# Development of Prediction Method for Dimensional Stability of 3D-Printed Objects
## 3 Results  
### Stacking Profiles  
All designed 3D objects were printed three times to assess the stacking profile, which was defined as the outline of the printed object in the XZ plane. The printed objects formed a rectangular bar without noticeable flaw (Figure 4a). The printed 3D objects, with a 45\({}^{\circ}\) inclination angle and support spaces of 5, 10, and 15 mm, are shown in Figure 4b. The stacking profiles were used to evaluate the dimensional accuracy compared to the original design. Measured profiles were expressed in red lines and compared to the designed profiles in black lines (Figure 5). The differences between measured and designed profiles were recorded and set as output for the dataset. Figure 4: Printed 3D objects of (**a**) all objects and (**b**) with 45\({}^{\circ}\) inclination angle and support spaces of 5 mm, 10 mm, and 15 mm. Figure 3: The flow chart for ANN model. raster angle, and inclination angle, and one output parameter, namely, the MSDE. The R\({}^{2}\) for the non-support object used three parameters, namely, layer thickness, raster angle, and inclination angle, and one output parameter, namely, the MSDE. The R\({}^{2}\)s are listed in Table 10.  
In the case of the supporting object, the \(p\)-values for support spacing, layer thickness, raster angle, and inclination angle were 0.043, 0.0, 0.0, 0.009, and 0.0, respectively. The \(t\)-values for the support spacing, layer thickness, raster angle, and inclination angle, which had \(p\)-values below 0.05, were 10.03, 8.48, \(-\)2.67, and \(-\)7.75, respectively. Their standard errors were 0.00226, 0.05653, 0.000251, and 0.000754. The constant term, represented by 0.08614 of the coefficient, had a standard error of 0.0418. The \(t\)-value was 2.06, and the \(p\)-value was 0.043, indicating a statistically significant relationship. This implies that even when all predictor variables are zero, the constant term has a significant impact on the dependent variable. The MSDE, which was representative as the output, can be calculated as 0.0861 + 0.0277 \(\times\) supporting space + 0.479 \(\times\) layer thickness \(-\) 0.000677 \(\times\) raster angle \(-\) 0.00584 \(\times\) inclination angle. The R\({}^{2}\) between the four input parameters and one output parameter was 0.759. In the case of the non-supporting object, the \(p\)-values for layer thickness, raster angle, and inclination angle were 0, 0.126, and 0.333, respectively. The \(t\)-values were 4.82 for layer thickness, \(-\)1.63 for raster angle, and 1 for inclination angle. Their standard errors were 0.08251, 0.000367, and 0.001796. The constant term, represented by \(-\)0.1115 of the coefficient, had a standard error of 0.1275. The \(t\)-value was \(-\)0.87, and the \(p\)-value was 0.396, indicating no statistically significant relationship. This suggests that when all other predictor variables are zero, the constant does not significantly influence the dependent variable. The MSDE was calculated as \(-\)0.111 + 0.397 \(\times\) layer thickness \(-\) 0.0006 \(\times\) raster angle + 0.00180 \(\times\) inclination angle. The R\({}^{2}\) between the three parameters and one output parameter was 0.659. In cases where support was utilized, support spacing, layer thickness, raster angle, and inclination angle were found to be statistically significant predictors of the dependent variable, as evidenced by \(p\)-values below 0.05. Support spacing and layer thickness exhibited positive relationships, while raster angle and inclination angle demonstrated negative relationships. In cases where support was not utilized, only layer thickness exhibited a \begin{table}
\begin{tabular}{c c c} \hline
**Object** & **R\({}^{2}\)** \\ \hline Support & 0.759 \\ Non-support & 0.659 \\ \hline \end{tabular}
\end{table} 
Table 10: The coefficient of determination (R\({}^{2}\)) of support and non-support objects.