Fault Diagnosis in Partially Observed Petri Nets Using Redundancies

This paper is devoted to the development of an approach to the diagnosability of a system described in the framework of partially observed Petri nets (POPNs) such that the developed fault diagnosis technique can be widely applicable to systems with mutable initial states and partial observations. Existing studies show that the diagnosability of a discrete event system (DES) can be improved by suitable sensor selections or redundancies. This paper proposes a redundancy-building method for a POPN with a certain sensor selection such that no matter how the POPN is initially marked, it achieves maximally structural diagnosability, i.e., the diagnosability of a system cannot be further improved based on the given sensor selection and knowledge of the plant model, which is critical and fundamental in fault recovery capabilities for operating large and complex DESs. To make the proposed method practically applicable, we do not require prior knowledge of faults or special structure of a system, instead we model faults as abnormal events occurring on transitions or places in the plant but not special transitions. Necessary and sufficient conditions for maximally structural diagnosability of a system are established. Redundancies (externally observable places) that guarantee behavior permissiveness and maximally structural diagnosability are built by solving integer linear programming problems.