Extreme Learning Machine and Its Application in Parameter Identification of Proton Exchange Membrane Fuel Cell

doi:10.16183/j.cnki.jsjtu.2021.453

Abstract

Abstract:

In order to develop an accurate model of proton exchange membrane fuel cell (PEMFC), it is essential to exactly identify unknown parameters in PEMFC. However, parameter identification of PEMFC is a multi-variable, multi-peak, and strongly coupled nonlinear optimization problem, of which traditional parameter identification methods often fail to achieve satisfactory results. In addition, noises generated under different operation conditions will hinder meta-heuristic algorithms (MhAs) to obtain accurate parameters. To handle these thorny obstacles, extreme learning machine based MhAs (ELM-MhAs) are proposed for PEMFC parameter identification, which can achieve denoising through ELM. ELM is used to train data to reduce or eliminate noises and provide more accurate and reliable fitness functions for MhAs, thus ensuring the accurate identification of PEMFC parameters by MhAs. To verify the feasibility and effectiveness of this strategy, 25 groups of voltage-current data are processed without denoising, with Bayesian regularization neural network (BRNN) denoising or with ELM denoising under two conditions—low temperature and low relative humidity; high temperature and high relative humidity, respectively. Subsequently, parameter identification results of six MhAs and a Levenberg-Marquardt backpropagation of different data are thoroughly compared. The simulation results indicate that ELM can significantly reduce the impact of noise on the data, while effectively improving the parameter identification accuracy of MhAs, compared with no denoising and BRNN denoising.

Key words: proton exchange membrane fuel cell (PEMFC), parameter identification, extreme learning machine (ELM), meta-heuristic algorithms (MhAs), denoising

CLC Number:

TN911

YANG Bo, ZENG Chunyuan, CHEN Yijun, SHU Hongchun, CAO Pulin. Extreme Learning Machine and Its Application in Parameter Identification of Proton Exchange Membrane Fuel Cell[J]. Journal of Shanghai Jiao Tong University, 2023, 57(4): 482-494.

Figures/Tables 14

Fig.1

Fig.2

Fig.3

Tab.1

Tab.2

Parameter identification results obtained at a low temperature and low relative humidity

算法	符号	ε₁	ε₂	ε₃	ε₄	λ	R_c/Ω	b/V	RMSE/V
ALO	N	-1.1997	0.0038	4.7755×10^-5	-1.9539×10^-4	22.7213	8.0000×10^-4	0.0136	1.4918×10^-3
	B	-0.8531	0.0027	4.6077×10^-5	-1.9240×10^-4	17.2486	3.0088×10^-4	0.0148	1.1955×10^-3
	E	-1.0622	0.0039	8.3563×10^-5	-1.9076×10^-4	19.5346	2.1396×10^-4	0.0162	1.1631×10^-3
DA	N	-1.1997	0.0038	4.4140×10^-5	-1.9063×10^-4	14.1016	4.8523×10^-4	0.0157	1.3099×10^-3
	B	-0.9920	0.0031	4.4408×10^-5	-1.9707×10^-4	15.4621	3.3040×10^-4	0.0136	1.3915×10^-3
	E	-0.8531	0.0030	7.0217×10^-5	-1.9588×10^-4	14.1585	5.2635×10^-4	0.0136	1.2992×10^-3
EO	N	-0.8828	0.0033	8.8483×10^-5	-1.8694×10^-4	20.2055	5.1412×10^-4	0.0180	1.7501×10^-3
	B	-1.1997	0.0041	6.8525×10^-5	-1.8486×10^-4	22.2448	8.0000×10^-4	0.0181	2.0123×10^-3
	E	-0.9576	0.0032	5.9925×10^-5	-1.9073×10^-4	17.4769	1.1767×10^-4	0.0152	8.2907×10^-4
GA	N	-0.8952	0.0033	8.1726×10^-5	-1.9717×10^-4	17.9935	1.0162×10^-4	0.0150	1.4024×10^-3
	B	-1.0374	0.0032	3.9417×10^-5	-1.9576×10^-4	22.9887	1.0260×10^-4	0.0143	1.7726×10^-3
	E	-0.8727	0.0034	9.4426×10^-5	-1.9046×10^-4	20.1161	2.1615×10^-4	0.0174	1.1935×10^-3
GWO	N	-0.8558	0.0026	4.1166×10^-5	-1.8835×10^-4	22.5918	6.0519×10^-4	0.0180	1.6007×10^-3
	B	-1.0634	0.0040	9.4119×10^-5	-1.8632×10^-4	20.0275	6.5140×10^-4	0.0173	1.5371×10^-3
	E	-1.1301	0.0041	8.3065×10^-5	-1.8739×10^-4	14.2505	1.9414×10^-4	0.0157	1.2038×10^-3
WOA	N	-0.8535	0.0026	4.3311×10^-5	-1.9027×10^-4	13.3911	1.0890×10^-4	0.0180	3.2404×10^-3
	B	-1.0351	0.0037	7.8048×10^-5	-1.8972×10^-4	14.7768	1.0000×10^-4	0.0136	1.5500×10^-3
	E	-1.1995	0.0041	6.3044×10^-5	-1.9065×10^-4	16.7606	4.0499×10^-4	0.0143	1.1961×10^-3
LMBP	N	-1.0282	0.0031	3.7294×10^-5	-1.8648×10^-4	20.7773	1.0000×10^-4	0.0193	2.5661×10^-3
	B	-1.1028	0.0039	7.5117×10^-5	-1.8040×10^-4	10.2563	8.0000×10^-4	0.0136	2.8427×10^-3
	E	-1.0619	0.0036	6.3838×10^-5	-1.8326×10^-4	19.4747	8.0000×10^-4	0.0188	2.4426×10^-3

Tab.2

Fig.4

Fig.5

Fig.6

Fig.7

Tab.3

Parameter identification results obtained at a high temperature and high relative humidity

算法		ε₁	ε₂	ε₃	ε₄	λ	R_c/Ω	b/V	RMSE/V
ALO	N	-0.8531	0.0028	5.4224×10^-5	-1.9381×10^-4	17.1927	1.6728×10^-4	0.0136	1.4200×10^-3
	B	-0.9590	0.0030	4.6983×10^-5	-1.9038×10^-4	15.0582	1.0000×10^-4	0.0136	1.2983×10^-3
	E	-0.8531	0.0027	4.5276×10^-5	-1.9218×10^-4	18.1940	4.4457×10^-4	0.0136	1.0970×10^-3
DA	N	-0.9377	0.0029	4.2164×10^-5	-1.9321×10^-4	18.9210	4.1854×10^-4	0.0136	1.1348×10^-3
	B	-1.1997	0.0040	6.2009×10^-5	-1.9179×10^-4	18.2714	3.5924×10^-4	0.0136	8.6808×10^-4
	E	-0.8531	0.0028	5.2448×10^-5	-1.9155×10^-4	20.7451	8.0000×10^-4	0.0136	7.9570×10^-4
EO	N	-0.9304	0.0032	6.7696×10^-5	-1.9272×10^-4	19.8194	1.6251×10^-4	0.0136	7.9879×10^-4
	B	-0.8564	0.0032	8.3113×10^-5	-1.9239×10^-4	22.0052	1.0000×10^-4	0.0136	6.8046×10^-4
	E	-1.1996	0.0040	6.3959×10^-5	-1.9278×10^-4	22.9997	2.3671×10^-4	0.0136	6.8623×10^-4
GA	N	-1.0365	0.0035	6.5236×10^-5	-1.9455×10^-4	22.8470	1.2145×10^-4	0.0137	1.1852×10^-3
	B	-1.0737	0.0033	4.0511×10^-5	-1.9059×10^-4	22.8380	1.1889×10^-4	0.0141	1.1625×10^-3
	E	-1.1406	0.0043	9.2910×10^-5	-1.9165×10^-4	22.7392	7.9682×10^-4	0.0136	6.6562×10^-4
GWO	N	-1.1997	0.0043	8.1015×10^-5	-1.9245×10^-4	22.3827	2.3883×10^-4	0.0136	6.6925×10^-4
	B	-0.8894	0.0027	4.1693×10^-5	-1.9289×10^-4	21.8924	4.9842×10^-4	0.0136	6.9529×10^-4
	E	-1.1327	0.0035	4.4503×10^-5	-1.9136×10^-4	19.5772	1.9583×10^-4	0.0137	6.3941×10^-4
WOA	N	-1.1493	0.0038	5.9464×10^-5	-1.8838×10^-4	17.7311	1.0096×10^-4	0.0151	1.7329×10^-3
	B	-0.8531	0.0026	3.8977×10^-5	-1.9118×10^-4	13.0255	1.0991×10^-4	0.0136	1.9095×10^-3
	E	-1.1540	0.0041	7.6040×10^-5	-1.9381×10^-4	18.6908	1.0000×10^-4	0.0136	1.2166×10^-3
LMBP	N	-0.97694	0.0033	5.9833×10^-5	-1.9507×10^-4	21.1973	1.0000×10^-4	0.0136	1.5649×10^-3
	B	-1.1155	0.0036	5.6620×10^-5	-1.9381×10^-4	22.3659	1.0000×10^-4	0.0136	8.8141×10^-4
	E	-1.1823	0.0036	3.8790×10^-5	-1.9396×10^-4	23.0000	1.0000×10^-4	0.0136	8.6141×10^-4

Tab.3

Fig.8

Fig.9

Fig.10

Fig.11

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