*5.1. Machine Learning Predictions of the Decarburization Rate dc*/*dt*

Figure 2 shows the correlation matrix between different features, which was generated by the available dataset. The correlation between two datasets varies between -1 and 1, with 0 implying no correlation. Correlation of +1 implies a perfect positive correlation (e.g., as x increases, so does y), and -1 implies a perfect negative correlation (as x increases, y decreases). Dark blue implies a strong positive correlation, and lighter pink shows a strong negative correlation. For example, there is a strong positive correlation between Total O2 flow and dO/dt, or there is a strong negative correlation between O2 waste gas and dc/dt.

Total oxygen flow has nearly perfect positive (>0.9) correlation with dc/dt (kg C/min) or dC/dt (kg C/s), total C removed, dO/dt, dOs/dt (0.71) and waste gas CO2 composition. The total oxygen flow was mainly used for decarburization escaping from the reactor as waste gas and remaining in the slag (oxidization of Si, Mn, Fe and P elements in the liquid metal). The former is directly linked with parameters dc/dt (or dC/dt), total C removed, dO/dt and waste gas CO2 composition, while the latter is in the form of dOs/dt. Furthermore, dc/dt (or dC/dt) has nearly perfect positive correlation with total O2 flow and waste gas CO2 composition and nearly perfect negative correlation with lance height and waste gas O2. Except the oxygen from steel scrap and iron ore coolant, the main oxygen comes from the total oxygen blown through the lance that is also the main oxygen source for decarburization. Thus, the dc/dt (or dC/dt) has a nearly perfect correlation with the total O2 flow. During the pilot plant experiment, O2 was blown at a fixed flow rate, and the refining performance in the converter was controlled by adjusting the lance height. The decarburization mainly occurred in two zones of a hot spot zone (at the vicinity of the location where the lance releases oxygen to the bath) and gas-slag-metal droplet emulsification zone (where the available area for slag/metal/gas reaction is high). Lower lance height increases the hot spot zone and the amount of metal droplets in the emulsification zone, and the latter increases the decarburization in the gas-slag-metal droplet zone. Therefore, the overall decarburization rate increases with decreasing the lance height, which explains the observed negative correlation. The decarburization rate is calculated from the waste gas composition according to the equation dc/dt *dc dt* <sup>=</sup> (*CO* <sup>+</sup> *CO*2) <sup>×</sup> *waste gas flow rate* <sup>×</sup> <sup>12</sup> 22.4 . This explains well the perfect positive correlation between dc/dt (or dC/dt) and waste gas CO2 concentration. From the above analysis, both the total O2 flow and the lance height are the controlling parameters for the decarburization, which indicates that the probability of predicting the decarburization rate by the combination of both parameters (see Section 5.3. Prediction of the dc/dt After Excluding Parameters). Finally, dO/dt has nearly perfect positive correlation with the total O2 flow, dc/dt (or dC/dt) and waste gas CO2 composition but nearly perfect negative correlation with the lance height and waste gas O2 content (similar explanation to that of the dc/dt or dC/dt dependence upon the parameters).


**Figure 2.** The correlations between different features within the dataset from the six-ton (6t) pilot plant trial. The figure has been vertically split into two parts, and the top and the bottom shown above are actually the left and right parts of the figure, respectively.
