Mathematical models of phenomena at gas blowing into ladle

Abstract

The paper describes the physical and cybernetic approach to the task of looking for an appropriate mathematical approximation-regression model of the measured standardised concentration of the tracer at a scale physical model of the casting ladle when blowing the steel by inert gas. The physical approach allows assembling an adequate mathematical model of the processes in the shape of a so-called white box, where the structure of the model are known. The cybernetic approach only draws on the measured inputs and outputs (so-called black box) as well as any additional conditions (so-called grey box) and the structure of the model is chosen according to them. These mathematical models are referred to as empirical models. The paper presents and compares four mathematical models – physically adequate one and three empirical ones.