## 2 Model Establishment and Analysis
### Secondary Optimization and Inverse Prediction of Part Thickness  
In multi-objective optimization, the objectives are to minimize the total mass of the fifth wheel and maximize the minimum fatigue life. There was a positive correlation between the two variables: The smaller the mass, the smaller the corresponding minimum fatigue life. To achieve coordinated optimization between the two, it is necessary to obtain the minimum value of f in Equation (7). \[f=M+\frac{1}{N3} \tag{7}\]  
In Equation (7), \(M\) is the total mass of the fifth wheel, and \(N3\) is the minimum fatigue life of condition 3 at this mass. Next, the mass (M) and minimum fatigue life under condition 3 (N3) from the 6000 datasets of the multi-objective optimization results were sorted. The mass (M) was sorted in ascending order. Data points from the 6(i \(-\) 1) + 1 th to the 6 ith positions were assigned a value of i. For example, data points from the 1 st to the 6 th positions were  
Figure 14: Comparison of the MAPEs of the three models. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Models** & **BP Neural Network** & **Random Forest Algorithm** & **Hybrid Model** \\ \hline MAPE of test set (\%) & 1.89 & 7.73 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: MAPE predicted by the three models. assigned a value of 1, and so on. Data points from the 6031 st to the 6000 th positions were assigned a value of 1000. Similarly, the minimum fatigue life under condition 3 (N3) was sorted in descending order, and data points from the 6(j \(-\) 1) + 1 th to the 6 jth positions were assigned a value of j. In practical applications, the fifth wheel must consider the fatigue performance while pursuing lightweight design. If an increase of 2-3 kg in weight can enhance the fatigue life by hundreds of thousands or even millions of cycles, it is definitely a better option. Therefore, the establishment of the evaluation index in this study is more inclined to the improvement of failure protection performance, with the lightweight being controlled within a 20% reduction. After comprehensive consideration, the evaluation index was set to 0.65i + 0.35j. Based on the established multi-objective optimization evaluation index, the minimum value among the 6000 datasets was identified, representing the optimal balance between lightweight design and fatigue performance. This set is the optimal solution. The thickness of each component in the optimal solution is listed in Table 10. The mass of the fifth wheel was 79.07 kg, and the minimum fatigue life reached 4.614 \(\times\) 10\({}^{6}\) cycles. Moreover, the maximum stress was 291.1 MPa under condition 2 and 447.0 MPa under condition 3, which is below the 600 MPa yield strength of SD600, meeting the strength requirements. The fatigue life distribution diagram is shown in Figure 15a, and the corresponding stress distribution diagrams are shown in Figure 16a,b. Single-objective optimization was conducted based on the optimal solution. In accordance with relevant fatigue test standards, N3 was constrained to exceed 2.0 \(\times\) 10\({}^{6}\) cycles, and the maximum stress under both conditions 2 and 3 was limited to less than 600 MPa. The range of each variable was bounded based on the data in Table 10, with the saddle body constrained to \(\pm\)1 mm and the other components constrained to \(\pm\)4 mm. Optimization was then performed to minimize the mass. The thickness of each component for the optimal design option from the single-objective optimization results is listed in Table 11. The mass of this group of results is 72.99 kg, while the fatigue life under condition 3, as shown in Figure 15b, reaches 3.714 \(\times\) 10\({}^{6}\) cycles. The position of the minimum life under condition 3 is also the element node-218,253. The maximum stress is 410.1 MPa under condition 2 and 458.9 MPa under condition 3, both of which are below the 600 MPa yield strength of SD600, satisfying the strength requirements. The corresponding stress distributions are shown in Figure 17a,b.