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TECHNICAL PAPERS

Mechanical Fault Detection Based on the Wavelet De-Noising Technique

[+] Author and Article Information
Jing Lin

National Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing, China e-mail: jinglin@mail.ioa.ac.cn

Ming J. Zuo, Ken R. Fyfe

Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada, T6G 2G8

J. Vib. Acoust 126(1), 9-16 (Feb 26, 2004) (8 pages) doi:10.1115/1.1596552 History: Received May 01, 2002; Revised March 01, 2003; Online February 26, 2004
Copyright © 2004 by ASME
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References

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Donoho,  D. L., and Johnstone,  I. M., 1994, “Ideal Spatial Adaptation by Wavelet Shrinkage,” Biometrika, 81(3), pp. 425–455.
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Bruce, A. G., Donoho, D. L. et al., 1994, “Smoothing and Robust Wavelet Analysis,” COMPSTAT, Proceedings in Computational Statistics, 11th Symposium, pp. 531–547.
Johnstone,  I. M., and Silverman,  B. W., 1997, “Wavelet Threshold Estimators for Data With Correlated Noise,” Journal of Royal Statistical Society Series B, 59(2), pp. 319–351.
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Pan,  Q., Zhang,  L., Dai,  G., and Zhang,  H., 1999, “Two Denoising Methods by Wavelet Transform,” IEEE Trans. Signal Process., 47(12), pp. 3401–3406.
Sardy,  S., Tseng,  P., , 2001, “Robust Wavelet Denoising,” IEEE Trans. Signal Process., 49(6), pp. 1146–1152.
Lin,  J., and Qu,  L., 2000, “Feature Extraction Based on Morlet Wavelet and Its Application for Mechanical Fault Diagnosis,” J. Sound Vib., 234(1), pp. 135–148.
Fan,  J. Q., Hall,  P., Martin,  M. A., and Patil,  P., 1996, “On Local Smoothing of Nonparametric Curve Estimators,” J. Am. Stat. Assoc., 91, pp. 258–266.
Nason, G. P., 1995, “Choice of the Threshold Parameter in Wavelet Function Estimation,” Antoniadis, A., and Oppenheim, G., eds., Wavelets and Statistics, Vol. 103 of Lecture Notes in Statistics, pp. 261–280, Springer-Verlag, New York.
Donoho,  D. L., and Johnstone,  I. M., 1995, “Adapting to Unknown Smoothness via Wavelet Shrinkage,” J. Am. Stat. Assoc., 90, pp. 1200–1224.
Neumann, M. H., and von Sachs, R., 1995, “Wavelet Thresholding: Beyond the Gaussian i.i.d. Situation,” Wavelets and Statistics, Vol. 103 of Lecture Notes in Statistics, pp. 281–300, Springer-Verlag.
Berkner, K., and Wells, R. O., Jr., 1998, “A Correlation-dependent Model for De-noising via Nonorhogonal Wavelet Transforms,” Technical Report CML TR98-07, Computational Mathematics Laboratory, Rice University, US.
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Figures

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Comparison between the pdf of the simulated impulses and the pdf of Gaussian noise with the same mean and standard deviation
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Comparison between the pdf of an impulse and the sparse distributions
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Comparisons among the sparse distributions with different α values
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Illustrations for hard-thresholding, soft-thresholding and MLE thresholding
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An impulse with very heavy Gaussian noise
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(a) Hard-thresholding using the Minimax threshold (b) Soft-thresholding using the Minimax threshold
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Result by MLE thresholding using the Morlet wavelet
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Signals from a gearbox with broken teeth
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Signals from the gearbox in normal state
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Signals from the gearbox with fatigue crack on teeth
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Spectrum (low frequency area) of the signal in Fig. 11
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MLE thresholding based on the Morlet wavelet for the signals from normal gearbox
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MLE thresholding based on Morlet wavelet for the signals from gearbox with cracks on a gear
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(a) Optimal minimax thresholding using hard-threshold (b) Optimal minimax thresholding using soft-threshold
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(a) Signal from a normal roller bearing (b) Signal from a roller bearing with the inner-race damaged
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(a) Spectrum of the signal in Figure 16(a) (b) Spectrum of the signal in Figure 16(b)
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(a) The de-noising result for the signals from the normal roller bearing (b) The de-noising result for the signals from the roller bearing with the inner-race damaged
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(a) Optimal minimax thresholding using hard-threshold (b) Optimal minimax thresholding using soft-threshold

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