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Multi-scale degradation forecasting of PEMFCs under non-stationary operating conditions: A novel spatio-temporal deep learning framework

Author

Listed:
  • Yang, Yijun
  • Han, Qingyang
  • Zhang, Zhizheng
  • Zhang, Hailun
  • Xue, Haoyuan
  • Sun, Wenxu
  • Jia, Lei

Abstract

Predicting the degradation is crucial for effective fuel cell health management, which directly impacts the reliability and cost-efficiency of proton exchange membrane fuel cells (PEMFC). While deep learning have achieved success in PEMFC degradation prediction, existing methods face challenges in modeling non-stationary, spatial correlations and long-term dependencies of multi-sensor data. To address these challenges, we propose SANformer, a novel Transformer-based spatio-temporal modeling framework. Specifically, SANformer consist of a Transformer based on spatial attention and a seasonal-trend decomposition module, which work in parallel to jointly capture complex spatial and temporal dependencies in degradation data. Furthermore, we introduce an adaptive non-stationary reconstruction attention (ANRA) mechanism that can dynamically reconstruct attention maps by identifying non-stationary factors from multi-sensor time series data. Experimental results on both static and quasi-dynamic datasets demonstrate that SANformer significantly outperforms existing state-of-the-art methods in prediction accuracy and maintains robust performance even under limited training data conditions.

Suggested Citation

  • Yang, Yijun & Han, Qingyang & Zhang, Zhizheng & Zhang, Hailun & Xue, Haoyuan & Sun, Wenxu & Jia, Lei, 2026. "Multi-scale degradation forecasting of PEMFCs under non-stationary operating conditions: A novel spatio-temporal deep learning framework," Renewable Energy, Elsevier, vol. 256(PD).
  • Handle: RePEc:eee:renene:v:256:y:2026:i:pd:s0960148125018063
    DOI: 10.1016/j.renene.2025.124142
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    References listed on IDEAS

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    1. Benaggoune, Khaled & Yue, Meiling & Jemei, Samir & Zerhouni, Noureddine, 2022. "A data-driven method for multi-step-ahead prediction and long-term prognostics of proton exchange membrane fuel cell," Applied Energy, Elsevier, vol. 313(C).
    2. Yu, Yang & Yu, Qinghua & Luo, RunSen & Chen, Sheng & Yang, Jiebo & Yan, Fuwu, 2024. "Degradation and polarization curve prediction of proton exchange membrane fuel cells: An interpretable model perspective," Applied Energy, Elsevier, vol. 365(C).
    3. Xuan Meng & Jian Mei & Xingwang Tang & Jinhai Jiang & Chuanyu Sun & Kai Song, 2024. "The Degradation Prediction of Proton Exchange Membrane Fuel Cell Performance Based on a Transformer Model," Energies, MDPI, vol. 17(12), pages 1-13, June.
    4. Li, Zhongliang & Outbib, Rachid & Giurgea, Stefan & Hissel, Daniel & Jemei, Samir & Giraud, Alain & Rosini, Sebastien, 2016. "Online implementation of SVM based fault diagnosis strategy for PEMFC systems," Applied Energy, Elsevier, vol. 164(C), pages 284-293.
    5. Deng, Zhihua & Wang, Haijiang & Liu, Hao & Chen, Qihong & Zhang, Jiashun, 2024. "Degradation prediction of proton exchange membrane fuel cell using a novel neuron-fuzzy model based on light spectrum optimizer," Renewable Energy, Elsevier, vol. 234(C).
    6. Zhu, Wenchao & Li, Changzhi & Xu, Yafei & Yang, Wenlong & Xie, Changjun, 2024. "High accuracy and adaptability of PEMFC degradation interval prediction with Informer-GPR under dynamic conditions," Energy, Elsevier, vol. 307(C).
    7. Lv, Jianfeng & Shen, Xiaoning & Gao, Yabin & Liu, Jianxing & Sun, Guanghui, 2024. "The seasonal-trend disentangle based prognostic framework for PEM fuel cells," Renewable Energy, Elsevier, vol. 228(C).
    8. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    9. Yang, Yang & Yu, Xiaoran & Zhu, Wenchao & Xie, Changjun & Zhao, Bo & Zhang, Leiqi & Shi, Ying & Huang, Liang & Zhang, Ruiming, 2023. "Degradation prediction of proton exchange membrane fuel cells with model uncertainty quantification," Renewable Energy, Elsevier, vol. 219(P2).
    10. El Aoumari, Abdelaziz & Ouadi, Hamid & El-Bakkouri, Jamal & Giri, Fouad, 2024. "Adaptive filtered high-gain observer for PEMFC systems in electric vehicles," Renewable Energy, Elsevier, vol. 231(C).
    11. Song, Ke & Huang, Xing & Huang, Pengyu & Sun, Hui & Chen, Yuhui & Huang, Dongya, 2024. "Data-driven health state estimation and remaining useful life prediction of fuel cells," Renewable Energy, Elsevier, vol. 227(C).
    12. Sheng, Chuang & Fu, Jun & Qin, HongChuan & Zu, YanMin & Liang, YeZhe & Deng, ZhongHua & Wang, Zhuo & Li, Xi, 2024. "Short-term hybrid prognostics of fuel cells: A comparative and improvement study," Renewable Energy, Elsevier, vol. 237(PB).
    13. Lei Fan & Jianhua Gao & Yanda Lu & Wei Shen & Su Zhou, 2023. "Empirical Degradation Models of the Different Indexes of the Proton Exchange Membrane Fuel Cell Based on the Component Degradation," Energies, MDPI, vol. 16(24), pages 1-19, December.
    14. Whitney Newey & Kenneth West, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
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