IEEE/CAA Journal of Automatica Sinica
Citation:  Z. N. Pang, X. S. Si, C. H. Hu, and Z. X. Zhang, “An agedependent and statedependent 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 
[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 controllimit 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 orderreplacement 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 modelbased 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 conditionbased 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 twophase degradation data based on changepoint 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 conditionbased 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 constantstress 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 timevarying 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 ageand statedependent 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 timevarying 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 timevarying operating conditions based on a twofactor 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 Wienerprocessbased 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 ageand statedependent 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 ageand statedependent 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 ageand statedependent 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 filterbased prognostics algorithm using Matlab,” Reliability Engineering &System Safety, vol. 115, pp. 161–169, 2013.

[24] 
M. E. Orchard, P. HeviaKoch, B. Zhang, and L. Tang, “Risk measures for particlefilteringbased stateofcharge prognosis in lithiumion 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 twophase 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 modelbased method for remaining useful life prediction considering unittounit 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 threesource 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,

[32] 
L. Feng, H. L. Wang, X. S. Si, and H. X. Zou, “A state spacebased prognostic model for hidden and agedependent 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. AïtSahalia, “Maximumlikelihood estimation of discretely sampled diffusions: A closedform approach,” Econometrica, vol. 70, no. 1, pp. 223–262, 2002. doi: 10.1111/14680262.00274

[37] 
A. V. Egorov, H. Li, and Y. Xu, “Maximum likelihood estimation of timeinhomogeneous diffusions,” J. Econometr., vol. 114, pp. 107–139, 2003. doi: 10.1016/S03044076(02)00221X

[38] 
Y. AïtSahalia, “Closedform 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 neldermead 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/prognosticdatarepository/, 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 damagemarker bivariate degradation model: A case study on lithiumion 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 discretetime binaryvalued multiagent 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.
