## 2 Data Generation
### Experimental Test Setup  
The experimental study was conducted at the Australian Maritime College's (AMC) Model Test Basin within the National Centre for Maritime Engineering & Hydrodynamics (NCMEH). A scaling factor of 1:36 was applied to the geometry, and the Qualisys Motion Capture System was utilized to measure the sphere's 6 Degrees of Freedom (DOFs). Sampling was performed at a rate of 200 Hz. Before the experiment, the Qualisys data underwent calibration. The primary objective was to gather high-quality data in considerable volume. A 1:6 porous beach was positioned at the aft end of the basin to mitigate wave reflections, as illustrated in Figure 3. A single taut mooring was employed to securely hold the model sphere from the basin floor to its bottom. Further details regarding the experimental model parameters are provided in Table 1. The model has been simplified to minimize the uncertainties and involve playmakers/parameters as much as possible. Figure 3: Model Test Basin layout. In order to assess the proposed theoretical data analysis framework, stochastic inputs of irregular waves by utilizing a distribution derived from the JONSWAP spectrum [24] were used. Subsequently, the test time frame was extended to 40 min to encompass a broad range of spectral constitutions sampled from the JONSWAP spectrum. Table 2 outlines the specifics of the input waves applied to the model with relevant parameters. More details about the test setup can be found in [25]. The heave decay test is performed by measuring the force applied to the single mooring with a load cell installed on the swivel, according to Figure 4, to find out the natural period of the sphere where the validation is presented in [7]. Figure 5 indicates the results of 6 DOF responses to waves for the sphere excited by unidirectional irregular waves in the form of time series. Note that data showed some discontinuity due to Qualisys glitches. However, they have been smoothened by move mean interpolation before further processing. Regardless, due to the very high sampling frequency, the contribution of those glitches was insignificant. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Value** & **Unit** \\ \hline Mooring Line Diameter & 5 & mm \\ Mooring Line Material & Ultra-high molecular weight polyethylene \\ Pretension on Mooring Line & 12.2 & kg \\ Sphere Diameter & 400 & mm \\ Sphere Mass & 4.305 & kg \\ Spring Stiffness & 20,568.75 & N/m \\ \hline \end{tabular}
\end{table} 
Table 1: Model and mooring line parameters. Figure 4: Swivel and load cell setup for heave decay test. The test specifications are outlined in Table 3, while the parametric spectrum formulation for JONSWAP, denoted as \(\mathrm{S}(\omega)\), is provided in Equation (2). Here, \(\alpha\) represents the spectral energy parameter, (\(\sigma\)1, \(\sigma\)2) signify the spectral width parameters, \(\gamma\) stands for the peak enhancement factor, and \(\mathrm{g}\) denotes the acceleration due to gravity. Wave parameters, such as the significant wave height \(\mathrm{H_{s}}\) and peak period \(\overline{\mathrm{T}}_{\mathrm{p}}\) in Equation (3), can subsequently be derived from statistical moments \(\mathrm{m_{n}}\) applied to \(\mathrm{S}(\omega)\) using Equation (4). To achieve comprehensive spectral coverage, the model underwent an extended run lasting 40 min. Given the symmetrical shape of the model, wave direction had no effect on the induced response. Therefore, the only variable parameter was the wave peak period chosen to minimize uncertainties.