# Research on the Prediction of Insertion Resistance of Wheel Loader Based on PSO-LSTM
## 3 LSTM and PSO
### PSO Optimization Process
In the sand sample groups, when the training set is 50%, the maximum value of ARE for the three samples is 4.35%. When the training set is 80%, the maximum value of ARE is 1.14% and the minimum value is only 0.60%. Meanwhile, the \(R^{2}\) of both the gravel sample groups and the sand sample groups with different proportions of training sets is greater than 0.9, which indicates that the predicted values fit the actual values better. Moreover, the \(RMSE\) values also showed a significant decrease compared with the LSTM model. Combining the data in Tables 7 and 9, it can be seen that different initial learning rates, the number of hidden layer units, and dropout probability have a large impact on the prediction results. The initial learning rate set in the LSTM model is 0.01, which is a high value, and the reasonable setting interval should be between 0.001 and 0.003, as shown in Tables 7 and 9. For the number of hidden layer units, the prediction performance is better when the setting is above 500. As for the dropout probability, there is no obvious

Figure 22: Sand samples with an insertion depth of 1000 mm. (**a**) The training set proportion of 50%; (**b**) The training set proportion of 60%; (**c**) The training set proportion of 70%; (**d**) The training set proportion of 80%. setting method, which is related to the changing trend of the sample data and other parameter settings. When the proportion of the training set is 80%, the resistance predicted by PSO-LSTM, the resistance calculated by empirical formula, and the true resistance for the gravel sample groups and the sand sample groups are shown in Figure 23.

Both in the gravel sample groups and in the sand sample groups, it is obvious that there is a large deviation between the resistance calculated by the empirical formula and the true resistance. In particular, the insertion resistance of the wheel loader is unique each time, which makes it difficult to obtain a more accurate resistance by empirical formula. The resistance predicted by PSO-LSTM is closer to the true resistance and can reflect the trend of resistance changes well, which is not available for the empirical formula. ### Discussion

In summary, the PSO-LSTM model developed in this study can predict the magnitude and trend of insertion resistance well, even when the training data are fewer, and considerable prediction results can be obtained. Moreover, the PSO-LSTM model has good stability, robustness, and generalization performance for various piles and insertion depths, which can reflect the change in insertion resistance of wheel loaders. This study provides a basis for subsequent research on the reduction in energy consumption of wheel loaders, energy-efficient operation, reasonable trajectory planning of shoveling, and operation in special operating environments. The research in this paper also has certain shortcomings. The PSO-LSTM model built in this paper is optimized only for the initial learning rate, the number of hidden layer units, and dropout probability; however, the parameters affecting the prediction performance

Figure 23: Resistance comparison. (**a**) The gravel pile with an insertion depth of 600 mm; (**b**) The gravel pile with an insertion depth of 800 mm; (**c**) The gravel pile with an insertion depth of 1000 mm; (**d**) The sand pile with an insertion depth of 600 mm; (**e**) The sand pile with insertion depth of 800 mm; (**f**) The sand pile with insertion depth of 1000 mm. also include the maximum number of iterations, the number of generations of learning rate attenuation and the learning rate attenuation rate, etc., which can be tried to optimize these parameters. At the same time, increasing the number of LSTM layers can prevent the overfitting situation to a certain extent. In this paper, only a single-layer LSTM model is constructed from the perspective of computational efficiency, and changing the single-layer LSTM into a two-layer LSTM can be considered in the future.