Comparison of finite difference and data-based models application to solve problem of steel billets temperature prediction

Within the whole cycle of technological conversion processes, which are widespread in the ferrous metallurgy, there are many energy-intensive technological units, energy-efficient control of which is a complicated task due to the non-stationarity of technological processes within them. One of such units is a continuous flame furnace, which is used for simple heating, homogenization, annealing and other operations. If the surface temperature of the billets at the furnace outlet could be known in advance (while they are still inside the furnace), it would be possible to adjust certain heating parameters, while staying within the technological instructions, in order to minimize the consumption of the combustible fuel. Therefore, in this paper we compare two models to predict the temperature of the billet surface after a simple heating in such a furnace: a model based on numerical differentiation of transient heat conduction equation and a tree-like one, which is obtained by machine learning and based on the technological data from the lower level of the furnace automation. It is supposed that such models can become the basis for a "digital twin" of the unit, which can be further used in Advanced Process Control (APC) systems. As a result of comparison, it is obtained that the error of the data-based model is 7.4 degrees Celsius lower on average comparing to the finite-difference one. It is assumed that this result is a consequence of the advantage of the first model "natural adaptation" to the technological unit.