Identification methods in nonlinear heat conduction. Part II: inverse problem using a reduced model

A method for solving nonlinear Inverse Heat Conduction Problems (IHCPs) using a Reduced Model (RM) is proposed in this numerical study. In a first step, RM is identified through a specific procedure using optimization techniques and a Detailed Model (DM). Compared to DM, RM allows drastic reduction of computing time without significant loss of accuracy. The second step is the sequential resolution of the inverse problem using RM, taking into account data at Future Time Steps in order to estimate a time-varying thermal input from the knowledge of simulated temperature measurements inside the domain. A transient 3D example with thermal conductivity linearly dependant on temperature illustrates the method. It is shown, on this example, that the proposed inversion algorithm using a simple Euler implicit scheme in time gives good results with RM, whereas it does not work with DM.