Fault detection for discrete event systems using Petri nets with unobservable transitions

Abstract

In this paper we present a fault detection approach for discrete event systems using Petri nets. We assume that some of the transitions of the net are unobservable, including all those transitions that model faulty behaviors. Our diagnosis approach is based on the notions of basis marking and justification, that allow us to characterize the set of markings that are consistent with the actual observation, and the set of unobservable transitions whose firing enable it. This approach applies to all net systems whose unobservable subnet is acyclic. If the net system is also bounded the proposed approach may be significantly simplified by moving the most burdensome part of the procedure off-line, thanks to the construction of a graph, called the basis reachability graph.

On the Equivalence of Observation Structures for Petri Net Generators

“…the supervisor in a supervisory control problem, or the intruder in an opacity problem) that knows the initial marking and the structure of the PN but observes the firing of transitions through a mask. A common assumption is that of considering the mask as a projection from the set of transitions T to an alphabet Σ which represents available sensors readings [5], [15], [18]. The mask is possibly evasive, i.e., the output label assigned to a transition may either be a symbol from the alphabet or the empty string ε to denote that the firing of the transition does not produce an observable reading.…”

“…This result can be explained by the following theorem concerning the coloring problem in infinite graphs. The future work will focus on characterizing a class of LPNOs whose LPNs or ALPNs can be obtained with polynomial complexity, using the basis reachability graph introduced in [15] to reduce the conversion complexity, …”

“…We point out that the notion of observation equivalence proposed in this paper is not related to what the observer sees (e.g., the observed language) but rather to what the observer can infer about the system's dynamical evolution. Thus the results presented herein are relevant to addressing a wide range of problems that are currently investigated in the DES literature, such as state estimation, failure diagnosis or opacity [4], [5], [15], [16].…”

Online Fault Diagnoser for Partially Observed Petri Nets

“…The unfolding approach for online asynchronous diagnosis is presented in [6]. This approach leads to an interpreted diagnosis in which the state explosion is well kept under control, but the online computational effort may increase significantly due to the online building of PN structures called diagnosis nets via unfolding.…”

A Program Model of Fuzzy Interpreted Petri Net to Control Discrete Event Systems

“…Others are associated with the validation of DES, which includes: diagnosis of an asynchronous system [11]; detecting and isolating fault events [12]; fault online detection [13]; fault diagnosis with unobservable transition [14]; model checking based on user specification [15]; formal verification with the use of structural reasoning and general unary hypothesis automaton (GUHA) methods [16]. Other research concerns the application of PNs to specific problems, e.g., to model flexible manufacturing systems (FMS) [17][18][19][20][21][22] or to model As a continuation of [53], which lacked a formal description of the proposed solution, this article may be included in the second trend of dealing with DES.…”