“RMS Based Health Indicators for Remaining Useful Lifetime Estimation of Bearings”

Authors: Andreas Klausen, Hyunh van Khang and Kjell G. Robbersmyr,
Affiliation: University of Agder
Reference: 2022, Vol 43, No 1, pp. 21-38.

Keywords: Ball bearings, Remaining useful life, Particle filter, Paris' law, Vibration measurement

Abstract: Estimating the remaining useful life (RUL) of bearings from healthy to faulty is important for predictive maintenance. The bearing fault severity can be estimated based on the energy or root mean square (RMS) of vibration signals, and a stopping criterion can be set based on a threshold given by an ISO standard. However, the vibration RMS is often not monotonically increasing with damage, which renders a challenge for predicting the RUL. This study proposes a novel method for splitting the vibration signal into multiple frequency bands before RMS calculations to generate multiple health indicators. Monotonic health indicators are identified using the Spearman coefficient, and the RUL is afterward estimated for each indicator using a suitable model and parameter update scheme. Historical failure data is not required to set any parameters. The proposed method is tested with the Paris' law, where parameters are updated by particle filters. Experimental results from two test rigs validate the performance of the proposed method.

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[1] Abboud, D., Elbadaoui, M., Smith, W., and Randall, R. (2019). Advanced bearing diagnostics: A comparative study of two powerful approaches, Mechanical Systems and Signal Processing. 114:604--627. doi:10.1016/j.ymssp.2018.05.011
[2] Ahmad, W., Khan, S.A., and Kim, J.-M. (2018). A Hybrid Prognostics Technique for Rolling Element Bearings Using Adaptive Predictive Models, IEEE Transactions on Industrial Electronics. 65(2):1577--1584. doi:10.1109/TIE.2017.2733487
[3] Akkad, K. and He, D. (2019). A Hybrid Deep Learning Based Approach for Remaining Useful Life Estimation, 2019. pages 1--6. doi:10.1109/ICPHM.2019.8819435
[4] An, D., Choi, J.-H., and Kim, N.H. (2013). Prognostics 101: A tutorial for particle filter-based prognostics algorithm using Matlab, Reliability Engineering & System Safety. 115:161--169. doi:10.1016/j.ress.2013.02.019
[5] An, H., Wang, G., Dong, Y., Yang, K., and Sang, L. (2019). Tool life prediction based on Gauss importance resampling particle filter, The International Journal of Advanced Manufacturing Technology. 103(9-12):4627--4634. doi:10.1007/s00170-019-03934-5
[6] Arulampalam, M., Maskell, S., Gordon, N., and Clapp, T. (2002). A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking, IEEE Transactions on Signal Processing. 50(2):174--188. doi:10.1109/78.978374
[7] Aye, S. and Heyns, P. (2017). An integrated Gaussian process regression for prediction of remaining useful life of slow speed bearings based on acoustic emission, Mechanical Systems and Signal Processing. 84:485--498. doi:10.1016/j.ymssp.2016.07.039
[8] Branch, M.A., Coleman, T.F., and Li, Y. (1999). A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems, SIAM Journal on Scientific Computing. 21(1):1--23. Publisher: Society for Industrial & Applied Mathematics (SIAM). doi:10.1137/s1064827595289108
[9] Cheng, C., Ma, G., Zhang, Y., Sun, M., Teng, F., Ding, H., and Yuan, Y. (2020). A Deep Learning-Based Remaining Useful Life Prediction Approach for Bearings, IEEE/ASME Transactions on Mechatronics. 25(3):1243--1254. Conference Name: IEEE/ASME Transactions on Mechatronics. doi:10.1109/TMECH.2020.2971503
[10] Gebraeel, N., Lawley, M., Liu, R., and Parmeshwaran, V. (2004). Residual Life Predictions From Vibration-Based Degradation Signals: A Neural Network Approach, IEEE Transactions on Industrial Electronics. 51(3):694--700. doi:10.1109/TIE.2004.824875
[11] Hol, J.D., Schon, T.B., and Gustafsson, F. (2006). On Resampling Algorithms for Particle Filters, In 2006 IEEE Nonlinear Statistical Signal Processing Workshop. IEEE, Cambridge, UK, pages 79--82. doi:10.1109/NSSPW.2006.4378824
[12] Hu, C., Youn, B.D., Wang, P., and TaekYoon, J. (2012). Ensemble of data-driven prognostic algorithms for robust prediction of remaining useful life, Reliability Engineering & System Safety. 103:120--135. doi:10.1016/j.ress.2012.03.008
[13] ISO. (1998). Mechanical vibration – Evaluation of machine vibration by measurements on non-rotating parts – Part 3 (Standard no, 10816-3). 1998.
[14] Khan, S.A., Prosvirin, A.E., and Kim, J.-M. (2018). Towards bearing health prognosis using generative adversarial networks: Modeling bearing degradation, In 2018 International Conference on Advancements in Computational Sciences (ICACS). IEEE, Lahore, pages 1--6. doi:10.1109/ICACS.2018.8333495
[15] Klausen, A., Folgerø, R.W., Robbersmyr, K.G., and Karimi, H.R. (2017). Accelerated Bearing Life-time Test Rig Development for Low Speed Data Acquisition, Modeling, Identification and Control: A Norwegian Research Bulletin, 2017. 38(3):143--156. doi:10.4173/mic.2017.3.4
[16] Klausen, A., Robbersmyr, K.G., and Karimi, H.R. (2017). Autonomous Bearing Fault Diagnosis Method based on Envelope Spectrum, IFAC-PapersOnLine, 2017. 50(1):13378--13383. doi:10.1016/j.ifacol.2017.08.2262
[17] Klausen, A., VanKhang, H., and Robbersmyr, K.G. (2018). Novel Threshold Calculations for Remaining Useful Lifetime Estimation of Rolling Element Bearings, In 2018 XIII International Conference on Electrical Machines (ICEM). IEEE, Alexandroupoli, pages 1912--1918. doi:10.1109/ICELMACH.2018.8507056
[18] Lei, Y., Li, N., Gontarz, S., Lin, J., Radkowski, S., and Dybala, J. (2016). A Model-Based Method for Remaining Useful Life Prediction of Machinery, IEEE Transactions on Reliability, 2016. 65(3):1314--1326. doi:10.1109/TR.2016.2570568
[19] Lei, Y., Li, N., Guo, L., Li, N., Yan, T., and Lin, J. (2018). Machinery health prognostics: A systematic review from data acquisition to RUL prediction, Mechanical Systems and Signal Processing. 104:799--834. doi:10.1016/j.ymssp.2017.11.016
[20] Lei, Y., Li, N., and Lin, J. (2016). A New Method Based on Stochastic Process Models for Machine Remaining Useful Life Prediction, IEEE Transactions on Instrumentation and Measurement, 2016. 65(12):2671--2684. doi:10.1109/TIM.2016.2601004
[21] Li, N., Lei, Y., Lin, J., and Ding, S.X. (2015). An Improved Exponential Model for Predicting Remaining Useful Life of Rolling Element Bearings, IEEE Transactions on Industrial Electronics. 62(12):7762--7773. doi:10.1109/TIE.2015.2455055
[22] Lu, C., Chen, J., Hong, R., Feng, Y., and Li, Y. (2016). Degradation trend estimation of slewing bearing based on LSSVM model, Mechanical Systems and Signal Processing, 2016. 76-77:353--366. doi:10.1016/j.ymssp.2016.02.031
[23] Lu, C., Wang, Y., Ragulskis, M., and Cheng, Y. (2016). Fault Diagnosis for Rotating Machinery: A Method based on Image Processing, PLOS ONE, 2016. 11(10):e0164111. doi:10.1371/journal.pone.0164111
[24] Ma, M. and Mao, Z. (2019). Deep Recurrent Convolutional Neural Network for Remaining Useful Life Prediction, In 2019 IEEE International Conference on Prognostics and Health Management (ICPHM). pages 1--4. doi:10.1109/ICPHM.2019.8819440
[25] Manjurul Islam, M., Prosvirin, A.E., and Kim, J.-M. (2021). Data-driven prognostic scheme for rolling-element bearings using a new health index and variants of least-square support vector machines, Mechanical Systems and Signal Processing. 160:107853. doi:10.1016/j.ymssp.2021.107853
[26] McFadden, P.D. and Smith, J.D. (1984). Model for the vibration produced by a single point defect in a rolling element bearing, Journal of Sound and Vibration. 96(1):69--82. Publisher: Elsevier BV. doi:10.1016/0022-460x(84)90595-9
[27] Pan, Z., Meng, Z., Chen, Z., Gao, W., and Shi, Y. (2020). A two-stage method based on extreme learning machine for predicting the remaining useful life of rolling-element bearings, Mechanical Systems and Signal Processing. 144:106899. doi:10.1016/j.ymssp.2020.106899
[28] Paris, P. and Erdogan, F. (1963). A Critical Analysis of Crack Propagation Laws, Journal of Basic Engineering. 85(4):528--533. Publisher: ASME International. doi:10.1115/1.3656900
[29] Peeters, C., Guillaume, P., and Helsen, J. (2017). A comparison of cepstral editing methods as signal pre-processing techniques for vibration-based bearing fault detection, Mechanical Systems and Signal Processing. 91:354--381. doi:10.1016/j.ymssp.2016.12.036
[30] Qian, Y. and Yan, R. (2015). Remaining Useful Life Prediction of Rolling Bearings Using an Enhanced Particle Filter, IEEE Transactions on Instrumentation and Measurement. 64(10):2696--2707. doi:10.1109/TIM.2015.2427891
[31] Qian, Y., Yan, R., and Gao, R.X. (2017). A multi-time scale approach to remaining useful life prediction in rolling bearing, Mechanical Systems and Signal Processing. 83:549--567. doi:10.1016/j.ymssp.2016.06.031
[32] Qian, Y., Yan, R., and Hu, S. (2014). Bearing Degradation Evaluation Using Recurrence Quantification Analysis and Kalman Filter, IEEE Transactions on Instrumentation and Measurement. 63(11):2599--2610. doi:10.1109/TIM.2014.2313034
[33] Qiu, H., Lee, J., Lin, J., and Yu, G. (2006). Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics, Journal of Sound and Vibration. 289(4-5):1066--1090. doi:10.1016/j.jsv.2005.03.007
[34] Rycerz, P., Olver, A., and Kadiric, A. (2017). Propagation of surface initiated rolling contact fatigue cracks in bearing steel, International Journal of Fatigue. 97:29--38. doi:10.1016/j.ijfatigue.2016.12.004
[35] Singleton, R.K., Strangas, E.G., and Aviyente, S. (2015). Extended Kalman Filtering for Remaining-Useful-Life Estimation of Bearings, IEEE Transactions on Industrial Electronics. 62(3):1781--1790. doi:10.1109/TIE.2014.2336616
[36] Singleton, R.K., Strangas, E.G., and Aviyente, S. (2017). The Use of Bearing Currents and Vibrations in Lifetime Estimation of Bearings, IEEE Transactions on Industrial Informatics. 13(3):1301--1309. doi:10.1109/TII.2016.2643693
[37] Spearman, C. (1904). The Proof and Measurement of Association between Two Things, The American Journal of Psychology. 15(1):72. Publisher: JSTOR. doi:10.2307/1412159
[38] Wang, B., Lei, Y., Li, N., and Yan, T. (2019). Deep separable convolutional network for remaining useful life prediction of machinery, Mechanical Systems and Signal Processing. 134:106330. doi:10.1016/j.ymssp.2019.106330
[39] Wang, D. and Tsui, K.-L. (2017). Statistical Modeling of Bearing Degradation Signals, IEEE Transactions on Reliability. 66(4):1331--1344. doi:10.1109/TR.2017.2739126
[40] Wang, W. (2002). A model to predict the residual life of rolling element bearings given monitored condition information to date, IMA Journal of Management Mathematics. 13(1):3--16. doi:10.1093/imaman/13.1.3
[41] Wang, Y., Peng, Y., Zi, Y., Jin, X., and Tsui, K.-L. (2016). A Two-Stage Data-Driven-Based Prognostic Approach for Bearing Degradation Problem, IEEE Transactions on Industrial Informatics. 12(3):924--932. doi:10.1109/TII.2016.2535368
[42] Zhang, P., Du, Y., Habetler, T.G., and Lu, B. (2011). A Survey of Condition Monitoring and Protection Methods for Medium-Voltage Induction Motors, IEEE Transactions on Industry Applications. 47(1):34--46. doi:10.1109/TIA.2010.2090839
[43] Zhu, J., Chen, N., and Peng, W. (2019). Estimation of Bearing Remaining Useful Life Based on Multiscale Convolutional Neural Network, IEEE Transactions on Industrial Electronics. 66(4):3208--3216. doi:10.1109/TIE.2018.2844856
[44] Zhu, J., Chen, N., and Shen, C. (2020). A new data-driven transferable remaining useful life prediction approach for bearing under different working conditions, Mechanical Systems and Signal Processing. 139:106602. doi:10.1016/j.ymssp.2019.106602

  title={{RMS Based Health Indicators for Remaining Useful Lifetime Estimation of Bearings}},
  author={Klausen, Andreas and van Khang, Hyunh and Robbersmyr, Kjell G.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}