## 2 Model Establishment and Analysis
### Multi-Objective Optimization
As shown in Figure 12, the scatter plot illustrates the relationship between weight and minimum fatigue life under condition 3. The black points represent the solution set values, the blue point in the lower right corner indicates the initial value, and the red points denote the Pareto frontier values. From the trend of the Pareto frontier values in the scatter plot above, it is evident that the trend of the points aligns with the actual situation. Specifically, the greater the mass, the greater the fatigue life. Next, the multi-objective optimization results were processed. First, outliers were removed. The total mass (M) of the fifth wheel fluctuates within a certain range due to the  
Figure 11: Components of the fifth wheel. (**a**)—Saddle body, (**b**)—Upper transverse plate (**c**)—Lower transverse plate, (**d**)—Reinforcing ribs, (**e**)—Lower reinforcing plate, (**f**)—Swing rod support seat, (**g**)—Guide plate, (**h**)—Carriages, (**i**)—Inner baffles, (**j**)—Outer baffles, (**k**)—force-transforming element. Figure 12: Scatter diagram of mass (M) and minimum fatigue life under condition 3 (N3). constrained thickness ranges of its components. The fatigue life data fall within the range of 1.0 \(\times\) 10\({}^{4}\) to 1.0 \(\times\) 10\({}^{7}\) cycles. In the calculated life results, the majority of the fatigue life values under condition 2 exceeded 1.0 \(\times\) 10\({}^{7}\) cycles, and the fatigue performance under condition 2 was consistently stronger than that under condition 3 across all data groups. Therefore, this study focused on analyzing the fatigue life under condition 3 as the primary indicator. After removing outliers, 6000 data points remained from the optimized dataset. Fatigue Life Prediction Based on a Hybrid Model of BP Neural Network and Improved Random Forest Algorithm  
To obtain the relationship between each component of the traction seat and the total mass and fatigue life of the traction seat, this study used 6000 sets of data calculated by the multi-objective genetic algorithm for training tests, with the thickness of the ten components as the input and the total mass and fatigue life as the output. Because there is a linear relationship between the thickness of the ten components and the total mass of the traction seat, the relationship equation between the mass and the thickness of each component was calculated as:  
\[ \begin{split}\text{M}=6.07\cdot x_{1}+0.499\cdot x_{2}+0.496 \cdot x_{3}+0.207\cdot x_{4}+0.231\cdot x_{5}+0.0688\cdot\\ x_{6}+0.0726\cdot x_{7}+0.394\cdot x_{8}+0.488\cdot x_{9}+0.404 \cdot x_{10}+7.70972\end{split}  \tag{6}\]  
In Equation (6), where M denotes the total mass of the fifth wheel, the [\(x_{1}\),\(x_{2}\),\(x_{3}\),\(x_{4}\)\(\cdots\)\(x_{10}\)] represent, respectively, the thickness of the saddle body, upper transverse plate, lower transverse plate, reinforcing ribs, lower reinforcing plate, swing rod support seat, guide plate, carriages, inner baffles, and outer baffles. The dataset generated by multi-objective optimization was imported after singular value processing. It was then divided into training and test sets and normalized for easier analysis. The normalized data were individually trained and predicted using the random forest model. The Mean Absolute Percentage Error (MAPE) of the predictions was calculated by adjusting the parameters of the random forest. The parameter set with the smallest MAPE was selected, and its predictions were fused with the original ten features to create a new dataset. This fused dataset was then used for training and prediction using a BP neural network, and the MAPE of the hybrid model was calculated. The model analysis processing flow is illustrated in Figure 13.  
Figure 13: Model analysis processing flow. The MAPE for fatigue life prediction by the BP neural network was calculated to be 1.89%, the average absolute percentage error for fatigue life prediction by random forest algorithm was 7.73%, and the MAPE for hybrid model prediction was 0.99%. Table 9 presents the results.