Fault diagnosis for non-Markovian timed stochastic discrete event systems

This paper concerns the fault diagnosis of stochastic discrete event systems that behave with non-Markovian dynamics. Partially observed Petri nets are used to model the system structure and the sensors. Stochastic processes with arbitrary probability density functions and various time semantics are used to model the dynamics including the failure processes. From the proposed modelling and the collected timed measurements, the probabilities of consistent trajectories are computed with a numerical scheme. The advantage of the proposed scheme is that it can be used for arbitrary probability density functions of the firing durations. It works for race or preselection choice policies. Diagnosis in terms of faults probability is established as a consequence. An example is presented to illustrate the method.