Research Papers

Periodic Impulsive Fault Feature Extraction of Rotating Machinery Using Dual-Tree Rational Dilation Complex Wavelet Transform

[+] Author and Article Information
ChunLin Zhang

State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: zhangclfly@stu.xjtu.edu.cn

Bing Li

State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: bli@mail.xjtu.edu.cn

BinQiang Chen

School of Physics and Mechanical &
Electrical Engineering,
Xiamen University,
Xiamen 361005, China
e-mail: cbq@xmu.edu.cn

HongRui Cao

State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: chr@mail.xjtu.edu.cn

YanYang Zi

State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: ziyy@mail.xjtu.edu.cn

ZhengJia He

State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: hzj@mail.xjtu.edu.cn

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received October 9, 2013; final manuscript received June 1, 2014; published online August 6, 2014. Assoc. Editor: Robert Gao.

J. Manuf. Sci. Eng 136(5), 051011 (Aug 06, 2014) (16 pages) Paper No: MANU-13-1366; doi: 10.1115/1.4027839 History: Received October 09, 2013; Revised June 01, 2014

Fault diagnosis of rotating machinery is very important to guarantee the safety of manufacturing. Periodic impulsive fault features commonly appear in vibration measurements when local defects occur in the key components like rolling bearings and gearboxes. To extract the periodic impulses embedded in strong background noise, wavelet transform (WT) is suitable and has been widely used in analyzing these nonstationary signals. However, a few limitations like shift-variance and fixed frequency partition manner of the dyadic WT would weaken its effectiveness in engineering application. Compared with dyadic WT, the dual-tree rational dilation complex wavelet transform (DT-RADWT) enjoys attractive properties of better shift-invariance, flexible time-frequency (TF) partition manner, and tunable oscillatory nature of the bases. In this article, an impulsive fault features extraction technique based on the DT-RADWT is proposed. In the routine of the proposed method, the optimal DT-RADWT basis is constructed dynamically and adaptively based on the input signal. Additionally, the sensitive wavelet subband is chosen using kurtosis maximization principle to reveal the potential weak fault features. The proposed method is applied on engineering applications for defects detection of the rolling bearing and gearbox. The results show that the proposed method performs better in extracting the fault features than dyadic WT and empirical mode decomposition (EMD), especially when the incipient fault features are embedded in the frequency transition bands of the dyadic WT.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Rao, B. K. N., Pai, P. S., and Nagabhushana, T. N., 2012, “Failure Diagnosis and Prognosis of Rolling-Element Bearings Using Artificial Neural Networks: A Critical Overview,” J. Phys.: Conf. Ser., 364, p. 012023. [CrossRef]
Aherwar, A., 2012, “An Investigation on Gearbox Fault Detection Using Vibration Analysis Techniques: A Review,” Aust. J. Mech. Eng., 10(2), pp. 169–184. [CrossRef]
Randall, R. B., 2011, Vibration-Based Condition Monitoring: Industrial, Aerospace and Automotive Applications, John Wiley & Sons, West Sussex, UK. [CrossRef]
Zheng, G. T., and Wang, W. J., 2001, “A New Cepstral Analysis Procedure of Recovering Excitations for Transient Components of Vibration Signals and Applications to Rotating Machinery Condition Monitoring,” ASME J. Vib. Acoust., 123(2), pp. 222–229. [CrossRef]
He, Z., Chen, J., and Wang, T., 2010, Theories and Applications of Machinery Fault Diagnosis, Higher Education Press, Beijing, People's Republic of China.
Gao, R. X., and Yan, R. Q., 2011, Wavelets: Theory and Applications for Manufacturing, Springer, New York.
Bracewell, R. N., and Bracewell, R., 1978, The Fourier Transform and its Applications, McGraw-Hill, New York.
Satish, L., 1998, “Short-Time Fourier and Wavelet Transforms for Fault Detection in Power Transformers During Impulse Tests,” IEE Proc.-Sci. Meas. Technol., 145(2), pp. 77–84. [CrossRef]
He, Q. B., Li, P., and Kong, F. R., 2012, “Rolling Bearing Localized Defect Evaluation by Multiscale Signature via Empirical Mode Decomposition,” ASME J. Vib. Acoust., 134(6), p. 061013. [CrossRef]
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C., and Liu, H. H., 1998, “The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis,” Proc. R. Soc. London A, 454(1971), pp. 903–995. [CrossRef]
Yuan, J., He, Z., Ni, J., Brzezinski, A. J., and Zi, Y., 2013, “Ensemble Noise-Reconstructed Empirical Mode Decomposition for Mechanical Fault Detection,” ASME J. Vib. Acoust., 135(2), p. 021011. [CrossRef]
Yan, R. Q., and Gao, R. X., 2008, “Rotary Machine Health Diagnosis Based on Empirical Mode Decomposition,” ASME J. Vib. Acoust., 130(2), p. 021007. [CrossRef]
Xiang, L., and Hu, A., 2012, “New Feature Extraction Method for the Detection of Defects in Rolling Element Bearings,” ASME J. Eng. Gas Turbines Power, 134(8), p. 084501. [CrossRef]
Wang, Y. X., He, Z. J., and Zi, Y. Y., 2010, “A comparative Study on the Local Mean Decomposition and Empirical Mode Decomposition and Their Applications to Rotating Machinery Health Diagnosis,” ASME J. Vib. Acoust., 132(2), p. 021010. [CrossRef]
Flandrin, P., Rilling, G., and Goncalves, P., 2004, “Empirical Mode Decomposition as a Filter Bank,” IEEE Signal Process. Lett., 11(2), pp. 112–114. [CrossRef]
Yuan, J., 2011, “Inner Production Principle of Mechanical Fault Diagnosis and Feature Extraction Based on Multiwavelet Transform,” Xi'an Jiaotong University, Xi'an, P. R. China.
Daubechies, I., 1992, Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, PA.
Holm-Hansen, B. T., Gao, R. X., and Zhang, L., 2004, “Customized Wavelet for Bearing Defect Detection,” ASME J. Dyn. Meas. Control, 126(4), pp. 740–745. [CrossRef]
Yan, R., and Gao, R. X., 2011, “Impact of Wavelet Basis on Vibration Analysis for Rolling Bearing Defect Diagnosis,” IEEE Instrumentation and Measurement Technology Conference (I2MTC), Binjiang, P. R. China, May 10–12, pp. 1–4. [CrossRef]
Yan, R. Q., Gao, R. X., and Chen, X. F., 2014, “Wavelets for Fault Diagnosis of Rotary Machines: A Review With Applications,” Signal Process., 96, pp. 1–15. [CrossRef]
Al-Raheem, K. F., Roy, A., Ramachandran, K. P., Harrison, D. K., and Grainger, S., 2008, “Application of the Laplace-Wavelet Combined With ANN for Rolling Bearing Fault Diagnosis,” ASME J. Vib. Acoust., 130(5), p. 051007. [CrossRef]
Wang, W. J., and Mcfadden, P. D., 1996, “Application of Wavelets to Gearbox Vibration Signals for Fault Detection,” J. Sound Vib., 192(5), pp. 927–939. [CrossRef]
Jena, D. P., Panigrahi, S. N., and Kumar, R., 2012, “Gear Fault Identification and Localization Using Analytic Wavelet Transform of Vibration Signal,” Measurement, 46(3), pp. 1115–1124. [CrossRef]
Sweldens, W., 1996, “The Lifting Scheme: A Custom-Design Construction of Biorthogonal Wavelets,” Appl. Comput. Harmonic Anal., 3(2), pp. 186–200. [CrossRef]
Jiang, H. K., He, A. J., Duan, C. D., and Cheng, P., 2006, “Gearbox Fault Diagnosis Using Adaptive Redundant Lifting Scheme,” Mech. Syst. Signal Process., 20(8), pp. 1992–2006. [CrossRef]
He, Z. J., Cao, H. R., Li, Z., Zi, Y. Y., and Chen, X. F., 2009, “The Principle of Second Generation Wavelet for Milling Cutter Breakage Detection,” Sci. China Ser. E, 52(5), pp. 1312–1322. [CrossRef]
Gao, L., Yang, Z., Cai, L., Wang, H., and Chen, P., 2010, “Roller Bearing Fault Diagnosis Based on Nonlinear Redundant Lifting Wavelet Packet Analysis,” Sensors, 11(1), pp. 260–277. [CrossRef]
Tafreshi, R., Sassani, F., Ahmadi, H., and Dumont, G., 2009, “An Approach for the Construction of Entropy Measure and Energy Map in Machine Fault Diagnosis,” ASME J. Vib. Acoust., 131(2), p. 024501. [CrossRef]
Lei, Y., He, Z., and Zi, Y., 2009, “A Combination of WKNN to Fault Diagnosis of Rolling Element Bearings,” ASME J. Vib. Acoust., 131(6), p. 064502. [CrossRef]
Peng, Z. K., Jackson, M. R., Rongong, J. A., Chu, F. L., and Parkin, R. M., 2009, “On the Energy Leakage of Discrete Wavelet Transform,” Mech. Syst. Signal Process., 23(2), pp. 330–343. [CrossRef]
Antoni, J., and Randall, R. B., 2006, “The Spectral Kurtosis: Application to the Vibratory Surveillance and Diagnostics of Rotating Machines,” Mech. Syst. Signal Process., 20(2), pp. 308–331. [CrossRef]
Liu, H., Huang, W., Wang, S., and Zhu, Z., 2014, “Adaptive Spectral Kurtosis Filtering Based on Morlet Wavelet and its Application for Signal Transients Detection,” Signal Process., 96, pp. 118–124. [CrossRef]
Antoni, J., 2007, “Fast Computation of the Kurtogram for the Detection of Transient Faults,” Mech. Syst. Signal Process., 21(1), pp. 108–124. [CrossRef]
Bayram, I., and Selesnick, I. W., 2011, “A Dual-Tree Rational-Dilation Complex Wavelet Transform,” IEEE Trans. Signal Process., 59(12), pp. 6251–6256. [CrossRef]
Mallat, S., 2008, A Wavelet Tour of Signal Processing: The Sparse Way, Academic Press, New York.
Szu, H., Sheng, Y., and Chen, J., 1992, “Wavelet Transform as a Bank of the Matched Filters,” Appl. Opt., 31(17), pp. 3267–3277. [CrossRef]
Wickerhauser, M. V., 1991, “Lectures on Wavelet Packet Algorithms,” Lecture Notes, INRIA.
Hilton, M. L., 1997, “Wavelet and Wavelet Packet Compression of Electrocardiograms,” IEEE Trans. Biomed. Eng., 44(5), pp. 394–402. [CrossRef]
Kingsbury, N. G., 1998, “The Dual-Tree Complex Wavelet Transform: A New Technique for Shift Invariance and Directional Filters,” 8th IEEE DSP Workshop, Bryce Canyon, Utah, Vol. 8.
Selesnick, I. W., Baraniuk, R. G., and Kingsbury, N. C., 2005, “The Dual-Tree Complex Wavelet Transform,” IEEE Signal Process. Mag., 22(6), pp. 123–151. [CrossRef]
Wang, Y., He, Z., and Zi, Y., 2010, “Enhancement of Signal Denoising and Multiple Fault Signatures Detecting in Rotating Machinery Using Dual-Tree Complex Wavelet Transform,” Mech. Syst. Signal Process., 24(1), pp. 119–137. [CrossRef]
Kingsbury, N., 2001, “Complex Wavelets for Shift Invariant Analysis and Filtering of Signals,” Appl. Comput. Harmonic Anal., 10(3), pp. 234–253. [CrossRef]
Chen, B., Zhang, Z., Sun, C., Li, B., Zi, Y., and He, Z., 2012, “Fault Feature Extraction of Gearbox by Using Overcomplete Rational Dilation Discrete Wavelet Transform on Signals Measured From Vibration Sensors,” Mech. Syst. Signal Process., 33, pp. 275–298. [CrossRef]
Yu, R., 2009, “A New Shift-Invariance of Discrete-Time Systems and Its Application to Discrete Wavelet Transform Analysis,” IEEE Trans. Signal Process., 57(7), pp. 2527–2537. [CrossRef]
He, W., Zi, Y., Chen, B., Wang, S., and He, Z., 2013, “Tunable Q-Factor Wavelet Transform Denoising With Neighboring Coefficients and Its Application to Rotating Machinery Fault Diagnosis,” Sci. China Tech. Sci., 56(8), pp. 1956–1965. [CrossRef]
Bayram, I., and Selesnick, I. W., 2009, “Frequency-Domain Design of Overcomplete Rational-Dilation Wavelet Transforms,” IEEE Trans. Signal Process., 57(8), pp. 2957–2972. [CrossRef]
Blu, T., 1993, “Iterated Filter Banks With Rational Rate Changes Connection With Discrete Wavelet Transforms,” IEEE Trans. Signal Process., 41(12), pp. 3232–3244. [CrossRef]
Niu, L. K., Cao, H. R., He, Z. J., and Li, Y. M., 2014, “Dynamic Modeling and Vibration Response Simulation for High Speed Rolling Ball Bearings,” ASME J. Manuf. Sci. Eng., 136(4), p. 041015. [CrossRef]


Grahic Jump Location
Fig. 1

Iterated FB implementation and frequency decomposition of dyadic DWT: (a) Two-level Mallat's pyramid algorithm of DWT; (b) frequency partition manner of dyadic DWT; and (c) frequency partition manner of WPT

Grahic Jump Location
Fig. 2

Iterated FBs for implementation of DTCWT

Grahic Jump Location
Fig. 3

TF atoms of dyadic WTs and their frequency response: (a) a typical wavelet basis of DTCWT; (b) frequency decomposition of DTCWT; (c) wavelet basis (Db 6 basis); and (d) frequency response of DWT (Db 6 basis)

Grahic Jump Location
Fig. 5

The analysis and synthesis FBs of DT-RADWT

Grahic Jump Location
Fig. 6

The first FB H(w) and G(w)

Grahic Jump Location
Fig. 7

Equivalent FB to the first FB and its properties: (a) an equivalent FB to the first FB and (b) properties of H1(w) and G1(w)

Grahic Jump Location
Fig. 11

The flow chart of the proposed method

Grahic Jump Location
Fig. 12

The test setup in case 1

Grahic Jump Location
Fig. 13

The vibration signal of the tested rolling bearing

Grahic Jump Location
Fig. 14

The log-amplitude FFT spectrum of the signal

Grahic Jump Location
Fig. 15

The characteristic kurtosis values of the candidate DT-RADWT bases: (a) q = p + 1; (b) q = p + 2; (c) q = p + 3; and (d) q = p + 4

Grahic Jump Location
Fig. 16

Waveforms of the two selected optimal DT-RADWT bases: (a) B6,7,4 and (b) B9,10,3

Grahic Jump Location
Fig. 17

The sensitive subband selection of the two optimal DT-RADWT bases: (a) B6,7,4 and (b) B9,10,3

Grahic Jump Location
Fig. 18

Reconstructed sensitive subband signals and their envelope spectra: (a) the D7 subband signal of the basis B6,7,4; (b) the D5 subband signal of the basis B9,10,3; (c) the envelope spectrum of the subband signal in (a); and (d) the envelope spectrum of the subband signal in (b)

Grahic Jump Location
Fig. 19

Local surface spalling fault on the outer race of the tested bearing: (a) a view of the disassembled axle box and (b) the defect on the outer race

Grahic Jump Location
Fig. 20

The IMFs using EMD

Grahic Jump Location
Fig. 21

Wavelet subband signals by using dyadic WTs: (a) DWT (Db 6 basis) and (b) SGWT

Grahic Jump Location
Fig. 22

The results by using SK: (a) the Kurtogram and (b) the purified signal

Grahic Jump Location
Fig. 23

The schematic sketch of the F3 finishing mill stand

Grahic Jump Location
Fig. 24

The vibration signal of the reduction gearbox

Grahic Jump Location
Fig. 25

The log-amplitude FFT spectrum of the vibration signal

Grahic Jump Location
Fig. 26

The characteristic kurtosis values of the candidate DT-RADWT bases: (a) s = 1; (b) s = 2; (c) s = 3; (d) s = 4; (e) s = 5; and (f) s = 6

Grahic Jump Location
Fig. 27

Waveform of the optimal basis B3,4,2

Grahic Jump Location
Fig. 28

Kurtosis values of subbands of B3,4,2

Grahic Jump Location
Fig. 29

The reconstructed D4 wavelet subband signal

Grahic Jump Location
Fig. 30

Wavelet subbands signals by using dyadic WTs: (a) DWT (Db 6 basis) and (b) SGWT

Grahic Jump Location
Fig. 31

The decomposition IMFs using EMD of Fig. 24

Grahic Jump Location
Fig. 32

Results by using SK of Fig. 24: (a) the Kurtogram and (b) the purified signal

Grahic Jump Location
Fig. 33

Local defects on the pinion gear in the reduction gearbox: (a) location of I1 and (b) location of I2




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