## 4 Results and Discussion
The user should firstly categorize the data as input and target data and then they should create an ANN network that describes the network in Figure 11. In this study, the sixteen combinations in Table 4 were categorized as input data, and the target data are the S/N ratio in Table 5. By using a feed-forward backpropagation network trained with Levenberg-Marquardt (LM) and a logsig transfer function for the two hidden layers, the results of the network can be illustrated in Figure 13. By the nntool function, the network automatically splits the input and target data into 75% as training data, 12.5% as validation data, and 12.5% as testing data. After the network is trained with several repetitions, the predicted values of THD are found to be very close to the simulation results. This is proven by the regression analysis in Figure 14, in which the magnitude of the training, validation, test, and all data is close to 1. Table 6 shows the comparison of the S/N ratio that resulted from the Taguchi and ANN methods. All predicted values of the S/N ratio resulting from the network shown in Figure 13 are almost the same as the S/N ratio resulting from the Taguchi method except for experiments number 8 and number 9. The predicted S/N ratio in experiment number 8 and in experiment number 9 are 1.62 and \(-4.09\), respectively. There is a deviation of 0.4 in experiment number 8 and a deviation of 0.14 in experiment number 9 when compared to the Taguchi method. Based on Equation (10), the percent error of experiment number 8 is 32.87% and this is 3.54% for experiment number 9. If the mean error is calculated for all the experiments (16 experiments), a mean error of 2.28% is calculated, which is less than  
Figure 12: S/N ratio response curve of THD. The performances of the proposed generator measured by the Ansys Maxwell software are shown below. * Distribution of magnetic flux density  
The distribution of the magnetic flux density is illustrated in Figure 16. Figure 16a shows its distribution in the symmetrical position of the proposed generator. To clearly see its distribution from Figure 16a, the stator cores located on the lower and upper sides are separated as shown in Figure 16b,c. To avoid the phenomena of demagnetizing the permanent magnet and to avoid increasing loss and temperature in the stator core, the maximum flux density in the stator core is firstly checked so that its magnitude does not exceed the permissible limit. In the stator teeth of Figure 16b,c, the maximum flux densities are 1.55 T and 1.6 T, respectively. The flux densities of 1.27 T and 1.28 T are the maximum flux density in the stator yoke of Figure 16b,c, respectively. If compared to reference [11], the maximum flux density on both the stator cores meets the requirement stated in reference [11]. This signifies that the phenomena of demagnetizing the permanent magnet can be avoided and the increasing loss and temperature in the stator core can be minimized in the proposed generator. * Voltage waveform  
The voltage waveform of the original generator and the proposed generator are shown in Figure 17a,b, respectively. Their measured harmonic orders are represented in Figure 17c. If compared to the original generator, the voltage waveform of the proposed generator is almost a pure sinusoidal waveform. In terms of the harmonic order from Figure 17c, as both generators are connected in a star connection, the 3 rd harmonic is zero in the original generator and the 5 th harmonic is zero in the proposed generator. The original generator generates the 5 th harmonic of 2.391 volts and the proposed generator generates the 3 rd harmonic of 0.2267 volts. The 7 th, 9 th, 11 th, and 13 th harmonic orders of the proposed generator all decrease with an average percentage of 71.08% when compared to the original generator. The calculated THD obtained from Equation (6) of the original generator is 8.53% and this is 0.65% for the proposed generator. From those results, a good improvement is achieved in term of THD for the proposed generator.