## 3 Simulation Results
### Prediction Based on Static Data
Table 10 compares the performance of the individual models when lime and dolomitic lime were added as input observations for modeling and melt temperature prediction. When the simulation results in Table 10 are compared with the results in Table 4, it can be stated that most models increased performance, except for the NN in the training phase. On the other hand, most models degraded performance in the test phase except for SVR models. Due to the performance index (PI), the RF model was the best in the training phase, and the piecewise-cubic MARS model was the best in the testing phase. \begin{table}
\begin{tabular}{l l l l l l l l l l l l l l l l} \hline \multicolumn{1}{c}{**Method**} & \multicolumn{2}{l}{**Training**} & \multicolumn{1}{c}{\multirowSimilarly, Table 11 compares the performance of the individual models when lime and dolomitic lime were added as additional input observations for modeling and predicting carbon content in the melt. When the simulation results in Table 11 are compared with the results in Table 6, it can be stated that in the training phase, most models increased performance except the piecewise-cubic MARS model and NN. Only SVR with a Gaussian kernel, NN, and the piecewise-linear MARS model in the test phase improved their performance. The other models demonstrate reduced performance in the testing phase. Due to the performance index (PI), the SVR model with a polynomial kernel was the best in the training phase, and the piecewise-linear type MARS model was the best in the testing phase. Due to the most effective model for predicting temperature on unknown data in the testing phase being the piecewise-cubic MARS model, its equation is presented in this paper (see Equation (31)). The list of corresponding basis functions for this model is shown in Figure 8:2 In addition, this regression model includes lime and dolomitic lime as supplementary observations. On the other hand, the best model for carbon prediction was the piecewise-linear MARS model (see Equation (32)) with the basis functions listed in Figure 8:3 Both models are listed in complete form and can be transferred to the monitoring system of the BOS plant. Variables \(x_{6}\), \(x_{11}\), \(x_{16}\), and \(x_{19}\) have the lowest relative importance and were not used in the MARS model (31). \begin{table}
\begin{tabular}{l l l l l l l l l l l l l l l} \hline \hline \multicolumn{1}{c}{**Method**} & \multicolumn{3}{c}{**Training**} & \multicolumn{6}{c}{**Testing**} \\ \hline  & \multicolumn{3}{c}{**Testing**} & \multicolumn{3}{c}{**Time (\%)**} & \multicolumn{3}{c}{**\(\tau_{\text{SP}}^{\text{\tiny{}}}\)**} & \multicolumn{3}{c}{**MSE**} & \multicolumn{3}{c}{**RMSE (\%)**} & \multicolumn{3}{c}{**RMSE (\%)**} & \multicolumn{3}{c}{**RMSE (\%)**} & \multicolumn{3}{c}{**RMSE (\%)**} & \multicolumn{3}{c}{**RMSE (\%)**} & \multicolumn{3}{c}{**PI**} \\ \hline SVR (polynomial kernel) & 2.1406 & 0.9710 & 0.9428 & 0.0000 & 0.0028 & 6.2736 & 169.6273 & **3.8180** & 0.0861 & 0.074 & 0.0040 & 0.0630 & 129.6704 & 47.7670 & 119.3862 \\ SVR (Gaussian kernel) & 0.0177 & 0.7426 & 0.5155 & 0.0001 & 0.0081 & 18.3250 & 899.9417 & 10.5157 & 0.3803 & 0.1464 & 0.0020 & 0.0126 & 25.9519 & 18.0279 & 18.3772 \\ NN & 0.6465 & 0.1047 & 0.0110 & 0.0004 & 0.0200 & 44.9654 & 1800.2484 & 0.70377 & 0.2020 & 0.0408 & 0.0003 & 0.0165 & 33.9825 & 25.1397 & 28.2077 \\ MARS (piecewise-linear) & 13.3011 & 0.6304 & 0.3794 & 0.0020 & 0.0009 & 20.1725 & 725.0240 & 123.7284 & 0.4102 & 0.1634 & **0.0001** & 0.0122 & 25.0742 & 17.3692 & **18.1645** \\ MARS (piecewise-cubic) & 22.7149 & 0.9456 & 0.3834 & 0.0001 & 0.0009 & 20.8945 & 1028.9977 & 13.0107 & 0.2757 & 0.0760 & 0.0002 & 0.0128 & 25.3574 & 18.1886 & 20.6616 \\ k-NN & 0.0010 & 0.5569 & 0.3101 & 0.0001 & 0.0009 & 21.6641 & 1022.7053 & 13.9148 & 0.1112 & 0.0124 & 0.0022 & 0.0137 & 28.1985 & 21.6607 & 25.3777 \\ RF & 71.9077 & 0.9087 & 0.8257 & 0.0000 & 0.0064 & 14.4773 & 849.7621 & 7.5849 & 0.3266 & 0.1067 & 0.0022 & 0.0126 & 25.8663 & 18.6019 & 19.4980 \\ \hline \hline \end{tabular}
\end{table}