## 3 Design of Experiments
### Latin Hypercube Sampling  
The design space created by the three design variables selected is certainly large; hence, an efficient and reliable method should be adopted to ensure that the sample points for the training of the surrogate model cover the whole design region. In the present study, the Latin Hypercube Sampling technique [34] has been applied to distribute the sample points evenly over the entire design space. The fifteen unique sample points generated are shown in Figure 3, which presents a set of four sub-figures. In Figure 3a, a three-dimensional representation of the sample points is shown by black dots in a non-dimensionalized parametric design space. The bounds for each of the axis, associated with each geometric design variable, are as indicated in Table 1. Next, in Figure 3b, the sample points are projected over a two-dimensional space of \(C/C_{\text{ref}}\) versus \(D/C_{\text{ref}}\), where both design variables have been non-dimensionalized by \(C_{\text{ref}}\). Similarly, in Figures 3c and Figure 3d, the sample points have been plotted on the two-dimensional space with axes of \(C/C_{\text{ref}}\) versus \(G/C_{\text{ref}}\) and \(D/C_{\text{ref}}\) versus \(G/C_{\text{ref}}\), respectively. In order to obtain the data required for the training of the surrogate model, 2D URANS numerical simulations are performed for each of the fifteen sample points. With the purpose of validating the CFD results for the force coefficients and flutter derivatives with experimental data, prototypes of the twin-decks are built by means of additive manufacturing, including rapid 3D printing, and then experiments are performed in the wind tunnel. However, performing experiments on all of the fifteen points is expensive, considering the cost of the prototypes as well as the costs involved with the wind tunnel operation. Hence, from the fifteen selected samples, a subset of three samples is chosen to be tested in the wind tunnel. In Figure 3, these three chosen deck designs have been marked by squares. The selected three points are case g01, case g04 and case g07 and, as shown in the figures, these points are distributed evenly over the design space. Table 2 shows the main geometrical features of the 15 samples, along with the corresponding corner angles, while, in Figure 4, the cross-section geometry of the set of samples adopted for the definition of the surrogate model are plotted (due to the symmetry of the cross-section geometry, only the left boxes are provided, along with the symmetry axis for reference). Based on the ample range of geometries considered, Figure 4 clearly depicts \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Symbol** & **Ref. Value** & **Lower Bound** & **Upper Bound** \\ \hline Width & \(C\) & \(C_{\text{ref}}=200\) mm & \(-5\%\) C\({}_{\text{ref}}\) & \(+5\%\) C\({}_{\text{ref}}\) \\ Depth & \(D\) & \(D_{\text{ref}}=0.143\) C\({}_{\text{ref}}\) & \(-10\%\) D\({}_{\text{ref}}\) & \(+25\%\) D\({}_{\text{ref}}\) \\ Gap/depth & \(G/D\) & & 2.5 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Design space with lower and upper bounds. the amplitude of the design domain that is being addressed in this application case and, therefore, the potential for surrogate-based aerodynamic and aeroelastic design.