Probabilistic Prognosis with Dynamic Bayesian Networks



Published Nov 3, 2020
Gregory Bartram Sankaran Mahadevan


This paper proposes a methodology for probabilistic prognosis of a system using a dynamic Bayesian network (DBN). Dynamic Bayesian networks are suitable for probabilistic prognosis because of their ability to integrate information in a variety of formats from various sources and give a probabilistic representation of the system state. Further, DBNs provide a platform naturally suited for seamless integration of diagnosis, uncertainty quantification, and prediction. In the proposed methodology, a DBN is used for online diagnosis via particle filtering, providing a current estimate of the joint distribution over the system variables. The information available in the state estimate also helps to quantify the uncertainty in diagnosis. Next, based on this probabilistic state estimate, future states of the system are predicted using the DBN and sequential or recursive Monte Carlo sampling. Prediction in this manner provides the necessary information to estimate the distribution of remaining use life (RUL). The prognosis procedure, which is system specific, is validated using a suite of offline hierarchical metrics. The prognosis methodology is demonstrated on a hydraulic actuator subject to a progressive seal wear that results in internal leakage between the chambers of the actuator.

Abstract 191 | PDF Downloads 216



diagnosis, prognosis, Dynamic Bayesian Network

Andrieu, C., Davy, M., & Doucet, A. (2003). Efficient particle filtering for jump Markov systems. Application to time-varying autoregressions. IEEE Transactions on Signal Processing, 51(7), 1762–1770.
Banjevic, D., & Jardine, A. K. S. (2006). Calculation of reliability function and remaining useful life for a Markov failure time process. IMA Journal of Management Mathematics, 17(2), 115–130.
Bartram, G., & Mahadevan, S. (2013). Dynamic Bayesian Networks for Prognosis. In Proceedings of the Annual Conference of the Prognostics and Health Management Society 2013. New Orleans, LA.
Bartram, G., & Mahadevan, S. (2013). Integration of Heterogeneous Information in SHM Models. Structural Control and Health Monitoring, Accepted.
Boyen, X., & Koller, D. (1998). Tractable inference for complex stochastic processes. In Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence (pp. 33–42). San Francisco, CA, USA: Morgan Kaufmann Publishers Inc. Retrieved from
Chinnam, R. B., & Baruah, P. (2003). Autonomous diagnostics and prognostics through competitive learning driven HMM-based clustering. In Proceedings of the International Joint Conference on Neural Networks, 2003 (Vol. 4, pp. 2466–2471 vol.4).
Dong, M., & Yang, Z. (2008). Dynamic Bayesian network based prognosis in machining processes. Journal of Shanghai Jiaotong University (Science), 13(3), 318–322.
Farrar, C. R., & Worden, K. (2012). Structural Health Monitoring: A Machine Learning Perspective. John Wiley & Sons.
Friedman, N., Murphy, K., & Russell, S. (1998). Learning the Structure of Dynamic Probabilistic Networks. In UAI’98 Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (pp. 139–147). Morgan Kaufmann Publishers Inc. Retrieved from
Gebraeel, N. Z., & Lawley, M. A. (2008). A neural network degradation model for computing and updating residual life distributions. Automation Science and Engineering, IEEE Transactions on, 5(1), 154–163.
Goebel, K., Saha, B., Saxena, A., Mct, N., & Riacs, N. (2008). A comparison of three data-driven techniques for prognostics. In 62nd Meeting of the Society For Machinery Failure Prevention Technology (MFPT) (pp. 119–131).
Goode, K. B., Moore, J., & Roylance, B. J. (2000). Plant machinery working life prediction method utilizing reliability and condition-monitoring data. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 214(2), 109–122.
Jardine, A. K. S., Lin, D., & Banjevic, D. (2006). A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical Systems and Signal Processing, 20(7), 1483–1510.
Jinlin, Z., & Zhengdao, Z. (2012). Fault prognosis for data incomplete systems: A dynamic Bayesian network approach. In Control and Decision Conference (CCDC), 2012 24th Chinese (pp. 2244–2249).
Kacprzynski, G. J., Sarlashkar, A., Roemer, M. J., Hess, A., & Hardman, B. (2004). Predicting remaining life by fusing the physics of failure modeling with diagnostics. JOM, 56(3), 29–35.
Karpenko, M., & Sepehri, N. (2003). Robust Position Control of an Electrohydraulic Actuator With a Faulty Actuator Piston Seal. Journal of Dynamic Systems, Measurement, and Control, 125(3), 413–423.
Khan, T., Udpa, L., & Udpa, S. (2011). Particle filter based prognosis study for predicting remaining useful life of steam generator tubing. In Prognostics and Health Management (PHM), 2011 IEEE Conference on (pp. 1 –6).
Koller, D., & Friedman, N. (2009). Probabilistic Graphical Models: Principles and Techniques. MIT Press.
Kozlowski, J. D. (2003). Electrochemical cell prognostics using online impedance measurements and model-based data fusion techniques. In 2003 IEEE Aerospace Conference, 2003. Proceedings (Vol. 7, pp. 3257–3270).
Kulakowski, B. T., Gardner, J. F., & Shearer, J. L. (2007). Dynamic modeling and control of engineering systems. Cambridge University Press.
Kwan, C., Zhang, X., Xu, R., & Haynes, L. (2003). A novel approach to fault diagnostics and prognostics. In IEEE International Conference on Robotics and Automation, 2003. Proceedings. ICRA ’03 (Vol. 1, pp. 604–609 vol.1).
Lin, D., & Makis, V. (2004). Filters and parameter estimation for a partially observable system subject to random failure with continuous-range observations. Advances in Applied Probability, 36(4), 1212–1230.
Liu, J., Saxena, A., Goebel, K., Saha, B., & Wang, W. (2010). An Adaptive Recurrent Neural Network for Remaining Useful Life Prediction of Lithium-ion Batteries. DTIC Document.
Lorton, A., Fouladirad, M., & Grall, A. (2013). A methodology for probabilistic model-based prognosis. European Journal of Operational Research, 225(3), 443–454.
MacCormick, B. W. (1995). Aerodynamics, Aeronautics, and Flight Mechanics. John Wiley & Sons, Incorporated.
Mahulkar, V., McGinnis, H., Derriso, M., & Adams, D. E. (2010). Fault Identification in an Electro-Hydraulic Actuator and Experimental Validation of Prognosis Based Life Extending Control. DTIC Document.
Naval Surface Warfare Center. (2011). Handbook of Reliability Prediction Procedures for Mechanical Equipment. West Bethesda, Maryland 20817-5700. Retrieved from
Orchard, M. E., & Vachtsevanos, G. J. (2009). A particle-filtering approach for on-line fault diagnosis and failure prognosis. Transactions of the Institute of Measurement and Control.
Pitt, M. K., & Shephard, N. (1999). Filtering via Simulation: Auxiliary Particle Filters. Journal of the American Statistical Association, 94(446), 590–599.
RIAC Automated Databook. (2006). (Version 2.22). Reliability Information Analysis Center. Retrieved from
Ristic, B., & Arulampalam, S. (2004). Beyond the Kalman filter : particle filters for tracking applications. Boston, MA: Artech House.
Saha, B., Celaya, J. R., Wysocki, P. F., & Goebel, K. F. (2009). Towards prognostics for electronics components. In 2009 IEEE Aerospace conference (pp. 1–7).
Saha, B., Goebel, K., & Christophersen, J. (2009). Comparison of prognostic algorithms for estimating remaining useful life of batteries. Transactions of the Institute of Measurement and Control, 31(3-4), 293–308.
Sankararaman, S., & Mahadevan, S. (2011). Uncertainty quantification in structural damage diagnosis. Structural Control and Health Monitoring, 18(8), 807–824.
Saxena, A., Celaya, J., Saha, B., Saha, S., & Goebel, K. (2010). Metrics for Offline Evaluation of Prognostic Performance. International Journal of Prognositcs and Health Management, (1). Retrieved from
Thompson, D. F., Pruyn, J. S., & Shukla, A. (1999). Feedback design for robust tracking and robust stiffness in flight control actuators using a modified QFT technique. International Journal of Control, 72(16), 1480 – 1497.
Tipping, M. E. (2001). Sparse Bayesian learning and the relevance vector machine. The Journal of Machine Learning Research, 1, 211–244.
Tobon-Mejia, D. A., Medjaher, K., Zerhouni, N., & Tripot, G. (2012). A Data-Driven Failure Prognostics Method Based on Mixture of Gaussians Hidden Markov Models. Reliability, IEEE Transactions on, 61(2), 491–503.
Tran, V. T., & Yang, B.-S. (2009). Machine Fault Diagnosis and Prognosis: The State of The Art. The International Journal of Fluid Machinery and Systems (IJFMS), 2(1), 61–71.
Vachtsevanos, G., & Wang, P. (2001). Fault prognosis using dynamic wavelet neural networks. In AUTOTESTCON Proceedings, 2001. IEEE Systems Readiness Technology Conference (pp. 857–870).
Vlok, P.-J., Wnek, M., & Zygmunt, M. (2004). Utilising statistical residual life estimates of bearings to quantify the influence of preventive maintenance actions. Mechanical Systems and Signal Processing, 18(4), 833–847.
Wang, W. (2002). A model to predict the residual life of rolling element bearings given monitored condition information to date. IMA Journal of Management Mathematics, 13(1), 3–16.
Wang, W. Q., Golnaraghi, M. F., & Ismail, F. (2004). Prognosis of machine health condition using neuro-fuzzy systems. Mechanical Systems and Signal Processing, 18(4), 813–831.
Wang, W., Scarf, P. A., & Smith, M. a. J. (2000). On the application of a model of condition-based maintenance. Journal of the Operational Research Society, 51(11), 1218–1227.
Yam, R. C. M., Tse, P. W., Li, L., & Tu, P. (2001). Intelligent Predictive Decision Support System for Condition-Based Maintenance. The International Journal of Advanced Manufacturing Technology, 17(5), 383–391.
Yan, J., Koç, M., & Lee, J. (2004). A prognostic algorithm for machine performance assessment and its application. Production Planning & Control, 15(8), 796–801.
Zhang, S., & Ganesan, R. (1997). Multivariable Trend Analysis Using Neural Networks for Intelligent Diagnostics of Rotating Machinery. Journal of Engineering for Gas Turbines and Power, 119(2), 378–384.
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