Research Papers

Nonstationary Vibration Signal Analysis Using Wavelet-Based Time–Frequency Filter and Wigner–Ville Distribution

[+] Author and Article Information
Chang Xu

Department of Aerospace
Engineering and Mechanics,
Harbin Institute of Technology,
No. 92 West Dazhi Street,
P.O. Box 137,
Harbin 150001, China
e-mail: xuchangcc@gmail.com

Cong Wang

Department of Aerospace
Engineering and Mechanics,
Harbin Institute of Technology,
No. 92 West Dazhi Street,
P.O. Box 137,
Harbin 150001, China
e-mail: alanwang@hit.edu.cn

Wei Liu

State Key Laboratory of Traction Power,
Southwest Jiaotong University,
Chengdu, Sichuan 610031, China
e-mail: Wei.Liu@rice.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 15, 2016; final manuscript received May 10, 2016; published online June 2, 2016. Assoc. Editor: Nicole Kessissoglou.

J. Vib. Acoust 138(5), 051009 (Jun 02, 2016) (9 pages) Paper No: VIB-16-1029; doi: 10.1115/1.4033641 History: Received January 15, 2016; Revised May 10, 2016

Vibration responses of nonlinear or time-varying dynamical systems are always nonstationary. Time–frequency representation becomes a necessary approach to analysis such signals. In this paper, a nonstationary vibration analysis method based on continuous wavelet transform (CWT) and Wigner–Ville distribution (WVD) is presented. In order to avoid the cross-terms in the original WVD, a time–frequency filter created by wavelet spectrum is employed to filter the time–frequency distribution (TFD). This process eliminates cross-terms and maintains high time–frequency resolution. The improved WVD is applied to both simulated and practical time-varying systems. Bat echolocation signal, train wheel vibration, and bridge vibration under a moving train are used to assess the proposed method. Comparison results show that the improved WVD is free of cross-terms, effective in identifying time-varying frequencies and is more accurate than the wavelet time–frequency spectrum.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Ghaffari, A. , Jafar, R. , and Morteza, T. , 2007, “ Time-Varying Transfer Function Extraction of an Unstable Launch Vehicle Via Closed-Loop Identification,” Aerosp. Sci. Technol., 11(2), pp. 238–244. [CrossRef]
Mourelatos, Z. P. , Majcher, M. , and Geroulas, V. , 2016, “ Time-Dependent Reliability Analysis of Vibratory Systems With Random Parameters,” ASME J. Vib. Acoust., 138(3), p. 031007. [CrossRef]
Mitu, A. M. , Sireteanu, T. , Giuclea, M. , and Solomon, O. , 2016, “ Simulation of Wide-Sense Stationary Random Time-Series With Specified Spectral Densities,” ASME J. Vib. Acoust., 138(3), p. 031011. [CrossRef]
Qian, S. , and Chen, D. , 1999, “ Joint Time-Frequency Analysis,” IEEE Signal Process. Mag., 16(2), pp. 52–67. [CrossRef]
Ta, M.-N. , and Lardiès, J. , 2006, “ Identification of Weak Nonlinearities on Damping and Stiffness by the Continuous Wavelet Transform,” J. Sound Vib., 293(1), pp. 16–37. [CrossRef]
Le, T.-P. , and Paultre, P. , 2012, “ Modal Identification Based on Continuous Wavelet Transform and Ambient Excitation Tests,” J. Sound Vib., 331(9), pp. 2023–2037. [CrossRef]
Ruzzene, M. , Fasana, A. , Garibaldi, L. , and Piombo, B. , 1997, “ Natural Frequencies and Dampings Identification Using Wavelet Transform: Application to Real Data,” Mech. Syst. Signal Process., 11(2), pp. 207–218. [CrossRef]
Le, T.-P. , and Argoul, P. , 2004, “ Continuous Wavelet Transform for Modal Identification Using Free Decay Response,” J. Sound Vib., 277(1), pp. 73–100. [CrossRef]
Ghanem, R. , and Romeo, F. , 2000, “ A Wavelet-Based Approach for the Identification of Linear Time-Varying Dynamical Systems,” J. Sound Vib., 234(4), pp. 555–576. [CrossRef]
Xu, X. , Shi, Z. , and You, Q. , 2012, “ Identification of Linear Time-Varying Systems Using a Wavelet-Based State-Space Method,” Mech. Syst. Signal Process., 26, pp. 91–103. [CrossRef]
Peng, Z. K. , and Chu, F. L. , 2004, “ Application of the Wavelet Transform in Machine Condition Monitoring and Fault Diagnostics: A Review With Bibliography,” Mech. Syst. Signal Process., 18(2), pp. 199–221. [CrossRef]
Staszewski, W. J. , and Wallace, D. M. , 2014, “ Wavelet-Based Frequency Response Function for Time-Variant Systems—An Exploratory Study,” Mech. Syst. Signal Process., 47(1), pp. 35–49. [CrossRef]
Feng, Z. , Liang, M. , and Chu, F. , 2013, “ Recent Advances in Time–Frequency Analysis Methods for Machinery Fault Diagnosis: A Review With Application Examples,” Mech. Syst. Signal Process., 38(1), pp. 165–205. [CrossRef]
Tang, B. , Liu, W. , and Song, T. , 2010, “ Wind Turbine Fault Diagnosis Based on Morlet Wavelet Transformation and Wigner-Ville Distribution,” Renewable Energy, 35(12), pp. 2862–2866. [CrossRef]
Zhang, H. X. , Li, J. , Lin, Q. , Qu, J. Z. , and Yang, Q. Z. , 2013, “ Contrast of Time-Frequency Analysis Methods and Fusion of Wigner-Ville Distribution and Wavelet Transform,” Adv. Mater. Res., 805, pp. 1962–1965. [CrossRef]
Shin, Y. S. , and Jeon, J. J. , 1993, “ Pseudo Wigner–Ville Time-Frequency Distribution and Its Application to Machinery Condition Monitoring,” Shock Vib., 1(1), pp. 65–76. [CrossRef]
Lerga, J. , and Sucic, V. , 2009, “ Nonlinear IF Estimation Based on the Pseudo WVD Adapted Using the Improved Sliding Pairwise ICI Rule,” IEEE Signal Process. Lett., 16(11), pp. 953–956. [CrossRef]
Ping, D. , Liu, X. , and Deng, B. , 2009, “ Cross-Term Suppression in the Wigner-Ville Distribution Using Beamforming,” Beamforming IEEE Conference on Industrial Electronics and Applications (ICIEA), Xi'an, China, May 25–27, pp. 1103–1105.
Cai, Y. P. , Li, A. H. , Li, R. B. , Li, X. L. , and Bai, X. F. , 2011, “ WVD Cross-Term Suppressing Method Based on Empirical Mode Decomposition,” Comput. Eng., 37(7), pp. 271–273.
Mann, S. , and Haykin, S. , 1992, “ Adaptive Chirplet Transform: An Adaptive Generalization of the Wavelet Transform,” Opt. Eng., 31(6), pp. 1243–1256. [CrossRef]
Spanos, P. , Giaralis, A. , and Politis, N. , 2007, “ Time–Frequency Representation of Earthquake Accelerograms and Inelastic Structural Response Records Using the Adaptive Chirplet Decomposition and Empirical Mode Decomposition,” Soil Dyn. Earthquake Eng., 27(7), pp. 675–689. [CrossRef]
Luo, J. , Yu, D. , and Liang, M. , 2012, “ Gear Fault Detection Under Time-Varying Rotating Speed Via Joint Application of Multiscale Chirplet Path Pursuit and Multiscale Morphology Analysis,” Struct. Health Monit., 11(5), pp. 526–537. [CrossRef]
Luo, J. , Yu, D. , and Liang, M. , 2012, “ Application of Multi-Scale Chirplet Path Pursuit and Fractional Fourier Transform for Gear Fault Detection in Speed Up and Speed-Down Processes,” J. Sound Vib., 331(22), pp. 4971–4986. [CrossRef]
Chen, G. , Chen, J. , and Dong, G. , 2013, “ Chirplet Wigner–Ville Distribution for Time–Frequency Representation and Its Application,” Mech. Syst. Signal Process., 41(1), pp. 1–13.
Wang, M. , Chan, A. L. , and Chui, C. K. , 1996, “ Wigner-Ville Distribution Decomposition Via Wavelet Packet Transform,” IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (TFSA), Paris, France, June 18–21, pp. 413–416.
Cohen, I. , Raz, S. , and Malah, D. , 1999, “ Adaptive Suppression of Wigner Interference-Terms Using Shift-Invariant Wavelet Packet Decompositions,” Signal Process., 73(3), pp. 203–223. [CrossRef]
Hlawatsch, F. , and Kozek, W. , 1994, “ Time-Frequency Projection Filters and Time-Frequency Signal Expansions,” IEEE Trans. Signal Process., 42(12), pp. 3321–3334. [CrossRef]
Feng, Z. , and Chu, F. , 2007, “ Nonstationary Vibration Signal Analysis of a Hydroturbine Based on Adaptive Chirplet Decomposition,” Struct. Health Monit., 6(4), pp. 265–279. [CrossRef]
Baraniuk, R. , 2009, Bat Echolocation Chirp, DSP Group, Rice University, Houston, TX.
Wang, S. , Chen, X. , Wang, Y. , Cai, G. , Ding, B. , and Zhang, X. , 2015, “ Nonlinear Squeezing Time–Frequency Transform for Weak Signal Detection,” Signal Process., 113, pp. 195–210. [CrossRef]
Chen, G. , Chen, J. , Dong, G. , and Jiang, H. , 2015, “ An Adaptive Non-Parametric Short-Time Fourier Transform: Application to Echolocation,” Appl. Acoust., 87, pp. 131–141. [CrossRef]
Liu, W. , Ma, W. , Luo, S. , Zhu, S. , and Wei, C. , 2015, “ Research Into the Problem of Wheel Tread Spalling Caused by Wheelset Longitudinal Vibration,” Veh. Syst. Dyn., 53(4), pp. 546–567. [CrossRef]
Liu, W. , Zhong, L. , Luo, S. , and He, X. , 2016, “ Research Into the Problem of Polygonal Wheel Wear on the Metro Train,” Proc. Inst. Mech. Eng., Part F, 230(1), pp. 43–55. [CrossRef]


Grahic Jump Location
Fig. 2

Spring–mass–damper model of a two degrees-of-freedom system

Grahic Jump Location
Fig. 3

Spring–mass–damper model vibration response

Grahic Jump Location
Fig. 4

Response of the spring–mass–damper model: (a) FT, (b) CWT, (c) WVD, and (d) improved WVD

Grahic Jump Location
Fig. 5

Time–frequency filter

Grahic Jump Location
Fig. 6

Improved WVD of signal with different noise levels: (a) SNR = ∞, (b) SNR = 20, (c) SNR = 10, and (d) SNR = 5

Grahic Jump Location
Fig. 7

Improved WVD of signal with SNR = 5: (a) CWT, (b) WVD, (c) improved WVD using mean value threshold, and (d) improved WVD using alternative value threshold

Grahic Jump Location
Fig. 8

(a) SPWVD and (b) improved WVD

Grahic Jump Location
Fig. 9

Instantaneous frequencies identification results (coarse line: SPWVD and smooth line: improved WVD)

Grahic Jump Location
Fig. 10

NLFM vibration signal: (a) FT, (b) CWT, (c)WVD, and (d) improved WVD

Grahic Jump Location
Fig. 11

Eptesicus fuscus bat echolocation signal

Grahic Jump Location
Fig. 12

Echolocation signal: (a) FT, (b) CWT, (c) WVD, and (d) improved WVD

Grahic Jump Location
Fig. 13

Vibration response of a train wheel

Grahic Jump Location
Fig. 14

Wheel vibration: (a) FT, (b) CWT, (c) WVD, and (d) improved WVD

Grahic Jump Location
Fig. 15

Vibration response of a bridge

Grahic Jump Location
Fig. 16

Bridge vibration: (a) FT, (b) CWT, (c) WVD, and (d) improved WVD




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In