Natalia M. Yaparova, Yury E. Kapelyushin

South Ural State University (NRU)

The article considers the problem of identifying an internal heat source and assessing its influence on changes in the temperature of a controlled object. The problem of identifying a heat source arises during thermal control of power transmission, during heat treatment, and during non-destructive testing of buildings, structures and materials. The mathematical model of heat transfer inside an object is represented by a heat conduction equation with an unknown source function, initial conditions, and boundary conditions formed on the basis of the results of noisy temperature measurements obtained near the surface of the object. The article proposes an approach to identifying an internal heat source based on the transition from an inverse problem to an integral equation, a numerical method for solving it, as well as an algorithm for calculating non-stationary internal heat fields that takes into account the influence of a heat source. The stability of the identification method with respect to the error of the initial data is ensured by the choice of regularization parameters. The proposed approach and methods, in contrast to the existing ones, make it possible to establish an explicit dependence of the desired function of the internal heat source on boundary measurements in a situation where the temperature fields near the surface of the object change with time. The article presents error estimates for numerical solutions found as a result of a comparative analysis with test values. The results of the experiment indicate that the proposed methods reduce the negative impact of noise on the accuracy of data processing and allow determining the internal thermal state of an object from indirect measurements with a sufficient level of accuracy and can serve as a basis for determining the influence of an internal heat source on the formation of internal non-stationary temperature fields.

heat transfer, technical systems, information processing method, inverse problem, integral equation, numerical method, regularization