On the problem of the parameters determination for a stationary source in a semi-bounded layered medium

Authors

UDC

517.9: 539.3

DOI:

https://doi.org/10.31429/vestnik-19-4-76-82

Abstract

In this paper, when solving the inverse problem of the parameters determination for a stationary radiation source (coordinates and intensity), formulated as an optimization problem for the residual functional of functions depending on the source parameters, we use conditional optimization methods based on the exact solution of the direct problem of the concentration calculation for a substance in a multilayer medium emitted by a stationary source using the matrix method based on the integral approach. The applied method of numerical inversion of Fourier integrals is based on the method of direct contour integration. The source is identified by the response of the pollutant distribution medium to the action of a stationary emission – a change in the concentration of an impurity at a given height based on additional "measurements", as which we chose the numerical values of the solution for the direct problem. To solve the optimization problem, local and global search methods, as well as genetic algorithms for global search, were used. Calculations carried out for various characteristics of the layered medium and the position of the source showed that the pattern search method allows us to find a more accurate solution than genetic algorithms, the convergence rate of which decreases near the minimum point. At the same time, the accuracy of restoring the initial intensity value of the pollutant source depends on the structure of the wind characteristics in the layered medium; an increase in wind speeds worsens the solution of the inverse problem. The number of measurement points has a significant impact on the accuracy of the source power value recovery when the measurement data has noise.

Keywords:

diffusion-convection, multilayer medium, matrix method, direct problem, inverse problem, conditional optimization methods

Author Infos

Olga N. Lapina

канд. физ.-мат. наук, доцент кафедры вычислительных технологий Кубанского государственного университета

e-mail: olga_ln@mail.ru

Aleksandr G. Nesterenko

канд. физ.-мат. наук, доцент кафедры физики и информационных систем Кубанского государственного университета

e-mail: agnest@mail.ru

Yuri G. Nikitin

канд. физ.-мат. наук, доцент кафедры теоретической физики и компьютерных технологий Кубанского государственного университета

e-mail: yug@fpm.kubsu.ru

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Issue

2022. Vol. 19. No. 4

Section

Mechanics

Pages

76-82

Submitted

2022-11-20

Published

2022-11-30

How to Cite

Lapina O.N., Nesterenko A.G., Nikitin Yu.G. On the problem of the parameters determination for a stationary source in a semi-bounded layered medium. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2022, vol. 19, no. 4, pp. 76-82. DOI: https://doi.org/10.31429/vestnik-19-4-76-82 (In Russian)

Copyright (c) 2022 Lapina O.N., Nesterenko A.G., Nikitin Yu.G.

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