Minimax Optimization Method in the Two-Dimensional Boundary-Value Inverse Heat Conduction Problem

Abstract

A method is proposed for the two-dimensional inverse heat conduction problem via reconstruction of the spatial and temporal density of a boundary heat flux. It is based on the optimal control theory for objects with distributed parameters. The method limits the set of desired solutions to the class of physically realized functions, which makes it possible to represent the desired-effect structure as a product of two one-variable functions. The problem of semi-infinite optimization, which minimizes temperature residuals in the uniform estimation metric, is formulated based on the parameterization of the desired characteristic (considered a control action). Analytical solution of the problem with the alternance properties of the desired optimal temperature deviations makes it possible to obtain the optimal values of the parameter vector.