Remaining Useful Life Prediction of Proton Exchange Membrane Fuel Cell Considering Long-Short Range Time Series Heterogeneity
Zha Pengtang1, Su Hongyu1, Gao Fengyang1, Han Yunfei1, Yue Wenhan2
1. Automation and Electrical Engineering Lanzhou Jiaotong University Lanzhou 730070 China; 2. Zhangye Power Supply Company State Grid Gansu Electric Power Company Zhangye 734000 China
Abstract：To improve the accuracy and stability of aging prediction for proton exchange membrane fuel cell (PEMFC), this study proposes a novel predictive modeling framework that explicitly distinguishes long-term and short-term time-series characteristics to capture the heterogeneity in fuel cell voltage degradation. PEMFC aging is simultaneously influenced by global, gradual degradation processes and local, abrupt fluctuations induced by complex electrochemical recovery phenomena. Traditional single-model approaches often struggle to accurately capture both types of characteristics, thereby reducing generalization capability and robustness under varying operating conditions. The proposed method first employs a multi-scale resolution decomposition strategy to separate the long-term and short-term components of the PEMFC voltage signal. The long-term component reflects the overall degradation trend and is modeled using the Mamba state-space architecture, which effectively represents long-range temporal dependencies and extracts smooth global aging trajectories. The short-term component represents transient, high-frequency fluctuations caused by recovery and other localized effects, and is modeled using a Transformer equipped with a local window attention mechanism. The Transformer excels at capturing nonlinear relationships and abrupt variations over short temporal spans, thereby modeling intricate short-term dynamics that are otherwise overlooked by global models. After the two components are modeled separately, a long-short router with learnable fusion weights is introduced to adaptively integrate the outputs through end-to-end training, enabling the model to automatically adjust their contribution ratios and generate the final prediction of the voltage degradation trajectory. This fusion strategy leverages the complementary strengths of the two architectures: the Mamba's global stability in trend estimation and the Transformer's high sensitivity to local fluctuations. The proposed method is validated using aging datasets collected under static, quasi-dynamic, and fully dynamic operating conditions, and is compared with several classical machine learning and deep learning methods, including backpropagation neural network (BP), long short-term memory (LSTM), extreme learning machine (ELM), gated recurrent unit (GRU), and Transformer. When the training set proportion is 55%, under static conditions, the proposed method improves RMSE by 81.77%, 10.62%, 85.51%, 85.26%, and 72.92% compared with BP, ELM, LSTM, GRU, and Transformer, respectively. Under quasi-dynamic conditions, RMSE is improved by 5%, 50%, 24%, 35%, and 42% relative to the same baselines. Under dynamic conditions, the proposed method achieves the lowest prediction error. Across different failure thresholds, the remaining useful life (RUL) prediction accuracy of the proposed method consistently surpasses that of the benchmark approaches. The results show that, under various training data proportions and failure voltage thresholds, the proposed fusion model achieves the lowest prediction error. It is capable of accurately tracking both long-term degradation trends and short-term fluctuation patterns, enabling high-precision estimation of RUL. Comprehensive simulation analyses highlight two major advantages of the proposed framework: (1) The proposed method enhances the joint perception of global degradation trends and local dynamic variations, thereby improving prediction stability and generalization capability under unknown operating conditions. (2) By integrating the state-space modeling strengths of Mamba with the local attention mechanism of the Transformer, and by employing a learnable-weight long-short router for adaptive fusion, the method effectively handles the complex temporal dependencies, nonlinear behaviors, and multi-scale dynamic characteristics inherent in PEMFC aging processes. (3) The proposed fusion model provides a robust and high-precision prediction tool for PEMFC systems across diverse operating environments, contributing to improved maintenance planning and operational reliability.
查鹏堂, 苏红宇, 高锋阳, 韩云飞, 岳文瀚. 考虑长-短程时间序列异质性的质子交换膜燃料电池剩余使用寿命预测方法[J]. 电工技术学报, 2026, 41(15): 5330-5344.
Zha Pengtang, Su Hongyu, Gao Fengyang, Han Yunfei, Yue Wenhan. Remaining Useful Life Prediction of Proton Exchange Membrane Fuel Cell Considering Long-Short Range Time Series Heterogeneity. Transactions of China Electrotechnical Society, 2026, 41(15): 5330-5344.
[1] 杨淇, 陈景文, 华志广, 等. 基于集成型极限学习机的氢燃料电池寿命预测[J]. 电工技术学报, 2025, 40(3): 964-974. Yang Qi, Chen Jingwen, Hua Zhiguang, et al.Research on PEMFC lifetime prediction based on ensemble extreme learning machine[J]. Transactions of China Electrotechnical Society, 2025, 40(3): 964-974. [2] 汪建锋, 王荣杰, 林安辉, 等. 质子交换膜燃料电池退化预测方法[J]. 电工技术学报, 2024, 39(11): 3367-3378. Wang Jianfeng, Wang Rongjie, Lin Anhui, et al.Degradation prediction method of proton exchange membrane fuel cell[J]. Transactions of China Electro-technical Society, 2024, 39(11): 3367-3378. [3] 潘光胜, 顾伟, 张会岩, 等. 面向高比例可再生能源消纳的电氢能源系统[J]. 电力系统自动化, 2020, 44(23): 1-10. Pan Guangsheng, Gu Wei, Zhang Huiyan, et al.Electricity and hydrogen energy system towards accomodation of high proportion of renewable energy[J]. Automation of Electric Power Systems, 2020, 44(23): 1-10. [4] 全睿, 程功, 周宇龙, 等. 基于增强型鲸鱼优化算法CNN-BiGRU-AT模型的燃料电池衰退预测[J]. 电工技术学报, 2025, 40(19): 6342-6358. Quan Rui, Cheng Gong, Zhou Yulong, et al.Enhanced whale optimization algorithm-based CNN-BiGRU-AT model for aging prediction of fuel cell[J]. Tran-sactions of China Electrotechnical Society, 2025, 40(19): 6342-6358. [5] 徐冰, 张敏, 杨文涛, 等. 质子交换膜燃料电池基于老化特征的剩余使用寿命混合预测方法[J]. 电工技术学报, 2025, 40(17): 5703-5714. Xu Bing, Zhang Min, Yang Wentao, et al.PEMFC hybrid prediction method for remaining useful life based on aging characteristics[J]. Transactions of China Electrotechnical Society, 2025, 40(17): 5703-5714. [6] Zhao Yan, Luo Maji, Yang Junwei, et al.Numerical analysis of PEMFC stack performance degradation using an empirical approach[J]. International Journal of Hydrogen Energy, 2024, 56: 147-163. [7] Jouin M, Gouriveau R, Hissel D, et al.Prognostics of PEM fuel cell in a particle filtering framework[J]. International Journal of Hydrogen Energy, 2014, 39(1): 481-494. [8] Chen Kui, Laghrouche S, Djerdir A.Fuel cell health prognosis using Unscented Kalman Filter: postal fuel cell electric vehicles case study[J]. International Journal of Hydrogen Energy, 2019, 44(3): 1930-1939. [9] 赵波, 张领先, 章雷其, 等. PEMFC剩余使用寿命直接预测的混合方法[J]. 中国电机工程学报, 2024, 44(21): 8554-8567. Zhao Bo, Zhang Lingxian, Zhang Leiqi, et al.A hybrid method for direct prediction of PEMFC remaining useful life[J]. Proceedings of the CSEE, 2024, 44(21): 8554-8567. [10] Liu Hao, Chen Jian, Hissel D, et al.Prognostics methods and degradation indexes of proton exchange membrane fuel cells: a review[J]. Renewable and Sustainable Energy Reviews, 2020, 123: 109721. [11] Ma Rui, Xie Renyou, Xu Liangcai, et al.A hybrid prognostic method for PEMFC with aging parameter prediction[J]. IEEE Transactions on Transportation Electrification, 2021, 7(4): 2318-2331. [12] Pan Rui, Yang Duo, Wang Yujie, et al.Performance degradation prediction of proton exchange membrane fuel cell using a hybrid prognostic approach[J]. International Journal of Hydrogen Energy, 2020, 45(55): 30994-31008. [13] 李浩, 李浩, 杨扬, 等. 基于改进鲸鱼算法优化GRU的PEMFC老化预测[J]. 中国电机工程学报, 2024, 44(20): 8166-8177. Li Hao, Li Hao, Yang Yang, et al.PEMFC aging prediction based on improved whale optimization algorithm optimized GRU[J]. Proceedings of the CSEE, 2024, 44(20): 8166-8177. [14] Jin Jiashu, Chen Yuepeng, Xie Changjun, et al.Degradation prediction of PEMFC based on data-driven method with adaptive fuzzy sampling[J]. IEEE Transactions on Transportation Electrification, 2024, 10(2): 3363-3372. [15] 潘诗媛, 华志广, 王光伟, 等. 基于级联回声状态网络的氢燃料电池剩余使用寿命预测[J]. 中国电机工程学报, 2025, 45(12): 4718-4727. Pan Shiyuan, Hua Zhiguang, Wang Guangwei, et al.Remaining useful life prediction of hydrogen fuel cell based on cascade echo state network[J]. Proceedings of the CSEE, 2025, 45(12): 4718-4727. [16] Lee W Y, Park G G, Yang T H, et al.Empirical modeling of polymer electrolyte membrane fuel cell performance using artificial neural networks[J]. International Journal of Hydrogen Energy, 2004, 29(9): 961-966. [17] Peng Yulin, Chen Tao, Xiao Fei, et al.Remaining useful lifetime prediction methods of proton exchange membrane fuel cell based on convolutional neural network-long short-term memory and convolutional neural network-bidirectional long short-term memory[J]. Fuel Cells, 2023, 23(1): 75-87. [18] Javed K, Gouriveau R, Zerhouni N, et al.Prognostics of proton exchange membrane fuel cells stack using an ensemble of constraints based connectionist networks[J]. Journal of Power Sources, 2016, 324: 745-757. [19] Cho K, van Merriënboer B, Bahdanau D, et al. On the properties of neural machine translation: encoder-decoder approaches[C]//Proceedings of SSST-8, Eighth Workshop on Syntax, Semantics and Structure in Statistical Translation, Doha, Qatar, 2014: 103-111. [20] Li Zhongliang, Zheng Zhixue, Outbib R.Adaptive prognostic of fuel cells by implementing ensemble echo state networks in time-varying model space[J]. IEEE Transactions on Industrial Electronics, 2020, 67(1): 379-389. [21] Jin Jiashu, Chen Yuepeng, Xie Changjun, et al.Remaining useful life prediction of PEMFC based on cycle reservoir with jump model[J]. International Journal of Hydrogen Energy, 2021, 46(80): 40001-40013. [22] Gouriveau R, Hilairet M, Hissel D, et al.IEEE PHM 2014 data challenge: Outline experiments scoring of results winners[C]//IEEE Conference. Prognostics Health Manage, Belfort, France, 2014. [23] Zuo Jian, Lü Hong, Zhou Daming, et al.Long-term dynamic durability test datasets for single proton exchange membrane fuel cell[J]. Data in Brief, 2021, 35: 106775. [24] 李永佳, 徐腊梅, 朱文超, 等. 基于电压低频特性的质子交换膜燃料电池性能退化预测[J]. 中国电机工程学报, 2026, 46(3): 1086-1097. Li Yongjia, Xu Lamei, Zhu Wenchao, et al.Prediction of proton exchange membrane fuel cell performance degradation based on low-frequency voltage characteristics. Proceedings of the CSEE, 2026, 46(3): 1086-1097. [25] Smith J T H, Warrington A, Linderman S W. Simplified state space layers for sequence modeling [PP/OL]. V3. arXiv(2023-03-03)[2025-10-19]. https://arxiv.org/abs/2208.04933. [26] 金亮, 尹振豪, 刘璐, 等. 基于残差U-Net和自注意力Transformer编码器的磁场预测方法[J]. 电工技术学报, 2024, 39(10): 2937-2952. Jin Liang, Yin Zhenhao, Liu Lu, et al.Magnetic field prediction method based on residual U-Net and self-attention transformer encoder[J]. Transactions of China Electrotechnical Society, 2024, 39(10): 2937-2952. [27] Yu Xiaoran, Yang Yang, Xie Changjun, et al.Remaining-useful-life time prediction of proton exchange membrane fuel cell considering model uncertainty quantification on the full-time scale[J]. IEEE Transactions on Transportation Electrification, 2024, 10(3): 7443-7455. [28] 赵波, 张领先, 章雷其, 等. 基于TCN和AUKF联合迭代的PEMFC寿命融合预测方法[J]. 中国电机工程学报, 2025, 45(9): 3609-3623, I0029. Zhao Bo, Zhang Lingxian, Zhang Leiqi, et al.PEMFC remaining useful life fusion method based on joint iteration of TCN and AUKF[J]. Proceedings of the Chinese Society for Electrical Engineering, 2025, 45(9): 3609-3623, I0029.
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