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Steady-State Model Enabled Dynamic PEMFC Performance Degradation Prediction via Recurrent Neural Network

Author

Listed:
  • Qiang Liu

    (School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China)

  • Weihong Zang

    (State-Assigned Electric Vehicle Power Battery Testing Center, China North Vehicle Research Institute, Beijing 100072, China)

  • Wentao Zhang

    (State-Assigned Electric Vehicle Power Battery Testing Center, China North Vehicle Research Institute, Beijing 100072, China)

  • Yang Zhang

    (State-Assigned Electric Vehicle Power Battery Testing Center, China North Vehicle Research Institute, Beijing 100072, China)

  • Yuqi Tong

    (State-Assigned Electric Vehicle Power Battery Testing Center, China North Vehicle Research Institute, Beijing 100072, China)

  • Yanbiao Feng

    (School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China)

Abstract

Proton exchange membrane fuel cells (PEMFC), distinguished by rapid refueling capability and zero tailpipe emissions, have emerged as a transformative energy conversion technology for automotive applications. Nevertheless, their widespread commercialization remains constrained by technical limitations mainly in operational longevity. Precise prognostics of performance degradation could enable real-time optimization of operation, thereby extending service life. This investigation proposes a hybrid prognostic framework integrating steady-state modeling with dynamic condition. First, a refined semi-empirical steady-state model was developed. Model parameters’ identification was achieved using grey wolf optimizer. Subsequently, dynamic durability testing data underwent systematic preprocessing through a correlation-based screening protocol. The processed dataset, comprising model-calculated reference outputs under dynamic conditions synchronized with filtered operational parameters, served as inputs for a recurrent neural network (RNN). Comparative analysis of multiple RNN variants revealed that the hybrid methodology achieved superior prediction fidelity, demonstrating a root mean square error of 0.6228%. Notably, the integration of steady-state physics could reduce the RNN structural complexity while maintaining equivalent prediction accuracy. This model-informed data fusion approach establishes a novel paradigm for PEMFC lifetime assessment. The proposed methodology provides automakers with a computationally efficient framework for durability prediction and control optimization in vehicular fuel cell systems.

Suggested Citation

  • Qiang Liu & Weihong Zang & Wentao Zhang & Yang Zhang & Yuqi Tong & Yanbiao Feng, 2025. "Steady-State Model Enabled Dynamic PEMFC Performance Degradation Prediction via Recurrent Neural Network," Energies, MDPI, vol. 18(10), pages 1-20, May.
  • Handle: RePEc:gam:jeners:v:18:y:2025:i:10:p:2665-:d:1661126
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    References listed on IDEAS

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    1. Zuo, Jian & Lv, Hong & Zhou, Daming & Xue, Qiong & Jin, Liming & Zhou, Wei & Yang, Daijun & Zhang, Cunman, 2021. "Deep learning based prognostic framework towards proton exchange membrane fuel cell for automotive application," Applied Energy, Elsevier, vol. 281(C).
    2. Liu, Yanjun & Li, Hao & Yang, Yang & Zhu, Wenchao & Xie, Changjun & Yu, Xiaoran & Guo, Bingxin, 2025. "Reliability assessment of PEMFC aging prediction based on probabilistic Bayesian mixed recurrent neural networks," Renewable Energy, Elsevier, vol. 246(C).
    3. Huang, Ruike & Zhang, Xuexia & Dong, Sidi & Huang, Lei & Li, Yuan, 2025. "Degradation prediction of PEM fuel cell using LSTM based on Gini gamma correlation coefficient and improved sand cat swarm optimization under dynamic operating conditions," Applied Energy, Elsevier, vol. 392(C).
    4. Tao, Zihan & Zhang, Chu & Xiong, Jinlin & Hu, Haowen & Ji, Jie & Peng, Tian & Nazir, Muhammad Shahzad, 2023. "Evolutionary gate recurrent unit coupling convolutional neural network and improved manta ray foraging optimization algorithm for performance degradation prediction of PEMFC," Applied Energy, Elsevier, vol. 336(C).
    5. Ma, Rui & Yang, Tao & Breaz, Elena & Li, Zhongliang & Briois, Pascal & Gao, Fei, 2018. "Data-driven proton exchange membrane fuel cell degradation predication through deep learning method," Applied Energy, Elsevier, vol. 231(C), pages 102-115.
    6. Zhang, Tong & Wang, Peiqi & Chen, Huicui & Pei, Pucheng, 2018. "A review of automotive proton exchange membrane fuel cell degradation under start-stop operating condition," Applied Energy, Elsevier, vol. 223(C), pages 249-262.
    7. Jouin, Marine & Bressel, Mathieu & Morando, Simon & Gouriveau, Rafael & Hissel, Daniel & Péra, Marie-Cécile & Zerhouni, Noureddine & Jemei, Samir & Hilairet, Mickael & Ould Bouamama, Belkacem, 2016. "Estimating the end-of-life of PEM fuel cells: Guidelines and metrics," Applied Energy, Elsevier, vol. 177(C), pages 87-97.
    8. Jouin, Marine & Gouriveau, Rafael & Hissel, Daniel & Péra, Marie-Cécile & Zerhouni, Noureddine, 2016. "Degradations analysis and aging modeling for health assessment and prognostics of PEMFC," Reliability Engineering and System Safety, Elsevier, vol. 148(C), pages 78-95.
    9. Chen, Huicui & Pei, Pucheng & Song, Mancun, 2015. "Lifetime prediction and the economic lifetime of Proton Exchange Membrane fuel cells," Applied Energy, Elsevier, vol. 142(C), pages 154-163.
    10. Yang, Jibin & Chen, Li & Zhang, Bo & Zhang, Han & Chen, Bo & Wu, Xiaohua & Deng, Pengyi & Xu, Xiaohui, 2025. "Remaining useful life prediction for vehicle-oriented PEMFCs based on organic gray neural network considering the influence of dual energy source synergy," Energy, Elsevier, vol. 322(C).
    11. Ko, Taehwan & Kim, Dukyong & Park, Jaewoong & Lee, Seung Hwan, 2025. "Physics-informed neural network for long-term prognostics of proton exchange membrane fuel cells," Applied Energy, Elsevier, vol. 382(C).
    12. Bressel, Mathieu & Hilairet, Mickael & Hissel, Daniel & Ould Bouamama, Belkacem, 2016. "Extended Kalman Filter for prognostic of Proton Exchange Membrane Fuel Cell," Applied Energy, Elsevier, vol. 164(C), pages 220-227.
    13. Liu, Hao & Chen, Jian & Hissel, Daniel & Su, Hongye, 2019. "Remaining useful life estimation for proton exchange membrane fuel cells using a hybrid method," Applied Energy, Elsevier, vol. 237(C), pages 910-919.
    14. Wu, Kangcheng & Du, Qing & Zu, Bingfeng & Wang, Yupeng & Cai, Jun & Gu, Xin & Xuan, Jin & Jiao, Kui, 2021. "Enabling real-time optimization of dynamic processes of proton exchange membrane fuel cell: Data-driven approach with semi-recurrent sliding window method," Applied Energy, Elsevier, vol. 303(C).
    15. Pei, Pucheng & Chen, Dongfang & Wu, Ziyao & Ren, Peng, 2019. "Nonlinear methods for evaluating and online predicting the lifetime of fuel cells," Applied Energy, Elsevier, vol. 254(C).
    16. Liu, Zhongyong & Sun, Hao & Xu, Lifeng & Mao, Lei & Hu, Zhiyong & Li, Jingguo, 2025. "Toward low-data and real-time PEMFC diagnostic: Multi-sine stimulation and hybrid ECM-informed neural network," Applied Energy, Elsevier, vol. 391(C).
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