Table of Contents Author Guidelines Submit a Manuscript
Shock and Vibration
Volume 2016 (2016), Article ID 9792807, 9 pages
http://dx.doi.org/10.1155/2016/9792807
Research Article

Undecimated Lifting Wavelet Packet Transform with Boundary Treatment for Machinery Incipient Fault Diagnosis

1School of Mechanical and Transportation Engineering, China University of Petroleum, Beijing 102249, China
2School of Material Science and Engineering, Xian University of Architecture and Technology, Xi’an 710055, China

Received 26 May 2015; Revised 22 July 2015; Accepted 25 August 2015

Academic Editor: José V. Araújo dos Santos

Copyright © 2016 Lixiang Duan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. V. Venkatasubramanian, R. Rengaswamy, K. Yin, and S. N. Kavuri, “A review of process fault detection and diagnosis: part I: quantitative model-based methods,” Computers and Chemical Engineering, vol. 27, no. 3, pp. 293–311, 2003. View at Publisher · View at Google Scholar · View at Scopus
  2. M. Liang and I. S. Bozchalooi, “An energy operator approach to joint application of amplitude and frequency-demodulations for bearing fault detection,” Mechanical Systems and Signal Processing, vol. 24, no. 5, pp. 1473–1494, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. Z. Zhong, Z. Jiang, Y. Long, and X. Zhan, “Analysis on the noise for the different gearboxes of the heavy truck,” Shock and Vibration, vol. 2015, Article ID 476460, 5 pages, 2015. View at Publisher · View at Google Scholar
  4. W. J. Wang, “Wavelet transform in vibration analysis for mechanical fault diagnosis,” Shock and Vibration, vol. 3, no. 1, pp. 17–26, 1996. View at Publisher · View at Google Scholar · View at Scopus
  5. Y. Lei, J. Lin, Z. He, and M. J. Zuo, “A review on empirical mode decomposition in fault diagnosis of rotating machinery,” Mechanical Systems and Signal Processing, vol. 35, no. 1-2, pp. 108–126, 2013. View at Publisher · View at Google Scholar · View at Scopus
  6. N. Baydar and A. Ball, “A comparative study of acoustic and vibration signals in detection of gear failures using Wigner-Ville distribution,” Mechanical Systems and Signal Processing, vol. 15, no. 6, pp. 1091–1107, 2001. View at Publisher · View at Google Scholar · View at Scopus
  7. W.-X. Yang and P. W. Tse, “Development of an advanced noise reduction method for vibration analysis based on singular value decomposition,” NDT & E International, vol. 36, no. 6, pp. 419–432, 2003. View at Publisher · View at Google Scholar · View at Scopus
  8. H. Hassanpour, A. Zehtabian, and S. J. Sadati, “Time domain signal enhancement based on an optimized singular vector denoising algorithm,” Digital Signal Processing, vol. 22, no. 5, pp. 786–794, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. J. Wang, R. X. Gao, and R. Yan, “Integration of EEMD and ICA for wind turbine gearbox diagnosis,” Wind Energy, vol. 17, no. 5, pp. 757–773, 2014. View at Publisher · View at Google Scholar · View at Scopus
  10. A. Sadhu and B. Hazra, “A novel damage detection algorithm using time-series analysis-based blind source separation,” Shock and Vibration, vol. 20, no. 3, pp. 423–438, 2013. View at Publisher · View at Google Scholar
  11. Z. K. Peng and F. L. Chu, “Application of the wavelet transform in machine condition monitoring and fault diagnostics: a review with bibliography,” Mechanical Systems and Signal Processing, vol. 18, no. 2, pp. 199–221, 2004. View at Publisher · View at Google Scholar · View at Scopus
  12. R. Yan, R. X. Gao, and X. Chen, “Wavelets for fault diagnosis of rotary machines: a review with applications,” Signal Processing, vol. 96, pp. 1–15, 2014. View at Publisher · View at Google Scholar · View at Scopus
  13. N. Saravanan and K. I. Ramachandran, “Incipient gear box fault diagnosis using discrete wavelet transform (DWT) for feature extraction and classification using artificial neural network (ANN),” Expert Systems with Applications, vol. 37, no. 6, pp. 4168–4181, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. H. Qiu, J. Lee, J. Lin, and G. Yu, “Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics,” Journal of Sound and Vibration, vol. 289, no. 4-5, pp. 1066–1090, 2006. View at Publisher · View at Google Scholar · View at Scopus
  15. J. Wang, R. X. Gao, and R. Yan, “Multi-scale enveloping order spectrogram for rotating machine health diagnosis,” Mechanical Systems and Signal Processing, vol. 46, no. 1, pp. 28–44, 2014. View at Publisher · View at Google Scholar · View at Scopus
  16. Y.-L. Chen, P.-L. Zhang, B. Li, and D.-H. Wu, “Denoising of mechanical vibration signals using quantum-inspired adaptive wavelet shrinkage,” Shock and Vibration, vol. 2014, Article ID 848097, 7 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. Pan, J. Chen, and X. Li, “Bearing performance degradation assessment based on lifting wavelet packet decomposition and fuzzy c-means,” Mechanical Systems and Signal Processing, vol. 24, no. 2, pp. 559–566, 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. R. Zhou, W. Bao, N. Li, X. Huang, and D. Yu, “Mechanical equipment fault diagnosis based on redundant second generation wavelet packet transform,” Digital Signal Processing: A Review Journal, vol. 20, no. 1, pp. 276–288, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. J. Yuan, Z. He, and Y. Zi, “Gear fault detection using customized multiwavelet lifting schemes,” Mechanical Systems and Signal Processing, vol. 24, no. 5, pp. 1509–1528, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. Y. He, X. Chen, J. Xiang, and Z. He, “Adaptive multiresolution finite element method based on second generation wavelets,” Finite Elements in Analysis and Design, vol. 43, no. 6-7, pp. 566–579, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. W. Bao, R. Zhou, J. Yang, D. Yu, and N. Li, “Anti-aliasing lifting scheme for mechanical vibration fault feature extraction,” Mechanical Systems and Signal Processing, vol. 23, no. 5, pp. 1458–1473, 2009. View at Publisher · View at Google Scholar · View at Scopus
  22. R. L. Claypoole, G. M. Davis, W. Sweldens, and R. G. Baraniuk, “Nonlinear wavelet transforms for image coding via lifting,” IEEE Transactions on Image Processing, vol. 12, no. 12, pp. 1449–1459, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. R. L. Claypoole, R. G. Baraniuk, and R. D. Nowak, “Adaptive wavelet transforms via lifting,” Report ECE TR-9304, 1999, https://scholarship.rice.edu/handle/1911/19808. View at Google Scholar
  24. B. Appleton and H. Talbot, “Recursive filtering of images with symmetric extension,” Signal Processing, vol. 85, no. 8, pp. 1546–1556, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  25. B. Wohlberg and C. M. Brislawn, “Symmetric extension for lifted filter banks and obstructions to reversible implementation,” Signal Processing, vol. 88, no. 1, pp. 131–145, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. L. Duan, L. Zhang, and J. Chen, “Boundary treatment of lifting wavelet transform based on Volterra series model and its application,” Chinese Journal of Scientific Instrument, vol. 33, no. 1, pp. 7–12, 2012. View at Google Scholar · View at Scopus
  27. D. Aiordachioaie, E. Ceanga, R. de Keyser, and Y. Naka, “Detection and classification of non-linearities based on Volterra kernels processing,” Engineering Applications of Artificial Intelligence, vol. 14, no. 4, pp. 497–503, 2001. View at Publisher · View at Google Scholar · View at Scopus
  28. W. Sweldens, “The lifting scheme: a custom-design construction of biorthogonal wavelets,” Applied and Computational Harmonic Analysis, vol. 3, no. 2, pp. 186–200, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. W. Sweldens, “The Lifting Scheme: a construction of second generation wavelets,” SIAM Journal on Mathematical Analysis, vol. 29, no. 2, pp. 511–546, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. A. Ben and T. Hugues, “Recursive filtering of images with symmetric extension,” Signal Processing, vol. 85, no. 8, pp. 1546–1556, 2005. View at Publisher · View at Google Scholar · View at Scopus
  31. D. Aiordachioaie, E. Ceanga, R. De Keyser, and Y. Naka, “Detection and classification of non-linearities based on Volterra kernels processing,” Engineering Applications of Artificial Intelligence, vol. 14, no. 4, pp. 497–503, 2001. View at Publisher · View at Google Scholar
  32. M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Physical Review A, vol. 45, no. 6, pp. 3403–3411, 1992. View at Publisher · View at Google Scholar · View at Scopus
  33. J. Zhang and X. Xiao, “Predicting low-dimensional chaotic time series using Volterra adaptive filters,” Acta Physica Sinica, vol. 49, no. 3, pp. 403–408, 1999. View at Google Scholar
  34. J. Hongkai, H. Zhengjia, D. Chendong, and C. Peng, “Gearbox fault diagnosis using adaptive redundant Lifting Scheme,” Mechanical Systems and Signal Processing, vol. 20, no. 8, pp. 1992–2006, 2006. View at Publisher · View at Google Scholar · View at Scopus