## 4 Model Lightweight Algorithm
### Response Surface Analysis Fitting and Precision Testing
According to Table 3, considering the present experiment with \(m=4\) independent variables and \(n=30\) experimental runs, the F-test critical value is \(F_{\alpha=0,01}=4.018\) at the  
Figure 7: The fitting response surface. significance level of \(\alpha\) = 0.01. Notably, given the substantial differences in the F-test values that correspond to each response surface of the objective functions, it is imperative to individually normalize the \(R_{1}\)-\(R_{5}\) single factors, the interaction factors, and their quadratic coupling terms to gain an intuitive understanding of the significance characteristics of each parameter. In this context, the F-test critical values for \(R_{1}\)-\(R_{5}\) are, respectively, \(F_{R_{1}(\alpha=0.01)}=7.85\times 10^{-3}\),\(F_{R_{2}(\alpha=0.01)}=2.91\times 10^{-3}\), \(F_{R_{3}(\alpha=0.01)}=1.88\times 10^{-2}\), \(F_{R_{4}(\alpha=0.01)}=2.77\times 10^{-4}\), and \(F_{R_{5}(\alpha=0.01)}=3.71\times 10^{-6}\), and their respective levels of significance are shown in Figure 8.  
It can be seen from Figure 8 that for objective function \(R_{1}\), variables A, B, C, D, and C\({}^{2}\) exhibit good significance. For objective function \(R_{2}\), variables B, C, D, and C\({}^{2}\) exhibit good significance. Similarly, for objective function \(R_{3}\), variables C, D, and C\({}^{2}\) exhibit  
Figure 8: The respective levels of significance. (**a**) The significance of single factors. (**b**) The two-way interaction significance. (**c**) The significance of quadratic coupling terms. good significance. For objective function \(R_{4}\), variables B, C, D, CD, B\({}^{2}\), C\({}^{2}\), and D\({}^{2}\) exhibit good significance. Finally, for objective function \(R_{5}\), variables B, C, and D exhibit good significance. It can also be seen that in the design of the top-stiffened double-layer steel truss bridge, among these four objective functions, the most influential are the first-order items of the four parameters to be optimized and the second-order items of the maximum length of the vertical stiffening bar, and the second-order interaction items of most of the other parameters are not significant. The incomplete quadratic polynomial response surface regression equations, simplified based on the results of parameter significance analysis, are represented by Equations (10)-(14). \[R_{1}=-817.11+8.38A+0.43B+3.29C+6.18D-0.23C^{2}, \tag{10}\]  
\[R_{2}=6.92\times 10^{7}-9.29\times 10^{4}B+1.33\times 10^{5}C-5.13\times 10^{5}D+8. 94\times 10^{3}C^{2}, \tag{11}\]  
\[R_{3}=4.54\times 10^{7}-1.84\times 10^{5}C-3.34\times 10^{5}D-1.28\times 10^{4}C^{2}, \tag{12}\]  
\[R_{4}=-9.00\times 10^{7}+5.02\times 10^{4}B-6.18\times 10^{4}C+5.63\times 10^{5}D+ 1.27\times 10^{3}CD\quad, \tag{13}\]  
\[-2.85\times 10^{2}B^{2}-3.72\times 10^{3}C^{2}-4.70\times 10^{3}D^{2}\]  
\[F_{m+1}=\frac{(S_{m}-S_{m+1})/(\eta_{m}-\eta_{m+1})}{S_{m+1}/\eta_{m+1}}, \tag{9}\]0  
After establishing the response surface equation, it is necessary to use the complex correlation coefficient \(R^{2}\) and corrected complex correlation coefficient \(R^{2}_{Adj}\) to test the fitting accuracy to ensure that the mathematical model can replace the FE method for the subsequent calculation and analysis of the structural response values. \[F_{m+1}=\frac{(S_{m}-S_{m+1})/(\eta_{m}-\eta_{m+1})}{S_{m+1}/\eta_{m+1}}, \tag{9}\]1  
\[F_{m+1}=\frac{(S_{m}-S_{m+1})/(\eta_{m}-\eta_{m+1})}{S_{m+1}/\eta_{m+1}}, \tag{9}\]2  
where \(y_{i}\) and \(\hat{y}_{i}\) refer to the response values of the FE method and the regression model for the \(i\)-th sampling point, respectively, and their mean values are \(\overline{y}=\frac{1}{n}\sum_{i=1}^{n}{y_{i}}\). The accuracy of response surface fitting is exhibited in \[F_{m+1}=\frac{(S_{m}-S_{m+1})/(\eta_{m}-\eta_{m+1})}{S_{m+1}/\eta_{m+1}}, \tag{9}\]3  
According to Figure 9, both \(R^{2}\) and \(R^{2}_{Adj}\) of objective functions \(R_{1}\)-\(R_{5}\) reach 0.95 or above, and their C.V. values are less than 3%.