## 5 Results and Discussion  
### Predictive Models  
Table 4 shows the regression coefficients for the three MLR models. The coefficients correspond to the explanatory variables in Table 3. They are computed when the responses (MRR or TWR) are expressed in mm3/min, while the values of \(F_{p}\), \(V_{f}\), and \(U\) are expressed in Hz, mm/min and V respectively. The units for the processing parameters are listed in Table 1.  
The three MLR models are built using the training data, which are collected by varying five processing parameters during the drilling experiments following a full factorial DoE. The effects of these processing parameters on the MRR and TWR can be investigated by analysing the training data. As shown in the main effect plots in Figure 4, the open voltage is the parameter having a higher influence on both responses at the investigated process conditions. The reason can be mainly attributed to the fact that the open voltage determines the energy input per discharge on the SARIX(r) machine tool, therefore strongly influencing the material removal and tool wear rate. The servo control parameters have also an influence on the MRR and TWR, which both increases with the gain factor. This is because an increase of the gain factor results in a more aggressive regulation of the servo control system. On the contrary, both the MRR and TWR decreases when increasing the reference voltage. This is due to the fact that a higher reference voltage corresponds to a less aggressive servo regulation since the reference voltage is closer to the open voltage level. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Response**} & \multicolumn{8}{c}{**Coefficients**} \\ \cline{3-10}  & & \(\mathbf{c_{0}}\) & \(\mathbf{c_{1}}\) & \(\mathbf{c_{2}}\) & \(\mathbf{c_{3}}\) & \(\mathbf{c_{4}}\) & \(\mathbf{c_{5}}\) & \(\mathbf{c_{6}}\) & \(\mathbf{c_{7}}\) & \(\mathbf{c_{8}}\) \\ \hline PP & MRR & \(-0.171\) & \(0.003\) & \(0.004\) & \(0.001\) & \(0.001\) & \(-0.003\) & - & - & - \\ DD & MRR & \(-0.000\) & \(0.000\) & \(0.001\) & \(0.001\) & - & - & - & - & - \\ PP + DD & MRR & \(0.002\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.001\) & \(0.000\) \\ PP & TWR & \(-0.303\) & \(0.007\) & \(0.004\) & \(0.002\) & \(0.001\) & \(-0.002\) & - & - & - \\ DD & TWR & \(-0.001\) & \(0.000\) & \(0.000\) & \(0.000\) & - & - & - & - & - \\ PP + DD & TWR & \(-0.083\) & \(0.003\) & \(0.001\) & \(0.000\) & \(0.000\) & \(0.001\) & \(0.001\) & \(0.043\) & \(0.000\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Regression coefficients for the predictive models. Figure 3: Schematic of micro-EDM drilling experiments using two-part specimens. The main effect plots show that the processing parameters can have considerably different effects on the MRR and TWR. These effects might depend on several factors, including the workpiece material, tool material, tool size and dielectric fluid. This means that it is difficult to predict which processing parameters are having a higher influence on the MRR and TWR before performing a series of preliminary drilling experiments. Therefore, the selection of the processing parameters to be considered as explanatory variables of a predictive model can be challenging and risky. On the contrary, when following data-driven approaches, the monitored quantities show a relatively high degree of correlation to the MRR and TWR (see Figure 5), which means that all explanatory variables included in the DD predictive model have an influence on the responses. This suggests that data-driven predictive models could have a higher prediction accuracy than traditional predictive models, especially when selecting a low number of explanatory variables or when using a set of training data in which limited variations of the processing parameters are considered. Figure 4: Main effect plots of the investigated processing parameters on the material removal rate (MRR) and tool wear rate (TWR).