Comparison of Finite-difference and Data-based Models of Temperature Transfer Process in Heating Furnaces for Cast Billet Temperature Prediction

The energy efficiency of the metallurgy is becoming more and more important today due to the permanently growing requirements to the final product quality. One of the modern methods to increase it is the production digitalization, which is mostly based on the concept of “Digital Twins” or “Digital Shadows” of technologically processes or units. As far as the metallurgy is concerned, the units with the highest energy consumption are furnaces. This fact makes it actual to try to develop “Digital Twins” of such furnaces. One of the main constituent parts of the “Digital Twin” is a kind of a mathematical model, such as finite-difference or data-based ones. In this research: 1) the finite-difference model of the steel heating process, which is based on the differential equation of transient heat conduction, is developed; 2) the obtained finite-difference model is compared with the data-based one, which is obtained as a result of application of the machine learning algorithms and extreme gradient boosting method modification (DART) to the data obtained from the furnace; 3) conclusions are made on the advantages and disadvantages of these models. The data-based model error is 7.4 degrees Celsius lower than the one obtained with the help of the finite-difference model.