2-DIMENSIONAL LINEAR TRANSIENT INVERSE HEAT-CONDUCTION PROBLEM - BOUNDARY-CONDITION IDENTIFICATION

This article deals with the identification of unknown time- and space- dependent boundary conditions for systems driven by the heat equation. We first consider a one-dimensional and single-input problem, dealing with the identification of the time-dependent heat flux on one side o f a one-dimensional linear thermal wall, from temperature and heat flu x measurements on the other side. We then focus on a quenching process ; our interest is to identify the time- and space-dependent heat flux on the boundary of a metal piece from temperature measurements perform ed inside the material (two-dimensional geometry). Those inverse probl ems are solved by use of a regularization method, and the solution is obtained by minimization of a quadratic criterion. Because of the line arity of the input-output relationship, the solution of this minimizat ion is derived from the linear quadratic optimal control theory (resol ution of a nonstationary Riccati equation). The robustness of the meth od for very small signal-to-noise ratio is shown. In the two-dimension al multi-input problem, the identification sensitivity to the localiza tion of the measurement points is analyzed. In both cases, we consider input that are discontinuous in time, in order to show the method acc uracy in the high-frequency domain.