*4.2. Analysis of the Selected Model*

The selected model for the analysis is the RF model with a variable batch 6 using domain-specific cleaning. This model was selected based on the relatively high *R*¯ <sup>2</sup> *<sup>μ</sup>*-value (0.457) while still keeping 90% of the data compared to the model using the expert cleaning type, which provided the highest *R*¯ 2 *<sup>μ</sup>*-value (0.490) but only keeping 64.2% of the data. Hence, the chosen model can be used in 90% of future heats given that the test data and training data come from the same distribution.

The main interactions of the variables Plate1, Internal1, HM, and Shredded on the EE consumption and the charged weight distributions of these scrap categories for each of the charge types A, B, and C, can be seen in Figure 9.

The EE contribution by Plate1 on charge type A is lower than for B and C. However, charge type B can have both a positive and negative EE contribution since the densest part of the distribution is present in the steepest EE interaction change for Plate1. Hence, it is hard to conclude whether charge type B gets a similar contribution as does charge type A or charge type C. Charge type C is commonly using zero, or next to zero, amount of Plate1. Hence there is a large contribution to EE by Plate1 for this charge type. The EE contribution by Internal1 is slightly lower for charge type A than charge types B and C. The EE contribution by HM on steel type A is higher than for charge types B and C, the latter two of which are charged similarly across all heats. For the Shredded scrap category, all charge types receive similar contributions to EE.

Based on these highlights, it is expected that charge type A has the lowest EE consumption, that charge type C has the highest EE consumption, and that the EE consumption of charge type B is in-between those of type A and type C. The following EE consumption, relative to the EE consumption by charge type A, was obtained based on the data from the heats used to create Figure 9: charge type B = 0.99 and charge type C = 1.02.

On the other hand, charge type B requires slightly less EE consumption on average than charge type A (1.00). This is likely because Plate1 being closer to a negative contribution to EE for charge type B than was previously anticipated. Furthermore, the analysis only focused on 4 of the 12 scrap categories, out of which 3 are of particular interest to the selected charge types. In addition, the model also uses a total of 21 input variables to predict the EE consumption of any given heat. However, given these caveats, the analysis is in line with what could be expected from the model analyzed as well as from expert domain knowledge.

The main utility of SHAP main interaction values is that it provides clarity on how specific values governed by the input variable distribution contribute to the EE consumption prediction. The SHAP main interaction values only show the univariate relationship between the input variable and the EE consumption prediction. It is possible to use the SHAP interaction effects between the input variables as explained in Section 3.5.1. However, the number of SHAP plots to analyze will be equal to an additional 20 for each input variable; giving a total of 441 SHAP interaction plots for a complete analysis of the selected model. Although experience and knowledge about the specific EAF can guide the selection of SHAP interaction plots, a further analysis of the SHAP plots is best left as a future point of study. The above analysis shows what can be done with the available tools. Although interesting, an exhaustive analysis is for obvious reasons out of scope of the present paper.

The SHAP main interaction effects on EE by each scrap category of the selected model can be observed in Figure 10. Thin plate, i.e., Plate1, has been confirmed by the steel plant engineers to contribute to less EE. This is evident since a steep drop can be observed. The reduced EE by Plate1 is eventually flattened out and increases when the amount of Plate1 approaches the upper limit of the furnace capacity. Internal1 contains heavy scrap with an apparent density of over 1.4 ton/m3. Heavy scrap takes longer time to melt which contributes to a steadily rising EE with an increased amount of Internal1 scrap. This has also been confirmed by the steel plant engineers, which refer to the use of Internal1 as the reciprocal of Plate1 in the steel plant charging strategies. One could observe a slight decrease in the EE contribution by increasing the amount of Plate2 and a slight increase in EE contribution for Internal2. However, these scrap categories consist of less than 1% of the total charged

weight in the studied heats. Hence, it is difficult to draw any clear conclusion on their contribution to the EE. Shredded scrap is charged based on operating practices rather than for specific charging strategies which results in steel with low amount of tramp elements. The EE contribution is decreasing with increased amount of Shredded scrap from the nominal amount used. This was not confirmed by the process engineers. The decreasing EE contribution could be a model artifact or because the shredded scrap does contribute to a decrease EE consumption in the process. The latter could be the case since shredded scrap is easily melted due to its high surface-area-to-volume ratio.

**Figure 9.** SHAP main interactions on EE by Plate1, Internal1, HM, and Shredded scrap categories. The three probability density plots below each plot show the distribution of the scrap category for each of the charge types A, B, and C, respectively. See Section 3.5.3 for an explanation of the different steel types. The y-axis of the scatter plot shows the SHAP main interactions on EE for each variable and the y-axes of the probability density plots show the frequency of each charge weight. The x-axes of both the SHAP plot and the probability density plot for each charge type are the amount charged of the scrap category. The values on the x-axes has been omitted due to proprietary reasons. The values governing the plots are from both the training and test data.

Incineration scrap is charged in low amounts, corresponding to only approximately 1.5% of the total charging weight on average for all heats and approximately 5% for the heats using charge types with lower requirements on impurity tramp elements. The increase in EE consumption is likely due to the melting requirements of the scrap weight rather than due to the surface-area-to-volume ratio. Also, skulls require higher EE according to the SHAP main interaction effect. This was confirmed by the steel plant engineers which reported that skulls are difficult to melt. Skulls are large concrete-like pieces of slag and metal mixture.

**Figure 10.** SHAP main interaction effects for the scrap categories for the selected model. The y-axes show the main interaction effect on EE while the x-axes show the amount of each charged scrap category. The values on the x-axes has been omitted due to proprietary reasons. The grey dots represent values from the training data and the black dots represent values from the test data.

The SHAP main interaction values for the base variables can be seen in Figure 11. Here, the focus will be on the variables whose EE contribution is counter-intuitive from the standpoint of a practitioner in physico-chemical modeling. Specifically, these are Burner *O*2, Carbon Injection, Burner oil, and Lance *O*2. According to the steel plant engineers, Burner oil is only effective up to a certain amount of *kg*, which is when the burner oxygen is used in tandem with burner oil. This agrees well with the observation from Figure 11. The burners are used in their maximum capacity when melting scrap. However, the burners still need to be active for the remainder of the heat to prevent the burners from getting clogged by slag and scrap. Thus, Burner oil is closely related to TTT, which is the reason Burner oil in higher amounts contributes positively to EE. Carbon injection, which should contribute to more heat generated by carbon boil, contributes positively to EE. This was confirmed by the steel plant engineers to be related to the continuous injection of carbon fines throughout the heat. As soon as liquid steel is present, carbon fines are injected to facilitate foaming slag. Similar to Burner oil, Carbon Injection is also closely related to TTT. In the steel plant of study, Lance *O*<sup>2</sup> is only used to clear the slag door to enable sampling of the steel melt temperature and composition. Therefore Lance *O*<sup>2</sup> does not have a consistent contribution to the EE.

**Figure 11.** SHAP Main interaction effects for the base variables for the selected model. The y-axes show the main interaction effect on EE while the x-axes show the increasing amount of each variable. See Table 2 for details about the definition of each variable. The values on the x-axes has been omitted due to proprietary reasons. The grey dots represent values from the training data and the black dots represent values from the test data.

The positive relationship Injection Carbon to EE can also be observed by its Pearson correlation coefficient in Table 9. For both the Pearson correlation and dCor, Injection Carbon has the highest value with respect to the EE. In addition, the SHAP feature importance (Figure 12) regards the Carbon Injection as almost twice as important as the Total weight when the model predicts the EE consumption.

The sometimes counter-intuitive relations between the input variables to the EE consumption prediction emphasize the importance of not only having a firm understanding of the physico-chemical and process experience on the relations governing the EAF. It is also important to understand the relationship between the governing factors to the EE consumption of the specific EAF that one intends to model.

It is important to observe that the total weight and TTT are among the three most important variables for the model when predicting on EE. Both variables are also correctly considered by the model with respect to what is known from process metallurgical experience. This agrees well with the results from the previously reported SHAP analysis of a statistical model, created by the authors of the present study, predicting the EE of an EAF [10].

**Figure 12.** SHAP feature importance for the selected model as defined in Equation (15). The bars show the feature importance on the training data and the dark dots show the feature importance on the test data.

**Table 9.** Correlation between the input variables and the EE consumption as defined in the transformer system. The input variables are ordered by dCor in the training data set. The values in parentheses are the Pearson correlation coefficients.


#### **5. Conclusions**

The main aim of this study was to investigate the effects of scrap in the performance of a statistical model predicting the EE consumption of an EAF. This was done using three distinct representations of the scrap types as well as SHAP main interaction effects which reveals the contributions from the scrap variables on each specific EE consumption prediction. In addition, the study extended a previously reported methodology used to create statistical models predicting the EE consumption of an EAF [2]. This was achieved by investigating the effects on the model performance using four different data

cleaning strategies, an additional statistical model framework, RF, and data from an EAF producing steel for tubes, rods, and ball-bearing rings as opposed to stainless steel.

The main conclusions of the study may be summarized as follows:
