Identification of thermal conductivity and the shape of an inclusion using the boundary elements method and the particle swarm optimization algorithm

Temperature measurements from the exterior boundary of a two-dimensional solid body containing an inclusion, under steady state conditions, are used to estimate the thermal conductivity and the shape of the inclusion. The particle swarm optimization algorithm (PSO), coupled with the boundary elements method, is used in this identification problem. A fitness function which is the summation of the squared differences between the measured and calculated temperatures at the locations on the exterior boundary is minimized. To avoid trapping into the local optimum points, the PSO algorithm which is a global optimization method is used instead of local optimization methods. The credibility of the PSO algorithm and its effectiveness in solving inverse problems is investigated. The effect of measurement errors and the size of the inclusion on the estimation process will be addressed.