Solving inverse problems in thermal engineering using a surrogate model

Sammanfattning: Through either measured or computed experimental data, inverse problems aim to determine parameters not straightforwardly given by measure. An inverse problem results in an optimization problem that requires many simulations of the direct problem which computations can be costly. One approach is to replace the reference model by a reduced model. A reduced model or surrogate is built by a statistical learning method (a theory on how to characterize the behaviour of a function based on observed data). In this case, uncertainties have a bigger effect on the problem and the errors introduced by the surrogate can significantly alter the convergence process. Furthermore, it is well known that the determination of input parameters via observed ones is an ill conditioned problem. As a result, the slightest measuring errors can engender tremendous gaps in the values of the reconstructed parameters, thus ruining their use. We can remedy that by adding a penalty in the optimization problem which would ensure a better stability during its resolution. Identification problems are here solved using a surrogate model. The issues of this approach on the resolution of the reference model are evaluated. Other specific substitution models known to be less reliable but better suited to inverse problems due to a regularization expression are constructed. Classical optimization methods including a penalty for the resolution of identification problems are implemented. The impact of the reliability of the surrogate model on the robustness and accuracy of the resolution is then carried out. In order to improve the surrogate model fidelity, sequential enrichment of the design of experiments is applied. Finally, the methodology is tested on a simplified thermal engineering example: the one dimensional heat conduction problem.