Fast solution of direct and inverse design problems concerning furnace operation conditions in steel industry

In this paper a fast numerical simulation tool able to accurately predict steel products heating in an industrial furnace is developed. This prediction tool is set up in two steps: firstly, a complete finite element model of the furnace is built up, and then a surrogate model based on the information extracted from the results of the previous one (alternatively, results of experimental tests could also be used) is developed.More precisely, the surrogate model developed in the second step is based on the computation of a numerical simulation database (using the finite element model) and the use of a High Order Singular Value Decomposition and interpolation techniques. Errors in the heating prediction provided by the surrogate model are comparable to the corresponding errors in the finite element model. Computation time instead is dramatically reduced: in the validation case presented in this paper (corresponding to a heat treatment furnace), computation time of the heating prediction in a desktop computer drops from around 2 h for the complete finite model to a few milliseconds for the surrogate model.The developed fast prediction tool is then applied to solve some design problems. Among them, a problem concerning the design of operation conditions able to minimize a functional involving the quality of the workpiece heat treatment and the fuel consumption is solved.

► Derivation of an accurate numerical model of an industrial furnace using free software tools.
► Derivation of an extremely inexpensive but accurate surrogate model from the previous one.
► Integration of the surrogate model in fast optimization strategies illustrated with some examples.