## 2 Materials and Methods
### Data Collection  
In order to obtain a heterogeneous dataset for training the regression models, the processing parameters applied in the micro-EDM drilling experiments are varied following a two-level full factorial Design of Experiments (DoE). Five processing parameters are varied, for a total of 32 experimental runs: pulse-on time (\(T_{\text{on}}\)), open voltage (\(U_{\text{o}}\)), charging frequency of the pulse generator (\(F\)), gain factor of the servo control loop (\(K\)) and reference gap voltage (\(U_{e}\)). The 32 experimental runs are performed in random order. The number of experimental runs is limited to only 32 experiments since the goal of this study is to compare the performance of different predictive models rather than showing the highest prediction accuracy, which can be achieved by each predictive model. It is believed that the accuracy of the predictive models would improve by increasing the number of experimental runs and therefore the amount of training data. The five processing parameters in the DoE are selected so as to include variations to some of the main factors influencing the material removal process in micro-EDM drilling, namely the energy input per discharge (\(T_{\text{on}}\), \(U_{\text{o}}\)), the cycle frequency of the power supply system (\(F\)) and the settings of the servo feed control system (\(K\), \(U_{\text{e}}\)). The levels of each parameter are set so as to cover a wide process window. The choice is carried out based on the recommendations from the machine vendor and previously-reported research work, which is carried out using a similar combination of tool and workpiece materials [22; 23; 24]. Table 1 is a summary of the factors and levels of the DoE. In all experimental runs, a constant tool rotation speed equal to 750 rpm is set and negative polarity is applied to the tool electrode. The energy index (\(E\)) and current index (\(I\)) are kept constant and equal to 301 and 70 respectively. According to the machine vendor, the energy index is the parameter determining the shape of the discharge pulses. The chosen energy index provides triangular-shaped pulses. When this energy index is selected, the current index can be used as a parameter to regulate the pulse peak current as shown in one of our previous studies [21]. Both the energy index and current index can vary the energy input per discharge pulse. In this study, the values of \(E\) and \(I\) are kept constant since the effects of variations to the discharge energy are already taken into account into the DoE by varying other processing parameters (\(T_{\text{on}}\), \(U_{\text{o}}\)). A second dataset is recorded for evaluating the prediction accuracy of the regression models at experimental conditions which are different from the ones applied when recording the training data. In this case, 10 experimental runs are performed by randomly varying the processing parameters within the process window defined by the DoE. In other words, this means that the five processing parameters that are included in the DoE are set randomly to a value between the minimum (Level - 1) and maximum (Level + 1) levels applied in the DoE. The processing parameters applied in each of these 10 experimental runs are listed in Table 2. All other processing parameters are kept constant and set as mentioned above. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Factor** & **Processing Parameter** & **Symbol** & **Unit** & **Level - 1** & **Level + 1** \\ \hline A & Pulse-on time & \(T_{\text{on}}\) & \(\mu\)s & 3 & 7 \\ B & Open voltage & \(U_{\text{o}}\) & V & 80 & 160 \\ C & Charging frequency & \(F\) & kHz & 40 & 100 \\ D & Gain factor & \(K\) & – & 20 & 80 \\ E & Reference voltage & \(U_{\text{e}}\) & V & 30 & 70 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Training dataset: Factors and levels of the DoE.