Forecasting of Potential Faults of a Technical System Based on Fuzzy Graphs and Fuzzy Cognitive Maps

Abstract

The development of a hierarchical step-by-step procedure for forecasting potential faults of a technical system based on fuzzy graphs and fuzzy cognitive maps is considered. Mathematically, this is based on the notion of a fuzzy binary preference relation. A fuzzy binary relation is always built on some set of objects. Since there are connections between objects and the consideration is conducted essentially at the level of a fuzzy graph, the connections between objects are described by the degree of affiliation and interpreted as «fault of object oi generates fault of object oj ». Next, it is necessary to allocate a hierarchy on this fuzzy graph, which will allow you to determine all possible scenarios for the occurrence of faults and the sequence of diagnostic measures. All problems of fault detection and localization, fault tolerance can be solved at the level of a fuzzy undirected graph, but obtaining an oriented graph additionally provides a fundamental opportunity for causal analysis of the occurrence and spread of faults in a technical system, their ranking by degree of importance, the influence of control actions on the behavior of the system.