Exact Nonlinear Filtering and Prediction in Process Model-Based Prognostics

##plugins.themes.bootstrap3.article.main##

##plugins.themes.bootstrap3.article.sidebar##

Published Mar 26, 2021
Jonathan A. DeCastro Liang Tang Kenneth A. Loparo Kai Goebel George Vachtsevanos

Abstract

Opportunities exist to apply nonlinear filtering to model-based prognostics in order to provide a systematic way of dealing with the propagation of system damage at some future time, whenever imprecise diagnostic information is obtained. Central to the prognostics problem is the ability to properly capture and manage uncertainties when predicting remaining useful life of a particular component of interest. The goal of this paper is to present a foundation for prediction and filtering of the failure process using nonlinear prognostic models and exact (finite-dimensional) filters. Specifically, we consider the use of non- linear filters to represent the uncertainty distributions exactly for certain classes of nonlinear systems, given a statistically-representative process model of remaining useful life. One such filter, known as the Beneš filter, is derived in this paper for a certain class of prognostic process model. The filter is applied to crack growth data and is shown to perform reasonably well in the context of the 1-D hyperbolic model. Although directly applicable to certain prognostic systems, the techniques descibed provide a theoretical foundation for approximate but less model-restrictive techniques for dynamic model-based prognostics such as particle filtering.

How to Cite

A. DeCastro , J. ., Tang, L., A. Loparo, K., Goebel , K. ., & Vachtsevanos , G. . (2021). Exact Nonlinear Filtering and Prediction in Process Model-Based Prognostics. Annual Conference of the PHM Society, 1(1). Retrieved from http://www.papers.phmsociety.org/index.php/phmconf/article/view/1529
Abstract 553 | PDF Downloads 169

##plugins.themes.bootstrap3.article.details##

Keywords

filtering, model based prognostics, model-based methods, particle filtering, prognostics, remaining useful life (RUL), uncertainty management

References
(Beneš, 1981) V. E. Beneš. Exact finite-dimensional for certain diffusions with nonlinear drift. Stochas- tics, 5(1/2):65–92, 1981.
(Chipman et al., 2001) H. Chipman, E. I. George, and R. E. McCulloch. The practical implementation of bayesian model selection. IMS Lecture Notes - Monograph Series, 38:65–116, 2001.
(Daum, 1986) F. E. Daum. Exact finite-dimensional nonlinear filters. IEEE Trans. on Automatic Control, AC-31(7):616–622, July 1986.
(Daum,1987) F.E.Daum.Solutionofthezakaiequation by separation of variables. IEEE Trans. on Automatic Control, AC-32(10):941–943, October 1987.
(Fuller, 1969) A. T. Fuller. Analysis of nonlinear stochastic systems by means of the fokkerplanck equation. Int. J. of Control, 9(6):603–655, June 1969.
(Goebel et al., 2008) K. Goebel, B. Saha, A. Saxena, J. R. Celaya, and J. P. Christophersen. Prognostics in battery health management. IEEE Instrumentation & Measurement Magazine, pages 33–40, August 2008.
(Mitter, 1983) S. K. Mitter. Lectures on nonlinear filtering and stochastic control. In S. K. Mitter and A. Moro, editors, Nonlinear Filtering and Stochastic Control, pages 170–207. New York: Springer- Verlag, 1983.
(Orchard et al., 2008) M. Orchard, G. Kacprzynski, K. Goebel, B. Saha, and G. Vachtsevanos. Advances in uncertainty representation and management for particle filtering applied to prognostics. In Int. Conf. on Prognostics and Health Management, Denver, CO, October 6–9 2008.
(Paola and Sofi, 2002) M. Di Paola and A. Sofi. Approximate solution of the fokkerplanck- kolmogorov equation. System and Control Letters, 17(4):369–384, 2002.
(Saxena et al., 2009) A. Saxena, J. Celaya, B. Saha, S. Saha, and K. Goebel. Evaluating algorithm performance metrics tailored for prognostics. In IEEE Aerospace Conference, March 2009.
(Wang and Zhang, 2000) R. Wang and Z. Zhang. Exact stationary solutions of the fokkerplanck equation for nonlinear oscillators under stochastic parametric and external excitations. Nonlinearity, 13:907–920, 2000.
(Zakai, 1969) M. Zakai. On the optimal filtering of diffusion processes. Zeitschrift fur Wahrschein- lichkeitstheorie und verwande Gebiete, 11(3):230– 243, 1969.
Section
Technical Research Papers

Most read articles by the same author(s)

1 2 3 4 5 6 > >>