A Probabilistic Analysis of Predictability in Discrete Event Systems

Predictability is a key property allowing one to expect in advance the occurrence of a fault in a system based on its observed events. Existing works give a binary answer to the question of knowing whether a system is predictable or not. In this paper, we consider discrete event systems where probabilities of the transitions are available. We show how to take advantage of this information to perform a Markov chain-based analysis and extract a variety of probability values that give a finer appreciation of the degree of predictability. This analysis is particularly important in case of non predictable systems. We consider a “light” analysis that focuses only on predictability as well as a “deep” analysis that handles in a uniform framework both predictability and diagnosability.

[1]  John G. Kemeny,et al.  Finite Markov chains , 1960 .

[2]  Alessandro Cimatti,et al.  Formal verification of diagnosability via symbolic model checking , 2003, IJCAI 2003.

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

[4]  Stéphane Lafortune,et al.  Predictability of event occurrences in partially-observed discrete-event systems , 2009, Autom..

[5]  Alban Grastien,et al.  Predictability of Event Occurrences in Timed Systems , 2013, FORMATS.

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

[7]  Farid Nouioua,et al.  Predictability analysis of distributed discrete event systems , 2013, 52nd IEEE Conference on Decision and Control.

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

[9]  Stéphane Lafortune,et al.  Predictability of Sequence Patterns in Discrete Event Systems , 2008 .

[10]  Luca Console,et al.  Diagnosis and Diagnosability Analysis Using PEPA , 2000, ECAI.

[11]  Farid Nouioua,et al.  A probabilistic analysis of diagnosability in discrete event systems , 2008, ECAI.

[12]  Jussi Rintanen,et al.  Diagnosability Testing with Satisfiability Algorithms , 2007, IJCAI.

[13]  Yannick Pencolé,et al.  Scalable Diagnosability Checking of Event-Driven Systems , 2007, IJCAI.

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

[15]  Philippe Dague,et al.  A General Algorithm for Pattern Diagnosability of Distributed Discrete Event Systems , 2012, 2012 IEEE 24th International Conference on Tools with Artificial Intelligence.