基于分解优化并行ESN的氢燃料电池寿命预测

doi:10.7527/S1000-6893.2024.30696

Abstract

Abstract:

Aiming at the problem of low voltage prediction accuracy caused by multi-time-scale aging characteristics of Proton Exchange Membrane Fuel Cell （PEMFC）， a Parallel Echo State Network （PESN） structure which based on Ensemble Empirical Mode Decomposition （EEMD） and Circulatory System based Optimization （CSBO） is proposed to improve the lifespan prediction accuracy of PEMFC. By utilizing EEMD to conduct modal decomposition on the original voltage signal， the historical data from various time points and the decomposed signals with distinct frequencies are taken as the parallel inputs for the different sub-reservoirs of ESN， thereby establishing a parallel ESN structure that allocates and superimposes outputs based on weights. The CSBO is then leveraged to optimize the relevant parameters of the parallel ESN structure. Subsequently， utilizing the optimized EPESN model， the prediction of the output voltage of PEMFC for the next several hundred hours is achieved. Specifically， under the steady-state and quasi-dynamic data training sets at 70%， the Root Mean Square Error （RMSE） of EPESN is reduced by 34.25% and 47.41% respectively， compared to that of ESN. Furthermore， when the dynamic 1 training duration is set at 300 h， the RMSE of EPESN is decreased by 15.30% compared to ESN. The results explicitly demonstrate that the EPESN structure is capable of enhancing the prediction accuracy for the lifespan of PEMFC.

Key words: proton exchange membrane fuel cell, life prediction, empirical mode decomposition, circulatory system based optimization, echo state network

CLC Number:

V237

Zhiguang HUA, Shiyuan PAN, Dongdong ZHAO, Xianglong LI, Manfeng DOU. Lifespan prediction of hydrogen fuel cell based on decomposition optimization parallel ESN[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(2): 330696.

Figures/Tables 27

Table 1

Fig.1

Fig.2

Fig.3

Fig.4

Table 2

Fig.5

Fig.6

Fig.7

Table 3

Table 4

Fig.8

Fig.9

Table 5

Table 6

Fig.10

Fig.11

Table 7

Table 8

Fig.12

Fig.13

Table 9

Table 10

Table 11

Table 12

Table 13

Fig.14

References 23

1	雷涛，闵志豪，付红杰，等. 燃料电池无人机混合电源动态平衡能量管理策略［J］. 航空学报， 2020， 41（ 12）： 324048.
	LEI T， MIN Z H， FU H J， et al. Dynamic balanced energy management strategies for fuel-cell hybrid power system of unmanned air vehicle［J］. Acta Aeronautica et Astronautica Sinica， 2020， 41（ 12）： 324048 （in Chinese）.
2	DIJOUX E， STEINER N Y， BENNE M， et al. Experimental validation of an active fault tolerant control strategy applied to a proton exchange membrane fuel cell［J］. Electrochem， 2022， 3（ 4）： 633- 652.
3	任圆圆，许亮，蔡远利. 质子交换膜燃料电池剩余使用寿命预测研究进展［J］. 电源技术， 2023， 47（ 8）： 984- 988.
	REN Y Y， XU L， CAI Y L. Progress on remaining useful life prediction of proton exchange membrane fuel cell［J］. Chinese Journal of Power Sources， 2023， 47（ 8）： 984- 988 （in Chinese）.
4	YUE M L， JEMEI S， ZERHOUNI N， et al. Proton exchange membrane fuel cell system prognostics and decision-making： Current status and perspectives［J］. Renewable Energy， 2021， 179： 2277- 2294.
5	LIU J W， LI Q， HAN Y， et al. PEMFC residual life prediction using sparse autoencoder-based deep neural network［J］. IEEE Transactions on Transportation Electrification， 2019， 5（ 4）： 1279- 1293.
6	ZHAO Y， LUO M J， YANG J W， et al. Numerical analysis of PEMFC stack performance degradation using an empirical approach［J］. International Journal of Hydrogen Energy， 2024， 56： 147- 163.
7	李奇，刘嘉蔚，陈维荣. 质子交换膜燃料电池剩余使用寿命预测方法综述及展望［J］. 中国电机工程学报， 2019， 39（ 8）： 2365- 2375.
	LI Q， LIU J W， CHEN W R. Review and prospect of remaining useful life prediction methods for proton exchange membrane fuel cell［J］. Proceedings of the CSEE， 2019， 39（ 8）： 2365- 2375 （in Chinese）.
8	赵冬冬，赵国胜，夏磊，等. 无人机用燃料电池阴极供气系统建模与控制［J］. 航空学报， 2021， 42（ 7）： 324659.
	ZHAO D D， ZHAO G S， XIA L， et al. Modeling and control of fuel cell cathode gas supply system for UAV［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（ 7）： 324659 （in Chinese）.
9	YAN C Z， CHEN J， LIU H， et al. Health management for PEM fuel cells based on an active fault tolerant control strategy［J］. IEEE Transactions on Sustainable Energy， 2021， 12（ 2）： 1311- 1320.
10	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.
11	ZHENG L， HOU Y P， ZHANG T， et al. Performance prediction of fuel cells using long short-term memory recurrent neural network［J］. International Journal of Energy Research， 2021， 45（ 6）： 9141- 9161.
12	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 & Management， 2019， 195（ S1）： 810- 818.
13	ZHU L， CHEN J. Prognostics of PEM fuel cells based on Gaussian process state space models［J］. Energy， 2018， 149： 63- 73.
14	REZK H， WILBERFORCE T， SAYED E T， et al. Finding best operational conditions of PEM fuel cell using adaptive neuro-fuzzy inference system and metaheuristics［J］. Energy Reports， 2022， 8： 6181- 6190.
15	DENG Z H， CHAN S H， CHEN Q H， et al. Efficient degradation prediction of PEMFCs using ELM-AE based on fuzzy extension broad learning system［J］. Applied Energy， 2023， 331： 120385.
16	LIU J W， LI Q， CHEN W R， 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.
17	JIN J S， CHEN Y P， XIE C J， 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.
18	LI S Y， LUAN W L， WANG C， 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.
19	LI Z L， ZHENG Z X， 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.
20	MEZZI R， YOUSFI-STEINER N， PÉRA M C， et al. An Echo State Network for fuel cell lifetime prediction under a dynamic micro-cogeneration load profile［J］. Applied Energy， 2021， 283： 116297.
21	MORANDO S， JEMEI S， HISSEL D， et al. ANOVA method applied to proton exchange membrane fuel cell ageing forecasting using an echo state network［J］. Mathematics and Computers in Simulation， 2017， 131： 283- 294.
22	GHASEMI M， AKBARI M A， JUN C， et al. Circulatory System Based Optimization （CSBO）： An expert multilevel biologically inspired meta-heuristic algorithm［J］. Engineering Applications of Computational Fluid Mechanics， 2022， 16（ 1）： 1483- 1525.
23	HUA Z G， ZHENG Z X， PAHON E， et al. Remaining useful life prediction of PEMFC systems under dynamic operating conditions［J］. Energy Conversion and Management， 2021， 231： 113825.

现有方法	优势	局限性
经验模型 ^{［ 5］}	易于实现、计算成本低	泛化能力差、依赖大量实验数据
机理模型 ^{［ 6］}	基于物理原理、预测准确	模型复杂、需要详细的系统知识
半经验半机理模型 ^{［ 7］}	结合物理原理和数据驱动、泛化能力强	模型复杂度中等、需要部分先验知识
数据驱动 ^{［ 12- 21］}	良好地捕捉非线性关系、快速收敛、适应性强	依赖高质量数据、可能过拟合
数据和模型驱动混合 ^{［ 7］}	结合数据和模型优势、预测精度高	方法复杂、需要大量数据和先验知识

参数	稳态	准动态	动态1	动态2
单体电池个数	5	5	96	8
运行功率/kW	1	1	1~5	1
单体电池活化面积/cm ²	100	100	100	220
工作电/A	70	70±7	20~99	0~110
测试时间/h	1 154	1 020	450	500
氢气输入/输出温度/℃	29/41	27/37	58	54/55
空气输入/输出温度/℃	42/51	43/51	58	56/57

训练时长/h	RMSE
训练时长/h	ESN	ELM	LSTM	EPESN
500	0.011 49	0.011 55	0.014 08	0.010 34
550	0.012 51	0.011 45	0.016 20	0.010 54
600	0.016 76	0.013 88	0.018 72	0.011 80
650	0.015 66	0.013 21	0.015 88	0.012 04
700	0.018 60	0.014 79	0.013 02	0.011 73
750	0.013 40	0.014 47	0.013 46	0.012 59
800	0.014 34	0.017 06	0.016 40	0.013 58

训练时长/h	MAPE
训练时长/h	ESN	ELM	LSTM	EPESN
500	0.002 47	0.002 82	0.003 71	0.002 31
550	0.002 98	0.002 36	0.004 02	0.002 43
600	0.004 04	0.003 15	0.004 93	0.002 51
650	0.003 81	0.003 08	0.003 73	0.002 59
700	0.004 70	0.002 79	0.003 16	0.002 63
750	0.003 05	0.003 52	0.003 18	0.002 70
800	0.003 29	0.003 48	0.003 46	0.003 07

训练时长/h	RMSE
训练时长/h	ESN	ELM	LSTM	EPESN
500	0.041 03	0.060 14	0.028 75	0.016 29
550	0.064 08	0.043 77	0.020 788	0.015 02
600	0.052 29	0.022 04	0.030 31	0.016 43
650	0.052 96	0.025 00	0.025 89	0.016 47
700	0.049 76	0.034 71	0.026 17	0.017 17
750	0.054 50	0.024 95	0.024 62	0.018 10
800	0.028 34	0.041 24	0.031 13	0.015 16

Lifespan prediction of hydrogen fuel cell based on decomposition optimization parallel ESN

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 27

References 23

Related Articles 15

Recommended Articles

Metrics

Comments

训练时长/h	RMSE/10 ^-2
训练时长/h	ESN-1R	ESN-2R	ESN-3R	ESN-4R	ESN-5R
500	4.10	1.60	2.24	1.94	2.20
550	6.40	1.55	1.99	1.80	1.91
600	5.23	1.75	4.98	1.63	1.66
650	5.30	3.22	5.11	1.98	2.11
700	4.98	2.13	4.11	2.25	2.16
750	5.45	1.86	2.04	2.21	1.87
800	2.83	1.95	3.24	2.34	1.74

不同工况	训练时长/h	RMSE/10 ^-2
不同工况	训练时长/h	EPESN	GA EPESN	PSO EPESN	CSBO EPESN
稳态	500	1.56	1.01	1.03	1.00
	650	1.66	1.28	1.20	1.20
	700	1.73	1.31	1.22	1.17
准动态	500	1.35	1.54	1.71	1.50
	550	1.11	1.53	1.99	1.53
	700	2.79	2.24	2.45	2.11

[1]	Tongzhou GAO, Xiaofan HE, Xiaolei WANG, Ziguang LI, Zhentao ZHU, Zhixin ZHAN. Fatigue life prediction of 2014-T6 aluminum alloy based on CDM theory and SVM model [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(7): 228952-228952.
[2]	Guishuang TIAN, Shaoping WANG, Jian SHI, Mo TAO. IGBT life prediction method driven by model and data [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(15): 630173-630173.
[3]	Binjie MOU, Jinsong JIANG, Kun YANG, Huanbing FU, Dehong MENG, Wei JIN. Acoustic fatigue design method for fighter inlet structure [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(14): 229603-229603.
[4]	Jiaxin YANG, Shengjin TANG, Liang LI, Xiaoyan SUN, Shuai QI, Xiaosheng SI. Remaining useful life prediction of implicit nonlinear Wiener degradation process based on multi-source information [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(12): 227662-227662.
[5]	Xiurui WANG, Kaishang LI, Hanghang GU, Yong ZHANG, Tiwen LU, Runzi WANG, Xiancheng ZHANG. A unified criterion for high⁃low cycle fatigue life prediction based on crystal plasticity theory [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(10): 427300-427300.
[6]	ZHANG Shengfei, LI Tianmei, HU Changhua, DU Dangbo, SI Xiaosheng. Missing data generation method and its application in remaining useful life prediction based on deep convolutional generative adversarial network [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(8): 225708-225708.
[7]	TONG Fulin, DONG Siwei, DUAN Junyi, LI Xinliang. Direct numerical simulation of separation bubble in shock wave/turbulent boundary layer interaction [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(7): 125437-125437.
[8]	MU Hanxiao, ZHENG Jianfei, HU Changhua, ZHAO Ruixing, DONG Qing. Remaining useful life prediction of multivariate degradation equipment based on CDBN and BiLSTM [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(7): 325403-325403.
[9]	CHEN Keming, TIAN Ruozhou, GUO Sujuan, WANG Runzi, ZHANG Chengcheng, CHEN Haofeng, ZHANG Xiancheng, TU Shandong. Creep fatigue life prediction of aero-engine turbine disc under cyclic thermal load [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 225290-225290.
[10]	QU Bingnan, JIANG Ping, ZHAO Luyang, LI Fengrong, WANG Yingguan. Passive direction finding algorithm of projectile based on short baseline sensor array [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(3): 325139-325139.
[11]	WANG Shaoping, GENG Yixuan, SHI Cun. Life estimation of aircraft hydraulic pump based on failure physics and data driven [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(10): 527347-527347.
[12]	ZHAO Dongdong, ZHAO Guosheng, XIA Lei, FANG Chun, MA Rui, HUANGFU Yigeng. Modeling and control of fuel cell cathode gas supply system for UAV [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(7): 324659-324659.
[13]	XIAO Yang, QIN Haiqin, XU Kejun, JIA Mingming, ZHANG Zhuzhu. Low cycle fatigue life prediction of FGH96 alloy based on modified SWT model [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(5): 524360-524360.
[14]	ZHANG Junrui, ZHENG Xitao, YUAN Lin, ZHONG Guiyong, LI Guochen. Fatigue life prediction method for hybrid multi-bolted joints based on damage weight [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(5): 524306-524306.
[15]	LI Qian, ZHANG Fulu, ZHAO Zihua. Very high cycle fatigue of nickel-based single-crystal and directionally solidified superalloys: Review [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(5): 524340-524340.

训练时长/h	RMSE
训练时长/h	ESN	ELM	LSTM	EPESN
250	3.643 70	4.815 00	4.517 70	3.634 50
275	4.691 50	6.329 00	5.051 10	3.778 80
300	4.462 30	5.145 10	5.638 40	3.779 40
325	4.600 60	4.224 20	4.833 70	3.857 20
350	4.768 60	3.044 90	3.951 90	3.014 80
375	2.815 50	3.980 70	3.970 20	3.044 90
400	4.856 60	3.471 40	3.318 80	3.118 80

训练时长/h	MAPE
训练时长/h	ESN	ELM	LSTM	EPESN
250	0.004 90	0.006 21	0.005 79	0.004 70
275	0.006 09	0.008 80	0.006 45	0.005 10
300	0.005 68	0.006 73	0.007 39	0.004 99
325	0.005 92	0.005 64	0.006 67	0.005 10
350	0.006 29	0.004 11	0.005 13	0.004 15
375	0.003 64	0.005 61	0.005 25	0.004 09
400	0.006 41	0.004 63	0.003 63	0.003 76

训练时长/h	RMSE/10 ^-3
训练时长/h	ESN	ELM	LSTM	EPESN
150	14.3	16.0	13.3	7.63
170	13.6	11.2	11.3	10.6
190	9.45	10.4	10.5	5.71
210	11.3	10.8	9.48	8.24
230	4.34	9.76	5.39	4.89
250	5.39	4.36	3.83	4.48
270	6.09	5.55	8.61	4.43

训练时长/h	MAPE/10 ^-2
训练时长/h	ESN	ELM	LSTM	EPESN
150	28.3	15.6	22.0	14.2
170	27.0	22.1	17.0	21.1
190	9.11	10.1	16.9	7.59
210	12.3	17.6	9.62	8.51
230	5.65	16.4	6.76	6.42
250	6.28	5.85	4.79	4.52
270	7.23	6.26	13.6	4.80