# Research on the Prediction of Insertion Resistance of Wheel Loader Based on PSO-LSTM
## 3 LSTM and PSO
### PSO Optimization Process
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Insertion** & **The Proportion** & **Initial** & **Number of Hidden** & **Dropout** \\
**Depth** & **of Training Set** & **Learning Rate** & **Layer Units** & **Probability** \\ \hline \multirow{4}{*}{600 mm} & 50\% & 0.0059 & 490 & 0.557 \\  & 60\% & 0.0029 & 234 & 0.643 \\  & 70\% & 0.0012 & 129 & 0.474 \\  & 80\% & 0.0009 & 414 & 0.515 \\ \hline \multirow{4}{*}{800 mm} & 50\% & 0.0024 & 624 & 0.312 \\  & 60\% & 0.0019 & 665 & 0.206 \\  & 70\% & 0.0031 & 658 & 0.616 \\  & 80\% & 0.0034 & 725 & 0.435 \\ \hline \multirow{4}{*}{1000 mm} & 50\% & 0.0014 & 633 & 0.528 \\  & 60\% & 0.0009 & 797 & 0.800 \\ \cline{1-1}  & 70\% & 0.0016 & 678 & 0.701 \\ \cline{1-1}  & 80\% & 0.0024 & 502 & 0.699 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: PSO-LSTM optimization parameters for the gravel sample groups. Figure 18: Gravel samples with an insertion depth of 800 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%. The prediction performance of the LSTM and PSO-LSTM models for inserting sand samples with depths of 600 mm, 800 mm, and 1000 mm are shown in Figures 20-22. The prediction performance indexes of LSTM and PSO-LSTM for sand sample groups with insertion depths of 600 mm, 800 mm, and 1000 mm are shown in Table 8, and the optimization parameters of PSO-LSTM are shown in Table 9.

In the LSTM model, when the training samples are fewer, it is easy to create an error accumulation, and the later predicted values of the timeseries show a large deviation from the actual values. This is more obvious in the gravel sample groups, where the \(ARE\)s of insertion depths of 600 mm, 800 mm, and 1000 mm are greater than 7% when the training set is 50%. In contrast, this value is relatively low in the sand sample groups, but the \(ARE\) is as high as 9.9% in the sample with an insertion depth of 1000 mm. The prediction accuracy is further improved with the increase in the number of training samples. When the training set reaches 80%, the \(ARE\) is only 2.56% in the sample with 800 mm insertion depth in the gravel experiment groups, but 7.18% in the sample with 600 mm insertion depth. While in the sand experiment groups, only the \(ARE\) of the sample with the 800 mm insertion

Figure 19: Gravel 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%. Figure 21: Sand samples with an insertion depth of 800 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%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Insertion** & **The Proportion** & **Initial** & **Number of Hidden** & **Dropout** \\
**Depth** & **of Training Set** & **Learning Rate** & **Layer Units** & **Probability** \\ \hline \multirow{3}{*}{600 mm} & 50\% & 0.0081 & 395 & 0.465 \\  & 60\% & 0.0097 & 414 & 0.259 \\  & 70\% & 0.0048 & 208 & 0.255 \\  & 80\% & 0.0012 & 633 & 0.504 \\ \hline \multirow{3}{*}{800 mm} & 50\% & 0.0086 & 368 & 0.743 \\  & 60\% & 0.0016 & 631 & 0.487 \\ \cline{1-1}  & 70\% & 0.0009 & 651 & 0.554 \\ \cline{1-1}  & 80\% & 0.0012 & 619 & 0.218 \\ \hline \multirow{3}{*}{1000 mm} & 50\% & 0.0011 & 625 & 0.500 \\ \cline{1-1}  & 60\% & 0.0022 & 768 & 0.495 \\ \cline{1-1}  & 70\% & 0.0021 & 756 & 0.453 \\ \cline{1-1}  & 80\% & 0.0082 & 647 & 0.653 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: PSO-LSTM optimization parameters for the sand sample groups. In the PSO-LSTM model, the prediction accuracy of all samples is improved over some range, even when the training set is sparser. The maximum value of \(ARE\) for the three samples in the gravel sample groups is 4.76% when the training set is 50%. When the training set is 80%, the maximum value of \(ARE\) is 2.28%.