# PEMFC RUL Prediction for Non-Stationary Time Series Based on Crossformer Model
## 5 Conclusions  
In the context of the urgent global demand for sustainable development, hydrogen energy is receiving considerable attention due to its clean and efficient characteristics. Consequently, hydrogen-powered vehicles, which use PEMFc as their power source, are rapidly gaining prominence. This paper focuses on PEMFc as the subject of study, with the objective of predicting their RUL. 1. This paper proposes a PEMFC RUL prediction model for non-stationary time series, called the De-stationary-Crossformer, which is an improved version of the Crossformer, incorporating non-stationary modeling techniques to enhance its capability in learning complex time series features. Compared to existing prediction methods based on LSTM, TCN, and the Transformer, the proposed model not only effectively captures short-term fluctuations but also leverages dependencies among multiple dimensions of the data, thereby improving prediction stability and accuracy. This study provides a new perspective on non-stationary time series modeling and fills the research gap in applying such methods to PEMFC lifetime prediction. 2. Compared to the Crossformer model, the model proposed in this paper demonstrates superior performance in both MSE and DTW evaluation metrics. Specifically, our model effectively addresses the issues of gradient vanishing and explosion commonly encountered in traditional time series prediction models such as LSTM and TCN, while also improving the ability to capture short-term fluctuations. Moreover, it overcomes the limitations of Transformer-based models in utilizing the dependencies between different dimensions of multivariate time series and capturing the non stationarity present in real-world datasets. The experimental results show that the MSE and DTW of our model improved by 17.73% and 8.98%, respectively, compared to the Crosformer model. 3. Through the plotting of the predicted and actual sequences for the experimental vehicles using five mainstream models and the De-stationary-Crosformer, it is observed that the model proposed in this paper significantly achieves the highest similarity between the predicted sequences and the actual sequences. 4. Through network model ablation experiments, the contribution of each major component of the De-stationary-Crosformer to enhancing the overall performance of the model is validated. Future work stemming from this paper could be approached from the following perspectives:  
1. To address existing limitations, the De-stationary-Crosformer improves the model's capability by adding or optimizing module structures, which leads to an increase in overall model parameters. However, this architectural design may still have limitations in handling extremely complex nonlinear features and long-range dependencies. Additionally, although the non-stationary attention mechanism enhances the model's ability to handle non-stationary time series data, it may become overly sensitive to noise and outliers in extreme cases, thus compromising the model's robustness. Future work will focus on optimizing and reducing model parameters to achieve a more lightweight model, improving computational efficiency. Furthermore, in terms of data processing, the more effective handling of outliers and noise is required to avoid the aforementioned extreme cases, thereby enhancing the model's practical applicability;
2. When predicting data for vehicles with significant and frequent fluctuations, the accuracy of the results produced by the De-stationary-Crosformer still needs improvement. Future efforts should focus on enhancing the model's capability to handle strongly non-stationary data;
3. This paper limits the scope of multi-step predictions in the PEMFC RUL forecasting task to 8-64 h. Future research could extend predictions to longer time steps. Conceptualization, N.Z. ; Methodology, K.W. and J.Z. ; Software, H.Z. and Z.Z. ; Validation, H.Z., Z.Z. and J.Z. ; Investigation, N.Z. ; Resources, J.Z. ; Data curation, H.Z., Z.Z. and K.W. ; Writing--original draft, N.Z. ; Writing--review & editing, N.Z.