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Bearing fault prognosis based on Cyclical Remaining Useful Life (CRUL)
[Pronostic des défauts de roulements basé sur la durée de vie résiduelle cyclique (CRUL)]
Comptes Rendus. Mécanique, Volume 353 (2025), pp. 1477-1495

Over the last decade, prognosis has become an interesting line of research in preventive maintenance for a variety of industrial applications. It generally focuses on estimating the Remaining Useful Life (RUL) of mechanical systems. In this context, this paper proposes a new prognosis approach based on cyclical prediction of RUL. The main idea lies in the integration of cyclical prediction of the degradation based on an appropriate adjustment of the data. The proposed degradation model can monitor continuously the evolution of degradation and finally provide an instantaneous estimation of RUL throughout the bearing life. First, the Simple Moving Average (SMA), Cumulative Moving Average (CMA), and Exponential Moving Average (EMA) filters are compared. Then, an exponential degradation model is constructed and fitted to the final $n$ data using both Principal Component Analysis (PCA) and model fitting. Finally, the developed model is evaluated in cyclical estimation of the bearing RUL using vibration data acquired from an endurance test rig. The results demonstrate an accurate prediction throughout each phase of bearing life, which confirms its ability to be applied to the prognosis of bearing failure.

Ces dernières décennies, le pronostic est devenu un axe de recherche intéressant en maintenance préventive pour diverses applications industrielles. Généralement, il se concentre sur l’estimation de la durée de vie résiduelle (RUL) des systèmes mécaniques. Dans ce contexte, cet article propose une nouvelle approche de pronostic basée sur des prédictions cycliques. L’idée principale réside dans l’intégration de la prédiction cyclique de la dégradation basée sur un ajustement approprié des données. Le modèle de dégradation proposé permet de suivre en continu l’évolution de la dégradation et de fournir une estimation instantanée de la RUL tout au long de la durée de vie du roulement. Dans un premier temps, les filtres de Moyenne Mobile Simple (SMA), de Moyenne Mobile Cumulative (CMA) et de Moyenne Mobile Exponentielle (EMA) sont comparés. Ensuite, un modèle de dégradation exponentielle est construit et ajusté aux $n$ données finales à l’aide de l’Analyse en Composantes Principales (ACP) et de l’ajustement du modèle. Enfin, le modèle développé est évalué en estimant la RUL du roulement de manière cyclique à l’aide de données vibratoires expérimentales, acquises à partir d’un banc d’essai d’endurance. Les résultats démontrent une prédiction précise tout au long de chaque phase de vie du roulement, confirmant sa capacité à être appliquée au pronostic des défauts des roulements.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmeca.332
Keywords: Bearings, prognosis, preventive maintenance, cyclical remaining useful life
Mots-clés : Roulements, pronostic, maintenance préventive, durée de vie résiduelle cyclique

Abderrahmane Ben Yagoub 1 ; Ridha Ziani 1

1 Laboratory of Applied Precision Mechanics, Institute of Optics and Precision Mechanics, Setif 1 University Ferhat Abbas, Setif 19000, Algeria
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Bearing fault prognosis based on {Cyclical} {Remaining} {Useful} {Life} {(CRUL)}},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {1477--1495},
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Abderrahmane Ben Yagoub; Ridha Ziani. Bearing fault prognosis based on Cyclical Remaining Useful Life (CRUL). Comptes Rendus. Mécanique, Volume 353 (2025), pp. 1477-1495. doi: 10.5802/crmeca.332

[1] Dhiraj Neupane; Jongwon Seok Bearing fault detection and diagnosis using case western reserve university dataset with deep learning approaches: A review, IEEE Access, Volume 8 (2020), pp. 93155-93178 | DOI

[2] Hasan Ocak; Kenneth A. Loparo Estimation of the running speed and bearing defect frequencies of an induction motor from vibration data, Mech. Syst. Signal Process., Volume 18 (2004) no. 3, pp. 515-533 | DOI

[3] Sandaram Buchaiah; Piyush Shakya Bearing fault diagnosis and prognosis using data fusion based feature extraction and feature selection, Meas., Volume 188 (2022), 110506 | DOI

[4] Pankaj Gupta; Mohan K. Pradhan Fault detection analysis in rolling element bearing: A review, Mater. Today: Proc., Volume 4 (2017) no. 2, 061001, pp. 2085-2094

[5] Mehdi Behzad; Hassan Izanlo; Ali Davoodabadi; Hesam Addin Arghand Fault detection of rolling element bearing using a temporal signal with artificial intelligence techniques, J. Theor. Appl. Vibr. Acoust., Volume 7 (2021) no. 1, pp. 55-71

[6] Mehdi Behzad; Sajjad Feizhoseini; Hesam Addin Arghand; Ali Davoodabadi; David Mba Failure threshold determination of rolling element bearings using vibration fluctuation and failure modes, Appl. Sci. (Switz.), Volume 11 (2021) no. 1, 160, 18 pages

[7] Abd Kadir Mahamad; Sharifah Saon; Takashi Hiyama Predicting remaining useful life of rotating machinery based artificial neural network, Comput. Math. Appl., Volume 60 (2010) no. 4, pp. 1078-1087 | DOI | Zbl

[8] D. Ho; R. B. Randall Optimisation of bearing diagnostic techniques using simulated and actual bearing fault signals, Mech. Syst. Signal Process., Volume 14 (2000) no. 5, pp. 763-788 | DOI

[9] P. D. McFadden; J. D. Smith Model for the vibration produced by a single point defect in a rolling element bearing, J. Sound Vib., Volume 96 (1984) no. 1, pp. 69-82 | DOI

[10] Olof G. Gustafsson; Tibor Tallian Detection of damage in assembled rolling element bearings, ASLE Trans., Volume 5 (1962) no. 1, 115190, pp. 197-209 | DOI

[11] Jay Lee; Fangji Wu; Wenyu Zhao; Masoud Ghaffari; Linxia Liao; David Siegel Prognostics and health management design for rotary machinery systems — Reviews, methodology and applications, Mech. Syst. Signal Process., Volume 42 (2014) no. 1–2, 105363, pp. 314-334 | DOI

[12] Jihed Hayouni Développement d’un modèle de pronostic pour les roulements des éoliennes, Ph. D. Thesis, Université du Québec à Rimouski (Canada) (2017)

[13] N. S. Jammu; P. K. Kankar A review on prognosis of rolling element bearings, Int. J. Eng. Sci. Technol., Volume 3 (2011) no. 10, pp. 7497-7503

[14] Seokgoo Kim; Joo-Ho Choi; Nam H. Kim Challenges and opportunities of system-level prognostics, Sensors, Volume 21 (2021) no. 22, 7655, 25 pages | DOI

[15] Kamal Medjaher; Diego Alejandro Tobon-Mejia; Noureddine Zerhouni Remaining useful life estimation of critical components with application to bearings, IEEE Trans. Reliab., Volume 61 (2012) no. 2, 109950, pp. 292-302 | DOI

[16] Diego Alejandro Tobon-Mejia; Kamal Medjaher; Noureddine Zerhouni; Gerard Tripot A mixture of gaussians hidden markov model for failure diagnostic and prognostic, 2010 IEEE International Conference on Automation Science and Engineering, IEEE (2010), 104703, pp. 338-343 | DOI

[17] Dawn An; Nam H. Kim; Joo-Ho Choi Practical options for selecting data-driven or physics-based prognostics algorithms with reviews, Reliab. Eng. Syst. Saf., Volume 133 (2015), pp. 223-236

[18] Xiao-Sheng Si; Wenbin Wang; Chang-Hua Hu; Dong-Hua Zhou Remaining useful life estimation — A review on the statistical data driven approaches, Eur. J. Oper. Res., Volume 213 (2011) no. 1, 115930, pp. 1-14 | MR

[19] Wei Kufi Yu; Tedric A. Harris A new stress-based fatigue life model for ball bearings, Tribol. Trans., Volume 44 (2001) no. 1, pp. 11-18 | DOI

[20] Arvid Palmgren The service life of ball bearings, Z. Vereines Deutscher Inge., Volume 68 (1924) no. 14, pp. 339-341

[21] Yawei Hu; Shujie Liu; Huitian Lu; Hongchao Zhang Remaining useful life model and assessment of mechanical products: a brief review and a note on the state space model method, Chin. J. Mech. Eng., Volume 32 (2019), pp. 1-20 | DOI

[22] Kamal Medjaher; Noureddine Zerhouni; Jihene Baklouti Data-driven prognostics based on health indicator construction: Application to PRONOSTIA’s data, 2013 European Control Conference (ECC), IEEE (2013), pp. 1451-1456 | DOI

[23] Theodoros H. Loutas; Dimitrios Roulias; George Georgoulas Remaining useful life estimation in rolling bearings utilizing data-driven probabilistic E-support vectors regression, IEEE Trans. Reliab., Volume 62 (2013) no. 4, 105654, pp. 821-832 | DOI

[24] Andrew KS Jardine; Daming Lin; Dragan Banjevic A review on machinery diagnostics and prognostics implementing condition-based maintenance, Mech. Syst. Signal Process., Volume 20 (2006) no. 7, pp. 1483-1510 | DOI

[25] Qing Zhang; Cheng Hua; Guanghua Xu A mixture Weibull proportional hazard model for mechanical system failure prediction utilising lifetime and monitoring data, Mech. Syst. Signal Process., Volume 43 (2014) no. 1–2, pp. 103-112 | DOI

[26] Wahyu Caesarendra; Achmad Widodo; Bo-Suk Yang Application of relevance vector machine and logistic regression for machine degradation assessment, Mech. Syst. Signal Process., Volume 24 (2010) no. 4, pp. 1161-1171 | DOI

[27] Jaouher Ben Ali; Brigitte Chebel-Morello; Lotfi Saidi; Simon Malinowski; Farhat Fnaiech Accurate bearing remaining useful life prediction based on Weibull distribution and artificial neural network, Mech. Syst. Signal Process., Volume 56 (2015), pp. 150-172 | DOI

[28] Junyu Guo; Zhiyuan Wang; He Li; Yulai Yang; Cheng-Geng Huang; Mohammad Yazdi; Hooi Siang Kang A hybrid prognosis scheme for rolling bearings based on a novel health indicator and nonlinear Wiener process, Reliab. Eng. Syst. Saf., Volume 245 (2024), 110014, 16 pages | DOI

[29] Fengtao Wang; Bei Wang; Bosen Dun; Xutao Chen; Dawen Yan; Hong Zhu Remaining life prediction of rolling bearing based on PCA and improved logistic regression model, J. Vibroeng., Volume 18 (2016) no. 8, pp. 5192-5203 | DOI

[30] J. Stuart Hunter The exponentially weighted moving average, J. Qual. Technol., Volume 18 (1986) no. 4, 113852, pp. 203-210 | DOI

[31] Lawrence R. Rabiner; Bernard Gold Theory and Application of Digital Signal Processing, Prentice Hall, 1975, 104931

[32] Chou Ya-Lun Statistical Analysis: With Business and Economic Applications, Holt, Rinehart and Winston, 1963

[33] Seng Hansun A new approach of moving average method in time series analysis, 2013 Conference on New Media Studies (CoNMedia), IEEE (2013), 118592, pp. 1-4 | DOI

[34] Yaxi Su; Chaoran Cui; Hao Qu Self-attentive moving average for time series prediction, Appl. Sci. (Switz.), Volume 12 (2022) no. 7, 3602 | DOI

[35] Akthem Rehab; Islam Ali; Walid Gomaa; M Nashat Fors Bearings fault detection using hidden Markov models and principal component analysis enhanced features (2021), 118188 | arXiv

[36] Jorge J. Moré The Levenberg-Marquardt algorithm: implementation and theory, Numerical analysis: Proceedings of the biennial Conference held at Dundee, June 28–July 1, 1977, Springer (2006), 116967, pp. 105-116 | MR

[37] Yangyang Zhang; Liqing Fang; Ziyuan Qi; Huiyong Deng A review of remaining useful life prediction approaches for mechanical equipment, IEEE Sens. J., Volume 23 (2023) no. 24, e7439, pp. 29991-30006 | DOI

[38] Naipeng Li; Yaguo Lei; Xiaofei Liu; Tao Yan; Pengcheng Xu Machinery health prognostics with multimodel fusion degradation modeling, IEEE Trans. Ind. Electron., Volume 70 (2022) no. 11, pp. 11764-11773 | DOI

[39] Jay Lee; Hai. Qiu; Gang Yu; Jing Lin IMS, University of Cincinnati. “Bearing Data Set”, NASA Ames Prognostics Data Repository, 113756 https://data.nasa.gov/dataset/ims-bearings (Accessed 2025-11-04)

[40] Hai Qiu; Jay Lee; Jing Lin; Gang Yu Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics, J. Sound Vib., Volume 289 (2006) no. 4–5, 105076, pp. 1066-1090 | DOI

[41] Abdenour Soualhi; Hubert Razik; Guy Clerc; Dinh Dong Doan Prognosis of bearing failures using hidden Markov models and the adaptive neuro-fuzzy inference system, IEEE Trans. Ind. Electron., Volume 61 (2013) no. 6, pp. 2864-2874 | DOI

[42] William Gousseau; Jérôme Antoni; François Girardin; Julien Griffaton Analysis of the Rolling Element Bearing data set of the Center for Intelligent Maintenance Systems of the University of Cincinnati (2016) | HAL

[43] NASA Prognostics Center of Excellence Data Set Repository https://www.nasa.gov/... (Accessed 2025-11-04) | arXiv

[44] James Kuria Kimotho; Walter Sextro An approach for feature extraction and selection from non-trending data for machinery prognosis, Proceedings of the European Conference of the PHM Society 2014, Vol. 2, No. 1, PHM Society (2014) | DOI

[45] Abderrahmane Ben Yagoub; Ridha Ziani Supplementary information to “Bearing fault prognosis based on Cyclical Remaining Useful Life (CRUL)”, Comptes Rendus. Mécanique, 2025 (2025), 115225 | DOI

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