DOI: 10.17587/prin.10.77-86

Approach to the Construction of Geometric Models of Multifactor Processes and Phenomena by the Method of Multidimensional Interpolation

E. V. Konopatskiy, e.v.konopatskiy@mail.ru, Donbas National Academy of Civil Engineering and Architecture, Makeyevka, 286123, Donetsk Peoples Republic

Corresponding author: Konopatskiy Evgeniy V., Associate Professor, Donbas National Academy of Civil Engineering and Architecture, Makeyevka, 286123, Donetsk Peoples Republic, E-mail: e.v.konopatskiy@mail.ru

The paper presents an approach to the theoretical foundations the geometric modeling of multifactor processes and phenomena by the method of multidimensional interpolation, which include the method of modeling the arcs of algebraic curves passing through the pre-set points and the fundamental algorithm of the multifactor processes modeling. The proposed method of multi-dimensional interpolation allows one to analytically determine and optimize geometric models based on a discrete array of points in the form of initial experimental and statistical information. This approach is particularly effective in modeling those processes and phenomena that have a large number of interrelated factors. These examples confirm the effectiveness of the method of multidimensional interpolation and approximation in relation to the geometric modeling problems of multifactor processes and phenomena. They include a two-factor process and optimization of the composition the combined aggregate of fine-grained concrete by means of multidimensional interpolation, a three-factor process — modeling of the distribution of strength characteristics throughout the volume of the concrete column, as well as an analytical description and optimization of the geometric model of the dependence of the pre-case of the compressive strength fine-grained degtepolymerbeton from 4 factors. The prospect of further research is the application of the method of multidimensional interpolation to the geometric modeling and optimization of socio-economic, thermodynamic and lighting processes and phenomena.

Keywords: geometric model, multifactor process, multidimensional interpolation, response function, influence factors, point equation, geometric model tree, curve arc, surface compartment, hypersurface compartment

pp. 77–86

For citation:
Konopatskiy E. V. Approach to the Construction of Geometric Models of Multifactor Processes and Phenomena by the Method of Multidimensional Interpolation, Programmnaya Ingeneria, 2019, vol. 10, no. 2, pp. 77—86.