# Aircraft Structural Stress Prediction Based on Multilayer Perceptron Neural Network
## 4 Model Construction and Result Analysis
### Peak Node Stress Prediction  
In engineering practice, the peak value of equivalent stress is particularly critical. Although the wing rib stress field prediction model established in Section 4.4 provides a good overall prediction of the wing rib stress field, the prediction error is somewhat higher in areas of stress concentration. Simulation results indicate that node 18,428 exhibits the maximum stress value on the wing rib. To enhance the accuracy of predicting the equivalent stress peak, an MLP neural network model is developed specifically for stress peak prediction. This model is compared with the RF model. The structure and parameter settings of the MLP model are detailed in Table 8.  
Table 9 presents the scores of the MLP and RF models on the validation and test sets for peak stress prediction. Analysis reveals that the MLP model exhibits a smaller prediction error and significantly higher accuracy compared to the RF model, reflecting its superior fitting ability and complex nonlinear mapping capabilities. Figure 9a illustrates the predictions of the MLP model on the training and test sets, while Figure 9b depicts the regression of peak equivalent force prediction. The correlation coefficients between the peak equivalent force and the MLP-predicted peak equivalent force are 0.999 for the  
Figure 8: Absolute Error Distribution for Stress Prediction. (**a**) Absolute Error Distribution for Validation and Test Sets in MLP Model; (**b**) Absolute Error Distribution for Validation and Test Sets in RF Model. validation set and 0.996 for the test set. The comparison graph and regression plots indicate that, while the MLP model accurately predicts various sizes of equivalent force values on the validation set, larger prediction errors are observed for higher equivalent force values on the test set. Figure 10 illustrates the stress concentration regions, and based on the FEM simulation results, three nodes (18,403, 35,182, and 35,207) with concentrated equivalent stresses are selected to establish the dataset and predict using the MLP model structure. Table 10 presents the prediction indicators of the MLP model for these different nodes. Figure 11 displays the predictions made by the MLP model for the stress concentration nodes. The MLP model demonstrates excellent performance in predicting the stresses at nodes 18,403, 35,182, and 35,207, reflecting its high accuracy in stress-concentrated regions. For node 18,403, the validation set shows an MSE of 0.026, an MAE of 0.121, and an R\({}^{2}\) of 0.999, indicating highly accurate fitting. In the test set, the MSE increases to 1.908 and the MAE to 0.982, yet the model maintains a high level of accuracy despite this increase. For node 35,182, the validation set records an MSE of 0.344, an MAE of 0.519, and an R\({}^{2}\) of 0.998, again demonstrating strong predictive power. The test set results show an MSE of 1.986 and an MAE of 1.108, which remain within acceptable limits. At node 35207, the validation set has an MSE of 0.152 and an MAE of 0.290, reflecting high prediction accuracy, while the test set performs with an MSE of 1.956 and an MAE of 0.875. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**NODE Number** & **Datasets** & **MSE** & **MAE** & **R\({}^{2}\)** & **MAPE** \\ \hline \multirow{2}{*}{18,403} & Validation set & 0.026 & 0.121 & 0.999 & 0.573\% \\  & Test set & 1.908 & 0.982 & 0.996 & 1.269\% \\ \hline \multirow{2}{*}{35,182} & Validation set & 0.344 & 0.519 & 0.998 & 1.204\% \\  & Test set & 1.986 & 1.108 & 0.996 & 1.507\% \\ \hline \multirow{2}{*}{35,207} & Validation set & 0.152 & 0.290 & 0.999 & 1.249\% \\  & Test set & 1.956 & 0.875 & 0.995 & 1.091\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Results of Various Indicators for Stress Prediction Models at Each Node.