基于改进长短期记忆网络的质子交换膜燃料电池长期老化预测

doi:10.13229/j.cnki.jdxbgxb.20240663

摘要/Abstract

摘要：

针对质子交换膜燃料电池（PEMFC）的长期老化预测问题，提出了一种基于局部加权散点平滑（LOWESS）去噪的二维网格长短期记忆网络（2D-G-LSTM）PEMFC输出电压预测方法。首先，通过LOWESS进行数据重构和平滑处理，获得消除噪声和尖峰后的平滑数据。其次，采用2D-G结构优化LSTM确定最优参数，并基于最优参数构建2D-G-LSTM，实现PEMFC输出电压在未来几百小时区间内的长期预测。最后，在代表静态和动态工况的2组老化数据集下对本文方法进行测试并与扩展卡尔曼滤波、长短期记忆网络、相关向量机、回声状态网络以及反向传播神经网络5种经典方法进行比较。结果表明，当静态和动态工况数据集的训练时长分别达到550 h和700 h时，与LSTM相比，本文方法的均方根误差和平均绝对百分比误差分别降低了51.19%、53.66%和43.88%、49.43%。因此，本文方法预测误差更小，PEMFC的长期老化趋势更接近真实值，并且能够在一定程度上提高PEMFC的老化预测精度。

关键词: 质子交换膜燃料电池, 长短期记忆网络, 局部加权散点平滑去噪, 二维网格结构, 老化预测

Abstract:

Aiming at the long-term aging prediction problem of Proton exchange membrane fuel cell （PEMFC）， this paper proposes a PEMFC output voltage prediction method of 2D-grid long short term memory networks（2D-G-LSTM） by denoising through locally weighted scatterplot smoothing （LOWESS）. First， data reconstruction and smoothing are performed by LOWESS to obtain smoothed data after eliminating noise and spikes. Second， a 2D-G structure is used to optimize the LSTM to determine the optimal parameters， and a 2D-G-LSTM is constructed based on the optimal parameters to achieve long-term prediction of the PEMFC output voltage over the next several hundred hour intervals. Finally， the proposed method is tested and compared with five classical methods， namely， extended Kalman filter， long short term memory network， correlation vector machine， echo state network， and back-propagation neural network， under two sets of aging datasets representing static and dynamic operating conditions， respectively. The results show that the root mean square error and the mean absolute percentage error of the proposed method are reduced by 51.19%， 53.66% and 43.88% and 49.43%， respectively， compared with LSTM when the training duration of the static and dynamic condition datasets reaches 550 h and 700 h， respectively. Therefore， the proposed method predicts a smaller error and the long-term aging trend of PEMFC is closer to the real value， and it can improve the aging prediction accuracy of PEMFC to some extent.

Key words: proton exchange membrane fuel cell, long short term memory network, locally weighted scatterplot smoothing denoising, 2D-grid structure, aging prediction

中图分类号:

TK91

查鹏堂,齐丰旭,杨雨泽,刘嘉,高锋阳. 基于改进长短期记忆网络的质子交换膜燃料电池长期老化预测[J]. 吉林大学学报(工学版), 2026, 56(1): 64-75.

Peng-tang ZHA,Feng-xu QI,Yu-ze YANG,Jia LIU,Feng-yang GAO. Long-term aging prediction of proton exchange membrane fuel cell based on improved long short term memory networks[J]. Journal of Jilin University(Engineering and Technology Edition), 2026, 56(1): 64-75.

图/表 15

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表2

实验期间采集的特征参数"

特征参数	物理意义
Time/h	时间
U₁~U₅/V；U_tot/V	单电池1~5电压；电堆电压
I/A；J/（A·cm^-2）	电流；电流密度
$T i n H 2$ /℃； $T o u t H 2$ /℃	氢气进口温度；氢气出口温度
T_inAIR/℃；T_outAIR/℃	空气进口温度；空气出口温度
T_inWAT/℃；T_outWAT/℃	冷却水进口温度；冷却水出口温度
$P i n H 2$ /10²Pa； $P o u t H 2$ /10²Pa	氢气进口压力；氢气出口压力
P_inAir/10²Pa；P_outAir/10²Pa	空气进口压力；空气出口压力
$D i n H 2$ /（L·mn^-1）； $D o u t H 2$ /（L·mn^-1）	氢气进口流速；氢气出口流速
D_inAir/（L·min^-1）； D_outAir/（L·min^-1）	空气进气流速；空气出口流速
D_WAT/（L·min^-1）	冷却水流速
HrAIRFC/%	空气湿度

表2

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表3

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表4

参考文献 25

[1]	高锋阳, 强雅昕, 高智山, 等. 计及驾驶风格的氢燃料电池有轨电车自适应能量管理策略[J]. 铁道科学与工程学报, 2024, 21(4): 1379-1390.
	Gao Feng-yang, Qiang Ya-xin, Gao Zhi-shan, et al. Counting and driving style hydrogen fuel cell trams adaptive energy management strategy[J]. Journal of Railway Science and Engineering, 2024, 21(4): 1379-1390.
[2]	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.
[3]	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): 3609-3624.
	Zhao Bo, Zhang Ling-xian, Zhang Lei-qi, et al. PEMFC remaining useful life fusion method based on joint iteration of TCN and AUKF[J]. Proceedings of the CSEE, 2025, 45(9): 3609-3624.
[4]	苏雨临, 连冠, 张大骋. 等效电路模型法预测动态工况下微型直接甲醇燃料电池剩余使用寿命[J]. 上海交通大学学报, 2024, 58(10): 1575-1584.
	Su Yu-lin, Lian Guan, Zhang Da-cheng. Equivalent circuit model-based prognostics for micro direct methanol fuel cell under dynamic operating conditions[J]. Journal of Shanghai Jiaotong University, 2024, 58(10): 1575-1584.
[5]	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 Hong-yuan, 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.
[6]	Bressel M, Hilairet M, Hissel D, et al. Extended kalman filter for prognostic of proton exchange membrane fuel cell[J]. Applied Energy, 2016, 164: 220-227.
[7]	胡捷, 苏建徽, 杜燕, 等. 基于最小二乘法的PEMFC电堆模型参数辨识[J]. 太阳能学报, 2021, 42(6):1-4.
	Hu Jie, Su Jian-hui, Du Yan, et al. Parameter identification of PEMFC stack model based on least square method[J]. Acta Energiae Solaris Sinica, 2021, 42(6): 1-4.
[8]	Chen K, 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]	Chen K, Laghrouche S, Djerdir A. Degradation prediction of proton exchange membrane fuel cell based on grey neural network model and particle swarm optimization[J]. Energy Conversion and Management, 2019, 195: 810-818.
[10]	Chen K, Laghrouche S, Djerdir A. Proton exchange membrane fuel cell degradation and remaining useful life prediction based on artificial neural network[C]∥Renewable Energy Research and Applications. Paris: Universit Bourgogne Franche-Comt, 2018: 14-17.
[11]	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): 4718-4728.
	Pan Shi-yuan, Hua Zhi-guang, Wang Guang-wei, et al. Remaining useful life prediction of hydrogen fuel cell based on cascade echo state network[J]. Proceedings of the CSEE, 2025, 45(12): 4718-4728.
[12]	李鹏程. 基于循环神经网络氢燃料电池寿命预测技术[D]. 成都: 电子科技大学自动化工程学院, 2021.
	Li Peng-cheng. The RUL prediction of hydrogen fuel cells based on recurrent neural network[D]. Chengdu: School of Automation Engineering, University of Electronic Science and Technology of China, 2021.
[13]	Wang F K, Cheng X B, Hsiao K C. Stacked long short-term memory model for proton exchange membrane fuel cell systems degradation[J]. Journal of Power Sources, 2020, 448(6): No.227591.
[14]	Zuo J, Lv H, Zhou D M, et al. Deep learning based prognostic framework towards proton exchange membrane fuel cell for automotive application[J]. Applied Energy, 2021, 281: No.115937
[15]	刘嘉蔚. 数据驱动的PEMFC发电系统故障诊断与寿命预测方法研究[D]. 成都: 西南交通大学电气工程学院, 2020.
	Liu Jia-wei. Data-driven fault diagnosis and life prediction methods for PEMFC power generation system[D]. Chengdu: School of Electrical Engineering, Southwest Jiaotong University, 2020.
[16]	张雪霞, 高雨璇, 陈维荣. 基于数据驱动的质子交换膜燃料电池寿命预测[J]. 西南交通大学学报, 2020, 55(2): 417-427.
	Zhang Xue-xia, Gao Yu-xuan, Chen Wei-rong. Data-driven based remaining useful life prediction for proton exchange membrane fuel cells[J]. Journal of Southwest Jiaotong University, 2020, 55(2): 417-427.
[17]	吴航宇, 王玮, 朱文超, 等. 基于ARIMA-BiGRU双数据驱动的燃料电池性能退化预测方法[J]. 中国电机工程学报, 2025, 45(7): 2690-2699.
	Wu Hang-yu, Wang Wei, Zhu Wen-chao, et al. A fuel cell performance degradation prediction method based on ARIMA-BiGRU dual data-driven approach[J]. Proceedings of the CSEE, 2025, 45(7): 2690-2699.
[18]	Werbos P J. Backpropagation through time: what it does and how to do it[J]. Proc IEEE, 1990, 78(10): 1550-1560.
[19]	刘嘉蔚, 李奇, 陈维荣, 等. 基于核超限学习机和局部加权回归散点平滑法的PEMFC剩余使用寿命预测方法[J]. 中国电机工程学报, 2019, 39(24): 7272-7279, 7500.
	Liu Jia-wei, Li Qi, Chen Wei-rong, et al. Remaining useful life prediction method of PEMFC based on kernel extreme learning machine and locally weighted scatterplot smoothing[J]. Proceedings of the CSEE, 2019, 39(24): 7272-7279, 7500.
[20]	Cleveland W S. LOWESS: a program for smoothing scatterplots by robust locally weighted regression[J]. American Statistician, 1981, 35(1): 54-54.
[21]	孙想, 吴保国, 吴华瑞, 等. 基于前置平滑的苗圃监测数据多元回归拟合方法[J]. 东北林业大学学报,2015, 43(12): 45-50.
	Sun Xiang, Wu Bao-guo, Wu Hua-rui, et al. Multiple regression fitting method of nursery monitoring data by pre-smoothing disposal[J]. Journal of Northeast Forestry University, 2015, 43(12): 45-50.
[22]	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): 8554-8568.
	Zhao Bo, Zhang Ling-xian, Zhang Lei-qi, et al. A hybrid method for direct prediction of PEMFC remaining useful life[J]. Proceedings of the CSEE, 2024, 44(21): 8554-8568.
[23]	FCLAB Research. IEEE PHM 2014 data challenge.2014[DB/OL].[2024-10-15]..
[24]	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研究[J]. 电工技术学报, 2024, 39(11): 3367-3378.
	Wang Jian-feng, Wang Rong-jie, Lin An-hui, et al. Research on degradation prediction method of proton exchange membrane fuel cell[J]. Transactions of China Electrotechnical Society, 2024, 39(11): 3367-3378.
[25]	Ma R, Xie R Y, Xu L C, et al. A hybrid prognostic method for PEMFC with aging parameter prediction[J]. IEEE Transactions on Transportation Electrification, 2021, 7(4): 2318-2331.

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物理参数	控制范围
冷却温度/℃	20~80
冷却流量/（L·min^-1）	0~10
气体温度/℃	20~80
气体相对湿度/%	0~100
空气流量/（L·min^-1）	0~100
氢气流量/（L·min^-1）	0~30
气体压力/bar	0~2
燃料电池电流/A	0~300

网格类型	参数	数值
2D-G-LSTM	输入层维数	20
	隐藏层神经元个数	60
	输出层维数	5
	批大小	56
	训练轮数	54
	学习率	0.001
	验证频率	10

工况	预测方法	f_RMSE	f_MAPE
静态（FC1）	BPNN^［25］	0.016 8	0.003 8
	ESN^［25］	0.027 1	0.007 1
	LOWESS-2D-G-LSTM	0.008 2	0.001 9
动态（FC2）	BPNN^［25］	0.023 6	0.006 1
	ESN^［25］	0.037 9	0.017 8
	LOWESS-2D-G-LSTM	0.019 5	0.005 1