Diagnosis on a sliding window for partially observable Petri nets

Abstract

In this paper, we propose an algebraic approach to investigate the diagnosis of partially observable labeled Petri nets based on state estimation on a sliding window of a predefined length h . Given an observation, the resulting diagnosis state can be computed while solving integer linear programming problems with a reduced subset of basis markings. The proposed approach consists in exploiting a subset of h observations at each estimation step, which provides a partial diagnosis relevant to the current observation window. This technique allows a status update with a ”forgetfulness” of past observations and enables distinguishing repetitive and punctual faults. The complete diagnosis state can be defined as a function of the partial diagnosis states interpreted on the sliding window. As the analysis shows that some basis markings can present an inconsistency with a future evolution, which possibly implies unnecessary computations of basis markings, a withdrawal procedure of these irrelevant basis markings based on linear programming is proposed.