# Prediction of Truck Fuel Consumption Based on Crossformer-LSTM Characteristic Distillation
## 5 Results and Discussion
### Model Robustness Validation  
To verify the robustness of the CLMFD model in the presence of various uncertainties, noise, and anomalous data, random masking was applied to the data (Xi'an to Shanyang; Xi'an to Bao Mao) to simulate anomalous conditions. Anomalous data samples refer to values in the dataset that are introduced due to factors such as data collection errors, transmission interference, noise, and sudden events (e.g., traffic accidents or extreme braking behaviors). These types of data may interfere with the model's training and prediction, affecting its practical application. By randomly masking a portion of the input data samples (i.e., setting different masking rates), we systematically simulate missing data  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Prediction Method** & **MSE** & **RMSE** & **MAE** & \(\mathbf{R^{2}}\) \\ \hline Crossformer & 0.0932 & 0.3159 & 0.2107 & 0.7150 \\ LSTM & 0.1005 & 0.3172 & 0.2070 & 0.7128 \\ CLMFD & 0.0962 & 0.3102 & 0.2078 & 0.6716 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Ablation Study Results for the CLMFD Model.  
Figure 8: Evaluation results of Xi’an–Baomao.  
or anomalous values, assessing the model's robustness and stability when data quality deteriorates, noise increases, and anomalous samples are present. The random masking rates were set to 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, and 0.40. By gradually increasing the masking rate, changes in model performance were observed using the MSE, MAE, R\({}^{2}\), and RMSE metrics to verify the CLMFD model's ability to resist interference.  
The experimental results, as shown in Figure 9, indicate that the CLMFD model outperforms the baseline models in terms of MSE, MAE, and R\({}^{2}\). In terms of RMSE, the performance of the CLMFD model is comparable to that of the Transformer model but better than other baseline models. As the masking rate increases, the changes in the evaluation metrics for CLMFD are minimal, indicating that the model exhibits considerable stability. Among the baseline models, the RF model performs the worst. When the masking rate exceeds 0.25, the R\({}^{2}\) value becomes negative, indicating that the model's fit is worse than simply using the average of the target variable, meaning the model's predictions are worse than random guessing. This suggests that the RF model may suffer from significant underfitting.  
From the above experiments, it is evident that the CLMFD model exhibits strong robustness and excellent predictive capabilities even in the presence of anomalous data. To further investigate the predictive capability of different components of the CLMFD model under anomalous data, tests were conducted with a masking rate of 0.05. The results, presented in Table 8, show that the CLMFD model outperforms both the Crosformer and LSTM models.  
By integrating the advantages of both models through multi-layer feature distillation, the CLMFD model improves generalization on unseen data and helps the student model learn more information from the teacher model, addressing anomalous data issues and enhancing model prediction performance.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MSE** & **RMSE** & **MAE** & **R\({}^{2}\)** \\ \hline Crosformer & 0.1051 & 0.3243 & 0.2105 & 0.6981 \\ LSTM & 0.1227 & 0.3502 & 0.2245 & 0.6498 \\ CLMFD & 0.1019 & 0.3065 & 0.2065 & 0.7319 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Prediction Results of CLMFD Model and Its Components on Anomalous Data.  
Figure 9: Prediction results of abnormal data with different mask rates.