Saturday , December 9 2023

Risk-Sensitive Particle-Filtering-based Prognosis Framework for Estimation of Remaining Useful Life in Energy Storage Devices

Dr. Marcos E. ORCHARD1, Liang TANG2, Bhaskar SAHA3, Kai GOEBEL4, Dr. George J. VACHTSEVANOS2,5

1 Electrical Engineering Department, Universidad de Chile
Santiago 8370451, Chile
2 Impact Technologies, LLC, Rochester, NY 14623, USA
3 MCT, Inc at NASA Ames Research Center,
MS 269-4, Moffett Field, CA. 94035, USA

4 NASA Ames Research Center,
MS 269-4, Moffett Field, CA. 94035, USA
5 School of Electrical and Computer Engineering, Georgia Institute of Technology,
Atlanta, GA 30332, USA

Abstract: Failure prognosis, and particularly representation and management of uncertainty in long-term predictions, is a topic of paramount importance not only to improve productivity and efficiency, but also to ensure safety in the system’s operation. The use of particle filter (PF) algorithms – in combination with outer feedback correction loops – has contributed significantly to the development of a robust framework for online estimation of the remaining useful equipment life. This paper explores the advantages and disadvantages of a Risk-Sensitive PF (RSPF) prognosis framework that complements the benefits of the classic approach, by representing the probability of rare events and highly non-monotonic phenomena within the formulation of the nonlinear dynamic equation that describes the evolution of the fault condition in time. The performance of this approach is thoroughly compared using a set of ad hoc metrics. Actual data illustrating aging of an energy storage device (specifically battery capacity measurements [A-hr]) are used to test the proposed framework.

Keywords: Risk-sensitive particle filtering, failure prognosis, nonlinear state estimation, battery prognosis.

>Full text
Dr. Marcos E. ORCHARD, Liang TANG, Bhaskar SAHA, Kai GOEBEL, Dr. George J. VACHTSEVANOS, Risk-Sensitive Particle-Filtering-based Prognosis Framework for Estimation of Remaining Useful Life in Energy Storage Devices, Studies in Informatics and Control, ISSN 1220-1766, vol. 19 (3), pp. 209-218, 2010.

1. Introduction

A number of approaches have been suggested in the recent years for uncertainty representation and management in prediction. Probabilistic, soft computing methods, and tools derived from evidential theory or Dempster-Shafer theory 1 have been explored for this purpose. Although probabilistic methods offer a mathematically rigorous methodology, they typically require a statistically sufficient database to estimate the required distributions. Soft-computing methods (fuzzy logic) offer an alternative when scarce data or contradictory data are available. Dempster’s rule of combination and similar concepts from evidential theory such as belief or plausibility (upper and lower bounds of probability) based on mass function calculations can support uncertainty representation and management tasks. Confidence Prediction Neural Networks (NN) 2 have also been used to represent and manage uncertainty using Parzen windows as the kernel and a structure based on Specht’s General Regression NN 3. For tuning of model hyper-parameters given observations, probabilistic reliability analysis tools employing an inner-outer loop Bayesian update scheme 4 have been employed.

Particle-filtering (PF) based prognostic algorithms 5-12 have been established as the de facto state of the art in failure prognosis. PF algorithms allow to avoid the assumption of Gaussian (or log-normal) probability density function (pdf) in nonlinear processes, with unknown model parameters, and simultaneously help to consider non-uniform probabilities of failure for particular regions of the state domain. Particularly, the authors in 6 have proposed a mathematically rigorous method (based on PF, function kernels, and outer correction loops) to represent and manage uncertainty in long-term predictions.

However, there are still unsolved issues regarding the proper representation for the probability of rare events and highly non-monotonic phenomena, since these events are associated to particles located at the tails of the predicted probability density functions.

This paper presents a solution for this problem. The paper is structured as follows: Section 2 introduces the basics of particle filtering (PF) and its application to the field of failure prognostics. Section 3 presents the proposed Risk-Sensitive PF (RSPF) framework and analyses the main advantages and disadvantages of its implementation, using actual failure data measuring battery capacity ([A-hr]). Section 4 utilizes performance metrics to assess prognostic results and evaluates the RSPF, when compared to the classic PF prognosis framework 5-10. Section 5 states conclusions.


  1. Shafer, G., A Mathematical Theory of Evidence, Princeton, N.J: Princeton University Press, 1976.
  2. Khiripet, N., G. Vachtsevanos, A. Thakker, T. Galie, A New Confidence Prediction Neural Network for Machine Failure Prognosis, Proceedings of Intelligent Ships Symposium IV, Philadelphia, PA, April 2-3, 2001.
  3. Specht, D. F., A General Regression Neural Network, IEEE Trans on Neural Networks, vol. 2, no. 6, November, 1991, pp. 568-76.
  4. Cruse, T. A., Probabilistic Systems Modeling and Validation, HCF 2004, March 16-18, 2004.
  5. Orchard, M., B. Wu, G. Vachtsevanos, A Particle Filter Framework for Failure Prognosis, Proceedings of World Tribology Congress III, Washington DC, Sept. 12-16, 2005.
  6. Orchard, M., G. Kacprzynski, K. Goebel, B. Saha, G. Vachtsevanos, Advances in Uncertainty Representation and Management for Particle Filtering Applied to Prognostics, 2008 International Conference on Prognostics and Health Management PHM 2008, Denver, CO, USA, October 9 – 12, 2008.
  7. Orchard, M., On-line Fault Diagnosis and Failure Prognosis Using Particle Filters. Theoretical Framework and Case Studies, Publisher: VDM Verlag Dr. Müller Aktiengesellschaft & Co. KG, Saarbrücken, Germany, April 2009, 108 pages. Atlanta: The Georgia Institute of Technology, Diss., 2007.
  8. Orchard, M. G. Vachtsevanos, A Particle Filtering Approach for On-Line Fault Diagnosis and Failure Prognosis, Transactions of the Institute of Measurement and Control, vol. 31, no. 3-4, June 2009, pp. 221-246.
  9. Orchard, M., F. TOBAR, G. Vachtsevanos, Outer Feedback Correction Loops in Particle Filtering-based Prognostic Algorithms: Statistical Performance Comparison, Studies in Informatics and Control, vol.18(4), December 2009, pp. 295-304.
  10. Orchard, M., L. Tang, K. Goebel, G. Vachtsevanos, A Novel RSPF Approach to Prediction of High-Risk, Low-Probability Failure Events, First Annual Conference of the Prognostics and Health Management Society, 2009, San Diego, CA, USA.
  11. Patrick, R., M. Orchard, B. Zhang, M. Koelemay, G. Kacprzynski, A. Ferri, G. Vachtsevanos, An Integrated Approach to Helicopter Planetary Gear Fault Diagnosis and Failure Prognosis, 42nd Annual Systems Readiness Technology Conference, AUTOTESTCON 2007, Baltimore, USA, September 2007.
  12. Zhang, B., T. Khawaja, R. Patrick, M. Orchard, A. Saxena, G. Vachtsevanos, A Novel Blind Deconvolution De-Noising Scheme in Failure Prognosis, IEEE Transactions on Instrumentation and Measurement, vol. 58, no. 2, February 2009, pp. 303-310.
  13. Andrieu, C., A. Doucet, E. Punskaya, Sequential Monte Carlo Methods for Optimal Filtering, in Sequential Monte Carlo Methods in Practice, A. Doucet, N. de Freitas, and N. Gordon, Eds. NY: Springer-Verlag, 2001.
  14. Arulampalam, M. S., S. Maskell, N. Gordon, T. Clapp, A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking, IEEE Transactions on Signal Processing, vol. 50, no. 2, Feb. 2002, pp. 174 – 188.
  15. Doucet, A., On Sequential Monte Carlo Methods for Bayesian Filtering, Technical Report, Engineering Department, University of Cambridge, UK, 1998.
  16. Doucet, A., N. de Freitas, N. Gordon, An introduction to Sequential Monte Carlo methods, in Sequential Monte Carlo Methods in Practice, A. Doucet, N. de Freitas, and N. Gordon, Eds. NY: Springer-Verlag, 2001.
  17. Thrun, S., J. Langford, V. Verma, Risk Sensitive Particle Filters, Neural Information Processing Systems (NIPS), Dec. 2001.
  18. Verma, V., G. Gordon, R. Simmons, S. Thrun, Particle Filters for Rover Fault Diagnosis, IEEE Robotics & Automation Magazine, pp. 56 – 64, June 2004.
  19. Vachtsevanos, G., F.L. Lewis, M.J. Roemer, A. Hess, B. Wu, Intelligent Fault Diagnosis and Prognosis for Engineering Systems, Hoboken, NJ, John Wiley and Sons, 2006.