## 4 Data Analysis Framework Application
### Irregular Waves Data  
So far, the approach has utilized deterministic inputs for improved control and monitoring. However, field wave data are stochastic, demanding evaluation of the approach with stochastic wave inputs. To achieve this, the sphere model underwent testing in the model test basin (MTB). During this experiment, three instruments were utilized for data collection: resistive wave probes, a FUTK QLA150 100 lb load cell, and a Qualisys motion capture system, which measured the free surface elevations, mooring loads, and motions of the sphere, respectively. The test was conducted to capture a broad range of spectral data sampled from the JONSWAP spectrum. The details of the test are reported in Table 3, and the parametric spectrum formulation for JONSWAP, S(\(\omega\)), is given in Equation (10), where \(\alpha\) denotes spectral energy parameter, \((\sigma_{1},\sigma_{2})\) are spectral width parameters, \(\gamma\) is peak enhancement factor, and \(g\) is the gravity acceleration. The wave parameters, such as significant wave height \(H_{s}\) and peak period \(T_{p}\) in Equations (11), later can be derived from statistical moment \(m_{n}\), applied on S(\(\omega\)) by Equation (12). \[\text{S}(\omega)=\frac{\alpha g^{2}}{16\pi^{4}}\omega^{-5}exp\Bigg{[}-\frac{5} {4}\bigg{(}\frac{\omega}{\omega_{p}}\bigg{)}^{-4}\Bigg{]}\gamma^{b} \tag{10}\]  
\[b=exp\Bigg{[}-\frac{1}{2\sigma^{2}}\bigg{(}\frac{\omega}{\omega_{m}}-1\bigg{)} ^{2}\Bigg{]},\sigma= \begin{cases}\sigma_{1}&for\ \omega\leq\omega_{p}\\ \sigma_{2}&for\ \omega>\omega_{p}\end{cases} \Bigg{\}}\]  
\[H_{s}=4\sqrt{m_{0}},\ T_{p}=2\ \pi\ \sqrt{\frac{m_{0}}{m_{2}}} \tag{11}\]  
\[m_{n}=\int_{0}^{\infty}\omega^{n}S(\omega)\ d\omega \tag{12}\]  
For regular waves, a single response was assessed, while for irregular waves, the final convolution vector was obtained by linearly adding four DOFs. This process involves surge and sway as translational motions forming vector \(\xi\), and roll and yaw as singular responses shaping vector \(\psi\). The method of vector addition and scalogram combination follows [24]. Four DOFs were used for consistency with ongoing research on advancing ships, using state-of-the-art simulator data from the MARITIME SIMULATION CENTRE of AMC. The size of the data segment corresponding to a window size vector was fixed at 40 s. Additionally, to further investigate the effect of resolution, a max-pooling filter was applied. This filter reduced the size of images from [256; 256; 1] to [32; 32; 1] as depicted in Figure 19. This operation served as a down-sampling technique, where the filter was applied to different sets of features in vector K instead of raw time series. As the filter slides over the original pixels, it selects the maximum value to form a new feature map. Considering input feature map as X, the image, with a size of \(\big{(}Width_{input},Height_{input}\big{)}\), and \(f\) as max-pooling window size with stride \(s\), the output feature map \(\varphi\) is characterized by Equation (13) [4]. Here \(i,j\) iterate over the spatial dimension. \[MaxPooling(\ X)_{i,j}=max_{a,b=0}^{f-1}X_{(i\times s+a),(j\times s+n)} \tag{13}\]  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Wave Test Parameters**} \\ \hline
**Scenario** & **Significant Wave Height (m), \(H_{s}\)** & **Peak Period, \(T_{p}\)** & **Run Time (s)** & \(\gamma\) & \(\sigma\)**1** & \(\sigma\)**2** & \(\alpha\) \\ \hline
1 & 0.05 & 1.4 & 2400 & 1 & 0.07 & 0.09 & 0.0081 \\
2 & 0.05 & 1.6 & 2400 & 1 & 0.07 & 0.09 & 0.0081 \\
3 & 0.05 & 1.8 & 2400 & 1 & 0.07 & 0.09 & 0.0081 \\ \hline \hline \endFigure 20 shows the feature spread from scenario 1's experiment to scenario 2's simulation over 40 min. Batch operation on the data limits detailed visualization, so RMSE quantifies the feature spread for various data generation processes. RMSE values are reported for each plane and the cumulative features on both projection planes, considering the outcomes in regular waves feature spread.