Methodology of Solving Inverse Heat Conduction and Thermoelasticity Problems for Identification of Thermal Processes

• Published in: Journal of engineering physics and thermophysics 2021-09, Vol.94 (5), p.1110-1116
• Main Authors: Matsevityi, Yu. M., Strel’nikova, E. A., Povgorodnii, V. O., Safonov, N. A., Ganchin, V. V.
• Format: Article
• Language: English
• Subjects: Algorithms; Analysis; Classical Mechanics; Complex Systems; Conduction heating; Conductive heat transfer; Engineering; Engineering Thermodynamics; Error analysis; Heat and Mass Transfer; Industrial Chemistry/Chemical Engineering; Influence functions; Inverse problems; Linear algebra; Methods; Nonlinear equations; Parameters; Regularization; Searching; Spline functions; Thermal stress; Thermodynamics; Thermoelasticity
• ISSN: 1062-0125; 1573-871X
• DOI: 10.1007/s10891-021-02391-w

An approach to solving the inverse problem of thermoelasticity that employs A. N. Tikhonov′s regularization principle and the method of influence functions has been suggested. The use of A. N. Tikhonov′s regularization with an efficient algorithm of the search for the regularization parameter makes it possible to obtain a stable solution of the inverse problem of thermoelasticity. The unknown functions of displacement and temperature are approximated by the Schoenberg splines, whereas the unknown coefficients of these functions are calculated by solving the system of linear algebraic equations. This system results from the necessary condition of the functional minimum based on the principle of least squares of the deviation of the calculated stress from the stress obtained experimentally. To regularize the solutions of the inverse heat conduction problems, this functional also employs a stabilizing functional with the regularization parameter as a multiplicative multiplier. The search for the regularization parameter is effected with the aid of an algorithm analogous to the algorithm of the search for the root of a nonlinear equation, whereas the use of the influence functions makes it possible to represent temperature stresses and temperature as a function of one and the same sought vector. This article presents numerical results on temperature identification by thermal stresses measured with an error characterized by a random quantity distributed by the normal law.