## 3 Results and Discussion
### Predictive Performance of ANN Model
Considering the measurement error of the actual concentration and the deviation between samples, the predictive performance was relatively good. In Figure 7b, the distributions of prediction errors were right-skewed, which means that the actual dissolved carbon concentrations were somewhat smaller than the predicted values. This suggests that the ANN model was under-fitted due to the lack of data for various operating conditions, as there were many operations with similar initial carbon concentration and the molten steel weight. However, if we determine the decarburization end time using the predicted value, the actual carbon concentration is always below the upper target range of the concentration. Thus, it is possible to determine the decarburization end time for steels without a target lower limit. Figure 7c shows the distribution of prediction errors according to the data collection period. In Period 1, the prediction error was evenly distributed around zero, but in Periods 2 and 3, it is right-skewed. There was facility maintenance work between Periods 1 and 2, so we estimated that changes in the facility and operating conditions might have affected the training of the prediction model. In particular, the circulation rate of the molten steel was increased due to facility improvement and as a result, the actual decarburization rate could be faster than Period 1 in the operation of Periods 2 and 3. Therefore, we expect that prediction accuracy will improve by iteratively training and upgrading the model by acquiring data that can reflect changes in facility and operating conditions. Figure 7d shows the distribution of prediction errors according to the target carbon concentration. It was confirmed that the smaller the target carbon concentration, the smaller the prediction error and deviation (Table 2). In general, the lower the target carbon concentration, the longer the operating time and the longer the slow decarburization reaction. In this case, the prediction error was small because the change in the carbon concentration in the molten steel was slow and the operating conditions were stable. On  
Figure 6: Prediction results of the ANN model for the target decarburization curves in two example operations (**a**) without and (**b**) with additional carbon. The solid and dotted lines represent the decarburization curve using the TDLAS analyzer and the predicted values of the ANN model, respectively. the other hand, if the target concentration is large, the operation is terminated when the variability in operating conditions and decarburization rate is relatively large. In this case, it seems necessary to train the model with more diverse data. Figure 8 shows the predicted and measured values of carbon concentration for each steel type. In general, steels are classified into many types according to the target carbon concentration and the allowable concentration range. As discussed above, the predicted carbon concentrations in the molten steel were generally higher than the measured values, \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Prediction Error**} & \multicolumn{3}{c}{**Target Carbon Content**} \\ \cline{2-4}  & **10 ppm** & **15 ppm** & **25 ppm** \\ \hline Mean & \(-\)2.09 ppm & \(-\)2.22 ppm & \(-\)2.80 ppm \\ Std. dev. & 3.56 ppm & 3.96 ppm & 4.47 ppm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Prediction error of the ANN model according to the target carbon contents. Figure 7: Predictive performance of endpoint carbon concentrations on test data. (**a**) Target vs. predicted values of the ANN model (blue line: regression line with slope 0.478; black line: ideal prediction line with slope 1.0; gray lines: the predicted values are within the ideal line \(\pm\) 5 ppm); (**b**) error distribution for all test data; (**c**) error distribution by the period of collected data; (**d**) box plot of prediction error by target values (filled circles represent the mean values of each steel type). but both predicted and measured values were within the allowable concentration ranges.