Fault Diagnosis in Discrete Event Systems Modeled by Partially Observed Petri Nets

Abstract

In this paper, we study fault diagnosis in discrete event systems modeled by partially observed Petri nets, i.e., Petri nets equipped with sensors that allow observation of the number of tokens in some of the places and/or partial observation of the firing of some of the transitions. We assume that the Petri net model is accompanied by a (possibly implicit) description of the likelihood of each firing sequence. Faults are modeled as unobservable transitions and are divided into different types. Given an ordered 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. To handle information from transition and place sensors in a unified manner, we transform a given partially observed Petri net into an equivalent (as far as state estimation and fault diagnosis is concerned) labeled Petri net (i.e., a Petri net with only transition sensors), and construct a translator that translates the sensing information from place and transition sensors into a sequence of labels in the equivalent labeled Petri net. Once this transformation is established, we focus on the computation of beliefs on faults in a given labeled Petri net and construct an online monitor that recursively produces these beliefs by tracking the existence of faulty transitions in execution paths that match the sequence of labels observed so far. Using the transformed labeled Petri net and the translated observation sequence, we can then compute the belief for each fault type in partially observed Petri nets in the same way as in labeled Petri nets.