## 4 Application
### Creating a Dataset and Performing Preparation  
3 DGAN model training requires datasets that are quite different and contain a large amount of data. This study used a synthetic dataset created by the authors. The main reason for using synthetic data is the insufficiency of real 3D model data for structural components. A parametric model of the structural component was assembled to create the synthetic dataset. In this model, parameter value ranges were determined by considering geometric boundary conditions. Figure 2 presents a parametric model of the structural components, showing the design parameters and boundary conditions. While the features shown in red on the part have fixed values, the features in blue can change parametrically. The determined parameters and boundary conditions are shown in Table 1. With the nine parameters used here, over 60 billion (\(8\times 11\times 16\times 8\times 9\times 16\times 51\times 76\times 11\)) design variants can be created. However, these concepts are insufficient for deep learning training  
Figure 2: Position of the considered structural component in the helicopter rotor assembly and parametric model. regarding data diversity. Although each of these designs is different from the other, their general geometries are quite similar to each other. Therefore, Voronoi diagrams were included in the parametric design process to increase data diversity. Applying Voronoi diagrams to the areas determined on the component created 4635 unique design variants. This dataset consists of models with different wall thicknesses, element sizes, Voronoi cell sizes, and Voronoi cell numbers. These variables help the dataset to mimic real data diversity. The parametric design process and some of the data obtained are shown in Figure 3. The dataset creation process was described in detail in a previous study prepared by the authors. The general process is summarized here. First of all, the area on which the Voronoi diagram would be applied was determined. In the second stage, Voronoi points were randomly placed in this predefined area. The distribution and number of points determine the size and shape of cells, creating diversity. In the third stage, Voronoi cells were created from point positions. In the fourth stage, the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter Name** & **Min. Value (mm)** & **Max. Value (mm)** & **Range of Change** \\ \hline Parameter A & 8 & 15 & 8 \\ Parameter B & 5 & 15 & 11 \\ Parameter C & 10 & 25 & 16 \\ Parameter D & 3 & 10 & 8 \\ Parameter E & 3 & 11 & 9 \\ Parameter F & 5 & 20 & 16 \\ Parameter G & 0 & 50 & 51 \\ Parameter H & 15 & 90 & 76 \\ Parameter I & 0 & 10 & 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter value ranges. Figure 3: Synthetic dataset creation process and samples from the created dataset. basic geometry for the hollow structure was created by offsetting each of the resulting Voronoi cells by a fixed value. This offset distance can be adjusted parametrically to control the detail and complexity of the design. In the final stage, the volumes between the walls of the Voronoi cells were evacuated and a unique structure with cavities was designed. For the training of the deep learning model, the 3D model dataset was subjected to certain processes. In the first stage, faulty or missing data were identified and removed from the dataset. Then, all data were standardized to a standard size to improve the performance of the generative design. Using the \"binvox\" library on Python 3.10, the models in OBJ format were converted into voxel format, which expresses an object as a collection of unit cubes. Since voxels can represent complex internal structures, they were chosen as the appropriate data representation method for the structural component data generated in this study. However, part resolution depends on the amount/size of voxels. For this study, the ideal grid size was determined as 128 \(\times\) 128 \(\times\) 128, depending on the computer processing capacity.