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Shock and Vibration
Volume 2016, Article ID 9792807, 9 pages
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.


Effective signal processing in fault detection and diagnosis (FDD) is an important measure to prevent failure and accidents of machinery. To address the end distortion and frequency aliasing issues in conventional lifting wavelet transform, a Volterra series assisted undecimated lifting wavelet packet transform (ULWPT) is investigated for machinery incipient fault diagnosis. Undecimated lifting wavelet packet transform is firstly formulated to eliminate the frequency aliasing issue in traditional lifting wavelet packet transform. Next, Volterra series, as a boundary treatment method, is used to preprocess the signal to suppress the end distortion in undecimated lifting wavelet packet transform. Finally, the decomposed wavelet coefficients are trimmed to the original length as the signal of interest for machinery incipient fault detection. Experimental study on a reciprocating compressor is performed to demonstrate the effectiveness of the presented method. The results show that the presented method outperforms the conventional approach by dramatically enhancing the weak defect feature extraction for reciprocating compressor valve fault diagnosis.