Mathematical and information models of decision support systems for explosion protection

Abstract

This paper is dedicated to the issue of mathematical and information modeling of the combustion-to-explosion transition that
makes it possible to create an adequate mathematical and information support for decision support systems (DSS) for automated
control of explosive objects. A simple mathematical model for the transition of combustion to explosion is constructed. This model is
based on solving mathematical problems of the hydrodynamic stability of flames and detonation waves. These problems are reduced
to solving eigenvalue problems for linearized differential equations of gas dynamics. Mathematical model is universal enough. It
provides opportunities for making simple analytical estimates for the explosive induction distance and the time of the shock wave
formation. The possibilities of the transition of slow combustion to both a deflagration explosion and a detonation wave are
considered. Theoretical estimates of the explosive induction distance and the time of the combustion-to-explosion transition are
obtained. These estimates are expressed by algebraic a formula, the use of which save computer resources and does not require
significant computer time. The application of fuzzy logic makes it possible to use the proposed mathematical model of the
combustion-to-explosion transition for real potentially explosive objects in industry and transport. Mathematical models of
potentially explosive objects are based on combination of the fuzzy logic and classical mathematical methods. These models give
possibilities for creating corresponding information models. Thus mathematical and information support of DSS for automated
control systems of explosive objects is developed. The main advantage of these DSS is that it makes it possible for decision makers
to do without experts. In particular, developed mathematical and information models create the base for software of DSS for
explosion safety of grain elevators. Appropriate software is developed and some calculations are performed. These calculations are
useful not only from the point of view of testing the proposed method of mathematical modeling of a grain elevator as a potentially
explosive object or testing the software itself, but also from the point of view of the grain elevator designing.