## 4 Results
### Simulative Results  
The springback behavior of the simulated process is shown in Figure 10. All figures show the occurring springback \(\Delta\alpha\) for the different configurations (**m**) plotted against the \begin{table}
\begin{tabular}{c c c c c} \hline
**Uncertainty** & **nu** & **lu** & **mu** & **hu** \\ \hline \(\delta E\) & \(\pm 0\) & \(\pm 2500\) & \(\pm 5000\) & \(\pm 10,000\) \\ \(\delta v\) & \(\pm 0\) & \(\pm 0.01\) & \(\pm 0.02\) & \(\pm 0.04\) \\ \(N\) & 3094 & 1725 & 3310 & 2069 \\ \hline \end{tabular}
\end{table} 
Table 3: Applied uncertainties of the four data sets. Figure 9: Die bending tool consisting of flexible punch (**a**) and die (**b**). target angle (\(\alpha_{\text{act}}^{\text{(loa)}}\)). The top row refers to data set nu (no uncertainty) and the bottom row to data set mu (medium uncertainty). It can be clearly seen that the highest springback occurs in the aluminum sheets with a thickness of 0.5 mm. This is expected, since in general, the springback increases with decreasing sheet thickness. It also increases with decreasing modulus of elasticity at similar tensile strength. For some material and sheet thickness combinations, springback increases with increasing forming angle (\(\alpha_{\text{act}}^{\text{(loa)}}\)), while it decreases for others. Since this behavior only occurs for materials of higher tensile strength, this leads to the following assumption. The applied stamping force is directly determined by the springs and their deflection, which remains equal for all materials and sheet thicknesses. This may mean that the applied force is not sufficiently high for thicker sheets of stiffer materials, like the used aluminum alloy and steel, at large angles. This assumption was confirmed by simulations with doubled spring stiffnesses, which can be seen in Figure 11.  
When comparing data set nu with mu, it is obvious that the variance of the springback increases with rising uncertainty. With the four data sets presented in Section 3, RL models are trained to learn the material-, sheet thickness- and angle-dependent springback behavior. The trained agents then predict the springback and compensate for it using the control loop. The results are  
Figure 11: Simulated springback for different spring stiffnesses of punch and die for DC01. Figure 10: Simulated springback behavior with constant material parameters (dataset nu, **top**) and material parameters subject to uncertainty (dataset mu, **bottom**). summarized for each data set in Figure 12 in the form of a Probability Density Function (PDF). An overview over the average and maximum deviations of the individual data sets is also shown in Table 4. The PDF of the agent belonging to data set nu shows that the mean deviation could be significantly reduced (\(|\overline{\Delta\alpha_{\text{ctrl}}}|=0.16^{\circ}\)). It can also be seen that both the mean and the maximum deviation increase with increasing uncertainty. To test whether the performance of the trained agents can be improved with knowledge of the applied uncertainty, a further series of tests is carried out. In these, the actual material properties (\(E+\delta E\) resp. \(v+\delta v\) instead of \(E\) resp. \(v\)) were fed to the agents, to see if the springback behavior of untrained configurations is learned. In a real environment, the feedback of the uncertainty or the actual material parameters could be achieved, for example, by measuring the forming forces in the process [27]. However, given the considerable difference between synthetically generated force signals and real measured signals, especially in the case of a flexible tool system, the approach described above was chosen. The results of these tests are also shown in Table 4 (gray values) and in the form of PDFs (Figure 13), separated by data set. The results presented in this study are derived from 30 training runs, with both the mean and maximum deviations being displayed. It shows clearly that with knowledge of the applied uncertainty, \(\Delta\alpha_{\text{ctrl}}\) can be reduced significantly.