Toward the Solution of Inverse Thermal Conductivity and Thermal Elasticity Problems

• Published in: Journal of engineering physics and thermophysics 2022-03, Vol.95 (2), p.374-379
• Main Authors: Matsevityi, Yu. M., Strel’nikova, E. A., Povgorodnii, V. O., Safonov, N. A., Ganchin, V. V.
• Format: Article
• Language: English
• Subjects: Algorithms; Classical Mechanics; Complex Systems; Engineering; Engineering Thermodynamics; Error analysis; Field theory; Heat and Mass Transfer; Heat transfer; Ill posed problems; Industrial Chemistry/Chemical Engineering; Influence functions; Inverse problems; Parallel processing; Parameter identification; Random variables; Regularization; Thermal conductivity; Thermodynamics
• ISSN: 1062-0125; 1573-871X
• DOI: 10.1007/s10891-022-02491-1

The article describes a method of solving inverse problems, which is based on the joint application of the A. N. Tikhonov regularization principle and of the method of influence functions that play an important role in obtaining stable solutions of ill-posed problems and in facilitating the computational process due to the preliminarily determined influence functions. The method is the result of development of the methodology previously developed by the authors for solving inverse problems, which is based on the various methods of regularizing solutions to multiparameter ill-posed problems of field theory, as well on the experience in identifying the parameters of mathematical models of various levels. The results of identification of heat transfer at the boundary of a body by displacements measured with an error characterized by a random variable distributed by the normal law are presented. The proposed method makes it possible to use experimental information obtained from several sensors. It is applicable to the study of heterogeneous media and combines the simplicity of programming with the ability of parallelizing the computational process, which meets modern requirements for methods and algorithms of solving direct and inverse problems.