## 6 XAI Empowered Decision Support
### Model Interpretability  
In manufacturing, the outcome is not only dependent on the process parameters independently, but also the interactions of the variables have an impact. In GBM, the interactions of the variables can be included in the model, and in this application, the interaction depth (the highest level of interactions between variables allowed during training the model) was three. Some of the variables may have quite a strong impact on interactions, but most of them do not interact actively with the other variables. In practice, the impact of the most important individual variables usually outperforms that of interactions. Figure 7 shows how strongly the variables of Model_HYBRID interact with each other based on the test set data. The interaction strength value corresponds to the proportion of explained variance of \(f(x)\) for each feature. The value is located between 0 when there is no interaction and 1 when all variation depends on a given feature's interactions. Clearly, the variable with the most interactions is the RAP speed. Additionally, the diameter of the roll in the fifth roughing mill pass, the reduction of the strip at first tandem pass, and the average pickling speed are on top of the interaction list. However, overall, the interaction strengths are quite weak. For each feature, it is possible to find the strongest interaction partners as well. In Figure 8, the interactions between the most important feature--the RAP speed--and other features are shown. The strongest pair is the RAP speed and the diameter of the roll at the fifth roughing mill pass (HOT ROLL DIAM RM5). However, overall, the values for the majority of the interaction pairs are quite low. Figure 6: Variable importance for Model_HYBRID. With Partial Dependence Plots (PDP), the effect of each variable on the response variable can be visualized together with the distribution of data points. From PDP in Figures 9 and 10, it is quite clear that the faster the steel strip goes, the lower the risk of surface roughness is in RAP-line. The decrease in roughness appears especially after 60 km/h. Figure 11 shows the relation between the diameter of the roll at the fifth roughing mill pass (HOT ROLL DIAM RM5) and the predicted response variable. The larger the diameter of the roll is (\(>\)96,000), the larger the risk of roughness is. Figure 12 presents the reduction of the strip at the first tandem pass (HOT REDUCTION TA). Clearly, with a reduction larger than 1.25, the risk of roughness is lower. To obtain a larger reduction, a larger rolling force is needed. The rolling force is proportional to the width of the strip and it relates to the pressure on the surface of the strip. Thus, it affects the quality of the surface. Some specific products, which are softer and more delicate as a result of their other mechanical properties, need to be rolled in a more sensitive way, and thus the rolling force and resulting reductions during individual passes are smaller as well. Figure 8: Interaction between the most important variable and other variables. Figure 7: The strength of the interactions of the variables. Figure 11: PDP of the diameter of the roll at the fifth roughing mill pass. Figure 10: PDP of the average pickling speed. Figure 9: PDP of the speed of the RAP process. Figure 13 shows the PDP of roughness and the interaction of the diameter of the roll at the fifth roughing mill pass and the speed of the RAP process, which is the pair of variables with the strongest interaction, as shown in Figure 8. As can be seen, roughness is at its lowest with a diameter of the roll under 960,000 and with a speed over 90. Roughness is at its highest with low speeds (\(<\)60) and especially when combined with a high diameter of the roll (\(>\)980,000). This tool is especially useful if the user needs to compromise between two parameters when trying to find the best manufacturing settings. The accumulated local effects (ALE) plots can be used in addition with PDP to visualize the effect of selected variables on the dependent variable, as well.