Information-Mathematical Representation of Steel Grades of Structural Elements in Applied Mechanics

There is a need to develop universal classification features by which it is possible to combine steels into groups and then find very similar properties in them. The aim of the work was to develop an indicator of the capacity of technical information of steel grades. Theoretical mathematical dependencies were derived on the basis of the formulas of combinatorics and information theory. Steel grade can be represented as an information object in the spaces of indicators and fusible chemical compositions. At the same time, each brand can include different “elementary” states. The number of mills is determined for one steel grade. However, to assess the degree of importance of steel grade, it is more convenient to use Shannon’s information entropy, measured in bits. The development of a new technology for the production of metal products leads either to quantitative changes in the direction of optimizing the characteristics of steel, or to the appearance of additional features. With each addition of a new characteristic, there will be a change in the degree of ordering of steels and an increase in entropy. The ratio of the related information about the state of the steel grade to the amount of its wealth can be interpreted as the capacity of the information object – steel. The higher the orderliness within the steel grade, the less the possibility of changing the information capacity. Thus, the unbalanced development of the steel grade leads to the maximization of the increase in information capacity, which complicates the ordering of steels. The obtained mathematical expressions make it possible to deter-mine the amount of information contained in information objects that determine the steel grade in the feature space. The practical application of the developed analytical description makes it possible, on the basis of the obtained mathematical dependencies, to qualitatively and quantitatively arrange steel grades, and to in-crease the debugging of technological processes in production.