极限学习机及其在质子交换膜燃料电池参数辨识中的应用

doi:10.16183/j.cnki.jsjtu.2021.453

摘要/Abstract

摘要：

为对质子交换膜燃料电池(PEMFC)进行精确建模,需要准确辨识PEMFC中的未知参数.然而,PEMFC的参数辨识是一个多变量、多峰值和强耦合的非线性优化问题,传统的参数辨识方法往往得不到满意的结果.此外,不同运行条件下产生的噪声会阻碍启发式算法(MhAs)获取精确的参数.针对该问题,提出一种基于极限学习机(ELM)的MhAs策略——ELM-MhAs,以实现PEMFC的参数辨识.利用ELM对数据进行训练以降低或消除噪声,为MhAs提供更为准确可靠的适应度函数,从而保证MhAs对PEMFC参数的精确辨识.为验证该策略的可行性和有效性,在低温、低相对湿度和高温、高相对湿度两种条件下,分别对25组电压-电流数据进行不降噪、贝叶斯正则神经网络(BRNN)降噪以及ELM降噪处理,随后对比不同数据中6种MhAs和列文伯格-马夸尔特反向传播法的参数辨识结果.实验结果表明,与不降噪和BRNN降噪处理相比,应用ELM能够显著减少数据噪声对实验数据的影响,从而有效提高MhAs的参数辨识精度.

关键词: 质子交换膜燃料电池, 参数辨识, 极限学习机, 启发式算法, 降噪处理

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

中图分类号:

TN911

杨博, 曾春源, 陈义军, 束洪春, 曹璞璘. 极限学习机及其在质子交换膜燃料电池参数辨识中的应用[J]. 上海交通大学学报, 2023, 57(4): 482-494.

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.

图/表 14

图1

图2

图3

表1

表2

低温低相对湿度下的参数辨识结果

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

表2

图4

图5

图6

图7

表3

高温、高相对湿度下的参数辨识结果

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

表3

图8

图9

图10

图11

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