## 6 Conclusions  
In this study, the shoveling trajectories of gravel and sand are optimized at different engine speeds. The corresponding optimized trajectories were obtained with the optimization objective of reducing the fuel consumption of shoveling operations. The results show that the optimized shoveling trajectory effectively reduces the fuel consumption of shoveling operation, and the main conclusions are as follows.  
1. In this study, the factors with a strong influence on the fuel consumption of shoveling operations are screened by experimental analysis and KPCA. The factors with a strong influence are initial velocity, the wheel loader displacement in the insertion phase, the shoveling weight, the operation time, and the wheel loader displacement in the scooping phase. KPCA results show that the cumulative contribution rate of the above five factors can reach 90%. Meanwhile, the grey relation coefficients between key factors of fuel consumption influence and fuel consumption are all greater than 0.75. It proves that the screening of key factors of fuel consumption influenced by KPCA is effective.
2. In this study, the fuel consumption model is established by SVM, and the penalty factor and kernel function parameters in SVM are optimized by CV. The SVM fuel consumption model has high stability and generalization ability, and the deviation between the predicted and true values of the model is small. In the gravel samples, its ARE is 4.91%, RMSE is 5.91, and R\({}^{2}\) is 0.9764. While in the sand samples, the ARE is 3.49%, RMSE is 3.08, and R\({}^{2}\) is 0.9494. The deviation between the true values and the predicted values from the SVM fuel consumption model is small.
3. In this study, the optimized shoveling trajectories are obtained by IPSO for shoveling gravel and shoveling sand at three engine speeds. Validation experiments are conducted based on the optimized trajectory and compared with the sample data fuel consumption and manually controlled shoveling fuel consumption. The results show that the optimized trajectory can significantly reduce the fuel consumption of shoveling operations. For shoveling gravel, the average fuel consumption of the validation experiment is reduced by 60.93%, 45.79%, and 49.10%, respectively, compared with the sample average fuel consumption with three engine speeds. For shoveling sand, the average fuel consumption in the validation experiment is reduced by 30.93%, 35.56%, and 28.59%, respectively, compared with the sample average fuel consumption with three engine speeds. Compared with manually controlled shoveling gravel and sand, fuel consumption can be reduced by 27.66% and 24.34%, respectively.  
Conceptualization, Y.C. and G.S.; methodology, Y.C.; software, G.S.; validation, G.S.; formal analysis, Y.C.; investigation, C.T.; resources, G.S.; data curation, G.S.; writing--original draft preparation, G.S.; writing--review and editing, Y.C.; visualization, C.T.; supervision, Y.C.; project administration, Z.W.; funding acquisition, Y.C. and Z.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (61962007), the Key Projects of Guangxi Natural Science Foundation (2018 GXNSFDA294001), and the S&T Fund of Guangxi Province (1598021-2).  
Not applicable.  
The data in this study are available from the corresponding authors upon request.  
The authors declare no conflict of interest.