Abstract
In this article, we propose an online fault diagnosis approach for labeled Petri nets. When observing an event, the reachability graph of the unobservable subnet (i.e., the net consisting of all places, unobservable transitions, and the attached arcs between them) is first constructed and then a topological sort (i.e., an ordered list of markings) of the reachability graph is obtained. According to the topological sort, each marking in the reachability graph is associated with a vector that contains diagnosis information to form a new graph, called a diagnosis graph. Based on the diagnosis graph constructed for each observed event, an online algorithm is developed to perform diagnosis. When the considered Petri net systems have a small amount of unobservable transitions, the proposed approach enjoys a high computational efficiency compared with the existing ones using integer linear programming.
Highlights
In recent decades, due to the rapid development of technology, large and complex systems are emerging in large numbers, which can be viewed as discrete event systems (DES) [1] at a certain level of abstraction
In [24], the faults are modeled as unobservable transitions and are identified by solving an integer linear programming (ILP) problem built according to the given fault-free Petri net and an observed Petri net language
MAIN RESULTS Before defining some new notations for the formal presentation of the approach, we formalize a proposition to prove that the reachability graph of an acyclic net is acyclic such that a topological sort of the reachability graph is possible
Summary
Due to the rapid development of technology, large and complex systems are emerging in large numbers, which can be viewed as discrete event systems (DES) [1] at a certain level of abstraction. In [24], the faults are modeled as unobservable transitions and are identified by solving an integer linear programming (ILP) problem built according to the given fault-free Petri net and an observed Petri net language. The diagnosis results are derived by assigning different objective functions to the ILP model and solving it This approach is extended to the case of labeled Petri nets in [28]. To avoid enumerating the whole reachability set of a Petri net, multiple approaches above-mentioned [25]–[30] solve the fault diagnosis problem using ILP technique. Given an observation (i.e., an event sequence) of a labeled Petri net, there may exist a huge number of transition sequences whose firings generate the observation, which implies that a large number of ILP models require to be solved to perform diagnosis (see Section V for an example).
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