# PEMFC RUL Prediction for Non-Stationary Time Series Based on Crossformer Model
## 4 Results and Discussion
### Results
#### 4.2.1 Network Model Comparative Experiment
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Models** & \multicolumn{2}{c}{**LSTnet**} & \multicolumn{2}{c}{**TCN**} & \multicolumn{2}{c}{**LSTM-ATTN**} & \multicolumn{2}{c}{**Transformer**} & \multicolumn{2}{c}{**Crossformer**} & \multicolumn{2}{c}{
\begin{tabular}{c} **De-Stationary-** \\ **Crosformer** \\ \end{tabular} } \\
**Steps** & **MSE** & **DTW** & **MSE** & **DTW** & **MSE** & **DTW** & **MSE** & **DTW** & **MSE** & **DTW** \\ \hline
**8** & 3.152 & 0.846 & 2.224 & 0.712 & 2.592 & 0.763 & 0.815 & 0.384 & 0.725 & 0.373 & **0.556** & **0.324** \\
**16** & 3.421 & 1.262 & 2.823 & 1.417 & 2.572 & 1.085 & 0.966 & 0.652 & 0.809 & 0.597 & **0.717** & **0.551** \\
**24** & 3.343 & 1.527 & 2.851 & 1.411 & 2.925 & 1.423 & 1.609 & 1.073 & 0.888 & 0.783 & **0.778** & **0.743** \\
**32** & 3.275 & 1.742 & 3.288 & 1.752 & 2.600 & 1.544 & 1.461 & 1.166 & 1.003 & 0.928 & **0.791** & **0.862** \\
**48** & 3.371 & 2.194 & 3.004 & 2.078 & 2.668 & 1.943 & 1.995 & 1.710 & 1.022 & 1.230 & **0.886** & **1.136** \\
**64** & 3.349 & 2.513 & 3.044 & 2.395 & 2.715 & 2.254 & 1.588 & 1.730 & 1.058 & 1.425 & **0.795** & **1.237** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparative experimental results of experimental vehicles at different time step lengths. To provide a clearer understanding of the similarity between the predicted and actual sequences designed in this chapter, Figure 9 displays the performance of six comparative models on the test set for the experimental vehicles. Figure 9d shows a comparison between the predicted and actual values using the LSTNet model. It can be observed that while the model performs well in predicting smooth trends, it struggles to adequately fit the actual fluctuations in the dataset, which exhibits a certain degree of non-stationarity. Figures 9c and 9e show the results of the LSTM and TCN models, respectively, indicating that while these models have some success in predicting the overall trend, they fail to effectively capture short-term fluctuations. Figures 9a and 9f display the results of the Transformer and Crossformer models. The Transformer-based model demonstrates strong sensitivity to both long-term trends and short-term fluctuations, while the Crossformer model further improves the capture of short-term voltage fluctuations, though it may slightly deviate from the true values in some cases. Figure 9b shows the performance of the proposed model, which clearly outperforms the other five models in terms of trend prediction and accuracy. This model not only captures short-term details and long-term trends but also addresses non-stationarity in the data more effectively. For example, in the 0-200 time range in Figure 9b, the predicted values are clearly superior to those of the other models. Therefore, the proposed model effectively addresses the non-stationarity of PEMFC data while maintaining high prediction accuracy. Figures 10 and 11 illustrate the error analysis of various models based on the mean squared error (MSE) and dynamic time warping (DTW) metrics, respectively. As is shown, the proposed model achieves the lowest MSE, with a highly concentrated distribution and almost no outliers, indicating high stability and low uncertainty in its error. This suggests that the proposed model's predictions are closely aligned with the actual values,  
Figure 9: Comparison of predicted and actual values across models. demonstrating high accuracy. Similarly, the proposed model also excels in the DTW metric, displaying a narrow error distribution and few outliers, which highlights its consistency and accuracy in temporal alignment. In contrast, the MSE distribution for the Crossformer and Transformer models ranks second lowest, with a relatively concentrated error spread but a few outliers. This suggests that while these models perform well overall, they exhibit deviations in certain instances.