Variational procedures for estimating the power of pollution sources in the passive admixture transfer model

Authors

UDC

51.37

DOI:

https://doi.org/10.31429/vestnik-21-3-26-31

Abstract

The paper considers variational algorithms for identifying capacities for a number of sources of constant power based on admixture concentration measurements at a finite time. In the process of implementing, the variational assimilation procedure, the main, conjugate and task in variations is solved. The search for the desired parameters is carried out iteratively. When implementing the filtering algorithm, the estimation method, the dual representation of the functional, the transformation of plane rotations of the redefined system of equations are used to construct an algebraic system of equations, which allows filtering data and finding the desired values of the source capacities. In this paper, an algorithm is proposed for searching for the power values of several sources by assimilating measurement data on the admixture concentration. When implementing a variation procedure, the integration of the main, conjugate tasks and tasks in variations is performed. The latter is necessary to find an iterative parameter in the process of gradient descent. An algorithm based on the application of the estimation method and a variational algorithm for filtering measurement data is presented. The latter is based on the use of the procedure of plane rotations of the original redefined system of equations and the minimization of a special kind of functional. An essential point in the construction of the algorithm is the linearity of the transfer equation, which allows us to consider its solution as the sum of solutions when specifying single point sources. Thus, to solve the problem of identifying the power of a number of sources, it is proposed, to use variational assimilation procedures based on solving related problems and minimizing the corresponding prediction quality functionals. In addition, an algorithm based on a variational filtering procedure for systems of linear algebraic equations is presented, which are based on the estimation method and solving a series of corresponding conjugate problems. The results can be used to solve various environmental problems in the waters of the Azov and Black Seas.

Keywords:

concentration of suspended matter, variational algorithm, assimilation, adjoint problem, variational filtration

Acknowledgement

The work was carried out within the framework of the state assignment on the topic FNNN-2021-0005 "Complex interdisciplinary studies of oceanological processes that determine the functioning and evolution of ecosystems in the coastal zones of the Black and Azov Seas" (code "Coastal Research").

Author Infos

Vladimir S. Kochergin

младший научный сотрудник отдела теории волн Федерального исследовательского центра «Морской гидрофизический институт РАН»

e-mail: vskocher@gmail.com

Sergey V. Kochergin

старший научный сотрудник отдела вычислительных технологий и математического моделирования Федерального исследовательского центра «Морской гидрофизический институт РАН»

e-mail: ko4ep@mail.ru

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Issue

2024. Vol. 21. No. 3

Section

Mechanics

Pages

26-31

Submitted

2024-07-24

Published

2024-09-24

How to Cite

Kochergin V.S., Kochergin S.V. Variational procedures for estimating the power of pollution sources in the passive admixture transfer model. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2024, vol. 21, no. 3, pp. 26-31. DOI: https://doi.org/10.31429/vestnik-21-3-26-31 (In Russian)

Copyright (c) 2024 Kochergin V.S., Kochergin S.V.

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