To download article.

DOI: 10.15507/2658-4123.036.202602.300-326

UDK 004.9:519.218.82

Algorithmization of Interpolation Model Methods in Processing Experimental Results

Vladimir V. Konovalov
Dr.Sci. (Eng.), Professor, Professor of the Department of Mechanical Engineering Technology, Penza State Technological University (1a/11 Gagarin St., Baidukova Ave., Penza 440039, Russian Federation), ORCID: https://orcid.org/0000-0002-5011-5354, Researcher ID: P-7520-2018, Scopus ID: 57193789361, This email address is being protected from spambots. You need JavaScript enabled to view it.

Alexander V. Moiseev
Cand.Sci. (Eng.), Associate Professor, Head of the Department of Mathematics and Physics, Penza State Technological University (1a/11 Gagarin St., Baidukova Ave., Penza 440039, Russian Federation), ORCID: https://orcid.org/0000-0001-9534-2465, Researcher ID: AAF-8891-2019, Scopus ID: 15731404900, This email address is being protected from spambots. You need JavaScript enabled to view it.

Vladimir Yu. Zaitsev
Cand.Sci. (Eng.), Associate Professor, Head of the Department of Mechanical Engineering Technology, Penza State Technological University (1a/11 Gagarin St., Baidukova Ave., Penza 440039, Russian Federation), ORCID: https://orcid.org/0000-0002-6230-0856, Researcher ID: Q-2601-2018, Scopus ID: 57204113621, This email address is being protected from spambots. You need JavaScript enabled to view it.

Marina V. Dontsova
Cand.Sci. (Eng.), Associate Professor, Associate Professor of the Department of Mechanical Engineering Technology, Penza State Technological University (1a/11 Gagarin St., Baidukova Ave., Penza 440039, Russian Federation), ORCID: https://orcid.org/0000-0003-2915-0881, Researcher ID: N-3708-2018, Scopus ID: 57216627822, This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract
Introduction. To solve the problem of bringing together the results of different experimental designs into a single regression model it is necessary to develop the methods for designing experiments, assessing the influence of intervals and levels of variation of the studied factors on the possible behavior of changes in process indicators, and to have the ability to compile (combine) the results of several sequential series of studies into a single system. The use of numerical methods and calculation technologies, and computerized management of technological machines, will allow adjusting rapidly their operating parameters at complex interplay of factors.
Aim of the Study. The study is aimed at algorithmizing the methodology for developing interpolation models when used for automated processing of the results of experimental studies using the mathematical experiment design theory and compilation of the models.
Materials and Methods. In the study, there was used the methodology for the analytical substantiation of expressions of interpolation functions describing the nature of indicator changes within the boundaries under consideration based on the results of previously completed studies, the development of a procedure for carrying out activities related to planning an experiment and obtaining interpolation expressions and computer models.
Results. There have been substantiated and implemented activities for developing a model combining a linear multifactor model and a particular function of one of the factors (the influence of the drum dispenser rotation frequency on its capacity).
Discussion and Conclusion. The implemented activities allowed us to recommend the following sequence of actions: implementing a full-factorial design for several coded factors with developing the process linear model, determining the preferred zone of their use; implementing an additional series of single-factor experiments within the previously investigated coded interval of the factor under study and the subsequent finding of the functional dependence of the process indicator on this factor; developing a computer program for combining the functions of both series of studies for the substitution of partial functions of the natural indicators of the factors into a multifactorial linear model of coded factors; determining the nature and numerical values of the process indicator for all factor values in order to use the results for further calculations in the mathematical description of the studied device operation, for example, a continuous mixer. The combination of linear multifactorial design models and different versions of functions of specific variables (factors), implemented as a computer model, makes it possible to obtain a complicated multifactorial dependence, which looks linear in the coded coordinates of the factors, and the partial values of the process indicator within the section of the multifactorial experiment design (–1; +1) are described by partial functions with current natural coordinates.

Keywords: full-factorial experimental design, multifactorial linear model, power function, regression model, combination of functions, interpolation studies, computer model

Conflict of interest: The authors declare that there is no conflict of interest.

For citation: Konovalov V.V., Moiseev А.V., Zaitsev V.Yu., Dontsova М.V. Algorithmization of Interpolation Model Methods in Processing Experimental Results. Engineering Technologies and Systems. 2026;36(2):300–326. https://doi.org/10.15507/2658-4123.26362.300-326

Authors contribution:
V. V. Konovalov – ideas; formulation or evolution of overarching research goals and aims; oversight and leadership responsibility for the research activity planning and execution, including mentorship external to the core team.
A. V. Moiseev – application of statistical, mathematical, computational, or other formal techniques to analyse or synthesize study data.
V. Yu. Zaitsev – development or design of methodology; creation of computer models.
M. V. Dontsova – preparation, creation and or presentation of the published work, specifically visualization data presentation.

All authors have read and approved the final manuscript.

Submitted 21.05.2025;
revised 22.12.2025;
accepted 09.02.2026

REFERENCES

This work is licensed under a Creative Commons Attribution 4.0 License.