Methods of converting multidimensional measuring information to a number by means of differential equations in partial derivatives

Authors

DOI:

https://doi.org/10.15587/1729-4061.2015.47581

Keywords:

metrological support, processing of images and video streams, elliptical and parabolic conversion

Abstract

We have proved that finite difference representation of differential equations in partial derivatives is the most effective method of converting multidimensional measuring information to a single number. The devised conversion methods use Laplace’s elliptic equations and Fourier’s parabolic equations.

To convert information,we have solved a number of tasks. We have devised a method of elliptic conversion of static images of the measured object by means of finite difference representation of Laplace’s differential equation in the second-order partial derivatives, which means a change of the current value of the pixel brightness to a new one that has two gradations of brightness––black and white. Pixel summation turns the relative number of black pixels into a single number as a result of elliptic conversion. We have improved the method of parabolic conversion of dynamic images of the measured object by means of finite difference representation of Fourier’s differential equation in the second-order partial derivatives,which means a change of the current value of the pixel brightness to a new one that has two gradations of brightness––black and white. Pixel summation turns the relative number of black pixels into a single number as a result of parabolic conversion. We have used the devised methods of industrial testing of metrological support for the technological process of continuous casting of copper ingots. The testing has proved technical and economic effectiveness of the approach.

The paper contains examples of technical and economic effectiveness of the devised methods in metallurgical production.

Author Biographies

Александр Леонидович Становский, Odessa National Polytechnical University Shevchenko 1, Odessa, Ukraine, 65044

Doctor of Technical Sciences, Professor

Department of Oilgas and chemical mechanical engineering

 

Александр Васильевич Шмараев, Odessa National Polytechnical University Shevchenko 1, Odessa, Ukraine, 65044

Department of Machine tools, Metrology and Certification

Игорь Валентинович Прокопович, Odessa National Polytechnical University Shevchenko 1, Odessa, Ukraine, 65044

Candidate of Technical Sciences, Associate Professor

Department of Technology and management of the casting process

Дмитрий Александрович Пурич, Odessa National Polytechnical University Shevchenko 1, Odessa, Ukraine, 65044

Candidate of Technical Sciences

Department of Road Transport 


Павел Степанович Швец, Odessa National Polytechnical University Shevchenko 1, Odessa, Ukraine, 65044

Candidate of Technical Sciences

Department of Еlectric cars 

Виктор Владимирович Бондаренко, Odessa National Polytechnical University Shevchenko 1, Odessa, Ukraine, 65044

Department of Radio Systems

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Published

2015-08-27

How to Cite

Становский, А. Л., Шмараев, А. В., Прокопович, И. В., Пурич, Д. А., Швец, П. С., & Бондаренко, В. В. (2015). Methods of converting multidimensional measuring information to a number by means of differential equations in partial derivatives. Eastern-European Journal of Enterprise Technologies, 4(4(76), 56–62. https://doi.org/10.15587/1729-4061.2015.47581

Issue

Vol. 4 No. 4(76) (2015): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

License

Copyright (c) 2015 Александр Леонидович Становский, Александр Васильевич Шмараев, Игорь Валентинович Прокопович, Павел Степанович Швец, Дмитрий Александрович Пурич, Виктор Владимирович Бондаренко

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