## 4 Results
### Experimental Results  
The same NN architecture was validated using experimental data. For each operating condition, five measurements were taken and subsequently averaged to minimize noise. The input to the NN consisted of the real and imaginary parts of the input impedance, \(Re(Z_{in})\) and \(Im(Z_{in})\). The output remained the inter-coil distance, again represented by 57 distinct distance values. The same NN structure was also employed to predict the capacitance values (\(C_{1}\), \(C_{2}\), and \(C_{3}\)) required for optimal AIMN performance. Optimal capacitance values were determined for each configuration and distance through simulation and subsequently validated experimentally, confirming matched performance in the experimental setup. These validated capacitance values served as the NN's target output, using the same impedance inputs \(Re(Z_{in})\) and \(Im(Z_{in})\). This process was repeated for all three experimentally measured configurations, each representing a different misalignment scenario. For the prediction of distance from \(Re(Z_{in})\) and \(Im(Z_{in})\), the MSE on the test dataset is 1.85, 0.03, and 1.49 for configurations 1, 2, and 3, respectively. As shown in Figure 13, during the test of the NN, the prediction error is very low. Additionally, the prediction of the capacitance value is very accurate, with MSE obtained on the test set, for cases 1, 2 and 3, respectively, as 0.31, 1.65, and 0.21. The low prediction error is reported in Figure 14 for \(C_{1}\), in Figure 15 for \(C_{2}\) and in Figure 16 for \(C_{3}\). The results obtained demonstrate high accuracy across all configurations for both distance and capacitance prediction. Building upon these initial findings, a further refinement was implemented using a two-stage NN approach. The first NN predicts the inter-coil distance, while the second NN leverages this predicted distance, along with impedance data, to determine the optimal capacitance values for impedance matching. This combined architecture, employing two smaller NNs, yielded even more accurate results compared with predicting capacitance directly from impedance alone. Specifically, the MSE was reduced to 0.18, demonstrating the benefit of incorporating distance information into the capacitance prediction process. Furthermore, this two-stage approach provides the additional advantage of explicitly predicting the inter-coil distance, a crucial parameter for adaptive WPT systems that adjust coil separation to maximize power transfer efficiency. The predicted results are visualized in Figure 17 for \(C_{1}\), in Figure 18 for \(C_{2}\), and in Figure 19 for \(C_{3}\). Figure 13: Predicted and original values of the distance from the impedance parameters. This test is performed on configuration 2, with \(\Delta x\) = 20 mm and \(\Delta y\) = 20 mm. The NN reaches an MSE of 0.03. These highly accurate results hold significant promise for the practical application of NNs in WPT systems. Compared with the NN architecture presented in [40], which employed five hidden layers with 15 neurons each, the compact NN developed in this study, with a single hidden layer of only 10 neurons, offers substantial advantages. Its smaller size translates to faster processing, reduced computational cost, and energy consumption, and importantly, facilitates straightforward implementation on a microcontroller. Furthermore, it is noteworthy that for capacitance value prediction, the smaller NN was trained using the optimized capacitance values derived from the larger simulation-trained NN described in [40]. This suggests that the smaller NN can be viewed as a result of data distillation from the original, more complex NN, effectively capturing the essential information for accurate capacitance prediction more efficiently. Figure 14: Prediction of the capacitance value \(C_{1}\) from the impedance parameters. Test performed on case 1, with \(\Delta x=0\) mm and \(\Delta y=0\) mm. The MSE on the test set is 0.31. Figure 15: Prediction of the capacitance value \(C_{2}\) from the impedance parameters.