## 4 SVM Fuel Consumption Model and IPSO Optimization
### SVM Model  
According to the results of KPCA, the initial velocity, the displacement of the wheel loader in the insertion phase, the shoveling weight, the operation time, and the displacement of the wheel loader in the scooping phase are selected as the input layer, and the fuel consumption as the output layer. Among 120 sets of gravel samples and sand samples, respectively, 100 sets of samples are randomly selected as the training set, and the other 20 sets are used as the test set. Meanwhile, the penalty factor \(g\) and the kernel function parameter \(c\) are optimized by combining them with the CV method. The optimal \(c\) and \(g\) for the gravel fuel consumption model are 3.03 and 143.58, respectively, and for the sand fuel consumption model, they are 4.32 and 123.52, respectively. The accuracy effect of the fuel consumption model is shown in Figure 9. Meanwhile, root mean square error (RMSE), average relative error (ARE), and goodness of fit R\({}^{2}\) are used in this study as indicators to evaluate the performance of the fuel consumption model. The smaller the RMSE and ARE, the smaller the deviation between the predicted value and the true value, and the higher the accuracy of the model. The value of R\({}^{2}\) is closer to 1, which indicates a higher degree of fit and higher accuracy of the model, and its calculation formula is as follows. The evaluation indicators of the fuel consumption model are shown in Table 6.  
\[RMSE=\sqrt{\frac{1}{n}{\sum\limits_{i=1}^{n}{{{({y_{i}}^{*}-{y_{i}})}^{2}}}}} \tag{19}\]  
\[ARE=\frac{1}{n}{\sum\limits_{i=1}^{n}{\left|{\frac{{{y_{i}}-{y_{i}}^{*}}}{{y_{ i}}}}\right|} \tag{20}\]  
\[R^{2}=1-\frac{\sum\limits_{i=1}^{n}{{{({y_{i}}-{y_{i}}^{*})}^{2}}}}{\sum \limits_{i=1}^{n}{{{({y_{i}}-{\overline{y}_{i}})}^{2}}}} \tag{21}\]  
where \(y_{i}\) is the true value, \({y_{i}}^{*}\) is the predicted value, \({\overline{y}_{i}}\) is the mean of the true value, and \(n\) is the number of samples.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type of Pile** & \begin{tabular}{c} **Initial** \\ **Velocity** \\ \end{tabular} & \begin{tabular}{c} **Displacement of Wheel** \\ **Loader in Insertion Phase** \\ \end{tabular} & \begin{tabular}{c} **Shoveling** \\ **Weight** \\ \end{tabular} & \
\begin{tabular}{c} **Operation** \\ **Time** \\ \end{tabular} &
\begin{tabular}{c} **Displacement of Wheel** \\ **Loader in Scooping Phase** \\ \end{tabular} \\ \hline Gravel & 0.792 & 0.782 & 0.834 & 0.789 & 0.779 \\ \hline Sand & 0.762 & 0.795 & 0.894 & 0.846 & 0.822 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Grey relation coefficients.  
In the gravel fuel consumption prediction model, the ARE is 4.91%, the RMSE is 5.91, and the R\({}^{2}\) is 0.9764. While in the sand fuel consumption prediction model, the ARE is 3.49%, the RMSE is 3.08, and the R\({}^{2}\) is 0.9494. In terms of prediction accuracy, the prediction accuracy of the gravel fuel consumption prediction model is lower than that of the sand fuel consumption prediction model. And in terms of fitting ability, the gravel fuel consumption prediction model has a better fitting ability. Overall, the SVM fuel consumption prediction model showed better prediction ability in both the gravel samples and the sand samples. The deviation between the predicted and true values of the model is slight, and the model has high stability and generalization ability. To further test the rationality of KPCA. Different dimensions of fuel consumption influence factors are selected as input layers in the SVM fuel consumption model. The same training set and test set are selected, and ARE is used as the evaluation indicator. The prediction performance of the gravel model and sand model is shown in Figure 10. When the dimension increases, the value of ARE decreases rapidly, and when the dimension is 5, the ARE of the gravel model and sand model reaches the lowest point. When the dimension continues to increase, the values of ARE both have a small increase.