Study of the diagnosability of automated production systems based on functional graphs

Functional graphs are a convenient representation that we have introduced to model automated production systems. They are useful for the monitoring and the supervision of manufacturing processes or other industrial processes, such as chemical processes. An approach based on relational theory and graph theory is presented in this paper. This approach allows to characterize formally structural properties of a functional graph and to map it into a set of relations translating all the complete paths existing in the initial graph. Two kinds of functional graphs are analyzed and algorithms exploiting their structures are presented. We introduce the concept of diagnosability as a system property that reflects the possibility to observe the behavior of a system with respect to faults. The diagnosability is defined and analyzed by means of computable states and mathematical relations. Propositions explaining causality relations between functions of a functional graph are given.

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