An Efficient Approach for Diagnosability and Diagnosis of DES Based on Labeled Petri Nets, Untimed and Timed Contexts

This PhD thesis deals with fault diagnosis of DES in both untimed and timed contexts using Petri net models. Some on-the-fly and incremental techniques are developed to reduce the state explosion problem while analyzing diagnosability. In the untimed context, an algebraic representation for labeled Petri net (LPN) is developed to feature the system behavior. The diagnosability of LPN models is tackled by analyzing a series of K-diagnosability problems, where K is increased progressively. Two models called respectively FM-graph and FM-set tree are developed and built on the fly to record the necessary information for diagnosability analysis and online diagnosis. Finally, a diagnoser is derived from the FM-set tree for online diagnosis. In the timed context, time interval splitting techniques are developed in order to generate a state representation of labeled time Petri net models, for which techniques from the untimed context can be used to analyze diagnosability and perform online diagnosis. Based on this, necessary and sufficient conditions for the diagnosability of LTPN models are determined. Moreover, we provide the solution for the minimum delay that ensures diagnosability. From a practical point of view, diagnosability analysis is performed on the basis of on-the-fly building of a structure that we call ASG and which holds fault information about the LTPN states. Generally, using on-the-fly analysis and incremental techniques makes it possible to build and investigate only a part of the state space. Analysis results obtained on some chosen benchmarks show the efficiency in terms of time and memory compared with the traditional approaches based on state enumeration.