Boundary Identification for a Blast Furnace*

In this paper, the authors discuss an inverse boundary problem for the axi-symmetric steady-state heat equation, which arises in monitoring the boundary corrosion for the blast-furnace. Measure temperature at some locations are used to identify the shape of the corrosion boundary.

The numerical inversion is complicated and consuming since the wear-line varies during the process and the boundary in the heat problem is not fixed. The authors suggest a method that the unknown boundary can be represented by a given curve plus a small perturbation, then the equation can be solved with fixed boundary, and a lot of computing time will be saved.

A method is given to solve the inverse problem by minimizing the sum of the squared residual at the measuring locations, in which the direct problems are solved by axi-symmetric fundamental solution method.

The numerical results are in good agreement with test model data as well as industrial data, even in severe corrosion case.