Physics-based intelligent prognosis for rolling bearing with fault feature extraction

  • Yanfei Lu
  • Qing Li
  • Steven Y. Liang


Successful condition monitoring of rotating machinery relies on the accurate prediction of the remaining life of the rotating components. This paper proposes a physics-based prognostic model for rolling element bearings using the realized volatility (RV) and wavelet neural network (WNN) to predict the remaining life of bearings. The proposed method overcomes the difficulties of forecasting the failure of bearings under various degradation patterns and improves the accuracy of prediction. The faulty signal is extracted using an AR filter to reveal the degradation trend. The prognosis is performed by calculating the RV and energy ratio, which are used to identify the abnormality of vibration in the system and degradation patterns before catastrophic failure occurs. Then, the WNN incorporated with physical inputs from the properties of the bearings predicts the failure cycles. The prediction yields a satisfactory result between the experimental and predicted failure cycle. The prognostic accuracy of the physics-based WNN model is compared with a widely used time-series model, the auto-regressive integrated moving average (ARIMA) model. The WNN model has an advantage of reducing error over the ARIMA model in various degradation patterns and overcomes the disadvantage of models requiring additional data after significant damage is present in the bearings.


Ball bearing Bearing degradation trend prognosis Forecasting Prognostics and health management Realized volatility Wavelet neural network 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


Author contributions

Y.L. and Q.L. created the model and analyzed the data; S.Y.L. provided feedback of the concept; Y.L. wrote the paper.


  1. 1.
    Group, W MR (1985) Report of large motor reliability survey of industrial and commercial installations, Part I. IEEE Trans Ind Appl 21(4):853–864Google Scholar
  2. 2.
    Kotzalas MN, Harris TA (2001) Fatigue failure progression in ball bearings. Trans Am Soc Mech Eng J Tribol 123(2):238–242Google Scholar
  3. 3.
    Tong W (2014) Mechanical design of electric motors. CRC pressGoogle Scholar
  4. 4.
    Graney BP, Starry K (2012) Rolling element bearing analysis. Mater Eval 70 (1)Google Scholar
  5. 5.
    Lundberg G, Palmgren A (1949) Dynamic capacity of rolling bearings. J Appl Mech Trans ASME 16(2):165–172Google Scholar
  6. 6.
    Harris T, Yu WK (1999) Lundberg-Palmgren fatigue theory: considerations of failure stress and stressed volume. J Tribol 121(1):85–89CrossRefGoogle Scholar
  7. 7.
    Li Y (1999) Dynamic prognostics of rolling element bearing condition. Georgia Institute of TechnologyGoogle Scholar
  8. 8.
    Liang SY, Li Y, Billington SA, Zhang C, Shiroishi J, Kurfess TR, Danyluk S (2014) Adaptive prognostics for rotary machineries. Proc Eng 86:852–857CrossRefGoogle Scholar
  9. 9.
    Gebraeel N, Lawley M, Liu R, Parmeshwaran V (2004) Residual life predictions from vibration-based degradation signals: a neural network approach. IEEE Trans Ind Electron 51(3):694–700CrossRefGoogle Scholar
  10. 10.
    Kim H-E, Tan AC, Mathew J, Choi B-K (2012) Bearing fault prognosis based on health state probability estimation. Expert Syst Appl 39(5):5200–5213CrossRefGoogle Scholar
  11. 11.
    Soualhi A, Razik H, Clerc G, Doan DD (2014) Prognosis of bearing failures using hidden Markov models and the adaptive neuro-fuzzy inference system. IEEE Trans Ind Electron 61(6):2864–2874CrossRefGoogle Scholar
  12. 12.
    Liu L, Wan J (2012) A study of Shanghai fuel oil futures price volatility based on high frequency data: long-range dependence, modeling and forecasting. Econ Model 29(6):2245–2253MathSciNetCrossRefGoogle Scholar
  13. 13.
    Barndorff-Nielsen OE, Shephard N (2002) Econometric analysis of realized volatility and its use in estimating stochastic volatility models. J R Stat Soc Ser B (Stat Methodology) 64(2):253–280MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Andersen TG, Bollerslev T, Diebold FX, Labys P (2003) Modeling and forecasting realized volatility. Econometrica 71(2):579–625MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Corsi F (2004) A simple long memory model of realized volatilityGoogle Scholar
  16. 16.
    Shirota S, Hizu T, Omori Y (2014) Realized stochastic volatility with leverage and long memory. Comput Stat Data Anal 76:618–641MathSciNetCrossRefGoogle Scholar
  17. 17.
    Li R, Sopon P, He D (2012) Fault features extraction for bearing prognostics. J Intell Manuf 23(2):313–321CrossRefGoogle Scholar
  18. 18.
    Chen Y, Yang B, Dong J (2006) Time-series prediction using a local linear wavelet neural network. Neurocomputing 69(4–6):449–465CrossRefGoogle Scholar
  19. 19.
    Pindoriya N, Singh S, Singh S (2008) An adaptive wavelet neural network-based energy price forecasting in electricity markets. IEEE Trans Power Syst 23(3):1423–1432CrossRefGoogle Scholar
  20. 20.
    Adamowski J, Chan HF (2011) A wavelet neural network conjunction model for groundwater level forecasting. J Hydrol 407(1–4):28–40CrossRefGoogle Scholar
  21. 21.
    Berenji HR, Wang Y (2006) In Wavelet neural networks for fault diagnosis and prognosis, IEEE Int Conf Fuzzy Syst; pp 1334–1339Google Scholar
  22. 22.
    Zhang Z, Wang Y, Wang K (2013) Fault diagnosis and prognosis using wavelet packet decomposition, Fourier transform and artificial neural network. J Intell Manuf 24(6):1213–1227CrossRefGoogle Scholar
  23. 23.
    Vachtsevanos G, Wang P (2001) In Fault prognosis using dynamic wavelet neural networks, AUTOTESTCON Proceedings, 2001 I.E. Systems Readiness Technology Conference, IEEE: pp 857–870Google Scholar
  24. 24.
    Lu Y, Rajora M, Zou P, Liang SY (2017) Physics-embedded machine learning: case study with electrochemical micro-machining. Mach Des 5(1):4CrossRefGoogle Scholar
  25. 25.
    Harris TA (2001) Rolling bearing analysis. John Wiley and sonsGoogle Scholar
  26. 26.
    Sawalhi N, Wang W, Becker A (2017) Vibration signal processing for spall size estimation in rolling element bearings using autoregressive inverse filtration combined with bearing signal synchronous averaging. Adv Mech Eng 9(5):1687814017703007CrossRefGoogle Scholar
  27. 27.
    Eshel G The yule walker equations for the AR coefficientsGoogle Scholar
  28. 28.
    Anderson TL (2017) Fracture mechanics: fundamentals and applications. CRC pressGoogle Scholar
  29. 29.
    Lewis M, Tomkins B (2012) A fracture mechanics interpretation of rolling bearing fatigue. Proc Inst Mech Eng J J Eng Tribol 226(5):389–405CrossRefGoogle Scholar
  30. 30.
    Camci F, Medjaher K, Zerhouni N, Nectoux P (2013) Feature evaluation for effective bearing prognostics. Qual Reliab Eng Int 29(4):477–486CrossRefGoogle Scholar
  31. 31.
    Nectoux P, Gouriveau R, Medjaher K, Ramasso E, Chebel-Morello B, Zerhouni N, Varnier C (2012) In PRONOSTIA: an experimental platform for bearings accelerated degradation tests, IEEE International Conference on Prognostics and Health Management, PHM'12., IEEE catalog number: CPF12PHM-CDR: pp 1–8Google Scholar
  32. 32.
    Doucoure B, Agbossou K, Cardenas A (2016) Time series prediction using artificial wavelet neural network and multi-resolution analysis: application to wind speed data. Renew Energy 92:202–211CrossRefGoogle Scholar
  33. 33.
    Okkan U (2012) Wavelet neural network model for reservoir inflow prediction. Sci Iran 19(6):1445–1455MathSciNetCrossRefGoogle Scholar
  34. 34.
    Skelton R, Vilhelmsen T, Webster G (1998) Energy criteria and cumulative damage during fatigue crack growth. Int J Fatigue 20(9):641–649CrossRefGoogle Scholar
  35. 35.
    Li Q, Liang SY, Yang J, Li B (2016) Long range dependence prognostics for bearing vibration intensity chaotic time series. Entropy 18(1):23CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.George W. Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.College of Mechanical EngineeringDonghua UniversityShanghaiChina

Personalised recommendations