Journal of Mechanical Science and Technology

, Volume 31, Issue 4, pp 1587–1601 | Cite as

Low-speed rolling bearing fault diagnosis based on EMD denoising and parameter estimate with alpha stable distribution

  • Qing Xiong
  • Yanhai Xu
  • Yiqiang Peng
  • Weihua Zhang
  • Yongjian Li
  • Lan Tang


When low-speed rolling bearings fail, it is hard to diagnose the extent of their damage. We developed a test rig to simulate the lowspeed rolling bearing operating condition, where bearings with various fault states are installed on the test wheelset and subjected to the same external loading condition. The collected bearing box acceleration time histories are processed with the Empirical mode decomposition (EMD) method combined with kurtosis criterion to filter the trend and noise components. Five characteristic parameters of Alpha stable distribution (ASD) are identified by fitting the ASD distribution to the vibration acceleration signals and computing the Probability density function (PDF). To highlight the advantage of ASD method in feature extraction, kurtosis also has be calculated. Through sensitivity and stability analysis of the six parameters and utilization of Least squares support vectors machine (LSSVM) with Particle swarm optimization (PSO), three most sensitive and stable feature parameters including the characteristic exponent α, the scale factor γ and the peak value of the PDF h are located and applied to evaluate the low-speed rolling bearings’ damage position and damage extent. The proposed method was validated by test data, and the results demonstrated that the ASD characteristics combined with PSO-LSSVM can not only achieve fault diagnosis of low-speed rolling bearings' damage position and damage extent, but also have better diagnosis accuracy and operational efficiency than other methods.


Low-speed rolling bearing Fault diagnosis Empirical mode decomposition Alpha stable distribution Particle swarm optimization algorithm Least squares support vector machine 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. C. Robinson and R. G. Canada, Monitoring slow speed machinery using integrator and selective correction of frequency spectrum, United States Patent, 5646350 (1997).Google Scholar
  2. [2]
    A. Widodo et al., Fault diagnosis of low speed bearing based on relevance vector machine and support vector machine, Expert Systems with Applications, 2009 (36) (2009) 7252–7261.CrossRefGoogle Scholar
  3. [3]
    Z. G. Zhang et al., Fault feature extraction of rolling element bearing based on improved EMD and spectral kurtosis, J. of Vibration, Measurement & Diagnosis, 33 (3) (2013) 478–482.MathSciNetGoogle Scholar
  4. [4]
    S. Zhang, Y. X. Zhang and J. P. Zhu, Rolling element bearing feature extraction based on combined wavelets and quantum-behaved particle swarm optimization, J. of Mechanical Science and Technology, 29 (2) (2015) 605–610.MathSciNetCrossRefGoogle Scholar
  5. [5]
    J. Harmouche and C. Delpha, Improved fault diagnosis of ball bearings based on the global spectrum of vibration signals, IEEE Transactions on Energy Conversion, 30 (1) (2015) 376–383.CrossRefGoogle Scholar
  6. [6]
    N. Canter, Using shock pulse for bearing analysis, Tribology & Lubrication Technology, 64 (4) (2008) 376–383.Google Scholar
  7. [7]
    Z. Li et al., Bearing condition monitoring based on shock pulse method and improved redundant lifting scheme, Mathematics and Computers in Simulation, 79 (3) (2008) 318–338.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    H. C. Wang et al., Application of resonance demodulation in rolling bearing fault feature extraction based on fast computation of kurtogram, J. of Vibration and Shock, 32 (1) (2013) 35–37.Google Scholar
  9. [9]
    S. M. Hou, Y. R. Li and Z. G. Wang, A resonance demodulation method based on harmonic wavelet transform for rolling bearing fault diagnosis, Structural Health Monitoring, 9 (4) (2010) 297–308.CrossRefGoogle Scholar
  10. [10]
    N. Wang et al., Study on fault diagnosis of low-speed rolling bearing using stress waves and wavelet analysis, J. of Vibration Engineering, 20 (3) (2007) 35–37.Google Scholar
  11. [11]
    L. S. Shi, Y. Z. Zhang and W. P. Mi, Application of Wigner Ville distribution based spectral kurtosis algorithm to fault diagnosis of rolling bearing, J. of Vibration, Measurement & Diagnosis, 31 (1) (2011) 27–31.Google Scholar
  12. [12]
    M. Kang, J. Kim and J. M. Kim, Reliable fault diagnosis for incipient low-speed bearings using fault feature analysis based on a binary bat algorithm, Information Sciences, 294 (2015) 423–438.MathSciNetCrossRefGoogle Scholar
  13. [13]
    T. Y. Wu, C. H. Lai and D. C. Liu, Defect diagnostics of roller bearing using instantaneous frequency normalization under fluctuant rotating speed, J. of Mechanical Science and Technology, 30 (3) (2016) 1037–1048.CrossRefGoogle Scholar
  14. [14]
    X. Y. Zhang et al., A novel bearing fault diagnosis model integrated permutation entropy, ensemble empirical mode decomposition and optimized SVM, Measurement, 69 (2015) 164–179.Google Scholar
  15. [15]
    Z. H. Wu and N. E. Huang, Ensemble empirical mode decomposition: a noise-assisted data analysis method, Advances in Adaptive Data Analysis, 1 (1) 1-41.Google Scholar
  16. [16]
    H. H. Liu and M. H. Han, A fault diagnosis method based on local mean decomposition and multi-scale entropy for roller bearings, Mechanism and Machine Theory, 75 (2014) 67–78.CrossRefGoogle Scholar
  17. [17]
    Z. J. Xu et al., A novel structure for covert communication based on alpha stable distribution, Information Technology J., 13 (9) (2014) 1673–1677.CrossRefGoogle Scholar
  18. [18]
    H. Sadreazam, M. O. Ahmad and M. N. S. Swamy, Contourlet domain image modeling by using the alpha-stable family of distributions, 2014 IEEE International Symposium on Circuits and Systems (ISCAS) (2014) 1288–1291.CrossRefGoogle Scholar
  19. [19]
    Z. H. Zheng et al., Radar target detection method in non-Gaussian correlated clutter backgrounds, J. of Signal Processing, 29 (8) (2013) 925–932.Google Scholar
  20. [20]
    C. N. Li, Research on statistical modeling for mechanical fault signal and related fault diagnosis methods, Ph.D. Thesis, Harbin Institute of Technology, Harbin, China (2010).Google Scholar
  21. [21]
    P. Wang, Diagnosis of rolling bearings based on feature parameters of alpha stable distribution, M.D. Thesis, Harbin Institute of Technology, Harbin, China (2011).Google Scholar
  22. [22]
    X. H. Zhang et al., Alpha stable distribution based morphological filter for bearing and gear fault diagnosis in nuclear power plant, Science and Technology of Nuclear Installations (2015) 1–15.Google Scholar
  23. [23]
    X. M. Yu and T. Shu, Fault diagnosis method for gearbox based on alpha-stable distribution parameters and support vector machines, Measurement & Control Technology, 31 (8) (2012) 23–30.Google Scholar
  24. [24]
    G. Yu and N. N. Shi, Gear fault signal modeling and detection based on alpha stable distribution, 2012 International Symposium on Instrumentation & Measurement, Sensor Network and Automatic (IMSNA) (2012) 471–474.CrossRefGoogle Scholar
  25. [25]
    G. Yu, C. N. Li and J. F. Zhang, A new statistical modeling and detection method for rolling element bearing faults based on alpha–stable distribution, Mechanical Systems and Signal Processing, 41 (1) (2013) 155–175.CrossRefGoogle Scholar
  26. [26]
    G. Samorodnitsky and M. S. Taqqu, Stable non-Gaussian random processes: stochastic models with infinite variance, Boca Raton, Florida, USA: Chapman & Hall/CRC (1994) 1–49.MATHGoogle Scholar
  27. [27]
    M. Shao and L. N. Chrysostomos, Signal processing with fractional lower order moments: stable processes and their applications, Proceedings of the IEEE, 81 (7) (1993) 986–1010.CrossRefGoogle Scholar
  28. [28]
    I. A. Koutrouvelis, An iterative procedure for the estimation of the parameters of stable laws, Communications in Statistics -Simulation and Computation, 10 (1) (1981) 17–28.MathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    J. A. K. Suykens and J. Vandewalle, Least squares support vector machine classifiers, Neural Processing Letters, 9 (3) (1999) 293–300.CrossRefMATHGoogle Scholar
  30. [30]
    J. A. K. Suykens et al., Least squares support vector machines, World Scientific, Singapore (2002).CrossRefMATHGoogle Scholar
  31. [31]
    V. N. Vapnik, The Nature of Statistical Learning Theory, Springer Verlag, New York (1999).MATHGoogle Scholar
  32. [32]
    Y. P. Gu, W. J. Zhao and Z. S. Wu, Study on the algorithm of least squares support vector machine, J. of Tsinghua University (Science and Technology), 50 (7) (2010) 1063–1071.MathSciNetMATHGoogle Scholar
  33. [33]
    H. N. Rong, G. X. Zhang and W. D. Jin, Selection of Kernel functions and parameters for support vector machines in system identification, J. of System Simulation, 18 (11) (2006) 3204–3208.Google Scholar
  34. [34]
    J. Kennedy, The particle swarm: Social adaptation of knowledge, IEEE International Conference on Evolutionary Computation (1997) 303–308.Google Scholar
  35. [35]
    I. Jacek and H. Dimitris, Applications of the empirical characteristic function to estimation and detection problems, Signal Processing, 65 (1998) 199–219.CrossRefMATHGoogle Scholar
  36. [36]
    N. E. Huang et al., The empirical mode decomposition and the Hilbert spectrum for non-linear and non-stationary time series analysis, Proceeding of the Royal Society, Lond. A 454) (1998) 903–995.CrossRefMATHGoogle Scholar
  37. [37]
    Y. P. Cai et al., Rolling bearings fault detection using improved envelop spectrum analysis based on EMD and spectral kurtosis, J. of Vibration and Shock, 30 (2) (2011) 167–172.Google Scholar
  38. [38]
    J. S. Lin, Fault diagnosis of rolling bearing based on empirical mode decomposition and spectrum kurtosis, J. of Mechanical Transmission, 36 (9) (2012) 76–79.Google Scholar
  39. [39]
    A. J. Hu, W. L. Ma and G. J. Tang, Rolling bearing fault feature extraction method based on ensemble empirical mode decomposition and kurtosis criterion, Proceedings of the CSEE, 32 (11) (2012) 106–111.Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Qing Xiong
    • 1
    • 2
  • Yanhai Xu
    • 2
  • Yiqiang Peng
    • 2
  • Weihua Zhang
    • 3
  • Yongjian Li
    • 3
  • Lan Tang
    • 2
  1. 1.Key Laboratory of Fluid and Power Machinery, Ministry of EducationXihua UniversityChengdu, SichuanChina
  2. 2.School of Automobile & TransportationXihua UniversityChengdu, SichuanChina
  3. 3.State Key Laboratory of Traction PowerSouthwest Jiaotong UniversityChengdu, SichuanChina

Personalised recommendations