Створення cеми- та восьми-факторних однорідних комп’ютерних планів експерименту з низькими розбіжностями

Abstract

Scientific research on the construction of efficient uniform computer designs of experiments is being carried out quite actively, and so far it has been proven that, the best results are achieved using Sobol’s quasi-sequences, but this is not observed in all cases of their arbitrary combination. Therefore, the construction of uniform designs even for a small number of factors requires additional research to ensure acceptable indicators of their uniformity. The work is devoted to the creation of multifactorial uniform computer designs of experiments based on quasi-random Sobol’s sequences with low discrepancy rates. The object of research is the process of creating uniform computer designs of experiments. The purpose of the work is to create multifactorial, namely seven- and eight-factor uniform designs of experiments with low rates of centered and wrap-around discrepancies, as well as to study their projection properties for a different number of filling points of a single hypercube. For the purpose of cataloging, seven- and eight-factor uniform computer designs of experiments were created, the quality of which was assessed simultaneously by a visual analysis of the scattering matrix of all two-dimensional projections and quantitative indicators of the uniformity of the set of vectors that form the design in hyperspace, namely, centered and wrap-around discrepancies. The trend of maintaining low indicators of these characteristics in multifactorial spaces, which is observed with a change in the number of design points, is confirmed. The results of the study can be used in the construction of metamodels of measurement processes for cases where it is necessary to ensure a high degree of accuracy in approximating a response hypersurface of a complex shape, solving inverse problems in real time.