## 6 Implementation of the Proposed Method and Solution Space Exploration
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Combinations of the Processing Parameters (Forming and Quenching Phase) Identified after**} \\ \multicolumn{5}{c}{**Solution Space Exploration**} \\ \hline
**Temperature at** & **Austenite \%** & **Cooling Rate** & **Deformation** & **Deformation** \\
**t = 0** & & **Amonium** & **Temperature** \\ \hline
1123.87 & 94.99 & 57.93 & 13.80 & 1064.08 \\ \hline
1121.85 & 96.02 & 62.67 & 12.84 & 1067.72 \\ \hline
1118.08 & 95.01 & 65.11 & 11.55 & 1065.76 \\ \hline
1122.25 & 96.49 & 58.26 & 17.28 & 1063.07 \\ \hline
1121.29 & 95.51 & 52.32 & 18.73 & 1063.04 \\ \hline
1117.11 & 97.44 & 71.48 & 11.28 & 1050.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Processing Parameter Combinations Satisfying Microstructure Requirements. Figure 11: Predicted Output and Actual Output Comparison for Step 3.1 (for Test Dataset). the input dataset and test dataset, respectively. The loss function for step 3.2 was calculated as shown in Table 12.  
Figure 12: Feasible Region of the Processing Parameters (Forming and Quenching). Figure 13: Predicted Output and Actual Output Comparison for Step 3.2 (for Input Dataset). For solution space exploration, the requirements on the austenite phase fraction % are received from step 3.1 as shown in Table 13. The austenite phase fraction requirements are provided in the ranges. Upon mapping these requirements with the results for the ANN model, a feasible region is identified as shown by the green rectangular area in Figure 15. Following the same procedure as in the last step, a plot was drawn. The redline in Figure 15 represents the austenite phase fraction values for each processing combination of the heating phase. Austenite was selected because the target for the heating phase is always to achieve as much austenite as possible. From the feasible region, a set of feasible values of _heating rate HR, soaking temperature,_ and _soaking time_ were identified as shown in Table 14. These identified combinations of the processing parameters for the heating phase satisfy the austenite phase fraction requirements received from step 3.1. After execution of our model for steps 2, 3.1 and 3.2 and exploring the solution space, the design set points for each space were identified that satisfy the requirements for each space. The method proposed and demonstrated for the hot stamping process can help designers with respect to (1) guidance from end goals to the processing goals, (2) adjustment of the variations and error being propagated, and modifications in model parameters, to \begin{table}
\begin{tabular}{c c} \hline \hline  & **Requirements from Step 3.1** \\ \cline{2-3}
**Limits** & **Austenite Phase Fraction \%** \\ \hline
**Lower** & 95 \\ \hline
**Upper** & 98 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Austenite Phase Fraction Requirements. Figure 14: Predicted Output and Actual Output Comparison for Step 3.2 (for Test Dataset). explore the possibilities in achieving any desired set of properties for a product that are less sensitive to variations and satisfy the design performance/requirements. The method is robust in the sense that requirements are specified in ranges, and the corresponding processing or microstructure parameters identified are also in ranges. Hence, the designer has the freedom to adjust the ranges to minimize the effects of uncertainty, according to the available manufacturing facility available. A comparison of the predicted output with the actual values present in the dataset shows that our proposed ANN model has acceptable generalization capability. The predicted values could be added to the actual dataset, once validated experimentally, for deeper and further research. Another important observation is the simplicity and straightforwardness of the proposed Design Space Exploration Framework (_DSEF_). The DSEF can help the designer to start straightaway from the end properties and trace back the PSPP spaces to realize the end product in a systematic manner in less time and in an efficient way.