This paper presents a mathematical framework for modeling prognostics at a system level, by combining the prognostics principles with the Plausible Petri nets (PPNs) formalism, first developed in M. Chiachío et al. [Proceedings of the Future Technologies Conference, San Francisco, (2016), pp. 165-172]. The main feature of the resulting framework resides in its efficiency to jointly consider the dynamics of discrete events, like maintenance actions, together with multiple sources of uncertain information about the system state like the probability distribution of end-of-life, information from sensors, and information coming from expert knowledge. In addition, the proposed methodology allows us to rigorously model the flow of information through logic operations, thus making it useful for nonlinear control, Bayesian updating, and decision making. A degradation process of an engineering sub-system is analyzed as an example of application using condition-based monitoring from sensors, predicted states from prognostics algorithms, along with information coming from expert knowledge. The numerical results reveal how the
information from sensors and prognostics algorithms can be processed, transferred, stored, and integrated with discreteevent maintenance activities for nonlinear control operations at system level.
How to Cite
Prognostic Information Management, system-level PHM, Petri nets
Antsaklis, P. J. (2000). Special issue on hybrid systems: theory and applications a brief introduction to the theory and applications of hybrid systems. Proceedings of the IEEE, 88(7), 879-887.
Arumlampalam, M., 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.
Bugarin, A. J., & Barro, S. (1994). Fuzzy reasoning supported by Petri nets. IEEE Transactions on Fuzzy Systems, 2(2), 135–150.
Cao, T., & Sanderson, A. C. (1993). Variable reasoning and analysis about uncertainty with fuzzy Petri nets. In International conference on application and theory of Petri nets (p. 126-145).
Cardoso, J., Valette, R., & Dubois, D. (1999). Possibilistic Petri nets. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 29(5), 573-582.
Chiachío, J., Chiachío, M., Sankararaman, S., Saxena, A., & Goebel, K. (2015). Prognostics design for structural health management. In Emerging design solutions in structural health monitoring systems (pp. 234–273). IGI Global.
Chiachío, M., Beck, J. L., Chiachío, J., & Rus, G. (2014). Approximate Bayesian computation by Subset Simulation. SIAM Journal on Scientific Computing,
Chiachío, M., Chiachío, J., Prescott, D., & Andrews, J. (2016). An information theoretic approach for knowledge representation using Petri nets. In Proceedings of Future Technologies Conference, 6-7 December 2016, San Francisco (pp. 165–172).
Chiachío, M., Chiachío, J., Saxena, A., & Goebel, K. (2016). An energy-based prognostic framework to predict evolution of damage in composite materials. In Structural health monitoring (shm) in aerospace structures (p. 447-477). Woodhead Publishing-Elsevier.
Chiachío, M., Chiachío, J., Shankararaman, S.,&Andrews, J. (2017). A new algorithm for prognostics using Subset Simulation. Reliability Engineering & System Safety, in press.
Daigle, M., Bregon, A., & Roychoudhury, I. (2014). Distributed prognostics based on structural model decomposition. IEEE Transactions on Reliability, 63(2), 495-510.
Daigle, M., & Kulkarni, S. (2013). Electrochemistry-based battery modeling for prognostics. In Proceedings of the annual conference of the prognostics and health management society, 2013 (Vol. 1, p. 249-261).
David, R. (1997). Modeling of hybrid systems using continuous and hybrid Petri nets. In Proceedings of the seventh international workshop on Petri nets and performance models (PNPM’97), 1997. (pp. 47–58).
Doucet, A., De Freitas, N., & Gordon, N. (2001). An introduction to sequential Monte Carlo methods. In A. Doucet, N. De Freitas, & N. Gordon (Eds.), Sequential Monte Carlo methods in practice (pp. 3–14). Springer.
Gomez, J., Rodrigues, L., Galvo, R., & Yoneyama, T. (2013). System level rul estimation for multiple-component systems. In Proceedings of Annual Conference of the Prognostics and Health Management Society (p. 74-83).
Javed, K., Gouriveau, R., & Zerhouni, N. (2017). State of the art and taxonomy of prognostics approaches, trends of prognostics applications and open issues towards maturity at different technology readiness levels. Mechanical Systems and Signal Processing, 94, 214–236.
J´ulvez, J., Di Cairano, S., Bemporad, A., & Mahulea, C. (2014). Event-driven model predictive control of timed hybrid Petri nets. International Journal of Robust and Nonlinear Control, 24(12), 1724-1742.
Khorasgani, H., Biswas, G., & Shankararaman, S. (2016). Methodologies for system-level remaining useful life prediction. Reliability Engineering and System Safety, 154, 8-18.
Konar, A., & Mandal, A. K. (1996). Uncertainty management in expert systems using fuzzy Petri nets. IEEE Transactions on Knowledge and Data Engineering, 8(1), 96-105.
Liu, B., Xu, Z., Xie, M., & Kuo, W. (2014). A value-based preventive maintenance policy for multi-component system with continuously degrading components. Reliability Engineering & System Safety, 132, 83-89.
Looney, C. G. (1988). Fuzzy Petri nets for rule-based decision making. IEEE Transactions on Systems, Man, and Cybernetics, 18(1), 178–183.
Murata, T. (1989). Petri nets: Properties, analysis and applications. Proceedings of the IEEE, 77(4), 541-580.
My¨otyri, E., Pulkkinen, U., & Simola, K. (2006). Application of stochastic filtering for lifetime prediction. Reliability Engineering and System Safety, 91(2), 200–208.
Petri, C. A. (1962). Kommunikation mit automaten (Unpublished doctoral dissertation). Institut fr Instrumentelle Mathematik an der Universitt Bonn.
Rus, G., Chiachío, J., & Chiachío, M. (2016). Logical inference for inverse problems. Inverse Problems in Science and Engineering, 24(3), 448-464.
Saha, B., Celaya, J. R., Wysocki, P. F., & Goebel, K. F. (2009). Towards prognostics for electronics components. In Aerospace conference, 2009 ieee (pp. 1–7).
Silva, M. (2016). Individuals, populations and fluid approximations: A Petri net based perspective. Nonlinear Analysis: Hybrid Systems, 22, 72–97.
Tarantola, A. (2005). Inverse problem theory and methods for model parameters estimation. SIAM.
Tarantola, A., & Mosegaard, K. (2007). Mapping of probabilities, theory for the interpretation of uncertain physical measurements. Cambridge University Press.
Tarantola, A., & Valette, B. (1982). Inverse problems = quest for information. Journal of Geophysics, 50(3), 159-170.
Vazquez, C. R., & Silva, M. (2015). Stochastic hybrid approximations of Markovian Petri nets. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 45(9), 1231–1244.
Zhou, K.-Q., & Zain, A. M. (2016). Fuzzy Petri nets and industrial applications: a review. Artificial Intelligence Review, 45(4), 405-446.
Zio, E., & Peloni, G. (2011). Particle filtering prognostic estimation of the remaining useful life of nonlinear components. Reliability Engineering and System Safety, 96(3), 403–409.
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.