Skip to main content
SpringerLink
Log in

Fault feature extraction of rolling element bearings based on wavelet packet transform and sparse representation theory

  • Published:
Journal of Intelligent Manufacturing Aims and scope Submit manuscript

Abstract

Extracting reliable features from vibration signals is a key problem in machinery fault recognition. This study proposes a novel sparse wavelet reconstruction residual (SWRR) feature for rolling element bearing diagnosis based on wavelet packet transform (WPT) and sparse representation theory. WPT has obtained huge success in machine fault diagnosis, which demonstrates its potential for extracting discriminative features. Sparse representation is an increasingly popular algorithm in signal processing and can find concise, high-level representations of signals that well matches the structure of analyzed data by using a learned dictionary. If sparse coding is conducted with a discriminative dictionary for different type signals, the pattern laying in each class will drive the generation of a unique residual. Inspired by this, sparse representation is introduced to help the feature extraction from WPT-based results in a novel manner: (1) learn a dictionary for each fault-related WPT subband; (2) solve the coefficients of each subband for different classes using the learned dictionaries and (3) calculate the reconstruction residual to form the SWRR feature. The effectiveness and advantages of the SWRR feature are confirmed by the practical fault pattern recognition of two bearing cases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  • Aharon, M., Elad, M., & Bruckstein, A. (2006). K-svd: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing, 54(11), 4311–4322.

    Article  Google Scholar 

  • Bahmani, S., Raj, B., & Boufounos, P. T. (2013). Greedy sparsity-constrained optimization. Journal of Machine Learning Research, 14, 807–841.

    Google Scholar 

  • Baillie, D. C., & Mathew, J. (1996). A comparison of autoregressive modeling techniques for fault diagnosis of rolling element bearings. Mechanical Systems and Signal Processing, 10(1), 1–17.

    Article  Google Scholar 

  • Baydar, N., & Ball, A. (2001). A comparative study of acoustic and vibration signals in detection of gear failures using Wigner–Ville distribution. Mechanical System and Signal Processing, 15(6), 1091–1107.

    Article  Google Scholar 

  • Beygi, S., Kafashan, M., Bahrami, H. R., & Mugler, D. H. (2012). The iterative shrinkage method for impulsive noise reduction from images. Measurement Science & Technology, 23(11), 114009.

    Article  Google Scholar 

  • Bilski, P. (2014). Data set preprocessing methods for the artificial intelligence-based diagnostic module. Measurement, 54, 180–190.

    Article  Google Scholar 

  • Blumensath, T., & Davies, M. E. (2007). Monte Carlo methods for adaptive sparse approximations of time-series. IEEE Transactions on Signal Processing, 55(9), 4474–4486.

    Article  Google Scholar 

  • Bokoski, P., & Juricic, D. (2012). Fault detection of mechanical drives under variable operating conditions based on wavelet packet renyi entropy signatures. Mechanical Systems and Signal Processing, 31, 369–381.

    Article  Google Scholar 

  • Bruckstein, A. M., Donoho, D. L., & Elad, M. (2009). From sparse solutions of systems of equations to sparse modeling of signals and images. Siam Review, 51(1), 34–81.

    Article  Google Scholar 

  • Cai, D., He, X. F. & Han, J. W. (2007). Spectral regression for efficient regularized subspace learning. In 2007 IEEE 11th international conference on computer vision (vol. 1–6, pp. 214–221).

  • Chen, S. S. B., Donoho, D. L., & Saunders, M. A. (1998). Atomic decomposition by basis pursuit. Siam Journal on Scientific Computing, 20(1), 33–61.

    Article  Google Scholar 

  • Coifman, R. R., & Wickerhauser, M. V. (1992). Entropy-based algorithms for best basis selection. IEEE Transactions on Information Theory, 38(2), 713–718.

    Article  Google Scholar 

  • Cui, J., & Wang, Y. R. (2011). A novel approach of analog circuit fault diagnosis using support vector machines classifier. Measurement, 44(1), 281–289.

    Article  Google Scholar 

  • Davis, G., Mallat, S., & Avellaneda, M. (1997). Adaptive greedy approximations. Constructive Approximation, 13(1), 57–98.

    Article  Google Scholar 

  • Dong, S. J., Tang, B. P., & Chen, R. X. (2013). Bearing running state recognition based on non-extensive wavelet feature scale entropy and support vector machine. Measurement, 46(10), 4189–4199.

    Article  Google Scholar 

  • Donoho, D. L., & Huo, X. M. (2001). Uncertainty principles and ideal atomic decomposition. IEEE Transactions on Information Theory, 47(7), 2845–2862.

    Article  Google Scholar 

  • Engan, K., Aase, S. O. & Husoy, J. H. (1999). Frame based signal compression using method of optimal directions (mod). In Iscas ’99: proceedings of the 1999 IEEE international symposium on circuits and systems (vol. 4, pp. 1–4).

  • Feng, Z. P., & Chu, F. L. (2007). Application of atomic decomposition to gear damage detection. Journal of Sound and Vibration, 302(1–2), 138–151.

    Article  Google Scholar 

  • Gao, R. X., & Yan, R. (2006). Non-stationary signal processing for bearing health monitoring. International Journal of Manufacturing Research, 1(1), 18–40.

    Article  Google Scholar 

  • Gharavian, M. H., Ganj, F. A., Ohadi, A. R., & Bafroui, H. H. (2013). Comparison of fda-based and pca-based features in fault diagnosis of automobile gearboxes. Neurocomputing, 121, 150–159.

    Article  Google Scholar 

  • He, Q. B. (2013). Vibration signal classification by wavelet packet energy flow manifold learning. Journal of Sound and Vibration, 332(7), 1881–1894.

    Article  Google Scholar 

  • Klein, R., Ingman, D., & Braun, S. (2001). Non-stationary signals: Phase-energy approach theory and simulations. Mechanical System and Signal Processing, 15(6), 1061–1089.

    Article  Google Scholar 

  • Lei, Y. G., He, Z. J., & Zi, Y. Y. (2008). A new approach to intelligent fault diagnosis of rotating machinery. Expert Systems with Applications, 35(4), 1593–1600.

    Article  Google Scholar 

  • Lewicki, M. S., & Sejnowski, T. J. (2000). Learning overcomplete representations. Neural Computation, 12(2), 337–365.

    Article  Google Scholar 

  • Li, B., Zhang, P. L., Liu, D. S., Mi, S. S., Ren, G. Q., & Tian, H. (2011). Feature extraction for rolling element bearing fault diagnosis utilizing generalized s transform and two-dimensional non-negative matrix factorization. Journal of Sound and Vibration, 330(10), 2388–2399.

    Article  Google Scholar 

  • Li, F. C., Meng, G., Ye, L., & Chen, P. (2008). Wavelet transform-based higher-order statistics for fault diagnosis in rolling element bearings. Journal of Vibration and Control, 14(11), 1691–1709.

    Article  Google Scholar 

  • Li, R. Y., Sopon, P., & He, D. (2012). Fault features extraction for bearing prognostics. Journal of Intelligent Manufacturing, 23(2), 313–321.

    Article  Google Scholar 

  • Liu, B., Ling, S. F., & Gribonval, R. (2002). Bearing failure detection using matching pursuit. Ndt & E International, 35(4), 255–262.

    Article  Google Scholar 

  • Mallat, S. G. (1989). A theory for multiresolution signal decomposition—The wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7), 674–693.

    Article  Google Scholar 

  • Marjanovic, G., & Solo, V. (2012). On l(q) optimization and matrix completion. IEEE Transactions on Signal Processing, 60(11), 5714–5724.

    Article  Google Scholar 

  • Mortada, M. A., Yacout, S., & Lakis, A. (2014). Fault diagnosis in power transformers using multi-class logical analysis of data. Journal of Intelligent Manufacturing, 25(6), 1429–1439.

    Article  Google Scholar 

  • Ocak, H., Loparo, K. A., & Discenzo, F. M. (2007). Online tracking of bearing wear using wavelet packet decomposition and probabilistic modeling: A method for bearing prognostics. Journal of Sound and Vibration, 302(4–5), 951–961.

    Article  Google Scholar 

  • Plumbley, M. D., Abdallah, S. A., Blumensath, T., & Davies, M. E. (2006). Sparse representations of polyphonic music. Signal Processing, 86(3), 417–431.

    Article  Google Scholar 

  • Polo, A. P. L., Coral, R. H. R., Sepulveda, J. A. Q., & Velez, A. L. R. (2009). Sparse signal recovery using orthogonal matching pursuit (omp). Ingenieria E Investigacion, 29(2), 112–118.

    Google Scholar 

  • Rubinstein, R., Bruckstein, A. M., & Elad, M. (2010). Dictionaries for sparse representation modeling. Proceedings of the IEEE, 98(6), 1045–1057.

    Article  Google Scholar 

  • Tropp, J. A. (2004). Greed is good: Algorithmic results for sparse approximation. IEEE Transactions on Information Theory, 50(10), 2231–2242.

    Article  Google Scholar 

  • Wang, G. F., & Cui, Y. H. (2013). On line tool wear monitoring based on auto associative neural network. Journal of Intelligent Manufacturing, 24(6), 1085–1094.

    Article  Google Scholar 

  • Wang, S. B., Huang, W. G., & Zhu, Z. K. (2011). Transient modeling and parameter identification based on wavelet and correlation filtering for rotating machine fault diagnosis. Mechanical Systems and Signal Processing, 25(4), 1299–1320.

    Article  Google Scholar 

  • Wells, L. J., Megahed, F. M., Niziolek, C. B., Camelio, J. A., & Woodall, W. H. (2013). Statistical process monitoring approach for high-density point clouds. Journal of Intelligent Manufacturing, 24(6), 1267–1279.

    Article  Google Scholar 

  • Yan, R. Q., Gao, R. X., & Chen, X. F. (2014). Wavelets for fault diagnosis of rotary machines: A review with applications. Signal Processing, 96, 1–15.

    Article  Google Scholar 

  • Yang, Z. S., Yu, Z. H., Xie, C., & Huang, Y. F. (2014). Application of hilbert-huang transform to acoustic emission signal for burn feature extraction in surface grinding process. Measurement, 47, 14–21.

    Article  Google Scholar 

  • Yu, H. C., Lin, K. Y., & Chien, C. F. (2014). Hierarchical indices to detect equipment condition changes with high dimensional data for semiconductor manufacturing. Journal of Intelligent Manufacturing, 25(5), 933–943.

    Article  Google Scholar 

  • Zarei, J., & Poshtan, J. (2007). Bearing fault detection using wavelet packet transform of induction motor stator current. Tribology International, 40(5), 763–769.

    Article  Google Scholar 

  • Zhang, Z. Y., Wang, Y., & Wang, K. S. (2013). Fault diagnosis and prognosis using wavelet packet decomposition, fourier transform and artificial neural network. Journal of Intelligent Manufacturing, 24(6), 1213–1227.

    Article  Google Scholar 

  • Zhao, D. L., Ma, W., & Liang, W. K. (2005). On data fusion fault diagnosis and simulation of hydroelectric units vibration. Proceedings of the CSEE, 25(20), 137–142.

    Google Scholar 

  • Zheng, M., Bu, J. J., Chen, C., Wang, C., Zhang, L. J., Qiu, G., et al. (2011). Graph regularized sparse coding for image representation. IEEE Transactions on Image Processing, 20(5), 1327–1336.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Key Basic Research Program of China (973 Program) under Grant No. 2014CB049500 and the Key Technologies R&D Program of Anhui Province under Grant No. 1301021005.

Author information

Authors and Affiliations

  1. Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China (USTC), Hefei, 230027, AnHui, People’s Republic of China

    Cong Wang, Meng Gan & Chang’an Zhu

Authors
  1. Cong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Meng Gan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chang’an Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cong Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, C., Gan, M. & Zhu, C. Fault feature extraction of rolling element bearings based on wavelet packet transform and sparse representation theory. J Intell Manuf 29, 937–951 (2018). https://doi.org/10.1007/s10845-015-1153-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10845-015-1153-2

Keywords

Search

Navigation