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Degradation trajectories prognosis for PEM fuel cell systems based on Gaussian process regression

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  • Deng, Huiwen
  • Hu, Weihao
  • Cao, Di
  • Chen, Weirong
  • Huang, Qi
  • Chen, Zhe
  • Blaabjerg, Frede

Abstract

The aging trajectory prognosis is an effective tool to prolong the lifespan and lower the cost of proton exchange membrane fuel cell (PEMFC) systems. In this paper, Gaussian process regression modeling frameworks based on sparse pseudo-input Gaussian process (SPGP) and variational auto-encoded deep Gaussian process (VAE-DGP) are proposed to predict the degradation trend and cope with model uncertainty for PEMFCs. The optimal hyper parameters and pseudo-input locations are obtained with conjugate gradient by maximizing the marginal likelihood. Besides, the variational parameters and closed-form variational lower bound are optimized through variable inference, radial basis function (RBF) kernel is utilized to determine the priori distribution of Gaussian process. Then stack voltage and output power are extracted as health indicators (HIs). To fully demonstrate the prediction performance, long-term experimental validation with static and dynamic aging tests are performed, single-input and multi-input structures are respectively constructed in SPGP and VAE-DGP for comparison with the existing models. The results show that the proposed methods outperform other data-driven methods, moreover, SPGP is more suitable for large data regime and VAE-DGP operates better with small data regime. Finally, the performance evolution is presented with 95% confidence interval to validate the mapping accuracy and reliability further.

Suggested Citation

  • Deng, Huiwen & Hu, Weihao & Cao, Di & Chen, Weirong & Huang, Qi & Chen, Zhe & Blaabjerg, Frede, 2022. "Degradation trajectories prognosis for PEM fuel cell systems based on Gaussian process regression," Energy, Elsevier, vol. 244(PA).
    • Handle: RePEc:eee:energy:v:244:y:2022:i:pa:s0360544221028188
    DOI: 10.1016/j.energy.2021.122569
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    References listed on IDEAS

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    1. Zhou, Daming & Gao, Fei & Breaz, Elena & Ravey, Alexandre & Miraoui, Abdellatif, 2017. "Degradation prediction of PEM fuel cell using a moving window based hybrid prognostic approach," Energy, Elsevier, vol. 138(C), pages 1175-1186.
    2. 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.
    3. 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).
    4. Zhou, Dengji & Yu, Ziqiang & Zhang, Huisheng & Weng, Shilie, 2016. "A novel grey prognostic model based on Markov process and grey incidence analysis for energy conversion equipment degradation," Energy, Elsevier, vol. 109(C), pages 420-429.
    5. 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.
    6. 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.
    7. Hua, Zhiguang & Zheng, Zhixue & Péra, Marie-Cécile & Gao, Fei, 2020. "Remaining useful life prediction of PEMFC systems based on the multi-input echo state network," Applied Energy, Elsevier, vol. 265(C).
    8. Wang, Yujie & Sun, Zhendong & Chen, Zonghai, 2019. "Development of energy management system based on a rule-based power distribution strategy for hybrid power sources," Energy, Elsevier, vol. 175(C), pages 1055-1066.
    9. Zhu, Li & Chen, Junghui, 2018. "Prognostics of PEM fuel cells based on Gaussian process state space models," Energy, Elsevier, vol. 149(C), pages 63-73.
    10. Fathabadi, Hassan, 2018. "Novel fuel cell/battery/supercapacitor hybrid power source for fuel cell hybrid electric vehicles," Energy, Elsevier, vol. 143(C), pages 467-477.
    11. 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.
    12. Pan, Rui & Yang, Duo & Wang, Yujie & Chen, Zonghai, 2020. "Health degradation assessment of proton exchange membrane fuel cell based on an analytical equivalent circuit model," Energy, Elsevier, vol. 207(C).
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    Cited by:

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    2. Yaping Wu & Xiaolong Wu & Yuanwu Xu & Yongjun Cheng & Xi Li, 2023. "A Novel Adaptive Neural Network-Based Thermoelectric Parameter Prediction Method for Enhancing Solid Oxide Fuel Cell System Efficiency," Sustainability, MDPI, vol. 15(19), pages 1-17, September.
    3. Li, Changzhi & Lin, Wei & Wu, Hangyu & Li, Yang & Zhu, Wenchao & Xie, Changjun & Gooi, Hoay Beng & Zhao, Bo & Zhang, Leiqi, 2023. "Performance degradation decomposition-ensemble prediction of PEMFC using CEEMDAN and dual data-driven model," Renewable Energy, Elsevier, vol. 215(C).
    4. SK Safdar Hossain & Bamidele Victor Ayodele & Syed Sadiq Ali & Chin Kui Cheng & Siti Indati Mustapa, 2022. "Comparative Analysis of Support Vector Machine Regression and Gaussian Process Regression in Modeling Hydrogen Production from Waste Effluent," Sustainability, MDPI, vol. 14(12), pages 1-14, June.
    5. Huu-Linh Nguyen & Sang-Min Lee & Sangseok Yu, 2023. "A Comprehensive Review of Degradation Prediction Methods for an Automotive Proton Exchange Membrane Fuel Cell," Energies, MDPI, vol. 16(12), pages 1-32, June.
    6. Aihua Tang & Yuanhang Yang & Quanqing Yu & Zhigang Zhang & Lin Yang, 2022. "A Review of Life Prediction Methods for PEMFCs in Electric Vehicles," Sustainability, MDPI, vol. 14(16), pages 1-18, August.
    7. Hasanien, Hany M. & Shaheen, Mohamed A.M. & Turky, Rania A. & Qais, Mohammed H. & Alghuwainem, Saad & Kamel, Salah & Tostado-Véliz, Marcos & Jurado, Francisco, 2022. "Precise modeling of PEM fuel cell using a novel Enhanced Transient Search Optimization algorithm," Energy, Elsevier, vol. 247(C).

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