Modeling the Functioning of the Mine Using the Algebra of Finite Automata DTA

Abstract

This article is a continuation of the authors' previous work devoted to the development of the algebra of finite automata of the special type DTA (Digital Twin Algebra), designed for mathematical modeling of the behavior of digital twins of production. In this work, the mathematical modeling of the functions of twins uses the DTA algebra apparatus in the form of systems of event-matched finite automata or event matched machines ‒ abbreviated ‒ EMM-systems, while automata (quasi-automata) of such systems are considered as having a specialized multi-sorted structure and an appropriate interpretation of behavior. The multi-sorted structure of automata is realized by dividing the states of quasi-automatic machines of EMM systems into non-intersecting classes, namely, the sets of their states are divided into two classes ‒ A (states of the modes of operation of an object modeled using FSA) and B (states of the production activity of an object). Such FSAs are called bipartite FSAs or abbreviated as BPA (Bipartite Automaton). Using a graphical view of such bipartite automata in the form of Moore diagrams, an example of describing the functioning of equipment and facilities of some imaginary mine of a mining enterprise is considered. This example demonstrates the clarity and adequacy of the means of the proposed apparatus for modelling the behavior of similar production facilities.

Keywords

• digital twin
• dt cyber-physical system
• dsp
• finite automata algebra
• mealy finite automaton
• mealy finite automaton diagrams
• mathematical modeling of production twins