## 3 Data Analysis Setup
### Evaluation for Deterministic Inputs (Regular Waves)
Figure 13: 3D representation of features spread and comparison with experimental results (**a**) and the same for black plane (**b**) for wave period 1.2 s.  
Figure 7.0 (**a**). comparison of experimental and simulation heave response to regular wave, period 2.8 s. (**b**) 3D representation of features spread and comparison with experimental results (**top**) and the same for black plane (**bottom**). To further analyze the behavior of features within a close spectral range, the obtained features from a period of 2.6 s (as new scenario A) were utilized for simulations with a period of 2.8 s (as scenario B). This involved subtracting the features obtained from the experiment for the heave response of 2.6 s from the simulation features and adding the residuals (\(\mathrm{t_{a,b},l_{a,b}}\)) to the simulation features of a period of 2.8 s (\(\mathrm{T_{a,b},L_{a,b}}\)). As per Figure 15, the features' spread shows a significant improvement compared to Figure 14b. Quantitatively, the RMSE for the black plane is 0.0611 for simulation and 0.0287 for the new features. In conclusion, it can be inferred that the technique performs effectively within a narrow frequency range and is functional for high-frequency components of distant frequencies. At this juncture, the features obtained from high and low frequencies are compared with a frequency range close to the natural frequency of the heave response in the sphere, which is found to be a period of 1.8 s. Thus, the features obtained from a period of 2.6 s are tested. Figure 16a displays the results of applying the residuals from the period of 2.6 s to 1.8 s. Visually, it is apparent that apart from regions below 0.5 in the color bar, the rest of the data spread deviates from the experiment. However, the RMSE for the region below 0.5 has improved by 0.0493 and 0.0404 for simulation and new features, even though the overall RMSE is 0.0479 and 0.0598 for simulation and new features, respectively. To further explore this observation, another higher frequency wave with a period of 1.1 s is utilized. As depicted in Figure 16b, despite improvements in spread, the new feature slightly deviates in the low-frequency region with a higher intensity of black pixels. For the region below 0.5, the RMSE of the new feature is 0.0404 versus 0.0447 for simulation. These findings necessitate a more direct examination of the wavelet coefficients in the form of black and white pixel scalogram images as presented in Figure 7.1  
Figure 7.2 3D representation of features spread and comparison with experimental results between period 2.6 and 2.8. Based on Figure 17a, the upper half of the image displays arbitrary spectral components represented as jagged white lines, which are absent in the corresponding simulated data image with a period of 1.1 s. Similarly, this is also evident in Figure 17b for a period of 1.8 s. Upon closer inspection of the lower half, the experimental and simulation data appear nearly identical in low-frequency contribution. It was anticipated that close frequencies would exhibit similar shapes in the lower region, given that the RMSE values remained consistent. To this end, Figure 18 presents images of experimental and simulation data for a period of 1.2 s. Notably, aside from the upper half, both exhibit remarkable similarity. Moreover, the images from periods 1.1 s (Figure 17a) and 1.2 s appear similar in the lower half as well. These observations underscore the efficiency of the new feature spread mechanism for close frequency ranges. For instance, using one scenario in a test can replicate several close frequencies with minimal computational costs. However, when dealing with distant frequencies, the high spectral content can be effectively extracted  
Figure 7.3 (a) 3D representation of spread and comparison with experimental results between period 1.8 s and 2.6 s, and 15 (b) 3D representation of spread and comparison with experimental results between period 1.8 s and 1.1 s.  
from one experimental scenario and added to the simulation data.