# Development of Prediction Method for Dimensional Stability of 3D-Printed Objects
## 3 Results
### Neural Network Regression Model Analysis  
In this study, the support cases (15\({}^{\circ}\), 30\({}^{\circ}\), and 45\({}^{\circ}\) of inclination angles) and non-support cases (60\({}^{\circ}\) and 75\({}^{\circ}\) of inclination angles) were trained without overfitting, as shown in Figure 11. The loss for the training dataset and the loss for the validation dataset decreased with each epoch number, and both loss datasets were converged after the 25 th and 90 th epoch for the MAE for support cases and the MAE for non-support cases, respectively.  
\begin{table}
\begin{tabular}{c c} \hline
**Regression Model** & **MAE** \\ \hline GPR & 0.020473 \\ SVM & 0.034762 \\ \hline \end{tabular}
\end{table}
Table 13: Mean absolute errors (MAEs) of the GPR and SVM models.  
Figure 10: Prediction versus experimental plot for (**a**) GPR and (**b**) SVM regression models.  
Figure 13-15 present the MSDEs observed for different support space widths (5 mm, 10 mm, and 15 mm) and layer thicknesses (0.2 mm, 0.4 mm, and 0.6 mm), considering the variations in inclination angle and raster angle. Figure 16, on the other hand, displays the MSDEs for cases where no support is used, with corresponding 0.2 mm, 0.4 mm, and 0.6 mm of layer thicknesses.  
In the case of utilizing support objects, an increase in inclination angle was found to result in a decrease in the MSDEs. Additionally, an increase in support space was observed to lead to an increase in the MSDEs. However, under the same inclination angle conditions, when the raster angles were set to 45\({}^{\circ}\), the MSDEs exhibited relatively lower  
Figure 16: Predicted mean squared dimensional error (MSDE) without support space with layer thickness (**a**) 0.2 mm, (**b**) 0.4 mm, and (**c**) 0.6 mm.  
Figure 14: Predicted mean squared dimensional error (MSDE) with 10 mm of support space with layer thickness (**a**) 0.2 mm, (**b**) 0.4 mm, and (**c**) 0.6 mm.  
Figure 15: Predicted mean squared dimensional error (MSDE) with 15 mm of support space with layer thickness (**a**) 0.2 mm, (**b**) 0.4 mm, and (**c**) 0.6 mm.  
values compared to other raster angles. In the case of utilizing the non-support object, as the inclination angle increased, the MSDEs also increased. Moreover, when the raster angle was 45\({}^{\circ}\), the MSDEs were observed to be lower compared to the errors associated with other raster angles.  
Increasing the inclination angle with support provides better support for overhanging features and complex geometries, maintaining structural integrity and reducing deformations. By mitigating the effects of gravity, the inclination angle with support reduces material sagging, warping, or overhangs and enables more controlled and accurate material deposition, resulting in reduced MSDEs [30]. A raster angle of 45\({}^{\circ}\) provides a more balanced deposition pattern during the printing process. This angle allows for a balanced distribution of stresses and forces, resulting in improved layer adhesion and reduced distortion. In contrast, at extreme angles such as 0\({}^{\circ}\) or 90\({}^{\circ}\), the deposition pattern may introduce more inherent weaknesses, leading to increased MSDEs and reduced dimensional accuracy [28; 31; 32].