# zbMATH — the first resource for mathematics

Fault diagnosis in discrete event systems modeled by partially observed Petri nets. (English) Zbl 1180.93069
Summary: 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.

##### MSC:
 93C65 Discrete event control/observation systems 93A30 Mathematical modelling of systems (MSC2010) 90B25 Reliability, availability, maintenance, inspection in operations research
UMDES
Full Text:
##### References:
 [1] Aghasaryan A, Fabre E, Benveniste A, Boubour R, Jard C (1998) Fault detection and diagnosis in distributed systems: An approach by partially stochastic Petri nets. Discret Event Dyn Syst Theory Appl Categ 8:203–231 · Zbl 0916.93074 · doi:10.1023/A:1008241818642 [2] Benveniste A, Fabre E, Haar S (2003a) Markov nets: Probabilistic models for distributed and concurrent systems. IEEE Trans Automat Contr 48:1936–1950 · Zbl 1364.93451 · doi:10.1109/TAC.2003.819076 [3] Benveniste A, Fabre E, Haar S, Jard C (2003b) Diagnosis of asynchronous discrete-event systems: A net unfolding approach. IEEE Trans Automat Contr 48:714–727 · Zbl 1364.93452 · doi:10.1109/TAC.2003.811249 [4] Cassandras CG, Lafortune S (2008) Introduction to discrete event systems (2nd Edition). Springer, New York · Zbl 1165.93001 [5] Chung SL (2005) Diagnosing PN-based models with partial observable transitions. Int J Comput Integr Manuf 18:158–169 · doi:10.1080/0951192052000288206 [6] Esparza J, Nielsen M (1994) Decidability issues for Petri nets–a survey. Bull Eur Assoc Theor Comput Sci 52:245–262 · Zbl 0791.68123 [7] Genc S, Lafortune S (2007) Distributed diagnosis of place-bordered Petri nets. IEEE Trans Autom Sci Eng 4:206–219 · doi:10.1109/TASE.2006.879916 [8] Giua A, Seatzu C (2005) Fault detection for discrete event systems using Petri nets with unobservable transitions. In: 44th IEEE Conf. on Decision and Control, Seville, pp 6323–6328 [9] Giua A, Corona D, Seatzu C (2005) State estimation of $$\lambda$$-free labeled Petri nets with contact-free nondeterministic transitions. Discret Event Dyn Syst Theory Appl Categ 15:85–108 · Zbl 1071.93028 · doi:10.1007/s10626-005-5239-4 [10] Giua A, Seatzu C, Corona C (2007) Marking estimation of Petri nets with silent transitions. IEEE Trans Automat Contr 52:1695–1699 · Zbl 1368.68261 · doi:10.1109/TAC.2007.904281 [11] Hadjicostis CN, Verghese GC (1999) Monitoring discrete event systems using Petri net embeddings. In: Application and Theory of Petri Nets 1999 (Series Lecture Notes in Computer Science, vol. 1639), pp 188–207 · Zbl 0934.93046 [12] Jiang S, Kumar R, Garcia HE (2002) Diagnosis of repeated failures in discrete event systems. In: 41st IEEE Conf. on Decision and Control, Las Vegas, pp 4000–4005 [13] Lefebvre D, Delherm C (2007) Diagnosis of DES with Petri net models. IEEE Trans Automat Sci Eng 4:114–118 · doi:10.1109/TASE.2006.872122 [14] Li L, Ru Y, Hadjicostis CN (2006) Least-cost firing sequence estimation in labeled Petri nets. In: Proc. of 45th IEEE Conf. on Decision and Control, San Diego, pp 416–421 [15] Murata T (1989) Petri nets: Properties, analysis and applications. Proc IEEE 77:541–580 · doi:10.1109/5.24143 [16] Pearl J (1988) Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, San Francisco · Zbl 0746.68089 [17] Peterson JL (1981) Petri net theory and the modelling of systems. Prentice-Hall, New Jersey · Zbl 0461.68059 [18] Ramadge PJ, Wonham WM (1989) The control of discrete event systems. Proc IEEE 77:81–98 · doi:10.1109/5.21072 [19] Ramírez-Treviño A, Ruiz-Beltrán E, Rivera-Rangel I, López-Mellado E (2007) Online fault diagnosis of discrete event systems. a Petri net-based approach. IEEE Trans Automat Sci Eng 4:31–39 · doi:10.1109/TASE.2006.872120 [20] Ru Y, Hadjicostis CN (2009a) Bounds on the number of markings consistent with label observations in Petri nets. IEEE Trans Automat Sci Eng 6:334–344 · doi:10.1109/TASE.2008.2009095 [21] Sampath M, Sengupta R, Lafortune S, Sinnamohideen K, Teneketzis D (1995) Diagnosability of discrete event systems. IEEE Trans Automat Contr 40:1555–1575 · Zbl 0839.93072 · doi:10.1109/9.412626 [22] Thorsley D, Teneketzis D (2005) Diagnosability of stochastic discrete-event systems. IEEE Trans Automat Contr 50:476–492 · Zbl 1365.93478 · doi:10.1109/TAC.2005.844722 [23] Thorsley D, Yoo TS, Garcia HE (2008) Diagnosability of stochastic discrete-event systems under unreliable observations. In: Proc. of the 2008 American Control Conference, Seattle, pp 1158–1165 [24] Ushio T, Onishi I, Okuda K (1998) Fault detection based on Petri net models with faulty behaviors. In: Proc. of IEEE Int. Conf. on Systems, Man, and Cybernetics, San Diego, pp 113–118 [25] Wu Y, Hadjicostis CN (2005) Algebraic approaches for fault identification in discrete-event systems. IEEE Trans Automat Contr 50:2048–2053 · Zbl 1365.93418 · doi:10.1109/TAC.2005.843877
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.