Fault diagnosis in discrete event systems modeled by Petri nets with outputs

In this paper, we study fault diagnosis in discrete event systems modeled by Petri nets with outputs, i.e., Petri nets with place sensors and transition sensors. Faults are modeled as unobservable transitions and are divided into different types. We assume that the Petri net model is accompanied by a description of the likelihood of each transition at any particular marking. Given a sequence of observations from place and transition sensors, our goal is to calculate the belief (namely, the degree of confidence) regarding the occurrence of faults belonging to each type. We first focus on the computation of beliefs in Petri nets with only transition sensors (i.e., labeled Petri nets) and we construct an online monitor that produces these beliefs by tracking the existence of faulty transitions in execution paths that match the sequence of labels observed so far. To handle place sensors, we transform a given Petri net with outputs into an equivalent labeled Petri net that translates the sensing information into a sequence of labels in the equivalent labeled Petri net. Using this transformation of Petri net and observation sequence, we can then compute the belief for each fault type in the same way as in labeled Petri nets.