The solution of nonlinear inverse boundary problem of heat conduction

• Дата: 2016
• Автори: Мацевитый, Ю. М., Сафонов, Н. А., Ганчин, В. В.
• Формат: Стаття
• Мова: Russian
• Опубліковано: Journal of Mechanical Engineering 2016
• Теми: inverse heat conduction problem; the method of weighted residuals in the form of Galerkin; heat flow; superposition principle; Tikhonov regularization method; stabilizer; regularization parameter; identification; approximation; Schoenberg splines of first; обратная граничная задача теплопроводности; метод взвешенных невязок в форме Галёркина; тепловой поток; принцип суперпозиции; метод регуляризации А. Н. Тихонова; функционал; стабилизатор; параметр регуляризации; идентификация; аппроксимация; сплайн Шёнбер; УДК 536.24; обернена гранична задача теплопровідності; метод зважених похибок у формі Гальоркіна; тепловий потік; принцип суперпозиції; метод регуляризації А. М. Тихо¬нова; функціонал; стабілізатор; параметр регуляризації; ідентифікація; апроксимація; сплайн Шьонберг
• Онлайн доступ: https://journals.uran.ua/jme/article/view/65238
• Назва журналу: Journal of Mechanical Engineering

In this paper, to obtain a stable solution of nonlinear inverse boundary problem of heat conduction the method of Tikhonov regularization with effectiveness-tive search algorithm regularizing parameter. Seeking the heat flux at the boundary of the time coordinate splines approximate Schoenberg first ste-interest. To apply the method of influence functions for the nonlinear heat conduction problem reduces it to a sequence of linear inverse boundary value problems using the diet-iteration process. This iterative process ends when the on-perёd specified accuracy for temperature recovery. The article presents a study on the use of the influence functions for approximating the solution of a linear edge-value problem of heat conduction. In particular it is shown that the influence functions are linearly independent in the time interval (0, ¥) at a fixed spatial variable. This fact is used to identify the temperature at the boundary or inside the area. Conducted numerous computational experiments using functional stabilizing zero and first order, and an analysis of the impact of the variance of the random error of measurement error in the obtained solution. The results of computational experiments revealed that for the class of first-order regularization was more effective than the regularization of the zero order. Also, the results of computational experiments show that by increasing the number of points where the specified Expo experimental temperature, increases the accuracy of the identification.