## 5 Results and Discussion  
The acquired signals along the three accelerometer axes, the combined signal, the angular speed, and the propeller torque of a test in the ICE operating mode of the HEPS are shown in Figure 5.  
The test in Figure 5 was performed at a constant angular speed and torque (Figure 5a,b), and the result signal (Figure 5f) was always positive. To completely describe the system dynamics, 22 time-features were calculated from the combined signals to describe the HEPS' dynamic behavior in the three configurations when the equilibrium point was inside the \(\pm\)5% limits of the propeller torque curve. The raw indexes were very noisy and overlapped in the three HEPS operating modes if the EM torque tended to zero: using a lowpass FIR filter, it was possible to improve the ICE, HYBM and HYBG differences. As an example, Figure 6 shows the angular speed, the total torque, and the EM torque in the three HEPS operating modes when the EM torque was around \(\pm\)5 Nm, while Figure 7 shows the raw and filtered trends of three indexes (RMS, kurtosis, and crest factor) to clarify the filter importance. Figure 5: ICE mode test: (**a**) angular speed, (**b**) total torque, (**c**) x-axis vibrational signal, (**d**) y-axis vibrational signal, (**e**) z-axis vibrational signal, and (**f**) combined signal. Figure 6: Parameter test trends: (**a**) angular speed, (**b**) total torque, and (**c**) EM torque. Figure 6 shows the coincidence between the three HEPS operating point configurations and how the EM torque contribution was negligible compared with that of the ICE. For this reason, the raw indices in Figure 7 tend to overlap, but using the FIR filter, the differentiation between the three different configurations could be improved. The 22 filtered time-features were divided into 50% training, 20% validation, and 30% test datasets using the Holdout method. The three datasets were standardized, and PCA analysis was performed on the training dataset. The PCA analysis results are shown in Figure 8.  
Analyzing the trend of the total variance explained as a function of 22 PCA cumulative number components (as the 22 filtered time-features) in Figure 8a, the first three principal directions were found to explain 96.10% of the original data variance: the first direction explains 69.53%, the second 24.42%, and the third 2.15% (Figure 8b). Since the first three PCs  
Figure 8: PCA analysis results: (**a**) total explained variance and (**b**) single PC component explained variance. Figure 7: Raw and filtered index trends: (**a**) RMS, (**b**) kurtosis, (**c**) crest factor. managed to explain over 95% of the index's total variance, only the first three components were used as input data to train, validate and test the model. The PCA transformation matrix calculated on the training dataset was also used to transform the validation and test datasets. The FNN model was trained and optimized using Bayesian Optimization to predict the HEPS' operating mode. The model was only trained with the torque/speed equilibrium point inside the \(\pm\)5% limit tests. The only used FNN input data were the three components obtained from the PCA analysis. The reduced number of inputs to the model reduced the calculation time of all phases (training, validation, and testing), as well as the optimization time. Figure 9 shows the last training loss curve and the Bayesian Optimization loss trend, and Table 1 reports the optimized FNN hyperparameters. The model was tested using the remaining dataset, which was never used during the training phase. In Figure 10, the confusion matrix of the test phase is shown. The confusion matrix showed that the model had a total accuracy of 97.44%, with the highest classification error of 4.4% for the ICE class. The model was not tested with the same number of the three classes, so the total accuracy was not a simple mean. The signals acquired with the torque/speed equilibrium points outside the \(\pm\)5% limits were processed like the training, validation, and testing datasets.