Computation of Diagnosable Fault-Occurrence Indices for Systems with Repeatable-Faults

We study discrete-event systems prone to such faults which can occur repeatedly. For the diagnosis of re- peatable faults, [5] introduced the notion of l-diagnosability requiring the diagnosis of the lth occurrence of a fault within a bounded delay. The present paper studies the identification of the set of all indices a for which the system is l-diagnosable. (These are precisely the occurrence indices for which a repeatable-fault can be diagnosed.) We first present a test to verify whether a fault is diagnosable for each occurrence index, i.e., whether it is “∀l-diagnosable”. For systems that fail this test, we further present a method to compute the set of all indices l for which the system is not l-diagnosable.

[1]  S. R. Das,et al.  Characterizing a confidence space for discrete event timings for fault monitoring using discrete sensing and actuation signals , 2000, IEEE Trans. Syst. Man Cybern. Part A.

[2]  Eleftheria Athanasopoulou,et al.  Probabilistic approaches to fault detection in networked discrete event systems , 2005, IEEE Transactions on Neural Networks.

[3]  W.M. Wonham,et al.  Fault diagnosis in timed discrete-event systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[4]  Gianfranco Lamperti,et al.  Diagnosis of discrete-event systems from uncertain temporal observations , 2002, Artif. Intell..

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

[6]  Shengbing Jiang,et al.  Diagnosis of repeated failures for discrete event systems with linear-time temporal-logic specifications , 2006, IEEE Transactions on Automation Science and Engineering.

[7]  Shengbing Jiang,et al.  A polynomial algorithm for testing diagnosability of discrete-event systems , 2001, IEEE Trans. Autom. Control..

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

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

[10]  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.

[11]  Shahin Hashtrudi-Zad,et al.  Fault diagnosis in discrete-event systems: incorporating timing information , 2005, IEEE Transactions on Automatic Control.

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

[13]  Peter F. Stadler,et al.  Circuit bases of strongly connected digraphs , 2003, Discuss. Math. Graph Theory.

[14]  A. Willsky,et al.  Observability of discrete event dynamic systems , 1990 .

[15]  Lawrence E. Holloway,et al.  Template languages for fault monitoring of timed discrete event processes , 2000, IEEE Trans. Autom. Control..

[16]  Demosthenis Teneketzis,et al.  Diagnosability of stochastic discrete-event systems , 2005, IEEE Transactions on Automatic Control.

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

[18]  Shengbing Jiang,et al.  Failure diagnosis of discrete event systems with linear-time temporal logic fault specifications , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

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

[20]  Gianfranco Lamperti,et al.  Flexible diagnosis of discrete-event systems by similarity-based reasoning techniques , 2006, Artif. Intell..

[21]  Andrew V. Goldberg,et al.  Scaling algorithms for the shortest paths problem , 1995, SODA '93.

[22]  H. D. Ratliff,et al.  Minimum cuts and related problems , 1975, Networks.

[23]  Marie-Odile Cordier,et al.  A formal framework for the decentralised diagnosis of large scale discrete event systems and its application to telecommunication networks , 2005, Artif. Intell..

[24]  Shengbing Jiang,et al.  Diagnosis of dense-time systems using digital-clocks , 2006, 2006 American Control Conference.

[25]  Stéphane Lafortune,et al.  Diagnosis of Intermittent Faults , 2004, Discret. Event Dyn. Syst..

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

[27]  Humberto E. Garcia,et al.  Model-based detection of routing events in discrete flow networks , 2005, Autom..

[28]  Robert E. Tarjan,et al.  Bounds on Backtrack Algorithms for Listing Cycles, Paths, and Spanning Trees , 1975, Networks.

[29]  Albert Benveniste,et al.  Diagnosis of asynchronous discrete-event systems: a net unfolding approach , 2003, IEEE Trans. Autom. Control..

[30]  Herbert Weinblatt,et al.  A New Search Algorithm for Finding the Simple Cycles of a Finite Directed Graph , 1972, JACM.

[31]  Robert E. Tarjan,et al.  Enumeration of the Elementary Circuits of a Directed Graph , 1972, SIAM J. Comput..