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Fault Diagnosis in Discrete Event Systems Modeled by Partially Observed Petri Nets

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Abstract

In this paper, we study fault diagnosis in discrete event systems modeled by partially observed Petri nets, i.e., Petri nets equipped with sensors that allow observation of the number of tokens in some of the places and/or partial observation of the firing of some of the transitions. We assume that the Petri net model is accompanied by a (possibly implicit) description of the likelihood of each firing sequence. Faults are modeled as unobservable transitions and are divided into different types. Given an ordered sequence of observations from place and transition sensors, our goal is to calculate the belief (namely, the degree of confidence) regarding the occurrence of faults belonging to each type. To handle information from transition and place sensors in a unified manner, we transform a given partially observed Petri net into an equivalent (as far as state estimation and fault diagnosis is concerned) labeled Petri net (i.e., a Petri net with only transition sensors), and construct a translator that translates the sensing information from place and transition sensors into a sequence of labels in the equivalent labeled Petri net. Once this transformation is established, we focus on the computation of beliefs on faults in a given labeled Petri net and construct an online monitor that recursively produces these beliefs by tracking the existence of faulty transitions in execution paths that match the sequence of labels observed so far. Using the transformed labeled Petri net and the translated observation sequence, we can then compute the belief for each fault type in partially observed Petri nets in the same way as in labeled Petri nets.

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Notes

  1. Possible paths are sequences of transitions that are consistent with a given sequence of observations.

  2. To avoid confusion between Σ and Σ′, we define a new label a 1 instead of using the original label a.

  3. T − T o ′ is the set of transitions that will generate neither token changes nor an observable transition label; therefore, such transitions will be mapped to ε in the constructed labeled Petri net. In other words, T − T o ′ = T ε , where T ε is obtained from L′ in (G, Σ′, L′).

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Acknowledgements

The authors would like to thank anonymous reviewers for very helpful comments on the initial submission of this paper and an earlier conference paper that included some of these results.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Yu Ru & Christoforos N. Hadjicostis

  2. Department of Electrical and Computer Engineering, University of Cyprus, 75 Kallipoleos Ave, P.O.Box 20537, 1678, Nicosia, Cyprus

    Christoforos N. Hadjicostis

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  1. Yu Ru
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Correspondence to Yu Ru.

Additional information

This material is based upon work supported in part by the National Science Foundation under NSF ITR Award 0426831 and NSF CNS Award 0834409. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of NSF. The research leading to these results has also received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreements INFSO-ICT-223844 and PIRG02-GA-2007-224877.

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Ru, Y., Hadjicostis, C.N. Fault Diagnosis in Discrete Event Systems Modeled by Partially Observed Petri Nets. Discrete Event Dyn Syst 19, 551–575 (2009). https://doi.org/10.1007/s10626-009-0074-7

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