A parameter estimation approach to solve the inverse problem of point heat sources identification

Abstract

This paper deals with an inverse problem that consists of the identification of multiple line heat sources placed in a homogeneous domain. In the inverse problem under investigation the location and strength of the line heat sources are unknown. The estimation procedure is based on the boundary element method. As the discrete problem is non-linear if the location of the line heat sources is unknown, an iterative procedure has to be applied to find out the location of the sources. The proposed approach has been tested for steady and transient experiments. In the present study we propose an original approach to solve the steady problem. As in the steady heat conduction case we have a limited number of unknown for each source, a “parameter estimation” approach can be applied to estimate the sources. Using the techniques of parameter estimation, we can also estimate the confidence interval of the estimated locations, which permits to design an optimal experiment. We intend to present some numerical and experimental 2D results.