## 3 Simulation Results
### Prediction Based on Static Data
\begin{array}{ll}\text{Carbon}\ \ (\%)=0.056331-0.00015156\times\text{BF1}+0.00035671 \times\text{BF2}\\ -0.026621\times\text{BF3}-0.030646\times\text{BF4}+0.00012233\times\text{BF5}+0.0 000014438\times\text{BF6}\\ -0.613\times\text{BF7}-0.00017452\times\text{BF8}-0.000000019273\times\text{BF9} \\ -0.00000000000088203\times\text{BF10}-0.0000023083\times\text{BF11}\\ -0.00000017825\times\text{BF12}-0.000010849\times\text{BF13}-0.00000080785\times \text{BF14}\\ +0.00024026\times\text{BF15}+0.00009186\times\text{BF16}+0.0000025541\times\text {BF17}\\ -0.00000045047\times\text{BF18}-0.0000000035607\times\text{BF19}+0.0000000023973 \times\text{BF20}\\ +0.0000000011266\times\text{BF21}-0.000000002276\times\text{BF22}\\ -0.00011272\times\text{BF23}-0.00011221\times\text{BF24}+0.00024054\times\text {BF25}.\end{array}  \tag{30}\]  
Variables \(x_{6}\), \(x_{7}\), \(x_{9}\), and \(x_{10}\) had the lowest relative importance and were not used in model (30). The list of corresponding basis functions is shown in Table 9.  
Figures 5-11 show the sequence of melts as they were performed in the steelmaking plant. These figures show a series of measured and predicted (i.e., simulated) endpoint melt temperatures. The black vertical line in the figures divides prediction in training and testing. These figures present a graphical comparison of the actual measured temperature with the simulated temperature for each method. The green bottom bars represent the calculated relative error in percentages. In graphic comparison, it can be seen that the lowest relative errors in the training phase were calculated in the case of the RF model (see Figure 11) and the highest in the case of NN (see Figure 7). In  
Figure 8: Prediction of endpoint melt temperature by piecewise-linear MARS model. Figure 6: Prediction of endpoint melt temperature by SVR model with the Gaussian kernel. Figure 7: Prediction of endpoint melt temperature by NN model. Figure 9: Prediction of endpoint melt temperature by piecewise-cubic MARS model. Figure 11: Prediction of endpoint melt temperature by RF model. Figure 12: Prediction of endpoint carbon concentration in melt by SVR model with a polynomial kernel. Figure 10: Prediction of endpoint melt temperature by \(k\)-NN model. Figure 16: Prediction of endpoint carbon concentration in melt by piecewise-cubic MARS model. Figure 14: Prediction of endpoint carbon concentration in melt by NN model. Figure 8:0 Prediction of endpoint carbon concentration in melt by SVR model with a Gaussian kernel. Figure 8:1 Prediction of endpoint carbon concentration in melt by piecewise-linear MARS model. In the previous analysis, lime was not considered as an input observation. Based on technological documentation, lime and dolomitic lime are added to the melt as slag-forming additives. The further analysis investigated the effect of added lime and dolomitic lime as additional input observations. Lime, together with magnesite, is used to cool the melt and MgO control in converter slag. To use two further observations, the list of variables in Table 1 was updated, by the following: \(x_{13}\) = amount of lime added to the melt (kg), \(x_{14}\) = amount of dolomitic lime added to the melt (kg), \(x_{15}\) = amount of added magnesite to the melt (kg), \(x_{16}\) = amount of Fe in pig iron (%), \(x_{17}\) = amount of after-blow oxygen (Nm\({}^{3}\)). When endpoint BOS melt temperature was modeled and predicted, the endpoint carbon concentration in melt and melting duration was regarded as the additional input observations (i.e., \(x_{18}\) = endpoint carbon concentration in the melt, \(x_{19}\) = melting duration). Otherwise, when carbon concentration in the melt was modeled and predicted, then melt temperature and melting duration was considered as input observations (i.e., \(x_{18}\) = endpoint melt temperature, \(x_{19}\) = melting duration). The total number of input observations for model training and target prediction was 19.