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where P c is a constant pressure value in the range [1, 1.5] atm, A and B are constants whose
nominal values are respectively, A=1895 °K and B=1.6 and n is commonly assumed to be
unitary, but some literature results provide n≈0.5 for [C]<0.08% and n≈1 otherwise.
Equation (1) can easily be inverted in order to predict [C] from [O] and T , but the prediction
obtained using the nominal values of the constant parameters is not very reliable compared
to the [C] measurements contained in a dataset provided by the steel manufacturer for the
steel grades of interest. A reliable prediction of the final Carbon content at the end of the
refining process is very important, as it allows to evaluate the process parameters (such as
the amount of inflated Oxygen and the duration of the refining process) required to achieve
the desired results optimizing the time and cost of the production process. By adopting a
simple two-layer MLP with 3 neurons in the hidden layer, the prediction error has been
reduced of 64% with respect to the prediction obtained through eq.(1).
This system presents the following advantages: i) the performance is acceptable, ii) the neural network
is very simple; iii) the training time is negligible. However the neural model has been not very well
perceived by the end-users mainly because it is difficult to attribute a precise physical meaning and
interpretation to the network parameters, such as it happens for the parameters of the formula (1).
Therefore the alternative solution of a fine tuning of the physical parameters around the
nominal values has finally been preferred.
4.4 Prediction of the time required by each stage of hot rolling mills
The efficiency and productivity of steel hot rolling mills is heavily affected by the possibility
of precisely estimating when the different manufacturing stages are completed, as this
avoids bottlenecks and provides important time and energy savings. For this reason, several
Mill Pacing Control (MPC) systems have been realised and implemented, which allow
optimising the production flow starting from the reheating furnaces, where slabs are heated
at a temperature between 1100°C and 1300°C for optimal workability before being rolled.
Hot steel rolling mills are usually composed of two main stages, namely the roughing mill ,
where the slab is firstly compressed, and the finishing mill, where the aimed thickness of the
hot rolled coil is reached. A further rolling stage can be afterwards required, named cold
rolling , which is pursued at far lower temperatures in order to produce flat products, such as
plate, sheets or coils of various thicknesses.
MPC systems allow shorten the discharging interval between two subsequent slabs
avoiding collisions. To this aim, schedule systems are developed and simulations are
performed in order to test new strategies without affecting the production cycle.
Colla et al. (Colla et al., 2010) applied neural networks to solve a particular mill pacing
problem, different from the usual one, namely the prediction of the total roughing time and
of the time required for passing the first gauge of the finishing mill. This investigation has
been pursued in order to increase the rolling efficiency and decrease the total rolling time.
The slabs that are subsequently rolled can differ in steel grade and other features, thus the
related rolling processes can require different times and energy amounts. The time required
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