To the problem of building a mathematical model of one-dimensional object

Authors

  • Тетяна Владиславівна Бойко National Technical University of Ukraine «Kyiv Polytechnic Institute», 03056, Kiev, Prospect Peremogy 37, Ukraine https://orcid.org/0000-0002-9710-8055
  • Алла Олександрівна Абрамова National Technical University of Ukraine «Kyiv Polytechnic Institute», 03056, Kiev, Prospect Peremogy 37, Ukraine https://orcid.org/0000-0003-3475-8584
  • Дмитро Олександрович Серебрянський Institute of Engineering Thermophysics, NAS of Ukraine, st. Zhelyabova, 2a, Kyiv, Ukraine, 03680, Ukraine https://orcid.org/0000-0002-6811-8932
  • Микола Віталійович Семенюк National Technical University of Ukraine «Kyiv Polytechnic Institute», 03056, Kiev, Prospect Peremogy 37, Ukraine https://orcid.org/0000-0003-0556-3649

DOI:

https://doi.org/10.15587/2312-8372.2015.41072

Keywords:

mathematical modeling, Chebyshev polynomials, approximation, method of least squares

Abstract

Methods of mathematical modeling of one-dimensional object using the method of least squares approximation and Chebyshev polynomials are investigated. Object is eight-stage centrifugal filter. The aim of the article is the building the mathematical relationship of aerodynamic drag depending on the gas flow. Approximating procedures of polynomial coefficients determination and calculation of residual variance in the system of Mathcad are developed. The influence of the degree of the polynomial degree on the accuracy of the results is analyzed. The obtained values of the residual variance indicate coincidence of results using both methods. From obtained results it can be argued that the investigated approximation methods give the same results, and to build approximating polynomial for the communication of parameters for input and output of object can be used both methods. If compared in terms of simplicity of constructing an algorithm method of least squares is simplest for implementation.

Author Biographies

Тетяна Владиславівна Бойко, National Technical University of Ukraine «Kyiv Polytechnic Institute», 03056, Kiev, Prospect Peremogy 37

Candidate of Technical Sciences, Associate Professor, Acting Head of Department

Department of Cybernetics of Chemical Technology Processes

Алла Олександрівна Абрамова, National Technical University of Ukraine «Kyiv Polytechnic Institute», 03056, Kiev, Prospect Peremogy 37

Candidate of Technical Sciences, Senior Lecturer

Department of Cybernetics of Chemical Technology Processes

Дмитро Олександрович Серебрянський, Institute of Engineering Thermophysics, NAS of Ukraine, st. Zhelyabova, 2a, Kyiv, Ukraine, 03680

Candidate of Technical Sciences, Senior Researcher

Микола Віталійович Семенюк, National Technical University of Ukraine «Kyiv Polytechnic Institute», 03056, Kiev, Prospect Peremogy 37

Graduate

Department of Cybernetics of Chemical Technology Processes

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Published

2015-04-02

How to Cite

Бойко, Т. В., Абрамова, А. О., Серебрянський, Д. О., & Семенюк, М. В. (2015). To the problem of building a mathematical model of one-dimensional object. Technology Audit and Production Reserves, 2(5(22), 16–21. https://doi.org/10.15587/2312-8372.2015.41072

Issue

Vol. 2 No. 5(22) (2015): Mathematical modeling. Information and control systems

Section

Mathematical Modeling: Original Research

License

Copyright (c) 2016 Тетяна Владиславівна Бойко, Алла Олександрівна Абрамова, Дмитро Олександрович Серебрянський, Микола Віталійович Семенюк

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