A Diagnoser-Based Approach to Diagnosis and Diagnosability of Repeated Faults of Discrete-Event Systems

Studies carried out in real plants have shown that repeated and/or intermittent fault events occur frequently during the operation of a system. Regarding the occurrence of repeated fault events, the problem becomes that of determining the number of occurrences of the fault event, namely, for a given <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\kappa \in \mathbb {Z}_+^{*}$</tex-math></inline-formula>, and based on the observation of events, be sure that the fault event has occurred at least <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\kappa$</tex-math></inline-formula> times (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\kappa$</tex-math></inline-formula>-diagnosability). In this article, the problem of repeated fault diagnosability is revisited, and a new algorithm that relies on a diagnoser-based automaton is proposed for the verification of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\kappa$</tex-math></inline-formula>-diagnosability. Based on the proposed test automaton, a necessary and sufficient condition for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\kappa$</tex-math></inline-formula>-diagnosability is presented. As a by-product of the proposed method to verify <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\kappa$</tex-math></inline-formula>-diagnosability, a diagnoser that can be used for online diagnosis is also developed.