IDEAS home Printed from https://ideas.repec.org/a/eee/renene/v256y2026ipds0960148125018063.html

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960148125018063
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.renene.2025.124142?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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).
    4. 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).
    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. 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.
    7. 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.
    8. 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).
    9. 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.
    10. 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).
    11. 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).
    12. 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).
    13. 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).
    14. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Feng, Ruizhe & Zhu, Shuzhao & Jiang, Ruixin & Cai, Xin & Lin, Rui, 2026. "Degradation prediction of the low-Pt loading proton exchange membrane fuel cell based on spatio-temporal Transformer network," Energy, Elsevier, vol. 342(C).
    2. Vitek, Francis, 2006. "Measuring the Stance of Monetary Policy in a Small Open Economy: A Dynamic Stochastic General Equilibrium Approach," MPRA Paper 802, University Library of Munich, Germany.
    3. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    4. Galvão, Ana Beatriz, 2013. "Changes in predictive ability with mixed frequency data," International Journal of Forecasting, Elsevier, vol. 29(3), pages 395-410.
    5. Daniel Buncic, 2012. "Understanding forecast failure of ESTAR models of real exchange rates," Empirical Economics, Springer, vol. 43(1), pages 399-426, August.
    6. Gradojevic, Nikola & Erdemlioglu, Deniz & Gençay, Ramazan, 2020. "A new wavelet-based ultra-high-frequency analysis of triangular currency arbitrage," Economic Modelling, Elsevier, vol. 85(C), pages 57-73.
    7. Cavit Pakel & Neil Shephard & Kevin Sheppard, 2009. "Nuisance parameters, composite likelihoods and a panel of GARCH models," OFRC Working Papers Series 2009fe03, Oxford Financial Research Centre.
    8. Lees, Kirdan & Matheson, Troy & Smith, Christie, 2011. "Open economy forecasting with a DSGE-VAR: Head to head with the RBNZ published forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 512-528, April.
    9. Mehmet Balcilar & Rangan Gupta & Stephen M. Miller, 2015. "The out-of-sample forecasting performance of nonlinear models of regional housing prices in the US," Applied Economics, Taylor & Francis Journals, vol. 47(22), pages 2259-2277, May.
    10. Sucarrat, Genaro, 2009. "Forecast Evaluation of Explanatory Models of Financial Variability," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy, vol. 3, pages 1-33.
    11. Domenico Giannone & Troy D. Matheson, 2007. "A New Core Inflation Indicator for New Zealand," International Journal of Central Banking, International Journal of Central Banking, vol. 3(4), pages 145-180, December.
    12. Peter Carr & Liuren Wu, 2023. "Decomposing Long Bond Returns: A Decentralized Theory," Review of Finance, European Finance Association, vol. 27(3), pages 997-1026.
    13. Diego Amaya & Jean-François Bégin & Geneviève Gauthier, 2022. "The Informational Content of High-Frequency Option Prices," Management Science, INFORMS, vol. 68(3), pages 2166-2201, March.
    14. Liu, Dandan & Jansen, Dennis W., 2007. "Macroeconomic forecasting using structural factor analysis," International Journal of Forecasting, Elsevier, vol. 23(4), pages 655-677.
    15. Corradi, Valentina & Swanson, Norman R., 2004. "Some recent developments in predictive accuracy testing with nested models and (generic) nonlinear alternatives," International Journal of Forecasting, Elsevier, vol. 20(2), pages 185-199.
    16. Ang, Andrew & Piazzesi, Monika & Wei, Min, 2006. "What does the yield curve tell us about GDP growth?," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 359-403.
    17. Diaa Noureldin & Neil Shephard & Kevin Sheppard, 2012. "Multivariate high‐frequency‐based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 907-933, September.
    18. Clarida, Richard H. & Sarno, Lucio & Taylor, Mark P. & Valente, Giorgio, 2003. "The out-of-sample success of term structure models as exchange rate predictors: a step beyond," Journal of International Economics, Elsevier, vol. 60(1), pages 61-83, May.
    19. Hamid Baghestani, 2010. "Evaluating Blue Chip forecasts of the trade-weighted dollar exchange rate," Applied Financial Economics, Taylor & Francis Journals, vol. 20(24), pages 1879-1889.
    20. Reus, Lorenzo & Carrasco, José A. & Pincheira, Pablo, 2020. "Do it with a smile: Forecasting volatility with currency options," Finance Research Letters, Elsevier, vol. 34(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:renene:v:256:y:2026:i:pd:s0960148125018063. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/renewable-energy .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.