## 3 Experiments
### Experimental Results and Grey Relational Analysis  
The experimentally processed samples are shown in Figure 9. The L16 (\(4^{4}\)) orthogonal array layout and experimental results are shown in Table 6. The experimental results were evaluated based on three processing properties: SR, RA, and ACD. Based on the discrete test result data, it was difficult to determine any connection between the parameters and observed performance. In order to determine these relationships, this paper uses the grey correlation analysis method to analyze the discrete experimental results. The analysis method requires fewer data, has lower data requirements and a simple principle, and is easy to understand and master. In this analysis method, the key is to calculate the degree of relevance, and to study discrete data by the degree of grey correlation. The steps to apply the grey correlation analysis method are as follows. First, it is inconvenient to compare the experimental data because the different data differ in units. Therefore, the experimental results are normalized in two different ways. If the performance has the characteristic of \"the higher, the better\", as seen in the average current density in one pulse width, the values can be calculated by using Equation (3):  
\[x_{i}^{*}(k)=\frac{x_{i}(k)-\min x_{i}(k)}{\max x_{i}(k)-\min x_{i}(k)} \tag{3}\]  
where \(i\) = 1,2...n, \(k\) = 1,2...m; n is the number of the experimental results type, and m is the number of experiments; \(x_{i}(k)\) is the value of the \(i\)th experimental result in the \(k\)th experiment; \(x_{i}^{*}(k)\) is the normalized value obtained from the grey relational analysis; max \(x_{i}(k)\) is the maximum value of sequence \(x_{i}(k)\); and min \(x_{i}(k)\) is the is the minimum value of sequence \(x_{i}(k)\). If the performance has the characteristic of \"the lower, the better,\" as seen in the surface roughness and replication accuracy, the values can be calculated by using Equation (4):  
\[x_{i}^{*}(k)=\frac{\max x_{i}(k)-x_{i}(k)}{\max x_{i}(k)-\min x_{i}(k)} \tag{4}\]  
The normalized data are shown in Table 7.  
Figure 8: Current waveform. Figure 7: Contour curves on (**a**) cathode tool and (**b**) machined specimen. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Parameters**} & \multicolumn{4}{c}{**Observed**} \\ \multirow{2}{*}{**Experiment**} & \multicolumn{4}{c}{**Performance**} & \multicolumn{4}{c}{**Performance**} \\ \cline{2-7}  & **A** & **B** & **C** & **D** & \begin{tabular}{c} **SR** \\ **(\(\mu\)m)** \\ \end{tabular} & \
\begin{tabular}{c} **RA** \\ **(mm)** \\ \end{tabular} &
\begin{tabular}{c} **ACD** \\ **(A/cm\({}^{2}\))** \\ \end{tabular} \\ \hline
1 & 1 & 1 & 1 & 1 & 0.59 & 0.0233 & 117.8 \\
2 & 1 & 2 & 2 & 2 & 1.43 & 0.0304 & 72.8 \\
3 & 1 & 3 & 3 & 3 & 0.27 & 0.0312 & 58.5 \\
4 & 1 & 4 & 4 & 4 & 0.52 & 0.0405 & 51.6 \\
5 & 2 & 1 & 2 & 3 & 0.58 & 0.0653 & 58.9 \\
6 & 2 & 2 & 1 & 4 & 0.23 & 0.0187 & 136.2 \\
7 & 2 & 3 & 4 & 1 & 0.77 & 0.0729 & 48.6 \\
8 & 2 & 4 & 3 & 2 & 0.21 & 0.0306 & 70.7 \\
9 & 3 & 1 & 3 & 4 & 0.70 & 0.1722 & 43.7 \\
10 & 3 & 2 & 4 & 3 & 0.86 & 0.2582 & 40.1 \\
11 & 3 & 3 & 1 & 2 & 0.63 & 0.0208 & 153 \\
12 & 3 & 4 & 2 & 1 & 0.16 & 0.0226 & 109.1 \\
13 & 4 & 1 & 4 & 2 & 0.86 & 0.1882 & 35.9 \\
14 & 4 & 2 & 3 & 1 & 2.68 & 0.1852 & 54.9 \\
15 & 4 & 3 & 2 & 4 & 0.70 & 0.0401 & 91.4 \\
16 & 4 & 4 & 1 & 3 & 0.54 & 0.0375 & 82.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Orthogonal array layout and experimental results.