Fault Diagnosis of Timed Discrete Event Systems using Dioid Algebra

This paper deals with the fault diagnosis problem in a concurrent Timed Discrete Event System (TDES). In a TDES, concurrency leads to more complexity in the diagnoser and appears where, at a certain time, some user must choose among several resources. To cope with this problem, a new model-based diagnoser is proposed in this paper. This diagnoser uses Durational Graph (DG), a main subclass of timed automata for representing the time evolution of the TDES. The proposed diagnoser predicts all possible timed event trajectories that may be generated by the DG This prediction procedure is complicated for nondeterministic DG's that are obtained for concurrent TDES's. To solve this problem, a new Dioid Algebra, Union-Plus Algebra is introduced in this paper. Based on this Algebra, a reachability matrix is defined for a DG that plays an essential role in predicting the time behavior of TDES. By using reachability matrix, a prediction procedure is carried on via an effective equation set that is similar to linear system state equations in ordinary algebra. These results provide a suitable framework for designing an observer-based diagnoser that is illustrated by an example.