IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v256y2025ics0951832024007774.html

Vibration response-based time-variant reliability and sensitivity analysis of rolling bearings using the first-passage method

Author

Listed:
  • Xie, Bin
  • Wang, Yanzhong
  • Zhu, Yunyi
  • E, Shiyuan
  • Wu, Yu

Abstract

The vibration response of rolling bearings exhibits random and uncertain characteristics due to factors such as random process loads, material property degradation, and uncertain dimensional parameters. The time-variant reliability of rolling bearings obtained based on such vibration response is more realistic and accurate. In this paper, a novel vibration response-based time-variant reliability and sensitivity analysis model of rolling bearings is proposed. First, the forces on the rolling bearing are analyzed and the stress distribution is derived. Then, the equivalent stiffness and damping in the bearing vibration equation are obtained based on the ball-raceway contact model. To approximate the real degradation process, the vibration equation considering the impact load is proposed, and the statistical characteristics of the impact load with time are obtained from degradation data of the conducted bearing tests. Subsequently, the first-passage method is adopted to efficiently evaluate the time-variant reliability of rolling bearings based on the vibration response. In addition, reliability sensitivity index is derived to analyze the influence of input parameters on the reliability of rolling bearings, which improves design efficiency and provides references for further structural optimization. The accuracy and validity of the proposed model and method are verified by two cases of different bearing types.

Suggested Citation

  • Xie, Bin & Wang, Yanzhong & Zhu, Yunyi & E, Shiyuan & Wu, Yu, 2025. "Vibration response-based time-variant reliability and sensitivity analysis of rolling bearings using the first-passage method," Reliability Engineering and System Safety, Elsevier, vol. 256(C).
    • Handle: RePEc:eee:reensy:v:256:y:2025:i:c:s0951832024007774
    DOI: 10.1016/j.ress.2024.110706
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832024007774
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2024.110706?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Wang, Jinsheng & Xu, Guoji & Yuan, Peng & Li, Yongle & Kareem, Ahsan, 2024. "An efficient and versatile Kriging-based active learning method for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    2. Chan, Jianpeng & Papaioannou, Iason & Straub, Daniel, 2022. "An adaptive subset simulation algorithm for system reliability analysis with discontinuous limit states," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    3. Wang, Zhonglai & Liu, Jing & Yu, Shui, 2020. "Time-variant reliability prediction for dynamic systems using partial information," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    4. Gao, Shuzhi & Zhang, Sixuan & Zhang, Yimin & Gao, Yue, 2020. "Operational reliability evaluation and prediction of rolling bearing based on isometric mapping and NoCuSa-LSSVM," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    5. Zhang, Yang & Xu, Jun & Beer, Michael, 2023. "A single-loop time-variant reliability evaluation via a decoupling strategy and probability distribution reconstruction," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    6. Dong, Y. & Teixeira, A.P. & Guedes Soares, C., 2020. "Application of adaptive surrogate models in time-variant fatigue reliability assessment of welded joints with surface cracks," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    7. Dong, Y. & Teixeira, A.P. & Guedes Soares, C., 2018. "Time-variant fatigue reliability assessment of welded joints based on the PHI2 and response surface methods," Reliability Engineering and System Safety, Elsevier, vol. 177(C), pages 120-130.
    8. Zhang, Xuan-Yi & Lu, Zhao-Hui & Wu, Shi-Yu & Zhao, Yan-Gang, 2021. "An Efficient Method for Time-Variant Reliability including Finite Element Analysis," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    9. Zhao, Zhao & Zhao, Yan-Gang & Li, Pei-Pei, 2023. "A novel decoupled time-variant reliability-based design optimization approach by improved extreme value moment method," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    10. Lyu, Hao & Qu, Hongchen & Yang, Zaiyou & Ma, Li & Lu, Bing & Pecht, Michael, 2023. "Reliability analysis of dependent competing failure processes with time-varying δ shock model," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    11. Chiron, Marie & Genest, Christian & Morio, Jérôme & Dubreuil, Sylvain, 2023. "Failure probability estimation through high-dimensional elliptical distribution modeling with multiple importance sampling," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    12. Li, Guofa & Wei, Jingfeng & He, Jialong & Yang, Haiji & Meng, Fanning, 2023. "Implicit Kalman filtering method for remaining useful life prediction of rolling bearing with adaptive detection of degradation stage transition point," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    13. Xie, Bin & Wang, Yanzhong & Zhu, Yunyi & Liu, Peng & Wu, Yu & Lu, Fengxia, 2024. "Time-variant reliability analysis of angular contact ball bearing considering the coupled effect of rolling contact fatigue damage and wear," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    14. Wang, Yanzhong & Xie, Bin & E, Shiyuan, 2022. "Adaptive relevance vector machine combined with Markov-chain-based importance sampling for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    15. Breitung, Karl, 1988. "Asymptotic crossing rates for stationary Gaussian vector processes," Stochastic Processes and their Applications, Elsevier, vol. 29(2), pages 195-207, September.
    16. Cui, L.X. & Du, Yi-Mu & Sun, C.P., 2023. "On system reliability for time-varying structure," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    17. Pepper, Nick & Crespo, Luis & Montomoli, Francesco, 2022. "Adaptive learning for reliability analysis using Support Vector Machines," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    18. Dai, Le & Guo, Junyu & Wan, Jia-Lun & Wang, Jiang & Zan, Xueping, 2022. "A reliability evaluation model of rolling bearings based on WKN-BiGRU and Wiener process," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    19. Lima, João P.S. & Evangelista, F. & Guedes Soares, C., 2023. "Hyperparameter-optimized multi-fidelity deep neural network model associated with subset simulation for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    20. Zheng, Weiming & Yuan, Xiukai & Bao, Xiya & Dong, Yiwei, 2025. "Adaptive support vector machine for time-variant failure probability function estimation," Reliability Engineering and System Safety, Elsevier, vol. 253(C).
    21. Li, Peiping & Wang, Yu, 2022. "An active learning reliability analysis method using adaptive Bayesian compressive sensing and Monte Carlo simulation (ABCS-MCS)," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    22. Zhou, Haoxuan & Wang, Bingsen & Zio, Enrico & Wen, Guangrui & Liu, Zimin & Su, Yu & Chen, Xuefeng, 2023. "Hybrid system response model for condition monitoring of bearings under time-varying operating conditions," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    23. Ouyang, Linhan & Che, Yushuai & Park, Chanseok & Chen, Yuejian, 2024. "A novel active learning Gaussian process modeling-based method for time-dependent reliability analysis considering mixed variables," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gong, Yi & Cheung, Sai Hung, 2026. "Adaptive physics-informed neural operator and subset simulation for high-dimensional reliability analysis with multiple stochastic processes in stochastic differential equations," Reliability Engineering and System Safety, Elsevier, vol. 268(C).
    2. Liu, Yongzhen & Li, Tao & Hu, Peng & Feng, Cong, 2026. "Modeling and reliability analysis of rolling bearing clearance based on assembly parameters," Reliability Engineering and System Safety, Elsevier, vol. 267(PB).
    3. Zhou, Di & Chen, Zhen & Chen, Zhaoxiang & Han, Jinrui & Pan, Ershun, 2025. "Dynamic reliability evaluation considering the stochastic evolving process based on extreme characteristics of system responses," Reliability Engineering and System Safety, Elsevier, vol. 260(C).
    4. Xiao, Sinan & Nowak, Wolfgang, 2026. "Reliability sensitivity analysis with multiple failure domains based on an extended two-stage Markov chain Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 266(PA).
    5. Wu, Shengnan & Zhang, Laibin & Liu, Tianqi & Liu, Tianhao & Liu, Yiliu, 2026. "A Machine learning-based framework for reliability prediction of metallic seals with manufacturing-induced dimensional uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 269(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Yang & Xu, Jun & Beer, Michael, 2023. "A single-loop time-variant reliability evaluation via a decoupling strategy and probability distribution reconstruction," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    2. Hao, Peng & Tian, Haojun & Yang, Hao & Zhang, Yue & Feng, Shaojun, 2025. "An efficient sequential Kriging model for structure safety lifetime analysis considering uncertain degradation," Reliability Engineering and System Safety, Elsevier, vol. 255(C).
    3. Xie, Bin & Wang, Yanzhong & Zhu, Yunyi & Liu, Peng & Wu, Yu & Lu, Fengxia, 2024. "Time-variant reliability analysis of angular contact ball bearing considering the coupled effect of rolling contact fatigue damage and wear," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    4. Ouyang, Linhan & Che, Yushuai & Park, Chanseok & Chen, Yuejian, 2024. "A novel active learning Gaussian process modeling-based method for time-dependent reliability analysis considering mixed variables," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    5. Jiang, Xia & Lu, Zhenzhou, 2024. "A novel quantile-based sequential optimization and reliability assessment method for safety life analysis," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    6. Liu, Bo & Li, Jia & Zhang, Wei & Shi, Lei & Li, Keke, 2026. "Cavitation reliability assessment of aviation fuel centrifugal pumps combining kriging and subset simulation important sampling," Reliability Engineering and System Safety, Elsevier, vol. 266(PA).
    7. Zhang, Yang & Xu, Jun & Gardoni, Paolo, 2024. "A loading contribution degree analysis-based strategy for time-variant reliability analysis of structures under multiple loading stochastic processes," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    8. Hu, Zhuo & Dang, Chao & Wang, Da & Beer, Michael & Wang, Lei, 2025. "Error-informed parallel adaptive Kriging method for time-dependent reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 262(C).
    9. Dong, Manman & Cheng, Yongbo & Wan, Liangqi, 2024. "A new adaptive multi-kernel relevance vector regression for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    10. Che, Yushuai & Ma, Yizhong & Chen, Hui & Ma, Yan, 2026. "Multi-fidelity Kriging structural reliability analysis with the fusion of non-hierarchical low-fidelity models," Reliability Engineering and System Safety, Elsevier, vol. 266(PA).
    11. Qian, Hua-Ming & Li, Yan-Feng & Huang, Hong-Zhong, 2021. "Time-variant system reliability analysis method for a small failure probability problem," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    12. Zha, Congyi & Pan, Chenrong & Sun, Zhili & Liu, Qin, 2024. "A single-loop reliability sensitivity analysis strategy for time-dependent rare events with both random variables and stochastic processes," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    13. Zhang, Long-Wen & Dang, Chao & Zhao, Yan-Gang, 2023. "An efficient method for accessing structural reliability indexes via power transformation family," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    14. Yu, Ting & Lu, Zhenzhou & Yun, Wanying, 2023. "An efficient algorithm for analyzing multimode structure system reliability by a new learning function of most reducing average probability of misjudging system state," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    15. Yu, Shui & Ren, Yuyao & Wu, Xiao & Guo, Peng & Li, Yun, 2024. "Dynamic pruning-based Bayesian support vector regression for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    16. Jian Wang & Xiang Gao & Zhili Sun, 2021. "A Multilevel Simulation Method for Time-Variant Reliability Analysis," Sustainability, MDPI, vol. 13(7), pages 1-16, March.
    17. Wang, Jinsheng & Xu, Guoji & Zhou, Jiaguo & Li, Yongle & Xue, Shihao & Mitoulis, Stergios-Aristoteles, 2026. "PAKP: Parallelized Adaptive Kriging method with Partial least squares for high-dimensional reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 265(PA).
    18. Nguyen, Phong T.T. & Manuel, Lance, 2024. "Uncertainty quantification in low-probability response estimation using sliced inverse regression and polynomial chaos expansion," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    19. Cui, Yifan & Hong, Fangqi & Kitahara, Masaru & Wei, Pengfei, 2025. "Time-variant reliability analysis using stratified Beta-sphere sampling and active learning," Reliability Engineering and System Safety, Elsevier, vol. 264(PA).
    20. van Essen, Sanne M. & Seyffert, Harleigh C., 2025. "Designing for dangerous waves – a new ‘Adaptive Screening’ method to predict extreme values of non-linear marine and coastal structure responses to waves," Reliability Engineering and System Safety, Elsevier, vol. 264(PB).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:256:y:2025:i:c:s0951832024007774. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.