We present a methodology for solving a non-linear inverse geometry heat transfer problem where the observations are temperature measurements at points inside the object and the unknown is the geometry of the volume where the problem is defined. The representation of the geometry is based on radial basis functions (RBFs) and the non-linear inverse problem is solved using the iteratively regularized Gauss-Newton method. In our work, we consider not only the problem with no geometry restrictions but also the bound-constrained problem.

The methodology is used for the industrial application of estimating the location of the 1150C isotherm in a blast furnace hearth, based on measurements of the thermocouples located inside it. We validate the solution of the algorithm against simulated measurements with different levels of noise and study its behaviour on different regularization matrices. Finally, we analyse the error behaviour of the solution.