## 4 Result and Discussion  
The regression results and real load are shown in Figures 5-16.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Meaning** & **Lower Limit** & **Higher Limit** \\ \hline Flight altitude (m) & 13,359 & 19,429 \\ Mach number & 0.6072 & 0.82 \\ Load factor & \(-2.5\) & 1 \\ Pitch acceleration & \(-0.2\) & 0.2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Range of input parameters.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Meaning** & **Unit** \\ \hline Shear force & N \\ Bending moment & N \(\times\) m \\ Torque moment & N \(\times\) m \\ \hline \hline \end{tabular}
\end{table}
Table 2: Output parameter.  
Figure 5: Shear forces of different methods.  
Figure 6: Comparison between the real shear force and regression shear force.  
Figure 7: \(Cont\).  
Figure 7: Detailed comparison between the real shear force and regression shear force.  
Figure 5-8 demonstrate the regression results of shear force, showing, respectively, the shear forces of different methods, a comparison between the real shear force and regression shear force, a detailed comparison between the real shear force and regression shear force, and the relative error of shear forces of different methods.  
Figure 8: Relative error of shear forces of different methods.  
Figure 10: Comparison between the real bending moment and regression bending moment.  
Figure 9: Bending moments of different methods.  
Figure 11: Detailed comparison between the real bending moment and regression bending moment.  
Figure 12: Relative error of bending moments of different methods.  
It can be seen that the regression bending moments are close to the actual bending moment, with most relative errors below 0.3. In comparison, the regression results of PCR and PLSR are very close, and there is no apparent difference seen in the graph.  
The detailed numerical comparison of the errors and relative errors of the regression results of PCR and PLSR is shown in Table 3. In the table, the reason for the large relative error in the 9 th case is that the numerical value itself is much smaller compared to other cases. Therefore, the calculated relative error is relatively large.  
Figure 14: Comparison between the real torque moment and regression torque moment.  
Figure 13: Torque moments of different methods.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & **Real Load** & **PCR** & **PLSR** & **Error of PCR** & **Error of PCR** & **Relative Error** \\  & & & & & & **Error of PCR** & **of PLSR** \\ \hline
1 & \(-8.4\times 10^{4}\) & \(-5.7\times 10^{4}\) & \(-5.8\times 10^{4}\) & \(2.6  
Figure 15: _Cont._  
close to 1. The regression of torque moment is relatively poor, which may be due to the small numerical value of the torque moment, leading to a large relative error.  
Comparing the results of PCR and PLSR, it can be observed that PLSR outperforms PCR in terms of MAE, MSE, RMSE, and R-square for all shear forces, bending moments, and torque moments. The improvements in the PLSR results can be attributed to the fact that PLSR takes into account the correlation between the response variables and the predictor variables, while PCR only considers the variance of the predictor variables.  
In summary, the predictive accuracy of the flight load regression model based on PCR and PLSR constructed in this paper is very high and is able to meet the needs of flight load engineering applications. In particular, the regression effect of PLSR is slightly better than that of PCR.  
By comparing various methods in Table 8, it becomes apparent that the computational time of regression models is significantly faster than that of panel methods, even with only 10 sets of operating conditions. If more datasets are calculated, the advantages of regression models will become even more apparent.