Skip to main content

Advertisement

Log in

A joint particle filter and expectation maximization approach to machine condition prognosis

  • Published:
Journal of Intelligent Manufacturing Aims and scope Submit manuscript

Abstract

This paper presents a probabilistic model based approach for machinery condition prognosis based on particle filter by integrating physical knowledge with in-process measurements into a state space framework to account for uncertainty and nonlinearity in machinery degradation process. One limitation of conventional particle filter is that condition prognosis is performed based on the model with predetermined parameters obtained from simulation studies or lab-controlled tests. Due to the stochastic nature of machinery defect propagation under varying operating conditions, model parameters may vary in practice which causes prediction errors. To address it, an integrated state prediction and parameter estimation framework based on particle filter and expectation-maximization algorithm is formulated and investigated. The model parameters are adaptively estimated based on expectation-maximization algorithm utilizing hidden degradation state and available in-process measurements. Particle filter is then performed on the identified model with estimated parameters following Bayesian inference scheme to improve the robustness and accuracy of machinery condition prognosis. The effectiveness of the developed method is demonstrated through a simulation study and an experimental run-to-failure bearing test in a wind turbine.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • An, D., Choi, J. H., & Kim, N. H. (2013). Prognostics 101: A tutorial for particle filter-based prognostics algorithm using Matlab. Reliability Engineering & System Safety, 115, 161–169.

    Article  Google Scholar 

  • Arulampalam, M. S., Maskell, S., Gordon, N., & Clapp, T. (2002). A tutorial on particle filters for online nonlinear/Non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, 50(2), 174–188.

    Article  Google Scholar 

  • Basin, M. V., Loukianov, A. G., & Hernandez-Gonzalez, M. (2013). Joint state and parameter estimation for uncertain nonlinear polynomial systems. International Journal of Systems Science, 44(7), 1200–1208.

    Article  Google Scholar 

  • Bechhoefer, E., & Bernhard, A. P. F. (2007). A generalized process for optimal threshold setting in HUMS. In Proceedings of 2007 IEEE Aerospace Conference (pp. 1–9.). Big Sky, MT, March 3–10.

  • Beckhoefer, E., He, D., & Dempsey, R. (2011). Gear health threshold setting based on a probability of false alarm. In Proceedings of Annual Conference of the Prognostics and Health Management Society (pp. 1–7). Montreal, Quebec, Canada, September 25–29.

  • Benkedjouh, T., Medjaher, K., Zerhouni, N., & Rechak, S. (2015). Health assessment and life prediction of cutting tools based on support vector regression. Journal of Intelligent Manufacturing, 26, 213–223.

    Article  Google Scholar 

  • Bousdekis, A., Magoutas, B., Apostolou, D., & Mentzas, G. (2016). Review, analysis and synthesis of prognostic-based decision support methods for condition based maintenance. Journal of Intelligent Manufacturing,. doi:10.1007/s10845-015-1179-5.

    Article  Google Scholar 

  • Dempster, A., Laird, N., & Rubin, D. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39(1), 1–38.

    Google Scholar 

  • Gokulachandran, J., & Mohandas, K. (2015). Comparative study of two soft computing techniques for the prediction of remaining useful life of cutting tools. Journal of Intelligent Manufacturing, 26, 255–268.

    Article  Google Scholar 

  • Gordon, N. J., Salmond, D. J., & Smith, A. F. M. (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings-F Radar and Signal Processing, 140(2), 107–113.

    Article  Google Scholar 

  • Heng, A., Zhang, S., Tan, A. C. C., & Mathew, J. (2009). Rotating machinery prognostics: State of the art, challenges, and opportunities. Mechanical Systems and Signal Processing, 23, 724–739.

    Article  Google Scholar 

  • Hue, C., Le Cadre, J. P., & Perez, P. (2002). Tracking multiple objects with particle filtering. IEEE Transactions on Aerospace and Systems, 38(3), 791–812.

    Article  Google Scholar 

  • Julier, S. J., & Uhlmann, J. K. (1997). A new extension of Kalman Filter to nonlinear systems. In Proceedings of 11th International Symposium on Aerospace/Defense sensing, simulation and controls, multi sensor fusion, tracking and resource management (pp. 1–12).

  • Jurkovie, Z., Cukor, G., Brezocnik, M., & Brajkovie, T. (2016). A comparison of machine learning methods for cutting parameters prediction in high speed turning process. Journal of Intelligent Manufacturing,. doi:10.1007/s10845-016-1206-1.

    Article  Google Scholar 

  • Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Transactions of the ASME-Journal of Basic Engineering, 82, 35–45.

    Article  Google Scholar 

  • Kwok, C., Fox, D., & Meila, M. (2003). Adaptive real-time particle filters for robot localization. In Proceedings of the 2003 IEEE International Conference on Robotics & Automation (pp. 2836-2841). Taipei, Taiwan, September 14–19.

  • Lever, P. J. A., Marefat, M. M., & Ruwani, T. (1997). A machine learning approach to tool wear behavior operational zones. IEEE Transactions on Industry Applications, 33(1), 264–73.

    Article  Google Scholar 

  • Liao, L. (2014). Discovering prognostic features using genetic programming in remaining useful life prediction. IEEE Transactions on Industrial Electronics, 61(5), 2464–2472.

    Article  Google Scholar 

  • Li, Y., Billington, S., Zhang, C., Kurfess, T., Danyluk, S., & Liang, S. (1999). Dynamic prognostic prediction of defect propagation on rolling element bearings. Tribology Transactions, 42(2), 385–392.

    Article  Google Scholar 

  • Liu, J., & West, M. (2001). Combined parameter and state estimation in simulation-based filtering. In Sequential Monte Carlo Methods in Practice (pp. 197–223). New York: Springer.

  • Liu, J., Wang, W., & Ma, F. (2011). A regularized auxiliary particle filtering approach for system state estimation and battery life prediction. Smart Materials and Structures, 20, 1–9.

    Google Scholar 

  • Malhi, A., Yan, R., & Gao, R. X. (2011). Prognosis of defect propagation based on recurrent neural networks. IEEE Transactions on Instrumentation and Measurement, 60(3), 703–711.

    Article  Google Scholar 

  • Mehta, P., Werner, A., & Mears, L. (2015). Condition based maintenance-systems integration and intelligence using Bayesian classification and sensor fusion. Journal of Intelligent Manufacturing, 26, 331–346.

    Article  Google Scholar 

  • Mkhadri, A. (1998). On the rate of convergence of the ECME algorithm. Statistics & Probability Letters, 37(1), 81–87.

    Article  Google Scholar 

  • Moon, T. K. (1996). The expectation-maximization algorithm. IEEE Signal Processing Magazine, 13(6), 47–60.

    Article  Google Scholar 

  • 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, 31(3/4), 221–246.

    Article  Google Scholar 

  • Paris, P. C., Gomez, M. P., & Anderson, W. E. (1961). A rational analytic theory of fatigue. The Trend in Engineering, 13, 9–14.

    Google Scholar 

  • Pedregal, D. J., & Carnero, M. C. (2006). State space models for condition monitoring: A case study. Reliability Engineering and System Safety, 91, 171–180.

    Article  Google Scholar 

  • Peng, Y., & Dong, M. (2011). A prognosis method using age-dependent hidden semi-Markov model for equipment health prediction. Mechanical Systems and Signal Processing, 25(1), 237–252.

    Article  Google Scholar 

  • Peng, Y., Dong, M., & Zuo, M. J. (2010). Current status of machine prognostics in condition-based maintenance: A review. International Journal of Advanced Manufacturing Technology, 50, 297–313.

    Article  Google Scholar 

  • Pham, H. T., & Yang, B. S. (2010). Estimation and forecasting of machine health condition using ARMA/GARCH model. Mechanical Systems and Signal Processing, 24, 546–558.

    Article  Google Scholar 

  • Qian, N. (1999). On the momentum term in gradient descent learning algorithms. Neural Networks, 12, 145–151.

    Article  Google Scholar 

  • Ragab, A., Yacout, S., Ouali, M. S., & Osman, H. (2016). Prognostics of multiple failure modes in rotating machinery using a pattern-based classifier and cumulative incidence functions. Journal of Intelligent Manufacturing,. doi:10.1007/s10845-016-1244-8.

    Article  Google Scholar 

  • Sarkeyli, A., Zain, A. M., & Sharif, S. (2015). A multi-performance prediction model based on ANFIS and new modified-GA for machining processes. Journal of Intelligent Manufacturing, 26, 703–716.

    Article  Google Scholar 

  • Schon, T. B., Wills, A., & Ninness, B. (2011). System identification of nonlinear state-space models. Automatica, 47(1), 39–49.

    Article  Google Scholar 

  • Storvik, G. (2002). Particle filters for state-space models with the presence of unknown static parameters. IEEE Transactions on Signal Processing, 50(2), 281–289.

    Article  Google Scholar 

  • Teti, R., Jemielniak, K., O’Donnell, G., & Dornfeld, D. (2010). Advanced monitoring of machining operations. CIRP Annals-Manufacturing Technology, 59, 717–739.

    Article  Google Scholar 

  • Vogl, G. W., Weiss, B. A., & Helu, M. (2016). A review of diagnostic and prognostic capabilities and best practices for manufacturing. Journal of Intelligent Manufacturing,. doi:10.1007/s10845-016-1228-8.

    Article  Google Scholar 

  • Wang, J., & Gao, R. X. (2013). Multiple model particle filtering for bearing life prognosis. In Proceedings of 2013 IEEE International Conference on Prognostics and Health Management (PHM 2013) (pp. 1–6). Gaithersburg, Maryland, USA, June 24–27.

  • Wang, J., Gao, R. X., & Yan, R. (2014). Multi-scale enveloping order spectrogram for rotating machine health diagnosis. Mechanical Systems and Signal Processing, 46(1), 28–44.

    Article  Google Scholar 

  • Zhang, Z., Wang, Y., & Wang, K. (2013). Fault diagnosis and prognosis using wavelet packet decomposition, Fourier transform, and artificial neural network. Journal of Intelligent Manufacturing, 24, 1213–1227.

    Article  Google Scholar 

  • Zhao, Z., Huang, B., & Liu, F. (2013). Parameter estimation in batch process using EM algorithm with particle filter. Computers and Chemical Engineering, 57, 159–172.

    Article  Google Scholar 

  • Zio, E., & Peloni, G. (2011). Particle filtering prognostics estimation of the remaining useful life of nonlinear components. Reliability Engineering and System Safety, 96, 403–409.

    Article  Google Scholar 

Download references

Acknowledgments

This work has been partially supported by the National Science Foundation of US (CMMI-1300999), the National Science foundation of China (Nos. 51504274 and 51674277), the National Key Research and Development Program of China (No. 2016YFC0802105), and the Science Foundation of China University of Petroleum (Nos. 2462014YJRC039 and 2462015YQ0403). Experimental support from Dr. Eric Bechhoefer (NRG Systems Company), and support from the Xi’an Jiaotong University for Zhaoyan Fan are sincerely appreciated. The authors would like to thank the anonymous reviewers for their constructive comments, which have helped improve the paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Robert X. Gao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, J., Gao, R.X., Yuan, Z. et al. A joint particle filter and expectation maximization approach to machine condition prognosis. J Intell Manuf 30, 605–621 (2019). https://doi.org/10.1007/s10845-016-1268-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10845-016-1268-0

Keywords

Navigation