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Nonlinear degradation modeling and prognostics: A Box-Cox transformation perspective

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  • Si, Xiao-Sheng
  • Li, Tianmei
  • Zhang, Jianxun
  • Lei, Yaguo

Abstract

Transforming nonlinear degradation paths into nearly linear ones has been widely used for nonlinear degradation modeling and prognostics. However, types of the current transformation functions are difficult to determine. This paper addresses issues in nonlinear stochastic degradation modeling and prognostics from a Box-Cox transformation (BCT) perspective. Specifically, the BCT is first used to transform the nonlinear degradation data into nearly linear data, and then the Wiener process with random drift is utilized to model the evolving process of the transformed data. To determine the model parameters, a two-stage estimation procedure is developed including offline stage and online stage. In the offline stage, the parameters are determined via maximum likelihood estimation method based on the historical degradation data and such estimated values are used to initialize the online stage. During the online stage, the Bayesian method is adopted to update the model parameters using the data of the degrading system in service, in which the hyperparameters are updated by the expectation maximization algorithm. A closed-form solution to remaining useful life with updated model parameters is further derived for prognostics. Finally, case studies for lithium-ion batteries and liquid coupling devices are provided to demonstrate the proposed approach.

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  • Si, Xiao-Sheng & Li, Tianmei & Zhang, Jianxun & Lei, Yaguo, 2022. "Nonlinear degradation modeling and prognostics: A Box-Cox transformation perspective," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
  • Handle: RePEc:eee:reensy:v:217:y:2022:i:c:s0951832021006165
    DOI: 10.1016/j.ress.2021.108120
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    1. Li, Rui & Verhagen, Wim J.C. & Curran, Richard, 2020. "A systematic methodology for Prognostic and Health Management system architecture definition," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    2. Kristen A. Severson & Peter M. Attia & Norman Jin & Nicholas Perkins & Benben Jiang & Zi Yang & Michael H. Chen & Muratahan Aykol & Patrick K. Herring & Dimitrios Fraggedakis & Martin Z. Bazant & Step, 2019. "Data-driven prediction of battery cycle life before capacity degradation," Nature Energy, Nature, vol. 4(5), pages 383-391, May.
    3. Zhang, Mimi & Gaudoin, Olivier & Xie, Min, 2015. "Degradation-based maintenance decision using stochastic filtering for systems under imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 245(2), pages 531-541.
    4. Wei-an Yan & Bao-wei Song & Gui-lin Duan & Yi-min Shi, 2017. "Real-time reliability evaluation of two-phase Wiener degradation process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(1), pages 176-188, January.
    5. Salman Jahani & Raed Kontar & Shiyu Zhou & Dharmaraj Veeramani, 2020. "Remaining useful life prediction based on degradation signals using monotonic B-splines with infinite support," IISE Transactions, Taylor & Francis Journals, vol. 52(5), pages 537-554, May.
    6. Wang, Han & Liao, Haitao & Ma, Xiaobing & Bao, Rui, 2021. "Remaining Useful Life Prediction and Optimal Maintenance Time Determination for a Single Unit Using Isotonic Regression and Gamma Process Model," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    7. Zhang, Zhengxin & Si, Xiaosheng & Hu, Changhua & Lei, Yaguo, 2018. "Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods," European Journal of Operational Research, Elsevier, vol. 271(3), pages 775-796.
    8. Si, Xiao-Sheng & Wang, Wenbin & Hu, Chang-Hua & Zhou, Dong-Hua, 2011. "Remaining useful life estimation - A review on the statistical data driven approaches," European Journal of Operational Research, Elsevier, vol. 213(1), pages 1-14, August.
    9. Li, Naipeng & Gebraeel, Nagi & Lei, Yaguo & Fang, Xiaolei & Cai, Xiao & Yan, Tao, 2021. "Remaining useful life prediction based on a multi-sensor data fusion model," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    10. Si, Xiao-Sheng & Wang, Wenbin & Chen, Mao-Yin & Hu, Chang-Hua & Zhou, Dong-Hua, 2013. "A degradation path-dependent approach for remaining useful life estimation with an exact and closed-form solution," European Journal of Operational Research, Elsevier, vol. 226(1), pages 53-66.
    11. Chiachío, Juan & Jalón, María L. & Chiachío, Manuel & Kolios, Athanasios, 2020. "A Markov chains prognostics framework for complex degradation processes," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
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