针对质子交换膜燃料电池(PEMFC)系统建模过程中存在的动态响应复杂、非线性关系难以准确表征等问题,提出一种基于多输入单输出Hammerstein结构的PEMFC整体系统建模与参数辨识新方法。首先,利用极限学习机(ELM)网络描述Hammerstein模型的输入非线性环节,构造能准确反映PEMFC系统动静态特性的模型框架。其次,利用关键项分离技术构造辨识模型,结合辅助模型思想推导辅助模型递推最小二乘(AM-RLS)算法和辅助模型遗忘梯度(AM-FG)算法对模型进行参数辨识。最后,将弹性网络(ElasticNet)与互信息分析(MIA)结合筛选与输出电能质量具有强关联性的可控变量,降低建模复杂度的同时提升计算效率。通过动态和稳态电流工况下的实测数据进行仿真验证,结果表明所建模型能够精准预测PEMFC的输出电压变化趋势,准确反映输出电能的质量波动情况。
Abstract
In response to the challenges associated with complex dynamic responses and inaccurate description of nonlinear relationships in proton exchange membrane fuel cell (PEMFC) modeling, this paper proposes a novel method for PEMFC modeling and parameter identification based on a multi-input single-output Hammerstein structure. Initially, an extreme learning machine (ELM) network is employed to capture the input nonlinearity within the Hammerstein model, thereby constructing a framework that precisely reflects both the dynamic and static characteristics of the PEMFC system. Subsequently, the key term separation technique is utilized to construct the identification model, from which the auxiliary model recursive least squares (AM-RLS) algorithm and the auxiliary model forgetting gradient (AM-FG) algorithm are derived for parameter identification by integrating the auxiliary model idea. Finally, by combining ElasticNet with mutual information analysis (MIA), controllable variables strongly correlated with the output power quality are screened, thereby reducing modeling complexity and improving computational efficiency. Through simulation verification using the measured data under dynamic and steady current conditions, the results indicate that the established model can accurately predict the variation trend of output voltage and exactly reflect the quality fluctuation of output power.
关键词
质子交换膜燃料电池 /
系统辨识 /
预测 /
ELM-Hammerstein模型 /
辅助模型思想
Key words
proton exchange membrane fuel cell (PEMFC) /
system identification /
prediction /
ELM-Hammerstein model /
auxiliary model idea
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参考文献
[1] RISCO-BRAVO A, VARELA C, BARTELS J, et al.From green hydrogen to electricity: a review on recent advances, challenges, and opportunities on power-to-hydrogen-to-power systems[J]. Renewable and sustainable energy reviews, 2024, 189: 113930.
[2] ZHANG C Z, ZHANG Y Q, WANG L, et al.A health management review of proton exchange membrane fuel cell for electric vehicles: failure mechanisms, diagnosis techniques and mitigation measures[J]. Renewable and sustainable energy reviews, 2023, 182: 113369.
[3] LI Y H, YANG F, CHEN D F, et al.Thermal-physical modeling and parameter identification method for dynamic model with unmeasurable state in 10-kW scale proton exchange membrane fuel cell system[J]. Energy conversion and management, 2023, 276: 116580.
[4] 陈永辉, 苏建徽, 解宝, 等. 基于HHO-FA的PEMFC电堆辨识建模[J]. 太阳能学报, 2024, 45(3): 282-289.
CHEN Y H, SU J H, XIE B, et al.Identification modeling of PEMFC stack based on HHO-FA[J]. Acta energiae solaris sinica, 2024, 45(3): 282-289.
[5] TZELEPIS S, KAVADIAS K A, MARNELLOS G E, et al.A review study on proton exchange membrane fuel cell electrochemical performance focusing on anode and cathode catalyst layer modelling at macroscopic level[J]. Renewable and sustainable energy reviews, 2021, 151: 111543.
[6] SHI Y, HE W, XIE B, et al.PEMFC fault diagnosis based on an equivalent circuit and OS-ELM framework[J]. IEEE transactions on industry applications, 2023, 60(1): 1277-1287.
[7] CHEN D F, WU W L, CHANG K Y, et al.Performance degradation prediction method of PEM fuel cells using bidirectional long short-term memory neural network based on Bayesian optimization[J]. Energy, 2023, 285: 129469.
[8] 袁铁江, 郭泽林, 胡辰康. 基于LSTM-MPC的PEMFC运行状态建模与容错控制[J]. 中国电机工程学报, 2024, 44(10): 3927-3937.
YUAN T J, GUO Z L, HU C K.Operating states modeling and fault-tolerant control of PEMFC based on LSTM-MPC[J]. Proceedings of the CSEE, 2024, 44(10): 3927-3937.
[9] CHAVAN S L, TALANGE D B.System identification black box approach for modeling performance of PEM fuel cell[J]. Journal of energy storage, 2018, 18: 327-332.
[10] ZHANG B, LIN F, ZHANG C Z, et al.Design and implementation of model predictive control for an open-cathode fuel cell thermal management system[J]. Renewable energy, 2020, 154: 1014-1024.
[11] ZHANG Q, WANG H W, LIU C L, et al.Establishment and identification of MIMO fractional Hammerstein model with colored noise for PEMFC system[J]. Chaos, solitons & fractals, 2024, 180: 114502.
[12] LYU L, SUN W, PAN J.Two-stage and three-stage recursive gradient identification of Hammerstein nonlinear systems based on the key term separation[J]. International journal of robust and nonlinear control, 2024, 34(2): 829-848.
[13] FAN Y M, LIU X M.Data filtering-based multi-innovation forgetting gradient algorithms for input nonlinear FIR-MA systems with piecewise-linear characteristics[J]. Journal of the Franklin Institute, 2021, 358(18): 9818-9840.
[14] ZHANG Q, WANG H W, LIU C L.MILM hybrid identification method of fractional order neural-fuzzy Hammerstein model[J]. Nonlinear dynamics, 2022, 108(3): 2337-2351.
[15] KAYEDPOUR N, SAMANI A E, DE KOONING J D M, et al. Model predictive control with a cascaded Hammerstein neural network of a wind turbine providing frequency containment reserve[J]. IEEE transactions on energy conversion, 2022, 37(1): 198-209.
[16] WANG D Q.Key-term separation based hierarchical gradient approach for NN based Hammerstein battery model[J]. Applied mathematics letters, 2024, 157: 109207.
[17] TANG Y G, BU C N, LIU M M, et al.Application of ELM-Hammerstein model to the identification of solid oxide fuel cells[J]. Neural computing and applications, 2018, 29(2): 401-411.
[18] XU K K, YANG H D, ZHU C J.A novel extreme learning machine-based Hammerstein-Wiener model for complex nonlinear industrial processes[J]. Neurocomputing, 2019, 358: 246-254.
[19] LIU Z P, CHEN J, FAN Q H, et al.A key-term separation based least square method for Hammerstein SOC estimation model[J]. Sustainable energy, grids and networks, 2023, 35: 101089.
[20] DING F, MA H, PAN J, et al.Hierarchical gradient- and least squares-based iterative algorithms for input nonlinear output-error systems using the key term separation[J]. Journal of the Franklin Institute, 2021, 358(9): 5113-5135.
[21] GOURIVEAU R, HILAIRET M, HISSEL D, et al.IEEE PHM 2014 data challenge: outline experiments scoring of results winners[C]//IEEE Conference. Prognostics Health Manage. Belfort, France, 2014.
[22] 于广宇, 董学平, 王祥民, 等. 弹性网下基于LSTM的分解炉出口温度预测[J]. 系统仿真学报, 2021, 33(5): 1078-1085.
YU G Y, DONG X P, WANG X M, et al.Decomposition furnace outlet temperature prediction based on ElasticNet and LSTM[J]. Journal of system simulation, 2021, 33(5): 1078-1085.
[23] ZOU H, HASTIE T.Regularization and variable selection via the elastic net[J]. Journal of the Royal Statistical Society series B: statistical methodology, 2005, 67(2): 301-320.
[24] HAN F, WANG T Y, LING Q H.An improved feature selection method based on angle-guided multi-objective PSO and feature-label mutual information[J]. Applied intelligence, 2023, 53(3): 3545-3562.
基金
国家自然科学基金(62103218); 太原科技大学科研启动基金(20222144); 山西省高等学校科技创新项目(2024L222)