Statistical modeling of heat exchange coefficient evolution during quenching

In the premium steelmaking industry, the heat treatment of steel products is a key process in order to obtain the good final properties and in a correct range of values. In general, the heating processes are well managed as the modeling and the piloting algorithms for the furnaces are today widespread in many production plants. Industry 4.0 target is a complete management of things inside the plants.To do that it is important to model all the processes in a sufficiently accurate way. One of the most complex processes in steelmaking heat treatment is quenching. Fast convective phenomena are always complex to model, in particular, if the model is strictly linked to the process set up. The literature is not very rich in models that can be used in real production processes; each case has his own particularities that imply the associated model is in general unique. A way to understand a quenching process is to create a large database of trials with a variation of the process set up. The first point is how large this trials database could reasonably be, considering all the constraints of measuring a real production process and how to optimize the creation of DOE (Design of Experiment) considering all the possible process parameters. The basic idea is to combine the database trials with a statistical tool in order to predict the HTC (Heat Transfer Coefficient) during quenching with each particular set up. We tried different regressions analysis in order to optimize the combination of parameters to obtain the smallest possible error. Our first idea was to use the simplest tool to have quickly the dimension of the complexity of the quenching HTC, so Multiple Linear Regression was used. To improve the first results Local Regression (LOESS) and Random Forest Regression were tested in the second moment. To validate all models we used Leave-one-out cross-validation method and Determination Coefficient techniques.