## 8 Results and Discussion  
The performance of the three-layer cascade-forward backpropagation ANN for smart tool wear curve reconstruction was evaluated using the root mean square error (RMSE):  
\[RMSE = \sqrt{\sum_{i=1}^{n}\frac{\left(\hat{y}_{i}-y_{i}\right)^{2}}{n}}\]  
where \(\hat{y}_{i}\) are the ANN predicted tool flank wear values and \(y_{i}\) are the measured tool flank wear values. The ANN results obtained reveal that the 5-5-1 ANN configuration provided the lowest RMSE values for smart tool wear curve reconstruction for almost all drilling test conditions in comparison with the 5-10-1 and 5-15-1 ANN configurations. In Table 2, the RMSE values for the 5-5-1 ANN configuration are reported for each drilling condition and for the time domain \(\text{FPV}_{\text{time}}\), the frequency domain \(\text{FPV}_{\text{freq}}\), the fractal analysis \(\text{FPV}_{\text{frac}}\). Moreover, the RMSE values obtained from a fourth FPV, called combined feature pattern vector \(\text{FPV}_{\text{comb}}\), which includes both time domain and fractal analysis features is a sensor fusion approach, are also reported in the last column of the table. From Table 2 and Figure 17a, it can be noted that the best overall ANN performance was obtained for drilling condition 9000 rpm-0.15 mm/rev with the lowest RMSE equal to 0.00037, whereas the worst overall RMSE, equal to 0.00514, was obtained for drilling condition 6000 rpm-0.15 mm/rev. Both the lowest and the highest RMSE values were obtained when using the time domain feature pattern vector, \(\text{FPV}_{\text{time}}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**RMSE for ANN Configuration 5-5-1**} \\ \hline
**Drilling Condition** & \multicolumn{3}{c}{**ANN Performance in Terms of RMSE for Different FPV**} \\ \hline (rotational speed-feed rate) & \(\text{FPV}_{\text{time}}\) & \(\text{FPV}_{\text{freq}}\) & \(\text{FPV}_{\text{frac}}\) & \(\text{FPV}_{\text{comb}}\) \\
2700 rpm–0.11 mm/rev & 0.00109 & - & 0.00045 & 0.00032 \\
2700 rpm–0.15 mm/rev & 0.00407 & 0.00221 & 0.00347 & 0.00321 \\
6000 rpm–0.11 mm/rev & 0.00249 & 0.00195 & 0.00046 & 0.00044 \\
6000 rpm–0.15 mm/rev & 0.00514 & 0.00134 & 0.00076 & 0.00241 \\
6000 rpm–0.20 mm/rev & 0.00061 & 0.00099 & 0.00125 & 0.00035 \\
9000 rpm–0.11 mm/rev & 0.00328 & - & 0.00154 & 0.00083 \\
9000 rpm–0.15 mm/rev & 0.00037 & 0.00121 & 0.00051 & 0.00034 \\
**Average RMSE** & 0.00244 & 0.00154 & 0.00120 & 0.00113 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance of the 5-5-1 artificial neural network (ANN) configuration expressed as root mean square error (RMSE) in tool wear curve reconstruction for each drilling condition and each constructed feature pattern vector (FPV). As regards the frequency domain feature pattern vector, \(\text{FPV}_{\text{freq}}\), the RMSE values ranged between 0.00099 (lowest RMSE) and 0.00221 (highest RMSE). In the case of the fractal analysis feature pattern vector, \(\text{FPV}_{\text{frac}}\), the lowest RMSE was equal to 0.00045 whereas the highest RMSE was 0.00347. The examination of the average RMSE values, evaluated by considering the RMSE values obtained with the same given FPV applied to all the drilling conditions (Table 2 and Figure 17b), indicates that the fractal analysis \(\text{FPV}_{\text{frac}}\) provided the best ANN performance in the classification of tool wear level, while the time domain \(\text{FPV}_{\text{time}}\) came second and the frequency domain \(\text{FPV}_{\text{freq}}\) came third in this ranking. Thus, to verify the robustness of smart tool wear curve reconstruction by making use of signal features obtained from diverse feature extraction methodologies, the time domain and the fractal analysis features were considered in a combined manner with the scope to construct an additional sensor fusion feature pattern vector, \(\text{FPV}_{\text{comb}}\).