This paper describes an Autoregressive Partially-hidden Markov model (ARPHMM) for fault detection and prognostics of equipments based on sensors’ data. It is a particular dynamic Bayesian network that allows to represent the dynamics of a system by means of a Hidden Markov Model (HMM) and an autoregressive (AR) process. The Markov chain assumes that the system is switching back and forth between internal states while the AR process ensures a temporal coherence on sensor measurements. A sound learning procedure of standard ARHMM based on maximum likelihood allows to iteratively estimate all parameters simultaneously. This paper suggests a modification of the learning procedure considering that one may have prior knowledge about the structure which becomes partially hidden. The integration of the prior is based on the Theory of Weighted Distributions which is compatible with the Expectation-Maximization algorithm in
the sense that the convergence properties are still satisfied. We show how to apply this model to estimate the remaining useful life based on health indicators. The autoregressive parameters can indeed be used for prediction while the latent structure can be used to get information about the degradation level. The interest of the proposed method for prognostics and health assessment is demonstrated on CMAPSS datasets.
How to Cite
CMAPSS datasets, Hidden Markov Model, Markov switching, Autoregressive process, Theory of Weighted Distributions
Cherfi, Z., Oukhellou, L., Cˆome, E., Denoeux, T., & Aknin, P. (2012). Partially supervised independent factor analysis using soft labels elicited from multiple experts: Application to railway track circuit diagnosis. Soft Computing, 16, 741–754.
Cˆome, E., Oukhellou, L., Denoeux, T., & Aknin, P. (2009). Learning from partially supervised data using mixture models and belief functions. Pattern recognition, 42(3), 334–348.
Dempster, A., Laird, N., & Rubin, D. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, 39(1), 1-38.
Denoeux, T. (2013). Maximum likelihood estimation from uncertain data in the belief function framework. Knowledge and Data Engineering, IEEE Transactions on, 25(1), 119–130.
Dubois, D. (2007). Uncertainty theories: a unified view. In Ieee cybernetic systems conference (p. 4-9). Dublin, Ireland.
Farrar, C. R., & Worden, K. (2013). Structural health monitoring: A machine learning perspective. John Wiley & Sons, Ltd.
Frederick, D., DeCastro, J., & Litt, J. (2007). User’s guide for the commercial modular aero-propulsion system simulation (C-MAPSS) (Tech. Rep.). Cleveland, Ohio 44135, USA: National Aeronautics and Space Administration (NASA), Glenn Research Center.
He, X., & De Roeck, G. (1997). System identification of mechanical structures by a high-order multivariate autoregressive model. Computers & structures, 64(1), 341–351.
Huang, C. (2001). Structural identification from ambient vibration measurement using the multivariate ar model. Journal of Sound and Vibration, 241(3), 337–359.
Javed, K., Gouriveau, R., & Zerhouni, N. (2013). Novel failure prognostics approach with dynamic thresholds for machine degradation. In Ieee iecon (p. 4402-4407). Austria.
Juesas, P., & Ramasso, E. (2016). Ascertainment-adjusted parameter estimation approach to improve robustness against misspecification of health monitoring methods. Mechanical Systems and Signal Processing. (Accepted) doi: doi:10.1016/j.ymssp.2016.03.022
Lehman, L., Nemati, S., & Mark, R. (2015). Hemodynamic monitoring using switching autoregressive dynamics of multivariate vital sign time series. In Computing in cardiology. Nice, France.
Lim, P., Goh, C. K., Tan, K. C., , & Dutta, P. (2016). Multimodal degradation prognostics based on switching kalman filter ensemble. IEEE Trans. on Neural Networks and Learning Systems.
Ling, Y., Shantz, C., Mahadevan, S., & Sankararaman, S. (2011). Stochastic prediction of fatigue loading using real-time monitoring data. International Journal of Fatigue, 33(7), 868 - 879. doi:
Ng, S., & Vogelsang, T. (2002). Forecasting autoregressive time series in the presence of deterministic components. The Econometrics Journal, 5(1), 196–224.
Patil, G. (2002). Weighted distributions (Vol. 4; A. H. El-Shaarawi & W. W. Piegorsch, Eds.). John Wiley & Sons, Ltd, Chichester. (pp. 2369-2377)
Rabiner, L. (1989). A tutorial on hidden Markov models and selected applications in speech recognition. Proc. of the IEEE, 77(2), 257–286.
Ramasso, E. (2009). Contribution of belief functions to hidden markov models with an application to fault diagnosis. In Ieee international worshop on machine learning for signal processing, mlsp’09. (pp. 1–6).
Ramasso, E. (2014). Investigating computational geometry for failure prognostics. Int. Journal on Prognostics and Health Management, 5(5), 1-18.
Ramasso, E. (2016, January). Segmentation of CMAPSS health indicators into discrete states for sequencebased classification and prediction purposes (Tech. Rep. No. 6839). FEMTO-ST institute.
Ramasso, E., & Denoeux, T. (2014). Making use of partial knowledge about hidden states in HMMs: an approach based on belief functions. Fuzzy Systems, IEEE Transactions on, 22(2), 395–405.
Ramasso, E., & Saxena, A. (2014). Performance benchmarking and analysis of prognostic methods for CMAPSS datasets. International Journal on Prognostics and Health Management, 5(2), 1-15.
Saha, B., & Goebel, K. (2008). Uncertainty management for diagnostics and prognostics of batteries using bayesian techniques. In Aerospace conference, 2008 ieee (pp. 1–8).
Saha, B., Goebel, K., & Christophersen, J. (2009). Comparison of prognostic algorithms for estimating remaining useful life of batteries. In Transactions of the institute of measurement and control.
Sankararaman, S., & Goebel, K. (2015). Uncertainty in prognostics and systems health management. Int. Journal of Prognostics and Health Management, 6, 1-14.
Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2008). Damage propagation modeling for aircraft engine runto- failure simulation. In International conference on prognostics and health management (pp. 1–9). Denver, CO, USA.
Serdio, F., Lughofer, E., Pichler, K., Buchegger, T., Pichler, M., & Efendic, H. (2013). Multivariate fault detection using vector autoregressive moving average and orthogonal transformation in residual space. In Annual conference of the prognostics and health management society (Vol. 4).
Serir, L., Ramasso, E., Nectoux, P., & Zerhouni, N. (2013). E2GKpro: An evidential evolving multi-modeling approach for system behavior prediction with applications. Mechanical Systems and Signal Processing, 37(1-2), 213 - 228.
Serir, L., Ramasso, E., & Zerhouni, N. (2011). An evidential evolving multimodeling approach for systems behavior prediction. In Annual conference of the prognostics and health management society, phm’11. Montreal, QC, Canada.
Serir, L., Ramasso, E., & Zerhouni, N. (2012). An evidential evolving prognostic approach and its application to pronostia’s data streams. In Annual conference of the prognostics and health management society, phm’12 (Vol. 3, pp. 9–pages).
Storch, H. V., & Zwiers, F. W. (1999). Statistical analysis in climate research. Cambridge University Press.
Thanagasundram, S., Spurgeon, S., & Schlindwein, F. S. (2008). A fault detection tool using analysis from an autoregressive model pole trajectory. Journal of Sound and Vibration, 317(35), 975 - 993. doi: http://dx.doi.org/10.1016/j.jsv.2008.03.044
Wang, T. (2010). Trajectory similarity based prediction for remaining useful life estimation (Unpublished doctoral dissertation). University of Cincinnati.
Wang, T., Yu, J., Siegel, D., & Lee, J. (2008). A similaritybased prognostics approach for remaining useful life estimation of engineered systems. In Int. conf. on prognostics and health management (p. 1-6).
Wang, W., & Wong, A. K. (2002). Autoregressive modelbased gear fault diagnosis. Journal of vibration and acoustics, 124(2), 172–179.
Yan, J., Ko, M., & Lee, J. (2004). A prognostic algorithm for machine performance assessment and its application. Production Planning & Control, 15(8), 796-801. doi: 10.1080/09537280412331309208
The Prognostic and Health Management Society advocates open-access to scientific data and uses a Creative Commons license for publishing and distributing any papers. A Creative Commons license does not relinquish the author’s copyright; rather it allows them to share some of their rights with any member of the public under certain conditions whilst enjoying full legal protection. By submitting an article to the International Conference of the Prognostics and Health Management Society, the authors agree to be bound by the associated terms and conditions including the following:
As the author, you retain the copyright to your Work. By submitting your Work, you are granting anybody the right to copy, distribute and transmit your Work and to adapt your Work with proper attribution under the terms of the Creative Commons Attribution 3.0 United States license. You assign rights to the Prognostics and Health Management Society to publish and disseminate your Work through electronic and print media if it is accepted for publication. A license note citing the Creative Commons Attribution 3.0 United States License as shown below needs to be placed in the footnote on the first page of the article.
First Author et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 United States License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.