In this paper, the authors discuss an inverse boundary problem for the axisymmetric steady-state heat equation, which arises in monitoring the boundary corrosion for the blast-furnace. Measure temperature at some loca...In this paper, the authors discuss an inverse boundary problem for the axisymmetric 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 axisymmetric fundamental solution method. The numerical results are in good agreement with test model data as well as industrial data, even in severe corrosion case.展开更多
基金the National Natural Science Foundation of China(No.10431030).
文摘In this paper, the authors discuss an inverse boundary problem for the axisymmetric 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 axisymmetric fundamental solution method. The numerical results are in good agreement with test model data as well as industrial data, even in severe corrosion case.
