ANALYSIS OF THE DISPERSED COMPOSITION OF CRUSHING PARTICLES

UDC 519.2

 

Volk Anatoliy Matveevich − PhD (Engineering), Associate Professor, Assistant Professor, the Department of Higher Mathematics. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: volk@belstu.by

 

DOI: https://doi.org/ 10.52065/2520- 6141-2023-272-2-2 (In Russian).

 

Key words: physical processes, dispersive composition, distribution characteristics, generalized gamma distribution, properties, statistical estimation of parameters, best likelihood method, Fisher information matrix, asymptotic efficiency, uniqueness.

For citation: Volk A. M. Analysis of the dispersed composition of crushing particles. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2023, no 2 (272), pp. 9–17. DOI: 10.52065/2520- 6141-2023-272-2-2 (In Russian).

 

Abstract

An analysis of methods for describing the dispersed composition of crushing particles is performed. A generalized gamma distribution is considered. This distribution generalizes Gamma distributions and is widely used in statistical methods of physical processes research, in remote sensing, in reliability theory, and in describing the dispersed composition of crushing particles. Its properties have been investigated and its numerical characteristics have been found. Equations for statistical estimation of parameters of given distribution have been obtained by the method of highest likelihood. The Fisher information matrix was found for the obtained estimations; its sign-positivity was shown, which proves their consistency, asymptotically efficiency, and uniqueness. A description of the dispersed composition of fuel atomized by diesel injectors is performed. A method for determining all the necessary characteristics used in the study of physical processes is given.

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References

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Поступила после доработки 17.04.2023