## 4 Target Structure and Pseudo Data Generation  
To validate the methodology proposed in this study, numerical simulations were conducted for the rectangular floating structure shown in Figure 6, and pseudo-measurement data were generated. The target structure has a length of 40 m, a width of 15 m, and a depth of 3.5 m. The main particulars and loading conditions for the target floating structure are shown in Table 1.  
Motion analysis was performed using the linear diffraction-radiation program, AQWA-13.0. The wave heading was set at 30\({}^{\circ}\) intervals, and the frequency was set at 0.05 rad/s intervals. The wave height was set to 1 m, referred to as the unit wave height. The analysis was conducted for all directions (360\({}^{\circ}\)), and the motion response for the unit wave height was measured.  
To represent the overall dynamic response of the structure, the motion was measured at the center of gravity (COG) of the structure. Measuring at the COG allows for a comprehensive analysis of the interaction between translational and rotational motions. Figure 7 shows the response amplitude operators (RAOs) for the target structure.  
Figure 5: Flow chart for the model application.  
Figure 6: Dimension of the target structure.  
The complex number representation addresses issues arising from the traditional degree-based expression. For instance, 10\({}^{\circ}\) and 350\({}^{\circ}\) correspond to physically close directions (a 20\({}^{\circ}\) difference), but when expressed in degrees, they appear to be far apart (340\({}^{\circ}\) difference). On the other hand, when represented as complex numbers, they appear as points that are close to each other on the complex plane, ensuring the continuity and accuracy of directional data. Equation (9) demonstrates the process of decoding wave direction data from its complex form back to degrees. Here, x and y represent the real and imaginary parts, respectively.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameters** & **Values** & **Units** \\ \hline Length & 40 & m \\ \hline Breadth & 15 & m \\ \hline Depth & 3.5 & m \\ \hline Draft & 1.75 & m \\ \hline Displacement & 1050 & M/T \\ \hline LCG & 20 & m \\ \hline TCG & 7.50 & m \\ \hline VCG & 1.75 & m \\ \hline K\({}_{\text{xx}}\) & 4.50 & m \\ \hline K\({}_{\text{yy}}\) & 11.69 & m \\ \hline K\({}_{\text{zz}}\) & 11.74 & m \\ \hline \end{tabular}
\end{table}
Table 1: Main parameters and loading conditions of the target structure.  
Figure 7: Response amplitude operators for the target structure. (**a**) RAOs, heave. (**b**) RAOs, roll. (**c**) RAOs, pitch.  
The complex transfer function obtained from the numerical simulations was combined with the assumed wave spectrum to generate the motion spectra. The wave spectrum was assumed to follow the modified Pierson-Moskowitz spectrum, as shown in Equation (10). For the purpose of validating the methodology, long-crested waves were assumed in this calculation. The wave parameters used in the model training are shown in Table 2. The wave height was selected from the range 1-7 m (seven values), and the wave period was selected from the range 3-9 s (seven values), resulting in a total of 49 different wave conditions for the dataset. Fixing the significant wave height at 1 m, the modified Pierson-Moskowitz wave spectra with periods ranging from 3 to 9 s are shown in Figure 8.  
\[\theta=\begin{cases}\arctan(\frac{y}{x})&\text{if $x>0$}\\ \arctan(\frac{y}{x})+90^{\circ}&\text{if $x<0$ and $y\geq 0$}\\ \arctan(\frac{y}{x})-90^{\circ}&\text{if $x<0$ and $y<0$}\\ 90^{\circ}&\text{if $x=0$ and $y>0$}\\ -90^{\circ}&\text{if $x=0$ and $y<0$}\end{cases} \tag{9}\]  
\[S(\omega)=\frac{1}{4\pi}{H_{\mathrm{s}}}^{2}(\frac{2\pi}{\overline{T}_{z}})^{ 4}\omega^{-5}e^{[-\frac{1}{\pi}(\frac{2\pi}{\overline{T}_{z}})^{4}\omega^{-4 }]} \tag{10}\]  
where \(H_{\mathrm{s}}\) is the significant wave height and \(\overline{T}_{z}\) is the mean wave period.