## 3 Data Analysis of Similarity Calculation Method for Infield and Outfield Environmental Tests
### Verification of Similarity Calculation Method for Infield and Outfield Tests  
In order to verify whether the outfield curve obtained by the similarity calculation method can fit the outfield test data well, the outfield curve obtained by the two-point translation and scaling transformation is verified by the test data obtained from the outfield sampling. The curve derived from the outfield is compared with the four-point interpolation curve and the polynomial fitting curve. Among the data of the outfield test, the points with temperature of 0, \(-\)15, \(-\)25, and \(-\)35 \({}^{\circ}\)C were selected to directly interpolate and fit the curve of material A. The interpolation curve of material A in the springback tests is as follows:  
\[L_{1}(T)=-0.00038049T^{3}-0.00815475T^{2}-0.09873783T+40.80853008 \tag{16}\]  
The interpolation curve of material A in the elongation tests is as follows:  
\[L_{2}(T)=-0.00000159T^{3}-0.00002311T^{2}-0.00057873T+0.99521616 \tag{17}\]  
In the outfield test data, the points with temperature of 10, \(-\)5, \(-\)20, and \(-\)35 \({}^{\circ}\)C were selected to directly interpolate and fit the curve of material B. The sampling point of material B is different from that of material A, because material B also has low temperature hardening when it is higher than 0 \({}^{\circ}\)C, while material A has no hardening when it is higher than 0 \({}^{\circ}\)C. When comparing with four point interpolation and transformation, the sampling points with better fitting are selected according to the distribution interval and density  
Figure 9: Transformation diagram. of the sampling points. The interpolation curve of material A in the springback tests is as follows:  
\[L_{1}(T)=-0.00002860T^{3}+0.00581235T^{2}-0.17353707T+41.96555913 \tag{18}\]  
The interpolation curve of material B in the elongation test is as follows:  
\[L_{2}(T)=-0.00000213T^{3}-0.00014557T^{2}-0.00142622T+0.98835368 \tag{19}\]  
The outfield interpolation curve and outfield scatter are shown in Figure 10, and the goodness of fit is shown in Table 7.  
The similarity calculation method of the low-temperature tests based on the translation and scaling transformation of the similar curve was adopted, and the infield tests curve obtained by polynomial fitting method was used. Substituting formula (7) into formula (11) yields the transformation parameters and the outfield curve based on the polynomial infield fitting curve and outfield sampling point. The scaling ratio, translation parameter, \(dT^{\prime}\) and the goodness of fit \(R^{2}\) are shown in Table 8, and the derived outfield curve is shown in Figure 11. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Fitting Type** & **A Springback** & **B Springback** & **A Elongation** & **B Elongation** \\ \hline Goodness of fit \(R^{2}\) & 0.9351 & 0.8764 & 0.8934 & 0.9242 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Goodness of fit of four-point sampling interpolation. Figure 10: Interpolation curves. (**a**) Springback (**b**) Elongation. Then the study compared the derived outfield curve obtained by scaling transformation with the similarity calculation method, four-point interpolation curve and outfield polynomial fitting curve in terms of the goodness of fit. The results are shown in Figure 12.  
Next, the study compared the curve derived from the two-point translation scaling transformation obtained by the similarity calculation method, the four point interpolation curve and the outfield polynomial fitting curve in terms of the goodness of fit. The higher the goodness of fit, the closer the fitted curve is to the outfield test results. The comparison shows that the best fitting curve is the outfield polynomial fitting curve, that the second best is the curve derived from the two-point translation scaling transformation using the similarity calculation method, and that the worst is the four-point interpolation fitting curve.