Predictive Model for the Cold Rolling Process through Sensitivity Factors via Neural Networks

The mathematical modeling of the rolling process involves several parameters that may lead to non-linear equations of difficult analytical solution. Such is the case of Alexander's model (Alexander 1972), considered one of the most complete in the rolling theory. This model requires excessive computational time, which prevents its application in on-line control and supervision systems. In this paper, the representation of the cold rolling process through Neural Networks trained with data obtained by Alexander's model is presented. This representation is based in sensitivity factors obtained by differentiating a neural network previously trained. The representation allows to obtain equations of the process for different operation points with low computational time. On the other hand, the representation based in sensitivity factors has predictive characteristics that can be used in predictive control techniques. Through predictive model, it is possible to eliminate the time delay in the feedback loop introduced by measurements of the outgoing thickness, normally with X-ray sensors. The predictive model can work as a virtual sensor implemented via software. An example of the application to a single stand rolling mill is presented.