Failure detection and localization for timed event graphs in ( max , + ) $(\max \limits ,+)$ -algebra

In this paper, we address the problem of failure detection and localization in a Timed Discrete Event System (TDES) such $(\max \limits ,+)$ -linear system graphically modeled by a Timed Event Graph (TEG). The considered failures are changes on holding times or tokens of the TEG places that can provoke shifts between an observed outcoming timed flow and an expected outcoming timed flow (for a given incoming timed flow). Indicators are built to first detect such shifts relying on the $(\max \limits ,+)$ algebraic framework and the residuation theory. An analysis of the indicators’ values provides information about time or event failure that could have happen. Then, thanks to the knowledge of the behavior of the system through its corresponding TEG, sets of failures that could explain the detected shifts are obtained. It comes from matrices of signatures for each indicator built on each observable output of the system. An example of application is proposed to experiment exhaustively failures of type time and event on each place of the TEG.