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Stochastic process-based degradation modeling and RUL prediction: from Brownian motion to fractional Brownian motion

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Abstract

Brownian motion (BM) has been widely used for degradation modeling and remaining useful life (RUL) prediction, but it is essentially Markovian. This implies that the future state in a BM-based degradation process relies only on its current state, independent of the past states. However, some practical industrial devices such as Li-ion batteries, ball bearings, turbofans, and blast furnace walls show degradations with long-range dependence (LRD), where the future degradation states depend on both the current and past degradation states. This type of degradation naturally brings two interesting problems, that is, how to model the degradations and how to predict their RULs. Recently, in contrast to the work that uses only BM, fractional Brownian motion (FBM) is introduced to model practical degradations. The most important feature of the FBM-based degradation models is the ability to characterize the non-Markovian degradations with LRD. Although FBM is an extension of BM, it is neither a Markovian process nor a semimartingale. Therefore, how to obtain the first passage time of an FBM-based degradation process has become a challenging task. In this paper, a review of the transition of RUL prediction from BM to FBM is provided. The peculiarities of FBM when addressing the LRD inherent in some practical degradations are discussed. We first review the BM-based degradation models of the past few decades and then give details regarding the evolution of FBM-based research. Interestingly, the existing BM-based models scarcely consider the effect of LRD on the prediction of RULs. Two practical cases illustrate that the newly developed FBM-based models are more generalized and suitable for predicting RULs than the BM-based models, especially for degradations with LRD. Along with the direction of FBM-based RUL prediction, we also introduce some important and interesting problems that require further study.

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Acknowledgements

This work was supported by National Key Research and Development Program of China (Grant No. 2018YFC0809300), National Natural Science Foundation of China (Grant Nos. 61903326, 61873143), China Postdoctoral Science Foundation (Grant No. 2019M662051), and Zhejiang Province Postdoctoral Science Foundation (Grant No. ZJ2019093).

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Authors and Affiliations

  1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Hanwen Zhang

  2. State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou, 310027, China

    Hanwen Zhang, Chunjie Yang & Youxian Sun

  3. Department of Automation, Tsinghua University, Beijing, 100084, China

    Maoyin Chen

  4. School of Automation and Electrical Engineering, Linyi University, Linyi, 276005, China

    Maoyin Chen

  5. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada

    Jun Shang

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  1. Hanwen Zhang
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  2. Maoyin Chen
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  3. Jun Shang
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  4. Chunjie Yang
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  5. Youxian Sun
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Correspondence to Maoyin Chen.

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Zhang, H., Chen, M., Shang, J. et al. Stochastic process-based degradation modeling and RUL prediction: from Brownian motion to fractional Brownian motion. Sci. China Inf. Sci. 64, 171201 (2021). https://doi.org/10.1007/s11432-020-3134-8

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  • DOI: https://doi.org/10.1007/s11432-020-3134-8

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