Теоретико-множественное представление функциональных моделей химических производств

The technique for the formalized description of functional models of chemical manufacturing is developed. The technique is based on graph theory. The model is described as a set of oriented labeled graphs that are hierarchically organized by the decompose relationship. First we describe the conversion of a single diagram to a labeled graph, including adding new nodes and edges. The nodes of the graph correspond to boxes, borders and branching points of the arrows at the diagram. The edges of the graph correspond to the arrows at the diagram. The graph descriptions of the model of base functional relationships such as output-input, output-control, output-mechanism are represented. We develop procedures to convert the border arrows and branch arrows. Conversion of branch arrows is performed depending on changes of the labels of branches. Branching of each arrow corresponds to a subgraph including several edges and perhaps additional nodes. Oriented labeled graphs are described by set-theoretic notation that contains the labels of the edges and the roles of nodes. The hierarchy of diagrams is specified by a decompose relationship, which includes the parent chart, the child chart and the decomposed box. As an example, we present the set-theoretic description of the functional model of vinyl acetate manufacturing. The application of mathematical apparatus built within the framework of graph theory for verification and analysis of functional diagrams based on the proposed formal description is an area for further research.