Abstract：For the life prediction issue of Proton Exchange Membrane Fuel Cells (PEMFC), a hybrid prediction method based on aging characteristics was proposed. The aging characteristics of PEMFC throughout its lifecycle could be decomposed into overall aging characteristics, voltage fluctuation characteristics, and voltage recovery characteristics. For the overall aging characteristics, the Square Root Unscented Kalman Filter (SRUKF) was utilized for prediction; for the voltage recovery characteristics, a second-order RQ-RLC equivalent circuit model was used to fit the electrochemical impedance spectroscopy data, obtaining an indirect relationship between recovery voltage and time; for the voltage fluctuation characteristics, the Xception-Long Short Term Memory (LSTM) network was employed for training and prediction. Finally, the prediction results of the three aging characteristics were superimposed to calculate the RUL prediction result for PEMFC. Based on the verification of two sets of operating condition data, the results show that compared to independent predictions by SRUKF and Xception-LSTM, the accuracy of the hybrid prediction method is improved by about 20%. Certainly, here is the translation with the sequence numbers replaced by ordinal terms: Firstly, the collection and preprocessing of voltage aging data. Preprocess the collected PEMFC data, which includes removing monitoring noise, outlier processing, and timestamp reconstruction; Secondly, voltage aging feature prediction. Utilize the PEMFC empirical model to represent the degradation trend and apply SRUKF to identify the hidden state of the voltage. The output of this module is the prediction of future voltage aging trends under the overall trend; Thirdly, voltage fluctuation feature prediction. This module is designed to analyze the periodic fluctuations of PEMFC voltage during long-term durability operation. The Xception-LSTM model is extensively trained with voltage fluctuation feature datasets for long-term prediction of these characteristics. Fourthly, EIS test data collection. Gather EIS experimental data of the stack at specific time points during long-term durability experiments at regular intervals. Fifthly, recovery voltage feature prediction. Based on EIS data, identify the parameters of the second-order RQ-RLC model and further establish the relationship between resistance parameters and recovery voltage. Lastly, overlay the results of the three feature predictions to obtain the long-term prediction of the aging voltage characteristic values, and calculate the RUL prediction value according to the aging voltage threshold. This paper proposes a hybrid prediction method based on aging characteristics, which decomposes the aging characteristics into overall aging features, voltage fluctuation features, and voltage recovery features, and carries out long-term predictions for the three types of features, finally overlaying the prediction results. The method was validated using data from two sets of operating conditions, FC1 and FC2, and the results indicate: (1) The short-term prediction results show that SRUKF has a smaller prediction error compared to UKF, and after incorporating the Xception network for feature extraction, the Xception-LSTM model exhibits better prediction performance; (2) Under both operating conditions, the hybrid prediction method has a high RUL prediction accuracy. For FC1, most prediction starting points can achieve an accuracy of over 95%, while for FC2, the accuracy can reach over 90%; (3) A comparison among the SRUKF, Xception-LSTM, and hybrid prediction methods shows that, compared to predicting a single aging feature, the RUL prediction accuracy is higher when combining multiple aging features.
[1] 全睿, 程功, 周宇龙, 等. 基于EWOA优化CNN-BiGRU-AT模型的燃料电池衰退预测[J/OL]. 电工技术学报, 1-17[2025-05-09]. https://doi.org/10.19595/j.cnki.1000-6753.tces.241835. Quan Rui, Cheng Gong, Zhou Yulong, et al. Enhanced whale optimization algorithm-based CNN-BiGRU-AT model for aging prediction of fuel cell[J/OL]. Transactions of China Electrotechnical Society, 1-17[2025-05-09]. https://doi.org/10.19595/j.cnki.1000-6753.tces.241835. [2] 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. [3] 谢宏远, 刘逸, 候权, 等. 基于粒子滤波和遗传算法的氢燃料电池剩余使用寿命预测[J]. 东北电力大学学报, 2021, 41(1): 56-64. Xie Hongyuan, Liu Yi, Hou Quan, et al.Prediction of the remaining useful life of PEMFC based on particle filter and genetic algorithm[J]. Journal of Northeast Electric Power University, 2021, 41(1): 56-64. [4] Liu Hao, Chen Jian, Zhu Chuyan, et al.Prognostics of proton exchange membrane fuel cells using a model-based method[J]. IFAC-PapersOnLine, 2017, 50(1): 4757-4762. [5] Ou Mingyang, Zhang Ruofan, Shao Zhifang, et al.A novel approach based on semi-empirical model for degradation prediction of fuel cells[J]. Journal of Power Sources, 2021, 488: 229435. [6] Li Songyang, Luan Weiling, Wang Chang, et al.Degradation prediction of proton exchange membrane fuel cell based on Bi-LSTM-GRU and ESN fusion prognostic framework[J]. International Journal of Hydrogen Energy, 2022, 47(78): 33466-33478. [7] 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. [8] He Kai, Mao Lei, Yu Jianbo, et al.Long-term performance prediction of PEMFC based on LASSO-ESN[J]. IEEE Transactions on Instrumentation and Measurement, 2021, 70: 3511611. [9] 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. [10] Liu Hao, Chen Jian, Hissel D, et al.Remaining useful life estimation for proton exchange membrane fuel cells using a hybrid method[J]. Applied Energy, 2019, 237: 910-919. [11] FCLAB Research. IEEE PHM 2014 Data Challenge [DB/OL]. 2014. http://eng.fclab.fr/ieee-phm-2014-data-challenge/. [12] 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. [13] Jouin M, Gouriveau R, Hissel D, et al.Degradations analysis and aging modeling for health assessment and prognostics of PEMFC[J]. Reliability Engineering & System Safety, 2016, 148: 78-95. [14] 符毅, 孔星炜, 董新民. 基于自适应SRUKF的无人机位姿预测方法[J]. 应用光学, 2019, 40(1): 21. Fu Yi, Kong Xingwei, Dong Xinmin.Adaptive square-root unscented Kalman filter for position and pose prediction of UAV[J]. Journal of Applied Optics, 2019, 40(1): 21. [15] Cheng Yujie, Zerhouni N, Lu Chen.A hybrid remaining useful life prognostic method for proton exchange membrane fuel cell[J]. International Journal of Hydrogen Energy, 2018, 43(27): 12314-12327. [16] Szegedy C, Ioffe S, Vanhoucke V, et al.Inception-v4, inception-ResNet and the impact of residual connec-tions on learning[C]//Proceedings of the 31st AAAI conference on artificial intelligence, San Francisco, CA, USA, 2017: 4278-4284. [17] Chollet F.Xception: deep learning with depthwise separable convolutions[C]//2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, USA, 2017: 1800-1807. [18] Yu Yong, Si Xiaosheng, Hu Changhua, et al.A review of recurrent neural networks: LSTM cells and network architectures[J]. Neural Computation, 2019, 31(7): 1235-1270. [19] Liu Jiawei, Li Qi, Chen Weirong, et al.Remaining useful life prediction of PEMFC based on long short-term memory recurrent neural networks[J]. International Journal of Hydrogen Energy, 2019, 44(11): 5470-5480. [20] Wang Yajie, Liu Hongmei, Lu Chen, et al.PEM fuel cell health state assessment using a geometrical approach and mahalanobis distance[C]//2016 12th World Congress on Intelligent Control and Automation (WCICA), Guilin, China, 2016: 1312-1316. [21] 鲜亮, 肖建, 贾俊波. 质子交换膜燃料电池交流阻抗谱实验研究[J]. 中国电机工程学报, 2010, 30(35): 101-106. Xian Liang, Xiao Jian, Jia Junbo.An experimental study on AC impedance spectroscopy of proton exchange membrane fuel cell[J]. Proceedings of the CSEE, 2010, 30(35): 101-106. [22] 刘相万, 杨扬, 朱文超, 等. 基于二阶RQ-RLC模型的质子交换膜燃料电池水管理故障诊断[J]. 中国电机工程学报, 2022, 42(21): 7893-7905. Liu Xiangwan, Yang Yang, Zhu Wenchao, et al.Second-order RQ-RLC model-based fault diagnosis for water management in proton exchange membrane fuel cells[J]. Proceedings of the CSEE, 2022, 42(21): 7893-7905. [23] 周唯逸, 郑万俊, 卫东, 等. 基于内阻特性的PEMFC发电效率建模与分析[J/OL]. 电源学报, 1-11[2025-04-21]. http://kns.cnki.net/kcms/detail/12.1420.TM.20250306.1623.015.html. Zhou Weiyi, Zheng Wanjun. Wei Dong, et al. Modeling and analysis of PEMFC power generation efficiency basedon internal resistance characteristics [J/OL]. Journal of Power Supply, 1-11[2025-04-21]. http://kns.cnki.net/kcms/detail/12.1420.TM.20250306.1623.015.html. [24] 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): 8166-8178. 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): 8166-8178. [25] Wang Chu, Li Zhongliang, Outbib R, et al.A novel long short-term memory networks-based data-driven prognostic strategy for proton exchange membrane fuel cells[J]. International Journal of Hydrogen Energy, 2022, 47(18): 10395-10408. [26] 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.
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