# Research on the Prediction of Insertion Resistance of Wheel Loader Based on PSO-LSTM
## 3 LSTM and PSO
### PSO Optimization Process
Meanwhile, only two typical piles, gravel and sand, are selected for experiments in this paper, and other kinds of piles are not tried, and conducting experiments in other special piles to verify the prediction performance of the model can be considered. ## 5 Conclusions

In this paper, a PSO-LSTM model is established and tested on gravel sample groups and sand sample groups with insertion depths of 600 mm, 800 mm, and 1000 mm. The results show that the PSO-LSTM model can predict the insertion resistance and its change trend during the insertion of wheel loaders with good accuracy, and the main conclusions are as follows:

1. This paper proposes using the insertion depth and cylinder pressure as the input layer, and the correlation between cylinder pressure and insertion resistance is examined by the Pearson correlation coefficient. Among them, the absolute values of Pearson correlation coefficients of the pressure values of the large chamber of the tilt cylinder, the small chamber of the tilt cylinder, and the large chamber of the lift cylinder are greater than 0.8 in both the gravel sample group and the sand sample group. The absolute values of the Pearson correlation coefficients of the majority of them are greater than 0.9. The absolute values of the Pearson correlation coefficients of the pressure of the small chamber of the lift cylinder are relatively low, but they are basically above 0.7, which proves that the correlation between the cylinder pressure data and the insertion resistance is high. 2. In this paper, we compare the prediction performance of the LSTM model and the PSO-LSTM model for insertion resistance. Experiments were conducted with 50%, 60%, 70%, and 80% of samples as training sets, respectively, in three different insertion depths of gravel sample groups and sand sample groups. The results show that in the LSTM model, the prediction accuracy gradually decreases due to the accumulation of errors, which is more obvious when the training-set samples are small. In contrast, in the PSO-LSTM model, the prediction performance of the model is greatly improved by optimizing the initial learning rate, the number of hidden layer units, and the dropout probability. In the gravel sample groups and sand sample groups with different proportions of training sets, both _RMSE_ and _ARE_ are significantly reduced. The values of \(R^{2}\) are all greater than 0.9, and the fit between the predicted and actual values is high. 3. In the PSO-LSTM model, when the training set was 80% of the total data, the _ARE_s of the gravel sample groups with insertion depths of 600 mm, 800 mm, and 1000 mm were 2.28%, 1.57%, and 1.53%, respectively. In contrast, the _ARE_s in the sand sample groups were 1.14%, 0.71%, and 0.60%, respectively. In general, the prediction accuracy of the sand sample groups is higher than that of the gravel sample groups, which is related to the pile characteristics and the mechanism of resistance generation. The insertion resistance of sand changes more smoothly, while the insertion resistance of gravel changes in a more fluctuating manner, which greatly increases the difficulty of predicting the insertion resistance for gravel. Conceptualization, Y.C. and G.S. ; methodology, Y.C. ; software, H.J. ; validation, G.S. ; formal analysis, Y.C. ; investigation, T.Z. ; resources, G.S. ; data curation, Y.C. ; writing--original draft preparation, G.S. ; writing--review and editing, Y.C. ; visualization, H.J. ; supervision, Y.C. ; project administration, Y.C. ; funding acquisition, Y.C. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the National Natural Science Foundation of China (61962007), the Key Projects of Guangxi Natural Science Foundation (2018 GXNSFDA294001), the S&T Fund of Guangxi Province (1598021-2). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data in this study are available from the corresponding authors upon request.