## 3 Taguchi and Artificial Neural Network (ANN) Methods  
The Taguchi method was formulated by Sir [PERSON] in the 1920s [16]. The method works by using the orthogonal array to analyze the information from the control factors and the levels to gain useful static information in the fewest experiments [17]. Knowing the number of the control factors and the levels, the correct orthogonal array can be chosen from the references. The generator with optimal rotor combination obtained from the process in Section 2.2, shown in Figure 9, is optimized again by the Taguchi method to acquire the lowest THD. As the lower and upper parts of the region marked by red are the same, the generator can be split in a symmetrical position to simplify its geometry, as shown in Figure 10.  
From Figure 10, the areas chosen as the control factors to improve the THD are marked with A, B, and C. The area marked with A indicates the air gap length, the area marked with B indicates the offset angle of the stator teeth on the upper side to the stator teeth on the lower side, and the area marked with C indicates the stator yoke height. The level of each control factor is tabulated in Table 3. The air gap lengths of 1 mm, 1.5 mm, 2 mm, and 2.5 mm are the levels of control factor (A). The offset angles of 0 degree, 1.5 degrees, 3 degrees, and 4.5 degrees in mechanical degree are the levels of control factor (B). The stator yoke heights of 19 mm, 17 mm, 15 mm, and 13 mm are the levels of control factor C. As there are four levels for each control factor, the \(\mathbf{L_{16}(4^{3})}\) sequence of the Taguchi orthogonal array is selected and the proper combinations of each level of the control factors are tabulated in Table 4. In the optimization process, the mean and variance of the experimental result obtained from Table 4, in this case, are combined into a single performance measure called the signal to noise (S/N) ratio. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{\(\mathbf{\alpha}_{i}\)} & \multirow{2}{*}{\(\mathbf{s_{o}}\)} & \multicolumn{6}{c}{**Harmonic Order**} & \multirow{2}{*}{**THD (\%)**} \\ \cline{3-3} \cline{5-8}  & & **1** & **3** & **7** & **9** & **11** & **13** \\ \hline \multirow{4}{*}{0.85} & 4.5 & 40.2488 & 5.2655 & 0.4533 & 0.371 & 0.137 & 0.1078 & 13.1702 \\  & 7 & 39.63 & 5.6814 & 0.3924 & 0.4114 & 0.0601 & 0.0779 & 14.40985 \\  & 9.5 & 38.5243 & 6.0454 & 0.2876 & 0.418 & 0.0268 & 0.0397 & 15.7481 \\  & 12 & 37.1757 & 6.2828 & 0.1638 & 0.3741 &Figure 10: Symmetrical position of the generator. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**No**} & \multicolumn{3}{c}{**Control Factor**} \\ \cline{2-4}  & **A** & **B** & **C** \\ \hline
1 & 1 (1) & 0 (1) & 19 (1) \\
2 & 1 (1) & 1.5 (2) & 17 (2) \\
3 & 1 (1) & 3 (3) & 15 (3) \\
4 & 1 (1) & 4.5 (4) & 13 (4) \\
5 & 1.5 (2) & 0 (1) & 17 (2) \\
6 & 1.5 (2) & 1.5 (2) & 19 (1) \\
7 & 1.5 (2) & 3 (3) & 13 (4) \\
8 & 1.5 (2) & 4.5 (4) & 15 (3) \\
9 & 2 (3) & 0 (1) & 15 (3) \\
10 & 2 (3) & 1.5 (2) & 13 (4) \\
11 & 2 (3) & 3 (3) & 19 (1) \\
12 & 2 (3) & 4.5 (4) & 17 (2) \\
13 & 2.5 (4) & 0 (1) & 13 (4) \\
14 & 2.5 (4) & 1.5 (2) & 15 (3) \\
15 & 2.5 (4) & 3 (3) & 17 (2) \\
16 & 2.5 (4) & 4.5 (4) & 19 (1) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Taguchi \(\mathbf{L_{16}}\) sequence. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Control Factor**} & \multicolumn{5}{c}{**Levels of Control Factor**} \\ \cline{2-5}  & & **1** & **2** & **3** & **4** \\ \hline Air gap length (mm) & A & 1 & 1.5 & 2 & 2.5 \\ Offset angle of stator tooth (mechanical degree) & B & 0 & 1.5 & 3 & 4.5 \\ Stator yoke height (mm) & C & 19 & 17 & 15 & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Control factors and levels of FP-AFPMG. Figure 9: The generator to be optimized by Taguchi method. In obtaining the optimal quality of the desired parameter, there are three types of the signal to noise ratio (S/N) function that can be applied to solve the issue discussed in this study.