2022/10/05 by Umberto Morelli, Patricia Barral, Morelli, Umberto Emil +7
Engineering · Mathematics · #FOS: Mathematics #Induction Heating and Inverter Technology #Metallurgical Processes and Thermodynamics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2210.02128
openalex publication_date 2022/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we investigate the estimation of the transient mold-slab heat flux in continuous casting molds given some thermocouples measurements in the mold plates. Mathematically, we can see this problem as the estimation of a Neumann boundary condition given pointwise state observations in the interior of the domain. We formulate it in a deterministic inverse problem setting. After introducing the industrial problem, we present the mold thermal model and related assumptions. Then, we formulate the boundary heat flux estimation problem in a deterministic inverse problem setting using a sequential approach according to the sequentiality of the temperature measurements. We consider different formulations of the inverse problem. For each one, we develop novel direct methodologies exploiting a space parameterization of the heat flux and the linearity of the mold model. We construct these methods to be divided into a computationally expensive offline phase that can be computed before the process starts, and a cheaper online phase to be performed during the casting process. To conclude, we test the performance of the proposed methods in two benchmark cases.