A New Approach for Diagnosability Analysis of Petri Nets Using Verifier Nets

In this paper, we analyze the diagnosability properties of labeled Petri nets. We consider the standard notion of diagnosability of languages, requiring that every occurrence of an unobservable fault event be eventually detected, as well as the stronger notion of diagnosability in K steps, where the detection must occur within a fixed bound of K event occurrences after the fault. We give necessary and sufficient conditions for these two notions of diagnosability for both bounded and unbounded Petri nets and then present an algorithmic technique for testing the conditions based on linear programming. Our approach is novel and based on the analysis of the reachability/coverability graph of a special Petri net, called Verifier Net, that is built from the Petri net model of the given system. In the case of systems that are diagnosable in K steps, we give a procedure to compute the bound K. To the best of our knowledge, this is the first time that necessary and sufficient conditions for diagnosability and diagnosability in K steps of labeled unbounded Petri nets are presented.

[1]  Alessandro Giua,et al.  Discrete event diagnosis using labeled Petri nets. An application to manufacturing systems , 2011 .

[2]  Stéphane Lafortune,et al.  Coordinated Decentralized Protocols for Failure Diagnosis of Discrete Event Systems , 2000, Discret. Event Dyn. Syst..

[3]  Jan Lunze,et al.  Sensor and actuator fault diagnosis of systems with discrete inputs and outputs , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  Stéphane Lafortune,et al.  Active diagnosis of discrete event systems , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[5]  J.H. van Schuppen,et al.  Decentralized failure diagnosis for discrete-event systems with costly communication between diagnosers , 2002, Sixth International Workshop on Discrete Event Systems, 2002. Proceedings..

[6]  Raja Sengupta,et al.  Diagnosability of discrete-event systems , 1995, IEEE Trans. Autom. Control..

[7]  Christoforos N. Hadjicostis,et al.  Fault Diagnosis in Discrete Event Systems Modeled by Partially Observed Petri Nets , 2009, Discret. Event Dyn. Syst..

[8]  YuanLin Wen,et al.  Diagnosability analysis based on T-invariants of Petri nets , 2005, Proceedings. 2005 IEEE Networking, Sensing and Control, 2005..

[9]  J. Prock.  A new technique for fault detection using Petri nets , 1991, Autom..

[10]  Alessandro Giua,et al.  Diagnosability of bounded Petri nets , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[11]  Farid Nouioua,et al.  Diagnosability verification with Petri net unfoldings , 2010, Int. J. Knowl. Based Intell. Eng. Syst..

[12]  V. S. Srinivasan,et al.  Fault detection/monitoring using time Petri nets , 1993, IEEE Trans. Syst. Man Cybern..

[13]  MuDer Jeng,et al.  A polynomial algorithm for checking diagnosability of Petri nets , 2005, 2005 IEEE International Conference on Systems, Man and Cybernetics.

[14]  Feng Lin,et al.  Diagnosability of discrete event systems and its applications , 1994, Discret. Event Dyn. Syst..

[15]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[16]  Richard M. Karp,et al.  Parallel Program Schemata , 1969, J. Comput. Syst. Sci..

[17]  H. Garcia,et al.  Event diagnosis of discrete-event systems with uniformly and nonuniformly bounded diagnosis delays , 2004, Proceedings of the 2004 American Control Conference.

[18]  Stefan Haar.  Qualitative diagnosability of labeled petri nets revisited , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[19]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[20]  Rüdiger Valk,et al.  Petri Nets and Regular Languages , 1981, J. Comput. Syst. Sci..

[21]  Shengbing Jiang,et al.  Failure diagnosis of discrete-event systems with linear-time temporal logic specifications , 2004, IEEE Transactions on Automatic Control.

[22]  Victor Khomenko,et al.  Diagnosability verification with parallel LTL-X model checking based on Petri net unfoldings , 2010, 2010 Conference on Control and Fault-Tolerant Systems (SysTol).

[23]  Stéphane Lafortune,et al.  Distributed Diagnosis of Discrete-Event Systems Using Petri Nets , 2003, ICATPN.

[24]  Alessandro Giua,et al.  Diagnosability analysis of unbounded Petri nets , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[25]  Alessandro Giua,et al.  Linear programming techniques for the identification of place/transition nets , 2008, 2008 47th IEEE Conference on Decision and Control.

[26]  Mariagrazia Dotoli,et al.  Fault Detection of Discrete Event Systems Using Petri Nets and Integer Linear Programming , 2008 .

[27]  Feng Lin,et al.  Design and test of mixed signal circuits: a discrete-event approach , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[28]  Feng Chu,et al.  Deadlock analysis of Petri nets using siphons and mathematical programming , 1997, IEEE Trans. Robotics Autom..

[29]  Antonio Ramírez-Treviño,et al.  Online Fault Diagnosis of Discrete Event Systems. A Petri Net-Based Approach , 2007, IEEE Transactions on Automation Science and Engineering.

[30]  Sheng-Luen Chung.  Diagnosing PN-based models with partial observable transitions , 2005, Int. J. Comput. Integr. Manuf..

[31]  Walter Ukovich,et al.  On-line fault detection in discrete event systems by Petri nets and integer linear programming , 2009, Autom..

[32]  Stéphane Lafortune,et al.  Failure diagnosis using discrete event models , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[33]  D UllmanJeffrey,et al.  Introduction to automata theory, languages, and computation, 2nd edition , 2001 .

[34]  Albert Benveniste,et al.  Diagnosis of asynchronous discrete event systems, a net unfolding approach , 2002, Sixth International Workshop on Discrete Event Systems, 2002. Proceedings..

[35]  Gianmaria De Tommasi,et al.  An Efficient Approach for Online Diagnosis of Discrete Event Systems , 2009, IEEE Transactions on Automatic Control.

[36]  Shahin Hashtrudi-Zad,et al.  Fault diagnosis in discrete-event systems: framework and model reduction , 2003, IEEE Trans. Autom. Control..

[37]  George Jiroveanu,et al.  The Diagnosability of Petri Net Models Using Minimal Explanations , 2010, IEEE Transactions on Automatic Control.

[38]  Christoforos N. Hadjicostis,et al.  Algebraic approaches for fault identification in discrete-event systems , 2005, IEEE Transactions on Automatic Control.

[39]  Stéphane Lafortune,et al.  Distributed Diagnosis of Place-Bordered Petri Nets , 2007, IEEE Transactions on Automation Science and Engineering.

[40]  Dimitri Lefebvre,et al.  Diagnosis of DES With Petri Net Models , 2007, IEEE Transactions on Automation Science and Engineering.

[41]  Jens Palsberg,et al.  Complexity Results for 1-safe Nets , 1993, FSTTCS.

[42]  Matthias Jantzen.  Complexity of Place/Transition Nets , 1986, Advances in Petri Nets.

[43]  Stéphane Lafortune,et al.  Polynomial-time verification of diagnosability of partially observed discrete-event systems , 2002, IEEE Trans. Autom. Control..

[44]  Toshimitsu Ushio,et al.  Fault detection based on Petri net models with faulty behaviors , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[45]  Christoforos N. Hadjicostis,et al.  Monitoring Discrete Event Systems Using Petri Net Embeddings , 1999, ICATPN.

[46]  Shengbing Jiang,et al.  Diagnosis of repeated/intermittent failures in discrete event systems , 2003, IEEE Trans. Robotics Autom..