Inverse Problems and Their Use for the Design of Aviation Navigation Equepment

Authors

DOI:

https://doi.org/10.20535/2521-1943.2026.10.1.344040

Keywords:

inverse problem, thermal stress, functions of influence, spline, identification, regularization

Abstract

The article proposes a method for determining the maximum thermal load from the temperature (thermal) stress measured with a certain error by solving the inverse problem of thermal conductivity and thermoelasticity. The determination of the maximum thermal load in the same way as the regulation of external and internal temperature and power loads, at which the temperature stresses or displacements in the structural elements within acceptable limits are achieved, are of significant theoretical value and are of great practical value, namely for non-destructive testing tasks. An expedient way of finding these quantities as a function of time and geometric coordinates is to solve the inverse problems of thermal conductivity and thermoelasticity, i.e., to determine the temperature field based on the field of temperature stresses. To obtain a stable solution to the inverse problem of thermoelasticity, A. N. Tikhonov's method is used with an effective search for the regularization parameter. The functional of A. N. Tikhonov reflects the deviation of the temperature stress obtained as a result of observation from that calculated on the basis of an approximate solution of the direct problem of thermoelasticity by the finite and boundary element’s methods. In this functional, the stabilizing functional with the regularization parameter is used as the term to the square of the indicated deviation. The search for the regularization parameter is carried out using an algorithm similar to the search algorithm for the root of a nonlinear equation. The use of influence functions in the method allows one to represent temperature and temperature stress depending on the same vector, which greatly facilitates the implementation of the iterative process. The proposed method allows, without bringing the research object to failure, to determine the load at which it will be destroyed i.e. this problem of non-destructive task. The-effectiveness of this method lies in the fact that its application reduces the cost of complex experimental studies of objects and eliminates the need to create analytical methods that accompany these studies.

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Published

2026-04-29

How to Cite

[1]
V. Povhorodnii, “Inverse Problems and Their Use for the Design of Aviation Navigation Equepment”, Mech. Adv. Technol., vol. 10, no. 1, Apr. 2026.

Issue

Vol. 10 No. 1 (2026): in progress

Section

Mechanics

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Copyright (c) 2026 Володимир Повгородній

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