## 6 Presentation and Analysis of Results
### Power Spectral Density (PSD) Plots  
As discussed in previous sections, averaged Power Spectral Densities (PSDs) are useful for identifying significant frequencies over the entire duration of a longer signal, especially when few transient events occur. Figures 13-16 compare radar and accelerometer measurement results for both the Multi-Passenger Test and PRND Test, demonstrating the similarities between micro-Doppler radar data and accelerometer data. This comparison helps identify which frequencies are most important for further analysis. Figures 17 and 18, on the other hand, display radar data alone for each test case on each side.  
The normalization method used was Max Normalization (i.e., Peak Scaling), computed as  
\[\mathrm{PSD}_{\mathrm{norm}}(f)=\frac{|\mathrm{PSD}(f)|}{|\mathrm{max}( \mathrm{PSD}(f))|}. \tag{7}\]  
This method is used when one is only interested in relative peaks and not absolute power levels. This method highlights dominant frequency components and displays the PSD values on the range of 0 to 1, with the peak scaled to 1.  
Figure 13: PSD comparisons between micro-Doppler radar and accelerometer data for the GMC. Acadia from the front side for multi-passenger case for 1 to 4 persons. Accelerometer data were collected on the windshield and the hood.  
Figure 14: PSD comparisons between micro-Doppler radar and accelerometer data for the GMC. Acadia from the back side for multi-passenger case for 1 to 4 persons. Accelerometer data were collected on the windshield and the hood.  
Figure 15: PSD comparisons between micro-Doppler radar and accelerometer data for the GMC. Acadia from the front side for OPRND case. Accelerometer data were collected on the windshield and the hood.  
Figure 16: PSD comparisons between micro-Doppler radar and accelerometer data for the GMC. Acadia from the back side for OPRND case. Accelerometer data were collected on the windshield and the hood.  
Figure 17: PSD comparisons between the number of persons for multi-passenger case for the GMC. Acadia from all four sides.  
To facilitate a proper comparison of the micro-Doppler and accelerometer data, normalization was necessary due to the large difference in magnitudes between the two datasets. The analysis reveals several tonal components that are common to both sensor modalities, suggesting that certain regions of the vehicle are prone to vibration. For instance, data collected from the front hood shows a dominant return near \(\sim\)30 Hz in both Doppler and vibration measurements, likely due to the proximity of the hood to the engine, which is the primary source of vibration.  
For each PSD shown in Figures 13-18, the 1 min signal was divided into five 5 s segments, each corresponding to a specific transmission mode. The choice of 5 s intervals, rather than using the entire 10 s signal, was made to avoid transient effects at the beginning of the transmission. The goal was to focus on the frequency content within the transmission mode itself. Upon review, there are only slight amplitude changes at certain frequencies (such as between 30-60 Hz), but these differences may not be substantial enough to be used for classification purposes via machine learning.  
Figures 19 and 20 show spectral densities representing only the transient component of each gear shift. Unlike the previous plots, these data were not averaged to provide a more detailed frequency spectrum, as they focus on the short-lived transient events. The signals are trimmed to one-second durations to capture the full transient response from each gear shift. Upon inspection, additional frequencies appear for different gear shifts, including 50, 80, and 100 Hz. Additionally, new peaks emerge below 30 Hz. This suggests that analyzing these transient responses could be a useful method for distinguishing between different gear shifts based on their unique frequency characteristics.  
Figure 18: PSD comparisons between gear shifts for PRND case for the GMC Acadia from all four sides.