242 Z. Mao and M. Todd Particle filtering is employed to fuse the data observation with the ARMA model, and a smooth time series with less uncertainty is obtained. Moreover, the framework forecasts the acceleration level, which can be used to determine the lifetime of the bearing, given an arbitrary decision threshold. Uncertainty bounds of the acceleration variance can be also propagated in the time axis, therefore the RUL uncertainty is characterized via standard deviation. For the data-driven flow adopted in this work, prediction of RUL is made considering the current state. Because of the uncertainties in data, and the incompleteness of model in characterizing the entire fatigue mechanism, the RUL prediction fluctuates with different stage of operation and training data. Future work will be focused on the model selection process, employing statistical machine learning algorithm, to have a better global characterization of the vibration energy curve. Also, more sensitive assessment indices will be investigated. Acknowledgments The authors acknowledge the Air Force Office of Scientific Research (AFOSR) Grant #FA9550-10-1-0455 (Dr. David Stargel, Program Manager) for support of this work. References 1. Burnham KP, Anderson DR (1998) Model selection and inference: a practical information-theoretic approach. Springer, New York 2. Vanik MW, Beck JL, Au SK (2000) Bayesian probabilistic approach to structural health monitoring. J Eng Mech 126:738–749 3. Sivia DS, David WIF, Knight KS (1993) An introduction to Bayesian model selection. Physica D 66:234–242 4. Sutrisno E, Oh H, Vasan ASS, Pecht M (2012) Estimation of remaining useful life of ball bearings using data driven methodologies. Prognostics and health management (PHM), 2012 IEEE Conference on, p 1, 7, 18–21 June 2012 5. Zhang B, Sconyers C, Byington C, Patrick R, Orchard M, Vachtsevanos G (2011) A probabilistic fault detection approach: application to bearing fault detection. IEEE Trans Ind Electron 58(5):2011, 2018 6. Rabiei M, Modarres M (2013) A recursive Bayesian framework for structural health management using online monitoring and periodic inspections. Reliab Eng Syst Saf 112:154–164 7. He D, Bechhoefer E, Dempsey P, Ma J (2012) An integrated approach for gear health prognostics. AHS international 68th annual forum and technology display, Fort Worth, TX, 1–3 May 2012 8. Zhang B, Sconyers C, Orchard M, Patrick R, Vachtsevanos G (2010) Fault progression modeling: an application to bearing diagnosis and prognosis. 2010 American Control Conference Marriott Waterfront, Baltimore, MD, USA, 30 June–02 July 2010 9. Bechhoefer E, Bernhard A, He D (2008) Use of Paris law for prediction of component remaining life. Aerospace conference, 2008 IEEE, pp 1, 9, 1–8 March 2008
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