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Theoretical analysis of adaptive harmonic window and its application in frequency extraction of vibration signal

自适应谐波窗及其在振动信号频率提取中的应用

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Abstract

The goal of this paper is to find an excellent adaptive window function for extracting the weak vibration signal and high frequency vibration signal under strong noise. The relationship between windowing transform and filtering is analyzed first in the paper. The advantage of adjustable time-frequency window of wavelet transform is introduced. Secondly the relationship between harmonic wavelet and multiple analytic band-pass filter is analyzed. The coherence of the multiple analytic band-pass filter and harmonic wavelet base function is discussed, and the characteristic that multiple analytic band-pass filter included in the harmonic wavelet transform is founded. Thirdly, by extending the harmonic wavelet transform, the concept of the adaptive harmonic window and its theoretical equation without decomposition are put forward in this paper. Then comparing with the Hanning window, the good performance of restraining side-lobe leakage possessed by adaptive harmonic window is shown, and the adaptive characteristics of window width changing and analytical center moving of the adaptive harmonic window are presented. Finally, the proposed adaptive harmonic window is applied to weak signal extraction and high frequency orbit extraction of high speed rotor under strong noise, and the satisfactory results are achieved. The application results show that the adaptive harmonic window function can be successfully applied to the actual engineering signal processing.

摘要

本文研究的目标在于寻找一个自适应的优秀窗函数, 来提取强噪声下微弱振动信号和高频段的振动信号。 首先分析了加窗变换与滤波的关系, 介绍了小波变换具有可变时频窗的优势。 其次分析了谐波小波与复解析带通滤波器的关系, 指出了复解析带通滤波器与谐波小波基函数的一致性, 发现了谐波小波变换对复解析带通滤波器的包含性。 然后对谐波小波变换进行拓展, 提出了不需要进行分层分解的自适应谐波窗的概念与理论表达式。 通过与汉宁窗对比, 分析了自适应谐波窗极其优秀的抑制泄漏能力, 和时频窗分析中心自由移动和任意改变尺度的优秀特性。 最后将所提出的自适应谐波窗应用到高速转子的强噪声下微弱周期信号的频率提取, 和高频轴心轨迹的提取中, 取得了满意的效果。 该应用效果显示出自适应谐波窗函数能够成功应用于实际工程信号处理中。

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References

  1. HEYDT G, FJELD P, LIU C. Applications of the windowed FFT to electric power quality assessment [J]. IEEE Transactions on Power Delivery, 1999, 14(4): 1411–1416. DOI: 10.1109/61.796235.

    Article  Google Scholar 

  2. FREDRIC J. On the use of windows for harmonic analysis with the discrete Fourier transform [J]. Proceedings of the IEEE, 1978, 66: 51–83. DOI: 10.1109/PROC.1978.10837.

    Article  Google Scholar 

  3. NUTTALL A. Some windows with very good sidelobe behavior [J]. IEEE Transactions on Acoustics Speech & Signal Processing, 1989, 29(1): 84–91. DOI: 10.1109/TASSP.1981.1163506.

    Article  Google Scholar 

  4. HA Y, PEARCE J. A new window and comparison to standard windows [J]. IEEE Transactions on Acoustics Speech & Signal Processing, 1989, 37(2): 298–301. DOI: 10.1109/29.21693.

    Article  Google Scholar 

  5. ZOU Mu-yan, LIU Rei-rong. I1-csch window function and its application [J]. ACATA Electronica Sinica, 1985, 13: 85–92. http://www.springer.com/engineering/electronics/journal/11767.

    Google Scholar 

  6. ZHANG Jie-qiu, LIANG Hong-chang, CHEN Yan-pu. A new family of windows—convolution windows and their applications [J]. Scientia Sinica Techologica, 2005, 48(4): 461–481. DOI: 10.1360/03ye0531.

    MathSciNet  Google Scholar 

  7. WEN He, TENG Zhao-sheng, GUO Si-yu. Hanning self convolution window function and its application of harmonic analysis [J]. Scientia Sinica Techologica, 2009, 52(2): 467–476. DOI: 10.1007/s11431-008-0356-6.

    MATH  Google Scholar 

  8. STUART W, ANDREAS A. Design of ultraspherical window functions with prescribed spectral characteristics [J]. EURASIP Journal on Applied Signal Processing, 2004, 13: 2053–2065. DOI: 10.1155/S1110865704403114.

    Google Scholar 

  9. AVCI K, NACAROG L. A cosine hyperbolic window family with its application to FIR filter design [C]// International Conference on Information and Communication Technologies: From Theory to Applications IEEE. 2008: 1–6. DOI: 10.1109/ICTTA.2008.4530047.

    Google Scholar 

  10. AVCI K, NACAROG L. Modification of cosh window family [J]. International Journal of Electronics and Communications, 2009, 63: 907–916. DOI: 10.1109/ICTTA.2008.4530048.

    Article  Google Scholar 

  11. MOTTAGHI M, SHAYESTEH M. New efficient window function, replacement for the hamming window [J]. Signal Processing Iet, 2011, 5(5): 499–505. DOI: 10.1049/iet-spr.2010.0272.

    Article  Google Scholar 

  12. WEN He, TENG Zhao-sheng, GUO Si-yu. Triangular self-convolution window with desirable sidelobe behaviors for harmonic analysis of power system [J]. IEEE Transactions on Instrumentation and Measurement, 2010, 59(3): 543–552. DOI: 10.1109/TIM.2009.2024702.

    Article  Google Scholar 

  13. ROHIT P, KUMAR M, JAISWAL A, SAXENA R. Design technique of bandpass FIR filter using various window function [J]. IOSR Journal of Electronics and Communication Engineering (IOSR-JECE), 2014, 6(6): 52–57. DOI: 10.9790/2834-0665257.

    Google Scholar 

  14. XIAO Ying, FENG Chang-jian. A time-frequency representation method of STFT with combining window functions [J]. Journal of Detection& Control, 2010, 32: 43–47. DOI: 10.3969/j.issn.1008-1194.2010.03.011.

    Google Scholar 

  15. LI Shun-ming. On phase holding by dyadic wavelet double transform in vibration signal detects [J]. Chinese Journal of Scientific Instrument, 2005, 26: 370–373. DOI: 10.3321/j.issn:0254–3087.2005.04.010. (in Chinese)

    Google Scholar 

  16. D'HEEDENE S, AMARATUNGA K, CASTRillón-candás J. Generalized hierarchical bases: a wavelet-ritz-galerkin framework for Lagrangian FEM [J]. Engineering Computations: International Journal for Computer-Aided Engineering and Software, 2005, 22(1): 15–37. DOI: 10.1108/02644400510572398.

    Article  MATH  Google Scholar 

  17. WIESLAW J, STASZEWSKI D, MARK W. Wavelet-based frequency response function for time-variant systems—An exploratory study [J]. Mechanical Systems and Signal Processing, 2014, 47(1, 2): 35–49. DOI: 10.1016/j.ymssp.2013.03.011.

    Google Scholar 

  18. LI Shun-ming. Harmonic wavelet packet method and used on accurate obtaining the orbit of rotor sub-frequency signal [J]. Chinese Journal of Mechanical Engineering, 2004, 40: 133–137. DOI: 10.3901/JME.2004.09.133. (in Chinese)

    Google Scholar 

  19. ZHANG Xian-da, BAO Zheng. Non-stationary signal analysis and processing [M]. Beijing: National Defence Industry Press, 1998. http://www.ndip.cn/. (in Chinese)

    Google Scholar 

  20. NEWLAND D. Harmonic wavelet analysis [J]. Proceedings of the Royal Society A Mathematical Physical & Engineering Sciences, 1993, 443(443): 203–225.

    Article  MATH  Google Scholar 

  21. NEWLAND D. An introduction to random vibrations, spectral and wavelet analysis, 3rd Edition [M]. New York: Longman, Harlow and John Wiley, 1993: 359–370. http://www.logobook.kz/prod_show.php?object_uid=11168166.

    Google Scholar 

  22. DING Kang, XIE Ming, ZHANG Bi-de, ZHAO Ling. Multiple analytic band-pass filter and its application in demodulation analysis [J]. Journal of Vibration Engineering, 2000, 13: 385–392. DOI: 10.16385/j.cnki.issn.1004-4523.2000.03.009. (in Chinese)

    Google Scholar 

  23. ZHANG Pei-yao, MA Xiao-jiang, WANG Ji-jun, ZHU Hong. Wavelet packet signal extraction algorithm and its application in fault diagnosis [J]. Journal of Dalian University of Technology, 1997, 39: 67–72. http://en.cnki.com.cn/Article_en/CJFDTOTAL-DLLG701.016.htm,1997-01/. (in Chinese).

    MATH  Google Scholar 

  24. PENG Zhi-ke, HE Yan-zao, CHEN Zhi-yong, CHU Fu-lei. Identification of the shaft orbit for rotating machines using wavelet modulus maxima [J]. Mechanical Systems and Signal Processing, 2002, 16(4): 623–635. DOI: 10.1006/mssp.2002.1494.

    Article  Google Scholar 

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Authors and Affiliations

  1. College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Shun-ming Li  (李舜酩) & Jin-rui Wang  (王金瑞)

  2. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Xiang-lian Li  (李香莲)

Authors
  1. Shun-ming Li  (李舜酩)
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  2. Jin-rui Wang  (王金瑞)
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  3. Xiang-lian Li  (李香莲)
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Correspondence to Shun-ming Li  (李舜酩).

Additional information

Foundation item: Project(51675262) supported by the National Natural Science Foundation of China; Project(6140210020102) supported by the Advance Research Field Fund Project of China; Project(2016YFD0700800) supported by the National Key Research and Development Plan of China

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Li, Sm., Wang, Jr. & Li, Xl. Theoretical analysis of adaptive harmonic window and its application in frequency extraction of vibration signal. J. Cent. South Univ. 25, 241–250 (2018). https://doi.org/10.1007/s11771-018-3733-8

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  • DOI: https://doi.org/10.1007/s11771-018-3733-8

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