Abstract
This article deals with the problem of fault prognosis in stochastic discrete event systems. For that purpose, partially observed stochastic Petri nets are considered to model the system with its sensors. The model represents both healthy and faulty behaviors of the system. Our goal is, based on a timed measurement trajectory issued from the sensors, to compute the probability that a fault will occur in a future time interval. To this end, a procedure based on an incremental algorithm is proposed to compute the set of consistent behaviors of the system. Based on the measurement dates, the probabilities of the consistent trajectories are evaluated and a state estimation is obtained as a consequence. From the set of possible current states and their probabilities, a method to evaluate the probability of future faults is developed using a probabilistic model. An example is presented to illustrate the results.
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Acknowledgments
This project (TERA-MRT MADNESS 2016) has been funded with the support from the European Union with the European Regional Development Fund (ERDF) and from the Regional Council of Normandie.
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This article belongs to the Topical Collection: Special Issue on Diagnosis, Opacity and Supervisory Control of Discrete Event Systems
Guest Editors: Christos G. Cassandras and Alessandro Giua
Appendix
Appendix
The subroutine Sil_events is given by the following recursive algorithm that computes the set SilTrajSet from a given trajectory (σ, M). This set contains, in addition to the considered trajectory (σ, M), all the possible continuations that do not provide any new label nor a change in the measured marking. This algorithm is similar to the unobservable reach operation proposed in Cassandras and Lafortune (2008) for partially observed DES.
Consist_event is given by the following algorithm. It computes, from a given trajectory (σ, M) that leads to the marking M ′ and measurement ejobs(Mjobs), the set of trajectories of type (σT, M), such that the event T provides the new label ejobs and leads to the new measured marking (Mjobs). The idea of this algorithm is similar to the one used for supervisory theory in Prosser et al. (1998).
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Ammour, R., Leclercq, E., Sanlaville, E. et al. Faults prognosis using partially observed stochastic Petri-nets: an incremental approach. Discrete Event Dyn Syst 28, 247–267 (2018). https://doi.org/10.1007/s10626-017-0252-y
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DOI: https://doi.org/10.1007/s10626-017-0252-y