Вариационные алгоритмы идентификации мощности импульсного источника загрязнения в модели переноса примеси

Abstract

To solve the problems of monitoring the environmental situation it is necessary to create computer systems that allow assessing the state of the environment. Such systems should allow for rapid assessment of the effects of pollution in the areas under investigation, especially in the areas of traditional shipping lanes and intensive construction of various communications. To solve such problems, it is necessary to have mathematical models and methods for solving inverse problems, when the input parameters of the model are determined using the measurement data due to their rapid assimilation. Variational algorithms for assimilation of incoming information are based on iterative minimization of the quadratic prediction quality function that characterizes deviations of the solution obtained from the used model from the measurement data. In this case, the mathematical model is a constraint on the variation of input parameters while minimizing the forecast quality functional. In this paper we propose the use of such procedures for the assimilation of data distributed in space and time. Based on the passive impurity transfer model, various approaches are considered to solve the problem of identifying the power of a point instantaneous source of pollution from time and space distributed measurement data. In this paper, we consider a variational method for identifying the power of a point instantaneous source of pollution based on solving adjoint  problems and the problem in variations. The proposed algorithm is obtained for the case when the measurement data is received at different times. In addition, the method of estimation and the variational method of filtering linear systems of equations are considered for searching for the required values. The initial values of the power of the pollution source are determined in the result of solving the redefined system of equations. The result obtained is consistent with all available information about the impurity concentration. The considered algorithms for identifying the power of the pollution source in relation to the passive impurity transfer model can be used to solve various environmental problems when studying the impact of anthropogenic pollution sources.