003,25(1):1-11.
[12]公茂盛,谢礼立. HHT方法在地震工程中的应用之初步探讨[J].世界地震工程,2003,19(3):257-263.
[13]段全生,贺振华,黄得济. HHT方法及其在地震信号处理中的应用[J].成都理工大学学报(自然科学版),2005,32(4):396-400.
[14]W. Huang,Z. Shen,N. E. Huang,et al. Engineering analysis of biological variables: an example of blood pressure over 1 day[J]. Proceeding of National Academic Science of United States of America,1998,95:4816-4821.
[15]H. Liang,Z. Lin,R. W. McCallum. Artifact reduction in electrogastrogram based on empirical mode decomposition method[J]. Medical & Biological Engineering & Computing,2000,38:35-41.
[16]P. L. Liu. Is the wind wave frequency spectrum outdated[J]. Ocean engineering,2000,27:557-588.
[17]熊学军,郭炳火,胡筱敏等. EMD方法和Hilbert谱分析的应用与探讨[J].黄渤海海洋,2002,20(2):12-21.
[18]胡劲松,杨世锡.基于HHT的转子横向裂纹故障诊断[J].动力工程,2004,24(2):218-221.
[19]Z. Chen,S. X. Zheng,Y. M. Sun. Gearbox vibration recognition using empirical mode decomposition method[J]. Journal of south China university of technology(Natural Science Edition),2002,30(9):61-64.
[20]X. M. Wang,F. L. Huang,J. J. Liu. Application of EMD to modal parameter identification of a bridge[J]. In: Proceedings of the 9th International Conference on Inspection,Appraisal,Repairs & Maintenance of Structures. Fuzhou,2005,443-448.
[21]王敏学,黄方林,陈政清,Hilbert-Huang变换在桥梁振动分析中的应用[J].铁道学报,2005,27(2):80-84.
[22]L. Xie,K. J. Wu,L. J. Pietrafesa. Empirical modes of land falling tropical cyclones in North Carolina[J]. In: 24th conference on Hurricanes and Tropical Meteorology. Fort Lauderdale,2000,P1:68
[23]T. Schlurmann,S. Schimmels,T. Dose. Spectral frequency analysis of freak waves using wavelet analysis (Morlet) and empirical mode decomposition[J]. In: Proceedings of the 4th International Conference on Hydroscience & Engineering. Seoul,2000,26-29.
[24]P. Flandrin,G. Rilling,P. Goncalves. Empirical mode decomposition as a filter bank[J]. IEEE Signal Processing Letters,2004,11(2):112-114.
[25]韩春明,郭华东,王长林等.基于EMD方法的多尺度边缘提取[J].高技术通讯,2003,6:13-17.
[26]J. N. Yang,Y. Lei,Z. Hou. Damage detection using empirical mode decomposition method and a comparison with wavelet analysis[J]. In: Proceedings of the 3rd International Workshop on Structural Health Monitoring. Stanford,2001,544-553.
[27]于德介,程军圣. EMD方法在齿轮故障诊断中的应用[J].湖南大学学报(自然科学版),2002,29(6):48-51.
[28]P. Chen,J. Zhang. The study of a new method for forecasting non-stationary series[J]. High Technology letters,2002,8(2):47-50.
[29]N. E. Huang. HHT: a review of the methods and many applications for nonsteady and nonlinear data analysis[J]. Laboratory for Hydroscience Processes,NASA Goddard Flight Center,Greenbelt,MD20071.
[30]钱勇,黄成军,陈陈等.基于经验模态分解的局部放电去噪方法[J].电力系统自动化,2005,29(12):53-56.
[31]谭善文,秦树人,汤宝平. Hilbert-Huang变换的滤波特性及其应用[J].重庆大学学报,2004,27(2):9-12.
[32]王世一.数字信号处理(修订版)[M].北京:北京理工大学出版社,2006.
[33]马耀庭,邵毅全.傅里叶变换在应用中的局限性及克服方法[J].内江师范学院学报. 2008,23(12):42-43.
[34]吴剑,代冀阳,孙秀霞.非平稳振动信号的角度域重采样小波解调分析方法[J].振动与冲击. 2009, 28(5):137-138
[35]N. E. Huang,Z. Shen,S. R. Long,et al. the empirical mode decomposition and the Hilbert spectrum for nonlinear and no-stationary time series analysis[J]. Proc. R. Soc. Lond. A, 1998, 454:903-995.
[36]于德介,程军圣,杨宇.机械故障诊断的Hilbert-Huang变换方法[M].北京:科学出版社,2006.
[37]P. G. Drazin. Nonlinear systems[M]. Cambridge,UK: Cambridge University Press,1992 .
[38]S. Q. Rice. Mathematical analysis of random noiseⅢ: statistical properties of random noise currents[J]. Bell Sys. Tech.,1945,24: 46-108.
[39]S. Q. Rice. Mathematical analysis of random noiseⅣ: noise through nonlinear devices[J]. Bell Sys. Tech.,1945,24:109-156
[40]N. E. Huang,Z. Shen,S. R. Long,et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and no-stationary time series analysis[J]. Proc. R. Soc. Lond. A, 1998, 454:903-995.
[41]N. E. Huang,Z. Shen,S. R. Long,et al. A new view of nonlinear water waves: the Hilbert Spectrum [J]. Annual Review of Fluid Mechanics, 1999, 31:417-457.
[42]胡广书.数字信号处理[M],北京:清华大学出版社,2003.
[43]刘俊斐.基于希尔伯特-黄(HHT)的海洋平台结构模态参数识别方法的研究[D],中国海洋大学硕士论文,2007.
[44]钟佑明,金涛,秦树人.希尔伯特-黄变换中的一种新包络线算法[J].数据采集与处理,2005,20(1):13-17.
[45]秦树人,季忠,尹爱军.工程信号处理[M],北京:高等教育出版社,2008.
[46]盖强,马孝江,张海勇等.一种消除局域波法中边界效应的新方法[J].大连理工大学学报,2002,42(1):115-117.
[47]陈忠,郑时雄. EMD信号分析方法边缘效应的分析[J].数据采集与处理,2003, 13(10):1054-1059.
[48]张郁山,梁建文,胡聿贤.应用自回归模型处理EMD方法中的边界问题[J].自然科学进展,2003,13(10):1054-1059.
[49]傅志方.振动模态分析与参数辨识[M].北京:机械工业出版社,1990.
[50]W. P. Huang,J. T. Jang,H. J. Li. Measurement of excessive vibration of a jacket platform[J]. Proceedings of International Symposium on Safety Science and Technology, ISSST, Tai’an China, 2002, 3:502-506.
[51]J. N. Yang,Y. Lei. Identification of natural frequencies and damping ratios of linear structures via Hilbert transform and empirical mode decomposition[J]. Proceedings of International Conference on Intelligent Systems and Control, IASTED/Acta press, Anaheim, CA, 1999:310-315.
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