Improved singular spectrum decomposition-based 1.5-dimensional energy spectrum for rotating machinery fault diagnosis

  • Xiaoan Yan
  • Minping JiaEmail author
Technical Paper


Fault diagnosis of rotating machinery has always been being a challenge thanks to the various effects of nonlinear factors. To address this problem, combining the concepts of improved singular spectrum decomposition with 1.5-dimensional energy spectrum in this paper, a novel method is presented for diagnosing the partial faults of rotating machinery. Within the proposed algorithm, waveform matching extension is firstly introduced to suppress the end effect of singular spectrum decomposition and obtain several singular spectrum components (SSCs) whose instantaneous features have physical meaning. Meanwhile, a new sensitive index is put forward to choose adaptively the sensitive SSCs containing the principal fault characteristic signatures. Subsequently, 1.5-dimensional energy spectrum of the selected sensitive SSC is conducted to acquire the defective frequency and identify the fault type of rotating machinery. The validity of the raised algorithm is proved through the applications in the fault detection of gear and rolling bearing. It turned out that the proposed method can improve signal’s decomposition results and is able to detect effectively the local faults of gear or rolling bearing. The studies provide a new perspective for the improvement in damage detection of rotating machinery.


Improved singular spectrum decomposition Sensitive index 1.5-Dimensional energy spectrum Rotating machinery Fault diagnosis 



This work was supported by the National Natural Science Foundation of China (Grant No. 51675098) and Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Project No. KYCX17_0059). The author would like to thank NCEPU for providing rotor and gear fault data, and thank the editor and the anonymous reviewers for their helpful comments.


  1. 1.
    Lei YG, Lin J, He ZJ, Zuo MJ (2013) A review on empirical mode decomposition in fault diagnosis of rotating machinery. Mech Syst Signal Process 35(1):108–126CrossRefGoogle Scholar
  2. 2.
    Li W, Zhu ZC, Jiang F, Zhou GB, Chen GA (2015) Fault diagnosis of rotating machinery with a novel statistical feature extraction and evaluation method. Mech Syst Signal Process 50:414–426CrossRefGoogle Scholar
  3. 3.
    Feng ZP, Liang M, Chu FL (2013) Recent advances in time–frequency analysis methods for machinery fault diagnosis: a review with application examples. Mech Syst Signal Process 38(1):165–205CrossRefGoogle Scholar
  4. 4.
    Gao HZ, Liang L, Chen XG, Xu GH (2015) Feature extraction and recognition for rolling element bearing fault utilizing short-time Fourier transform and non-negative matrix factorization. Chin J Mech Eng 28(1):96–105CrossRefGoogle Scholar
  5. 5.
    Pachori RB, Nishad A (2016) Cross-terms reduction in the Wigner-Ville distribution using tunable-Q wavelet transform. Signal Process 120:288–304CrossRefGoogle Scholar
  6. 6.
    Gao ZW, Cecati C, Ding SX (2015) A survey of fault diagnosis and fault-tolerant techniques—part I: fault diagnosis with model-based and signal-based approaches. IEEE Trans Ind Electron 62(6):3757–3767CrossRefGoogle Scholar
  7. 7.
    Huang NE, Zheng S, Long SR, Wu MC, Shih H, Zheng Q, Yen N, Tung C, Liu H (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc A Lond 454:903–995MathSciNetCrossRefGoogle Scholar
  8. 8.
    Smith JS (2005) The local mean decomposition and its application to EEG perception data. J R Soc Interface 2:443–454MathSciNetCrossRefGoogle Scholar
  9. 9.
    Frei MG, Osorio I (2007) Intrinsic time-scale decomposition: time–frequency–energy analysis and real-time filtering of non-stationary signals. Proc R Soc A 463:321–342MathSciNetCrossRefGoogle Scholar
  10. 10.
    Gilles J (2013) Empirical wavelet transform. IEEE Trans Signal Process 61(16):3999–4010MathSciNetCrossRefGoogle Scholar
  11. 11.
    Dragomiretskiy K, Zosso D (2014) Variational mode decomposition. IEEE Trans Signal Process 62:531–544MathSciNetCrossRefGoogle Scholar
  12. 12.
    Chandra NH, Sekhar AS (2016) Fault detection in rotor bearing systems using time frequency techniques. Mech Syst Signal Process 72:105–133CrossRefGoogle Scholar
  13. 13.
    Hu AJ, Yan XA, Xiang L (2015) A new wind turbine fault diagnosis method based on ensemble intrinsic time-scale decomposition and WPT-fractal dimension. Renew Energy 83:767–778CrossRefGoogle Scholar
  14. 14.
    Mandic DP, Rehman NU, Wu Z, Huang NE (2013) Empirical mode decomposition-based time-frequency analysis of multivariate signals: the power of adaptive data analysis. IEEE Signal Process Mag 30(6):74–86CrossRefGoogle Scholar
  15. 15.
    Yan X, Jia M, Xiang L (2016) Compound fault diagnosis of rotating machinery based on OVMD and a 1.5-dimension envelope spectrum. Meas Sci Technol 27(7):075002CrossRefGoogle Scholar
  16. 16.
    Bonizzi P, Karel JM, Meste O, Peeters RL (2014) Singular spectrum decomposition: a new method for time series decomposition. Adv Adapt Data Anal 6(4):1450011MathSciNetCrossRefGoogle Scholar
  17. 17.
    Bonizzi P, Karel JM, Zeemering S, Peeters RL (2015) Sleep apnea detection directly from unprocessed ECG through singular spectrum decomposition. In: IEEE 2015 computing in cardiology conference. Nice, France, Sept 2015, pp 309–312Google Scholar
  18. 18.
    Zhong XY, Zeng LC, Zhao CH (2013) Application of local mean decomposition and 1.5 dimension spectrum in machinery fault diagnosis. Chin Mech Eng 24:452–457Google Scholar
  19. 19.
    Chen L, Zi YY, He ZJ, Cheng W (2009) Research and application of ensemble empirical mode decomposition principle and 1.5 dimension spectrum method. J Xi’an Jiaotong Univ 43(5):94–98Google Scholar
  20. 20.
    Jiang HK, Xia Y, Wang XD (2013) Rolling bearing fault detection using an adaptive lifting multiwavelet packet with a 1.5 dimension spectrum. Meas Sci Technol 24(12):125002CrossRefGoogle Scholar
  21. 21.
    Cai JH, Li XQ (2016) Gear fault diagnosis based on empirical mode decomposition and 1.5 dimension spectrum. Shock Vib 2016(3):1–10Google Scholar
  22. 22.
    Rodriguez PH, Alonso JB, Ferrer MA, Travieso CM (2013) Application of the Teager–Kaiser energy operator in bearing fault diagnosis. ISA Trans 52(2):278–284CrossRefGoogle Scholar
  23. 23.
    Feng ZP, Zuo MJ, Hao RJ, Chu FL, Lee J (2013) Ensemble empirical mode decomposition-based Teager energy spectrum for bearing fault diagnosis. J Vib Acoust 135(3):031013CrossRefGoogle Scholar
  24. 24.
    Zeng M, Yang Y, Zheng JD, Cheng JS (2015) Normalized complex Teager energy operator demodulation method and its application to fault diagnosis in a rubbing rotor system. Mech Syst Signal Process 50:380–399CrossRefGoogle Scholar
  25. 25.
    Zhang DC, Yu DJ, Zhang WY (2015) Energy operator demodulating of optimal resonance components for the compound faults diagnosis of gearboxes. Meas Sci Technol 26(11):115003CrossRefGoogle Scholar
  26. 26.
    Bozchalooi IS, Liang M (2010) Teager energy operator for multi-modulation extraction and its application for gearbox fault detection. Smart Mater Struct 19(7):075008CrossRefGoogle Scholar
  27. 27.
    Tang G, Wang X (2014) Fault diagnosis for roller bearings based on EEMD de-noising and 1.5-dimensional energy spectrum. J Vib Shock 33(1):6–10Google Scholar
  28. 28.
    Muruganatham B, Sanjith MA, Krishnakumar B, Murty SS (2013) Roller element bearing fault diagnosis using singular spectrum analysis. Mech Syst Signal Process 35(1):150–166CrossRefGoogle Scholar
  29. 29.
    Vautard R, Yiou P, Ghil M (1992) Singular-spectrum analysis: a toolkit for short, noisy chaotic signals. Physica D 58(1):95–126CrossRefGoogle Scholar
  30. 30.
    Hu AJ, An LS, Tang GJ (2008) New process method for end effects of Hilbert–Huang transform. Chin J Mech Eng 44(4):154–158CrossRefGoogle Scholar
  31. 31.
    Meng Z, Gu HY, Li SS (2013) Restraining method for end effect of B-spline empirical mode decomposition based on neural network ensemble. Chin J Mech Eng 49(9):106–112CrossRefGoogle Scholar
  32. 32.
    Cheng JS, Yu DJ, Yang Y (2007) Application of support vector regression machines to the processing of end effects of Hilbert–Huang transform. Mech Syst Signal Process 21(3):1197–1211CrossRefGoogle Scholar
  33. 33.
    Yang JW, Jia MP (2006) Study on processing method and analysis of end problem of Hilbert–Huang spectrum. J Vib Eng 19(2):283–288Google Scholar
  34. 34.
    Li P, Gao J, Xu D, Wang C, Yang X (2016) Hilbert–Huang transform with adaptive waveform matching extension and its application in power quality disturbance detection for microgrid. J Mod Power Syst Clean Energy 4(1):19–27CrossRefGoogle Scholar
  35. 35.
    Peel MC, Pegram GGS, McMahon TA (2007) Empirical mode decomposition: improvement and application. In: Modsim 2007 International congress on modelling and simulation, Christchurch, New Zealand, Dec 2007, pp 2996–3002Google Scholar
  36. 36.
    Guo W, Peter WT, Djordjevich A (2012) Faulty bearing signal recovery from large noise using a hybrid method based on spectral kurtosis and ensemble empirical mode decomposition. Measurement 45(5):1308–1322CrossRefGoogle Scholar
  37. 37.
    Tse PW, Wang D (2013) The design of a new sparsogram for fast bearing fault diagnosis: part 1 of the two related manuscripts that have a joint title as “two automatic vibration-based fault diagnostic methods using the novel sparsity measurement—parts 1 and 2”. Mech Syst Signal Process 40(2):499–519CrossRefGoogle Scholar
  38. 38.
    Gao Q, Duan C, Fan H, Meng Q (2008) Rotating machine fault diagnosis using empirical mode decomposition. Mech Syst Signal Process 22(5):1072–1081CrossRefGoogle Scholar
  39. 39.
    Cheng JS, Yang Y, Yang Y (2012) A rotating machinery fault diagnosis method based on local mean decomposition. Digit Signal Process 22(2):356–366MathSciNetCrossRefGoogle Scholar
  40. 40.
    Antoni J (2006) The spectral kurtosis: a useful tool for characterising non-stationary signals. Mech Syst Signal Process 20(2):282–307CrossRefGoogle Scholar
  41. 41.
    He WP, Zi YY, Chen BQ, Wu F, He ZJ (2015) Automatic fault feature extraction of mechanical anomaly on induction motor bearing using ensemble super-wavelet transform. Mech Syst Signal Process 54:457–480CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringSoutheast UniversityNanjingPeople’s Republic of China

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