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Volume 9 Issue 5
May  2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2022  >  9(5): 907-921
Z. N. Pang, X. S. Si, C. H. Hu, and Z. X. Zhang, “An age-dependent and state-dependent adaptive prognostic approach for hidden nonlinear degrading system,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 5, pp. 907–921, May 2022. doi: 10.1109/JAS.2021.1003859
Citation: Z. N. Pang, X. S. Si, C. H. Hu, and Z. X. Zhang, “An age-dependent and state-dependent adaptive prognostic approach for hidden nonlinear degrading system,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 5, pp. 907–921, May 2022. doi: 10.1109/JAS.2021.1003859
shu

An Age-Dependent and State-Dependent Adaptive Prognostic Approach for Hidden Nonlinear Degrading System

doi: 10.1109/JAS.2021.1003859

  • Department of Automation, Rocket Force University of Engineering, Xi’an 710025, China

Funds:  This work was supported by the National Key R&D Program of China (2018YFB1306100), the National Natural Science Foundation of China (61922089, 61833016, 62073336, 61903376, 61773386), the National Science Foundation of Shannxi Province (2020JQ-489, 2020JM-360)
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    Abstract
  • Remaining useful life (RUL) estimation approaches on the basis of the degradation data have been greatly developed, and significant advances have been witnessed. Establishing an applicable degradation model of the system is the foundation and key to accurately estimating its RUL. Most current researches focus on age-dependent degradation models, but it has been found that some degradation processes in engineering are also related to the degradation states themselves. In addition, due to different working conditions and complex environments in engineering, the problems of the unit-to-unit variability in the degradation process of the same batch of systems and actual degradation states cannot be directly observed will affect the estimation accuracy of the RUL. In order to solve the above issues jointly, we develop an age-dependent and state-dependent nonlinear degradation model taking into consideration the unit-to-unit variability and hidden degradation states. Then, the Kalman filter (KF) is utilized to update the hidden degradation states in real time, and the expectation-maximization (EM) algorithm is applied to adaptively estimate the unknown model parameters. Besides, the approximate analytical RUL distribution can be obtained from the concept of the first hitting time. Once the new observation is available, the RUL distribution can be updated adaptively on the basis of the updated degradation states and model parameters. The effectiveness and accuracy of the proposed approach are shown by a numerical simulation and case studies for Li-ion batteries and rolling element bearings.

     

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    • References(49)
  • [1]
    M. Pecht, Prognostics and Health Management of Electronics. New York, NY, USA: John Wiley, 2008.
    [2]
    X. S. Si, T. M. Li, and Q. Zhang, “Optimal replacement of degrading components: A control-limit policy,” SCIENCE CHINA Information Sciences, vol. 64, no. 10, p. 209205, 2021.
    [3]
    X. S. Si, C. H. Hu, T. M. Li, and Q. Zhang, “A joint order-replacement policy for deteriorating components with reliability constraint,” SCIENCE CHINA Information Sciences, vol. 64, no. 8, p. 189203, 2021.
    [4]
    A. Lorton, M. Fouladirad, and A. Grall, “Methodology for probabilistic model-based prognosis,” Eur. J. Oper. Res., vol. 225, pp. 443–454, 2013. doi: 10.1016/j.ejor.2012.10.025
    [5]
    X. S. Si, T. M. Li, Q. Zhang, and X. Hu, “An optimal condition-based replacement method for systems with observed degradation signals,” IEEE Trans. Rel., vol. 67, no. 3, pp. 1281–1293, 2018. doi: 10.1109/TR.2018.2830188
    [6]
    X. S. Si, W. B. Wang, C. H. Hu, and D. H. Zhou, “Remaining useful life estimation–A review on the statistical data driven approaches,” Eur. J. Oper. Res., vol. 213, no. 1, pp. 1–14, 2011. doi: 10.1016/j.ejor.2010.11.018
    [7]
    P. P. Wang, Y. C. Tang, S. J. Bae, and Y. He, “Bayesian analysis of two-phase degradation data based on change-point Wiener process,” Rel. Eng. Syst. Saf., vol. 170, pp. 244–256, 2018. doi: 10.1016/j.ress.2017.09.027
    [8]
    X. S. Si, T. M. Li, Q. Zhang, and C. H. Hu. “Prognostics for linear stochastic degrading systems with survival measurements,” IEEE Trans. Ind. Electron., DOI: 10.1109/TIE.2019.2908617, 2019.
    [9]
    A. C. Xu, L. J. Chen, B. X. Wang, and Y. C. Tang, “On modeling bivariate Wiener degradation process,” IEEE Trans. Rel., vol. 67, no. 3, pp. 897–906, 2018. doi: 10.1109/TR.2018.2791616
    [10]
    M. E. Cholette, H. Y. Yu, P. Borghesani, M. Lin, and K. Geoff, “Degradation modeling and condition-based maintenance of boiler heat exchangers using Gamma processes,” Rel. Eng. Syst. Saf., vol. 183, pp. 184–196, 2019. doi: 10.1016/j.ress.2018.11.023
    [11]
    P. H. Jiang, X. W. Bing, and T. W. Fang, “Inference for constant-stress accelerated degradation test based on Gamma process,” Applied Mathematical Modelling, vol. 67, pp. 123–134, 2019. doi: 10.1016/j.apm.2018.10.017
    [12]
    W. W. Peng, Y. F. Li, Y. J. Yang, J. H. Mi, and H. Z. Huang, “Bayesian degradation analysis with inverse Gaussian process models under time-varying degradation rates,” IEEE Trans. Rel., vol. 66, no. 1, pp. 84–96, 2017. doi: 10.1109/TR.2016.2635149
    [13]
    J. B. Guo, C. X. Wang, J. Cabrera, and E. A. Elsayed, “Improved inverse Gaussian process and bootstrap: Degradation and reliability metrics,” Reliability Engineering &System Safety, vol. 178, pp. 269–277, 2018.
    [14]
    W. W. Peng, S. P. Zhu, and L. J. Shen, “The transformed inverse Gaussian process as an age-and state-dependent degradation model,” Applied Mathematical Modelling, vol. 75, pp. 837–852, 2019. doi: 10.1016/j.apm.2019.07.004
    [15]
    Z. S. Ye, N. Chen, and Y. Shen, “A new class of Wiener process models for degradation analysis,” Rel. Eng. Syst. Safety, vol. 138, pp. 58–67, 2015.
    [16]
    J. X. Zhang, C. H. Hu, X. He, X. S. Si, Y. Liu, and D. H. Zhou, “Lifetime prognostics for furnace wall degradation with time-varying random jumps,” Rel. Eng. Syst. Safety, vol. 167, pp. 338–350, 2017. doi: 10.1016/j.ress.2017.05.047
    [17]
    N. P. Li, N. Gebraeel, Y. G. Lei, L. K. Bian, and X. S. Si, “Remaining useful life prediction of machinery under time-varying operating conditions based on a two-factor state space model,” Rel. Eng. Syst. Safety, vol. 186, pp. 88–100, 2019. doi: 10.1016/j.ress.2019.02.017
    [18]
    Z. X. Zhang, X. S. Si, C. H. Hu, and Y. G. Lei, “Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods,” Eur. J. Oper. Res., vol. 271, no. 3, pp. 775–796, 2018. doi: 10.1016/j.ejor.2018.02.033
    [19]
    P. C. Paris and F. Erdogan, “A critical analysis of crack propagation laws,” Journal of Fluids Engineering, vol. 85, no. 4, pp. 528–533, 1963.
    [20]
    M. Giorgio, M. Guida, and G. Pulcini, “A parametric Markov chain to model age-and state-dependent wear processes”, in Complex Data Modelling and Computationally Intensive Statistical Methods”, Milan, Italy: Springer, 2010, pp. 85–97.
    [21]
    M. Giorgio, M. Guida, and G. Pulcini, “An age-and state-dependent Markov model for degradation processes,” IIE Transactions, vol. 43, pp. 621–632, 2011.
    [22]
    Z. X. Zhang, X. S. Si, and C. H. Hu, “An age-and state-dependent nonlinear prognostic model for degrading systems,” IEEE Trans. Rel., vol. 64, no. 4, pp. 1214–1228, 2015. doi: 10.1109/TR.2015.2419220
    [23]
    D. An, J. H. Choi, and N. H. Kim, “Prognostics 101: A tutorial for particle filter-based prognostics algorithm using Matlab,” Reliability Engineering &System Safety, vol. 115, pp. 161–169, 2013.
    [24]
    M. E. Orchard, P. Hevia-Koch, B. Zhang, and L. Tang, “Risk measures for particle-filtering-based state-of-charge prognosis in lithium-ion batteries,” IEEE Trans. Industrial Electronics, vol. 60, no. 11, pp. 5260–5269, Nov. 2013. doi: 10.1109/TIE.2012.2224079
    [25]
    N. P. Li, Y. G. Lei, L. Guo, T. Yan, and J. Lin, “Remaining useful life prediction based on a general expression of stochastic process models,” IEEE Trans. Industrial Electronics, vol. 64, pp. 5709–5718, Jul. 2017. doi: 10.1109/TIE.2017.2677334
    [26]
    H. W. Zhang, D. H. Zhou, M. Y. Chen, and X. P. Xi, “Predicting remaining useful life based on a generalized degradation with fractional Brownian motion,” Mech. Syst. Signal Process, vol. 115, pp. 736–752, 2019. doi: 10.1016/j.ymssp.2018.06.029
    [27]
    X. S. Si, W. Wang, C. H. Hu, D. H. Zhou, and M. G. Pecht, “Remaining useful life estimation based on a nonlinear diffusion degradation process,” IEEE Trans. Rel., vol. 61, no. 1, pp. 50–67, 2012. doi: 10.1109/TR.2011.2182221
    [28]
    J. X. Zhang, C. H. Hu, X. He, X. S. Si, Y. Liu, and D. H. Zhou, “A novel lifetime estimation method for two-phase degrading systems,” IEEE Trans. Rel., vol. 68, no. 2, pp. 689–709, 2018.
    [29]
    N. P. Li, Y. G. Lei, T. Yan, N. B. Li, and T. Y. Han, “A Wiener process model-based method for remaining useful life prediction considering unit-to-unit variability,” IEEE Trans. Industrial Electronics, vol. 66, no. 3, pp. 2092–2101, 2019. doi: 10.1109/TIE.2018.2838078
    [30]
    J. F. Zheng, X. S. Si, C. H. Hu, Z. X. Zhang, and W. Jiang, “A nonlinear prognostic model for degrading systems with three-source variability,” IEEE Trans. Rel., vol. 65, no. 2, pp. 736–750, 2016. doi: 10.1109/TR.2015.2513044
    [31]
    J. X. Li, Z. H. Wang, Y. B. Zhang, H. M. Fu, C. R. Liu, and S. Krishnaswamy, “Degradation data analysis based on a generalized Wiener process subject to measurement error,” Mech. Syst. Signal Process,, vol. 94, pp. 57–72, 2017. doi: 10.1016/j.ymssp.2017.02.031
    [32]
    L. Feng, H. L. Wang, X. S. Si, and H. X. Zou, “A state space-based prognostic model for hidden and age-dependent nonlinear degradation process,” IEEE Trans. Automation Science and Engineering, vol. 10, no. 4, pp. 1072–1086, 2013. doi: 10.1109/TASE.2012.2227960
    [33]
    X. S. Si, T. M. Li, and Q. Zhang, “A general stochastic degradation modelling approach for prognostics of degrading systems with surviving and uncertain measurements,” IEEE Trans. Reliability, vol. 68, no. 3, pp. 1080–1100, 2019. doi: 10.1109/TR.2019.2908492
    [34]
    H. Z. Fang, N. Tian, Y. B. Wang, M. C. Zhou, and M. A. Haile, “Nonlinear Bayesian estimation: From Kalman filtering to a broader horizon,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 2, pp. 401–417, 2018. doi: 10.1109/JAS.2017.7510808
    [35]
    Z. X. Zhang, X. S. Si, C. H. Hu, X. X. Hu, and G. X. Sun, “An adaptive prognostic approach incorporating inspection influence for deteriorating systems,” IEEE Trans. Rel., vol. 68, no. 1, pp. 302–316, 2018.
    [36]
    Y. Aït-Sahalia, “Maximum-likelihood estimation of discretely sampled diffusions: A closed-form approach,” Econometrica, vol. 70, no. 1, pp. 223–262, 2002. doi: 10.1111/1468-0262.00274
    [37]
    A. V. Egorov, H. Li, and Y. Xu, “Maximum likelihood estimation of time-inhomogeneous diffusions,” J. Econometr., vol. 114, pp. 107–139, 2003. doi: 10.1016/S0304-4076(02)00221-X
    [38]
    Y. Aït-Sahalia, “Closed-form likelihood expansions for multivariate diffusions,” Ann. Statisti., vol. 36, no. 2, pp. 906–937, 2008. doi: 10.1214/009053607000000622
    [39]
    J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the nelder-mead simplex method in low dimensions,” SIAM Journal of Optimization, vol. 9, no. 1, pp. 112–147, 1998. doi: 10.1137/S1052623496303470
    [40]
    P. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations. New York, NY, USA: Springer, 1995.
    [41]
    B. Saha and K. Goebel. Battery Data Set, in NASA Ames Prognostics Data Repository, National Aeronautics and Space Administration (NASA)’s Ames Research Center: Moffett Field, CA, USA, 2007. [Online]. Available: http://ti.arc.nasa.gov/tech/dash/pcoe/prognostic-data-repository/, Accessed on: Jan. 22, 2014.
    [42]
    X. S. Si, “An adaptive prognostic approach via nonlinear degradation modeling: Application to battery data,” IEEE Trans. Ind. Electron., vol. 62, no. 8, pp. 5082–5096, 2015. doi: 10.1109/TIE.2015.2393840
    [43]
    G. Dong, Z. Chen, J. Wei, and Q. Ling, “Battery health prognosis using Brownian motion modeling and particle filtering,” IEEE Trans. Ind. Electron., vol. 65, no. 11, pp. 8646–8655, 2018. doi: 10.1109/TIE.2018.2813964
    [44]
    B. Wang, Y. G. Lei, N. P. Li, and N. B. Li, “A hybrid prognostics approach for estimating remaining useful life of rolling element bearings,” IEEE Trans. Ind. Electron., vol. 69, no. 1, pp. 401–412, 2018.
    [45]
    J. Feng, P. Kvam, and Y. Tang, “Remaining useful lifetime prediction based on the damage-marker bivariate degradation model: A case study on lithium-ion batteries used in electric vehicles,” Eng. Failure Anal.,vol. 70, pp. 323–342, 2016.
    [46]
    T. Wang, M. Hu, and Y. L. Zhao, “Consensus control with a constant gain for discrete-time binary-valued multi-agent systems based on a projected empirical measure method,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1052–1059, 2019. doi: 10.1109/JAS.2019.1911594
    [47]
    K. L. Son, Mi. Fouladirad, A. Barros, E. Levrat, and B. Lung, “Remaining useful life estimation based on stochastic deterioration models: A comparative study,” Rel. Eng. Syst. Safety, vol. 112, pp. 165–175, 2013. doi: 10.1016/j.ress.2012.11.022
    [48]
    N. Li, Y. Lei, J. Lin, and S. X. Ding, “An improved exponential model for predicting remaining useful life of rolling element bearings,” IEEE Trans. Ind. Electron., vol. 62, no. 12, pp. 7762–7773, 2015. doi: 10.1109/TIE.2015.2455055
    [49]
    A. Saxena, J. Celaya, B. Saha, S. Saha, and K. Goebel, “Metrics for offline evaluation of prognostic performance,” Int. J. Prognostics and Health Management, vol. 1, pp. 1–20, 2010.
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    Highlights

    • The influence of the degradation rate change among different units is explicitly considered
    • An age- and state-dependent nonlinear degradation model considering the unit-to-unit variability is proposed
    • The uncertainty of the hidden state from the observations is incorporated into the RUL estimation
    • The approximate analytical RUL distribution is obtained from the concept of the FHT
    • The model parameters and hidden states can be updated by KF and EM algorithm to update the RUL distribution and realize real-time RUL estimation

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