Reliable predictability of patterns in decentralized discrete-event systems

Predictability is an important property which is used to predict the failures which is not observable for the sensors straightly before they occur. In an automation system, in addition to the failure caused by a single event, there also exist pattern failures caused by event strings composed of multiple events. In order to prevent some local sites malfunction, the issue of reliable predictability of patterns is considered in this paper, where the prediction information may be distributed at physically separated sites. Our contributions are listed mainly as follows: Firstly, the k-reliable pattern copredictability in decentralized DESs is defined with formal languages. Generally speaking, for a decentralized system where there are r local sites, it is said to be k-reliably pattern copredictable (1≤k≤r) if there are at least r-k+1 local agents which can predict every occurrences of the pattern failure for every pattern failure, it indicates that the prognostication capability will be maintained while r-k local sites in malfunction state. Then two nondeterministic automata respectively named codiagnoser and coverifier from the given system are constructed in this paper, and two algorithms of verifying the reliable copredictability of pattern are presented by constructing the codiagnoser and coverifier respectively for the purpose of attain the capability of prognostication. Especially, two necessary and sufficient conditions under the codiagnoser and coverifier are proposed. Moreover, for the decentralized DESs, the verification algorithm related to the k-reliable pattern copredictability is proposed after presenting the necessary and sufficient conditions for reliable pattern copredictability. It is worth noting that a polynomial complexity algorithm is used in constructing the coverifier and verifying the k-reliable pattern copredictability.