Diagnosis of Structural and Temporal Faults for $k$ -Bounded Non-Markovian Stochastic Petri Nets

Abstract

This paper concerns the diagnosis of faults for stochastic discrete event systems that behave according to non-Markovian dynamics. ${k}$ -bounded partially observed Petri nets are used to model the system structure and the sensors. Stochastic processes with probability density functions (pdf) of finite support define the dynamics. Structural and temporal faults are considered. Structural faults correspond to specific sequences of events that should satisfy precedence conditions defined with patterns. Temporal faults are defined with time constraints that must be fulfilled by the firing durations. The probabilities of consistent trajectories are computed with a numerical scheme from the collected timed measurements. The advantage of the proposed scheme is that it can be used for a large variety of pdf that may be defined either with an analytical or a numerical description. It works also for various time semantics. Diagnosis in terms of probability for faulty patterns and temporal constraints is established as a consequence.