*4.1. EE consumption Models*

*R*¯ 2 *<sup>μ</sup>*-values for all variable batches and data cleaning strategies are shown in Figure 8. Consistency throughout the variable batches can be observed for all four cleaning strategies when the RF model framework is used. The consistency among the variable batches means, for the RF model framework that the deciding factor for the performance is the variable batch and not the hyper-parameters of the statistical model framework. This is a wanted outcome since the performance of a model should mainly be dependent on factors stemming from the application domain and not based on an optimization of parameters in an abstract framework.

Variable batches (VB) 1 and 2 produce models with the lowest *R*¯ <sup>2</sup> *<sup>μ</sup>*-values. These are also the VB that *do not* use scrap representation variables. This provides evidence that scrap types are relevant factors when determining the EE consumption of the EAF and that scrap should not be treated collectively using only the total weight of all charged scrap.

The best performing models are those from VB 5 and 6 which use categories from the visual scrap representation. This provides evidence that a categorization based on scrap shapes is an optimal approach when creating a statistical model predicting the EE in the steel plant under study.

The performance of the models using the visual scrap representation are, performance-wise, followed by the models using the plant scrap representation (VB 3 and 4) and the density scrap representation (VB 7 and 8), respectively. Essentially, this indicates that a too fine or a too coarse representation of the charged scrap are sub-optimal for a statistical model predicting the EE. The steel plant scrap representation has numerous scrap types that contain the same scrap with respect to shape and dimension. The only difference is varying alloying content from Ni, Cr, and Mo, which does not significantly affect the melting time.

The coarse representation is based on the apparent density of the scrap, which does not take into account the shape of the scrap. Scrap shapes are closely related to the area-to-volume ratio, which is the strongest factor determining the melting time of scrap in the EAF since the stirring in the EAF is low during a large part of the melting phase. For example, HM has the same apparent density as skulls, which consist of bulky mixtures of solid slag and metal that takes long time to melt. Likewise, thin and thick plate have similar densities but different area-to-volume ratios.

The consistency among the four sets of VB between the four cleaning strategies for both statistical model frameworks further strengthens the evidence regarding the effects of the chosen scrap representations on the predictive performance of the models.

The performance and meta data of the best models and meta data from each cleaning strategy and model framework are shown in Table 8. In general, the ANN models perform similarly or better than the RF models with regards to the *R*¯ <sup>2</sup> *<sup>μ</sup>*-values. However, the ANN models always have a smaller mean error and standard deviation of error, i.e., Δ*<sup>μ</sup>* and Δ*σ*.

With regards to the modeling meta data, the ANN and RF models had the same VB for the best models on the data from each cleaning strategy. This is also a wanted outcome based on the same reasoning as before regarding the importance priority between the domain-specific factors and the abstract model-based factors.

The total amount of cleaned data points was 25.8 percentages higher for the *Expert* cleaning strategy compared to the *Domain-specific* cleaning strategy. The *R*¯ <sup>2</sup> *<sup>μ</sup>*-values only increased slightly using the *Expert* cleaning strategy; 0.035 and 0.039 for the RF and ANN models, respectively. Using the statistical cleaning method Tukey's fences, the amount of data cleaned were 11 and 13.3 percentages higher than the *Domain-specific* cleaning strategy. As opposed to the *Expert* cleaning strategy, the *R*¯ <sup>2</sup> *<sup>μ</sup>*-values were worse for the models involving Tukey's fences. *Tukey* reported reduced *R*¯ 2 *<sup>μ</sup>*-values of 0.049 and 0.077 for the RF and ANN models, respectively. For the *Tukey-Domain-specific* the reduction in *R*¯ <sup>2</sup> *<sup>μ</sup>* were 0.053 and 0.078, respectively. These results lead to two important findings. First, the usage of statistical cleaning heuristics results in a model performance that is sub-par to models using data cleaned by the usage of domain-specific knowledge; the *Expert* and *Domain-specific* cleaning strategies. Second, using data cleaned by an *Expert* yields models with the best performance, which illuminates the importance of knowledge about the specific EAF operations one intends to model. However, the large relative percentage of data loss using the *Expert* cleaning strategy (34.2%) as opposed to the *Domain-specific* cleaning strategy (10%) tilts the chosen cleaning strategy in favor of the latter since the data loss percentage directly relates to the percentage of future heats the model can predict on. This finding is closely tied to the practical usefulness of the model.

**Figure 8.** *R*¯ <sup>2</sup> *<sup>μ</sup>*-values for each variable batch (VB 1-8 on the abscissa) and cleaning strategy. **VB 1–2:**Without scrap representation. **VB 3–4:** Steel plant scrap representation. **VB 5-6:** Visual scrap representation. **VB 7–8:** Density scrap representation.

**Table 8.** The performance and meta data of the best models, and the meta data for the four cleaning strategies. The values in parentheses show the values from the ANN models.

