## 5 Results and Discussion
### Real-Time Wear Prediction and Hole Depth Control  
Figure 8a,b show the cross sections of some micro-EDM holes, which were drilled by applying the control strategy presented in Section 4 but choosing different predictive models. In both images it can be seen that the actual hole depth (\(H_{a}\)) is closer to the target hole depth (\(H_{t}\)) when selecting the PP+DD model or DD model for predicting the tool wear. The depth error (\(\Delta H\)) is below 10 \(\upmu\)m when \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Material Removal Prediction**} & \multicolumn{3}{c}{**Tool Wear Prediction**} \\ \hline  & **PP** & **DD** & **PP + DD** & **PP** & **DD** & **PP + DD** \\ \hline
**NRMSE** & 0.4275 & 0.1289 & 0.1564 & 0.5235 & 0.0921 & 0.0551 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Normalised mean square error (NRMSE) for the regression models. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Run** & \multicolumn{2}{c}{**Material Removal Prediction**} & \multicolumn{3}{c}{**Tool Wear Prediction**} \\ \hline
**\#** & **PP** & **DD** & **PP + DD** & **PP** & **DD** & **PP + DD** \\ \hline
1 & 0.0518 & 0.0013 & 0.0022 & 0.0679 & 0.0016 & 0.0001 \\
2 & 0.0697 & 0.0037 & 0.0081 & 0.1435 & 0.0086 & 0.0021 \\
3 & 0.0411 & 0.0062 & 0.0131 & 0.1080 & 0.0049 & 0.0009 \\
4 & 0.0070 & 0.0067 & 0.0 the DD + PP model is selected, while it is as high as 62 \(\upmu\)m when the PP model is applied to drill a hole of target depth equal to 2.5 mm. This indicates that tool wear prediction based on data-driven approaches can be considerably more accurate than traditional approaches based on the sole processing parameters. However, it is noteworthy to mention that in this study real-time tool wear prediction is tested in drilling micro holes having an aspect ratio in the range 5-7. This is similar to the aspect ratio of the micro holes that were drilled for generating the training data, which was equal to 5.7. Future investigations will focus on proving the advantages of the DD model in drilling holes having a significantly higher aspect ratio than the ones drilled for generating the training data. In this case, a more advanced strategy for calculating the average values of the monitored quantities (\(F_{p}\), \(V_{f}\), and \(U\)) might also be required. In order to further study the capability of the different predictive models, the micro-EDM drilling experiments were repeated 7 times for each predictive model, for a total of 21 drilled holes. The depth errors for each predictive model are shown in Figure 9. The average depth error when applying the PP + DD model is the lowest. It is roughly 50% lower than the average depth error for the PP model. The deviation between the results is also significantly lower when the PP + DD model or DD model are applied instead of the PP model. The results show that implementing PP + DD or DD model into the control strategy has a clear improvement both on accuracy and precision of the drilling process if compared to the PP model. This demonstrates the significance of data-driven approaches for robust in-process monitoring and controlling strategy in micro-EDM drilling. Figure 8: Cross sections of micro-EDMed blind holes. In both images, the three holes are drilled by applying the in-process wear prediction strategy and selecting the following MLR models (from left to right): PP + DD, DD, and PP. The target hole depths are **(a)** 1500 \(\upmu\)m and **(b)** 2500 \(\upmu\)m. The images are taken by means of a ZEISS® SteREO Discovery V20 microscope (Carl Zeiss Microscopy GmbH, Germany). Figure 9: Depth error (\(\Delta H\)) for the control strategy when applying different predictive models. The average depth error considering 7 holes is shown. The error bars are the standard deviations. In this work, the average values of the amount of normal discharge pulses per unit time, feed rate and gap voltage are considered.