This article concerns fault diagnosis and prognosis for stochastic discrete event systems. For this purpose, partially observed stochastic Petri nets are introduced that include the sensors used to measure events and markings and the Markovian stochastic dynamics used to represent failure processes. Timed observation sequences result from this modeling, and the probabilities of timed and untimed marking trajectories consistent with a given timed observation sequence are systematically computed. Diagnosis in terms of fault probability is obtained as a consequence and compared with the belief of faults that is usually used for diagnosis issues. Confidence factors based on fault probabilities are also proposed. Finally, state estimation and fault prediction are investigated, and probability of future faults is obtained as a consequence. An application case is studied to illustrate the method.
BlankeMKinnaertMLunzeJ. Diagnosis and fault tolerant control. New York: Springer-Verlag, 2003.
2.
PetersonJL. Petri net theory and the modelling of systems. Upper Saddle River, NJ: Prentice Hall, 1981.
3.
RuYHadjiscotisH. Fault diagnosis in discrete event systems modeled by partially observed Petri nets. Discrete Event Dyn S2009; 19: 551–575.
4.
CabasinoMPGiuaAPocciM. Discrete event diagnosis using labeled Petri nets. An application to manufacturing systems. Control Eng Pract2011; 19: 989–1001.
5.
MahuleaCSeatzuCCabasinoM. Fault diagnosis of discrete-event systems using continuous Petri nets. IEEE T Automat Contr2012; 42(4): 970–984.
6.
DotoliMPia FantiMManginiAM. Identification of the unobservable behaviour of industrial automation systems by Petri nets. Control Eng Pract2011; 19: 958–966.
7.
RenganathanKBhaskarV. Modeling, analysis and performance evaluation for fault diagnosis and Fault Tolerant Control in bottle-filling plant modeled using Hybrid Petri nets. Appl Math Model2012; 37: 4842–4859.
8.
BasileFChiacchioPDe TommasiG. An efficient approach for online diagnosis of discrete event systems. IEEE T Automat Contr2009; 54(4): 748–759.
9.
LiLHadjicostisC. Least-cost transition firing sequence estimation in labeled Petri nets with unobservable transitions. IEEE T Automat Contr2011; 8(2): 394–403.
10.
Ramírez-TreviñoARuiz-BeltranERivera-RangelI. Online fault diagnosis of discrete event systems. A Petri net-based approach. IEEE T Autom Sci Eng2007; 4(1): 31–39.
CabasinoMPGiuaALafortuneS. A new approach for diagnosability analysis of Petri nets using verifier net. IEEE T Automat Contr2012; 57(12): 3104–3117.
13.
DotoliMFantiMPManginiAM. On-line fault detection in discrete event systems by Petri nets and integer linear programming. Automatica2009; 45: 2665–2672.
14.
LefebvreDDelhermC. Diagnosis of DES with Petri net models. IEEE T Autom Sci Eng2007; 4(1): 114–118.
15.
WuYHadjicostisCN. Algebraic approaches for fault identification in discrete-event systems. IEEE T Automat Contr2005; 50(12): 2048–2053.
16.
UshioTOnishiLOkudaK. Fault detection based on Petri net models with faulty behaviors. In: Proceedings of the IEEE international conference on systems, man and cybernetics, San Diego, CA, 11–14 October 1998. New York: IEEE.
17.
Alcaraz-MejíaMLópez-MelladoERamírez-TreviñoA. Petri net based fault diagnosis of discrete event systems. In: Proceedings of the IEEE international conference on systems, man and cybernetics, Washington, D.C., USA, 5–8 October 2003. New York: IEEE.
18.
MadalinskiAKhomenkoV. Predictability verification with parallel LTL-X Model checking based on Petri net unfoldings. In: Proceedings of IFAC-SAFEPROCESS, Mexico City, 29–31 august 2012, IFAC and AMCA.
19.
LefebvreD. State estimation and fault prediction with partially observed Petri nets. In: Proceedings of the IEEE-ETFA, Cagliari, 10–13 September, New York : IEEE.
20.
ShengbingJKumarR. Failure diagnosis of discrete-event systems with linear-time temporal logic specifications. IEEE T Automat Contr2004; 49(6): 934–945.
21.
GencSLafortuneS. Predictability of event occurrences in partially-observed discrete-event systems. Automatica2009; 45: 301–311.
22.
ShuSLinFYingH. Detectability of discrete event systems. IEEE T Automat Contr2007; 52(12): 2356–2359.
23.
ShuSLinFYingH. State estimation and detectability of probabilistic discrete event systems. Automatica2008; 44(12): 3054–3060.
24.
SampathMSenguptaRLafortuneS. Diagnosability of discrete event systems. IEEE T Automat Contr1995; 40(9): 1555–1575.
25.
LefebvreD. Diagnosis with Petri nets according to partial events and states observation. In: Proceedings of the IFAC-SAFEPROCESS, Mexico City, 29–31 August 2012, IFAC and AMCA.
26.
LefebvreD. On-line fault diagnosis with partially observed Petri nets. IEEE T Automat Contr, forthcoming.
27.
MolloyM. Performance analysis using stochastic Petri nets. IEEE T Comput1982; 31: 913–917.
28.
El AkchiouiNLeclercqELefebvreD. Modeling and analysis of large systems with high availability constraints. In: Proceedings of the 43rd ESReDA seminar, Rouen, 21–23, October 2012, ESReDA.
29.
RausandMHoylandA. System reliability theory: models, statistical methods, and applications. Hoboken, NJ: Wiley, 2004.
30.
BobbioAPuliafitoATelekM. Recent developments in stochastic Petri nets. J Circuit Syst Comp1998; 8(1): 119–158.
31.
OuldElMehdiSLeclercqELefebvreD. Identification of stochastic and deterministic stochastic Petri net models for reliability analysis. Proc IMechE Part O: J Risk and Reliability2009; 223(1): 13–26.
32.
LefebvreD. Design and time parameters identification for non-Markovian Petri net models: application to the reliability analysis. Proc IMechE Part O: J Risk and Reliability2011; 225(1): 1–18.
33.
LefebvreD. Approximation of the asymptotic mean marking of SPNs with contPNs. Nonlinear Anal2012; 6: 972–987.
34.
LefebvreD. An algorithm of linear complexity for the diagnosis of discrete event systems. In: Proceedings of the 2013 IFAC Conference on Manufacturing Modelling, Management, and Control : 287–292, Saint Petersbourg, 19–21, June 2013, New York: IEEE and IFAC.
35.
VanderbeiR. Linear programming: foundations and extension. New York: Springer, 2007.
