Efficient computational strategies for the control process of continuous casting machines

Resumen

In continuous casting machineries, monitoring the mold is essential for the safety and quality of the process. Then, the objective of this thesis is to develop mathematical tools for the real-time estimation of the mold-steel heat flux which is the quantity of interest when controlling the mold behaviour. We approach this problem by first considering the mold modelling problem (direct problem). Then, we plant the heat flux estimation problem as the inverse problem of estimating a Neumann boundary condition having as data pointwise temperature measurements in the interior of the mold domain given by the thermocouples that are buried inside the mold plates. In formulating the inverse problem, we consider both the steady and unsteady-state case. For the numerical solution of these problems, we develop several methodologies. We consider traditional methods such as Alifanov's regularization as well as novel methodologies that exploit the parametrization of the sought heat flux. We develop the latter methods to have an offline-online decomposition with a computationally efficient online part. Moreover, in the unsteady-state case, we propose a novel, incremental, data-driven model order reduction technique to achieve the real-time performance of the online phase. Finally, we test all discussed methods on academic and industrial benchmark cases. The results show that the proposed novel numerical tools outclass traditional methods both in performance and computational cost. Moreover, they prove to be robust with respect to the measurements noise and confirm that the computational cost is suitable for real-time estimation of the heat flux.