Method of Minimax Optimization in the Coefficient Inverse Heat-Conduction Problem

Consideration has been given to the inverse problem on identification of a temperature-dependent thermal-conductivity coefficient. The problem was formulated in an extremum statement as a problem of search for a quantity considered as the optimum control of an object with distributed parameters, whi...

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Vydané v:Journal of engineering physics and thermophysics Ročník 89; číslo 4; s. 1008 - 1013
Hlavní autori: Diligenskaya, A. N., Rapoport, É. Ya
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.07.2016
Springer
Predmet:
Analysis
Classical Mechanics
Coefficients
Complex Systems
Electric properties
Engineering
Engineering Thermodynamics
Heat and Mass Transfer
Industrial Chemistry/Chemical Engineering
Intervals
Inverse problems
Mathematical analysis
Mathematical models
Methods
Minimax technique
Optimization
Parameters
Thermal conductivity
Thermodynamics
coefficient inverse heat-conduction problem
parametric optimization
minimax-optimization method
ISSN:1062-0125, 1573-871X
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Shrnutí:Consideration has been given to the inverse problem on identification of a temperature-dependent thermal-conductivity coefficient. The problem was formulated in an extremum statement as a problem of search for a quantity considered as the optimum control of an object with distributed parameters, which is described by a nonlinear homogeneous spatially one-dimensional Fourier partial equation with boundary conditions of the second kind. As the optimality criterion, the authors used the error (minimized on the time interval of observation) of uniform approximation of the temperature computed on the object′s model at an assigned point of the segment of variation in the spatial variable to its directly measured value. Pre-parametrization of the sought control action, which a priori records its description accurate to assigning parameters of representation in the class of polynomial temperature functions, ensured the reduction of the problem under study to a problem of parametric optimization. To solve the formulated problem, the authors used an analytical minimax-optimization method taking account of the alternance properties of the sought optimum solutions based on which the algorithm of computation of the optimum values of the sought parameters is reduced to a system (closed for these unknowns) of equations fixing minimax deviations of the calculated values of temperature from those observed on the time interval of identification. The obtained results confirm the efficiency of the proposed method for solution of a certain range of applied problems. The authors have studied the influence of the coordinate of a point of temperature measurement on the exactness of solution of the inverse problem.
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ISSN:1062-0125
1573-871X
DOI:10.1007/s10891-016-1462-0