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.

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Fig. 2

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

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Fig. 3

Spring–mass–damper model vibration response

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Fig. 4

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

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Fig. 5

Time–frequency filter

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Fig. 6

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

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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

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Fig. 8

(a) SPWVD and (b) improved WVD

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Fig. 9

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

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Fig. 10

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

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Fig. 11

Eptesicus fuscus bat echolocation signal

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Fig. 12

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

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Fig. 13

Vibration response of a train wheel

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Fig. 14

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

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Fig. 15

Vibration response of a bridge

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Fig. 16

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



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