## 3 Data Analysis Setup
### Evaluation for Deterministic Inputs (Regular Waves)
\[\mathrm{W_{a,b}}=\mathrm{w_{a,b}}-\mathrm{w_{a,b}^{\prime}},\mathrm{Q_{a,b}}= \mathrm{q_{a,b}}-\mathrm{q_{a,b}^{\prime}} \tag{8}\]  
Considering the same operation for scenario B with \(\mathrm{V_{a,b}}\), the vector of response simulation for period 1.0 s and \(\mathrm{t_{a,b}}\) and \(\mathrm{l_{a,b}}\), the projection vectors, the new vectors that will be compared with scenario B (experimental data) can be obtained from Equation (9). \(\mathrm{T_{a,b}}\) denotes the enhanced features on white planes and \(\mathrm{L_{a,b}}\) on black planes. \[\mathrm{T_{a,b}}=\mathrm{W_{a,b}}+\mathrm{t_{a,b}},\mathrm{L_{a,b}}=\mathrm{Q_ {a,b}}+\mathrm{l_{a,b}} \tag{9}\]  
As it had been surmised, the new feature spread in the resulted vectors must show a closer distribution to the experimental data of new period 1.0 s in comparison with the simulation. Figure 12 indicates the features spread for vectors on the black plane for wave period 1.0, scenario B. As can be seen visually, the cyan color data represent the new spread that is qualitatively closer to experimental data. Regardless, the result must be evaluated quantitatively, so the root mean square error (RMSE) value between features has been adopted to quantify the overall magnitude of error. In the black projection plane, the RMSE between new features and experimental data was found to be 0.0738, whereas the RMSE between RAO-based simulation and experimental data is 0.0872. However, cyan and blue points matched for the white plane, and the RMSE for both is 0.792. To conclude, the proposed feature space framework has improved the simulation data in a higher frequency range, even though further investigation is necessary to check the functionality of a broader spectral range. Figure 11: Features enhancement framework. While the proposed method has shown effectiveness for frequencies in a narrow range, it is essential to explore a broader spectrum. To achieve this, periods of 1.2 s, 2.6 s, 2.8 s, and 1.8 s have been selected for analysis. Beginning with a period of 1.2 s, which is close to the base period of 1.1 s, the residual features are combined with simulation data based on RAO with a period of 1.2 s as indicated in Figure 13. Figure 14 displays the time series of the heave responses for both experimental and simulated data. In Figure 13, the RMSE values for the black plane are determined to be 0.0415 for the new feature and 0.0450 for the RAO-based simulation. Meanwhile, the RMSE difference for the white plane is negligible, both at 0.0099. Upon observing the spread in both Figures 12 and 13, it becomes apparent that the enhancement in features is predominantly concentrated in the lower height range below 0.5 on the color bar. By calculating the RMSE within this range, the new feature exhibits a significant decrease from 0.0084 to 0.0034. This improvement is attributed to the scaling property of the wavelet, which offers fine temporal resolution for high-frequency ranges and superior spectral resolution for low-frequency ranges. Figure 12: 3D representation of features spread and comparison with experimental results (**a**) and the same for black plane (**b**). The deducted features obtained from period 1.1 s (t\({}_{a,b}\),l\({}_{a,b}\)) has been utilized to low-frequency wave with a period of 2.8 s. Figure 14a illustrates the time series of heave response for both experiment and simulation (simulation is subscripted RAO), while Figure 14b displays the feature distribution. In this scenario, the RMSE value for the white plane is as expected, but it is lower for RAO-based simulation. However, for the high-frequency range of wavelet coefficients, less than 0.5 on the color bar, the RMSE for the new feature is 0.0062 compared to 0.0096 for the simulation. This indicates that the uncertainty in the test, regardless of the exciting force, remains relatively identical, which could be utilized for a specific range between different frequencies. This characteristic arises from the wavelet's ability to extract nuanced temporal features in the high-frequency components of the data.