Theoretıcal Bases Of Optımızatıon Of Concrete Mıcrostructure Wıth Applıcatıon Of The Improved Method Of Mathematıcal Plannıng Of Experıments

Abstract

The article lays out the theoretical basesof using the improved method of mathematical design of experiments in solving optimization problems of selecting the composition and improving the microstructure of modified concrete. The method of mathematical planning of experiments are recommended for optimizing the composition and structure of multicomponent composite building materials with a relatively fine-grained and predominantly homogeneous structure. In this article, the authors, based on the analysis of fundamental research in this direction, propose an improved methodology for mathematical design of experiments, which is called “design of experiments using eigenvalue regression”. The essence of the developed method consists in the most accurate representation of a random function by a small number of series members. For this purpose, a system of orthonormal functions (eigenvectors) is introduced, the values of which depend on the statistical properties of the process under study, called optimal. As the result of using this technique, the obtained regression equations on eigenvalues make it possible to more accurately reproduce experimental data regarding the regression equation obtained by the classical method, which is an important factor in optimizing the composition and structure of modified concrete using mathematical modeling methods.