Parameter optimization for a PEMFC model with a hybrid genetic algorithm

Many steady‐state models of polymer electrolyte membrane fuel cells (PEMFC) have been developed and published in recent years. However, models which are easy to be solved and feasible for engineering applications are few. Moreover, rarely the methods for parameter optimization of PEMFC stack models were discussed. In this paper, an electrochemical‐based fuel cell model suitable for engineering optimization is presented. Parameters of this PEMFC model are determined and optimized by means of a niche hybrid genetic algorithm (HGA) by using stack output‐voltage, stack demand current, anode pressure and cathode pressure as input–output data. This genetic algorithm is a modified method for global optimization. It provides a new architecture of hybrid algorithms, which organically merges the niche techniques and Nelder–Mead's simplex method into genetic algorithms (GAs). Calculation results of this PEMFC model with optimized parameters agreed with experimental data well and show that this model can be used for the study on the PEMFC steady‐state performance, is broader in applicability than the earlier steady‐state models. HGA is an effective and reliable technique for optimizing the model parameters of PEMFC stack. Copyright © 2005 John Wiley & Sons, Ltd.     

A hybrid multi-variable experimental model for a PEMFC

A hybrid model composed of a least square support vector machine (LS-SVM) model and a pressure-incremental model is developed to dispose operation conditions of current, temperature, cathode and anode gas pressures, which have major impacts on a proton exchange membrane fuel cell's (PEMFC) performance. The LS-SVM model is built to incorporate current and temperature and a particle swarm optimization (PSO) algorithm is used to improve its performance. The optimized LS-SVM model fits the experimental data well, with a mean squared error of 0.0002 and a squared correlation coefficient of 99.98%. While a pressure-incremental model with only one empirical coefficient is constructed to for anode and cathode pressures with satisfactory results. Combining these two models together makes a powerful hybrid multi-variable model that can predict a PEMFC's voltage under any current, temperature, cathode and anode gas pressure. This black-box hybrid PEMFC model could be a competitive solution for system level designs such as simulation, real-time control, online optimization and so on.     

基于多模型的Z型流道燃料电池的性能优化

建立三维质子交换膜燃料单电池（PEMFC）数值模型,探究Z型流道PEMFC流道参数（角度、宽度、深度）、运行参数（温度、氢气湿度、氧气化学计量比）对燃料电池性能的影响,并建立多神经网络（MNN）模型,对上述参数进行优化。研究结果表明,最佳流道参数为角度-宽度-深度为25°-1.15 mm-0.85 mm,最佳运行参数为温度-湿度-化学计量比为349.15 K-0.60-4.5。通过对比优化前后的Z型流道PEMFC的性能可看出,优化后的Z型流道PEMFC在稳态特性及瞬态特性方面得到明显改善。     

Coupling flow channel optimization and Bagging neural network to achieve performance prediction for proton exchange membrane fuel cells with varying imitated water-drop block channel

The proton exchange membrane fuel cell (PEMFC) flow channel structure obviously affects the reaction gas distribution and electrochemical reactions. In this study, the imitated water-drop block heights and widths within the channel are optimized for better PEMFC performance. A machine learning-based Bagging neural network is applied for the first time to predict PEMFC output performance based on different block structure parameters. First, the proposed imitated water-drop block height and width are optimized by changing parameters. Then, a database is established. Finally, after the Bagging model is validated, the performance is compared with the back-propagation (BP) neural network. Results indicate that the mass transfer and the electrochemical reaction are improved under the optimal width and height of imitated water-drop block for PEMFC. The Bagging prediction model uses less training data to obtain high-precision prediction results in 10 s. The performance prediction model can effectively improve the efficiency of channel optimization.     

Nonlinear multivariable modeling of locomotive proton exchange membrane fuel cell system

A nonlinear multivariable model of a locomotive proton exchange membrane fuel cell (PEMFC) system based on a support vector regression (SVR) is proposed to study the effect of different operating conditions on dynamic behavior of a locomotive PEMFC power unit. Furthermore, an effective informed adaptive particle swarm optimization (EIA-PSO) algorithm which is an adaptive swarm intelligence optimization with preferable search ability and search rate is utilized to tune the hyper-parameters of the SVR model for the improvement of model performance. The comparisons with the experimental data demonstrate that the SVR model based on EIA-PSO can efficiently approximate the dynamic behaviors of locomotive PEMFC power unit and is capable of predicting dynamic performance in terms of the output voltage and power with a high accuracy.     

Performance optimization of polymer electrolyte membrane fuel cells using the Nelder-Mead algorithm

The direct-search simplex method for function optimization has been adapted to performance optimization of polymer electrolyte membrane fuel cells (PEMFCs). The established method is strongly application oriented and uses only experimentally determined data for optimization. It is not restricted to discrete parameters optimums and does not require the use of third-party software or computational resources. Hence, it is easy to implement in fuel cell testing stations. The optimization consists of finding, for a given fuel cell load, an optimum set of values of the 7 fuel cell operating parameters: the fuel cell temperature, the reactants' stoichiometric ratios, the reactants' inlet relative humidity, and the reactants' outlet pressures, resulting in the highest fuel cell performance. The performance is measured using a scalar function of the operating parameters and the load and can be defined according to needs.Two PEMFC performance functions: the fuel cell voltage and the system-related fuel cell efficiency were optimized using the procedure for practically sized PEMFC stacks of two designs. With respect to the nominal operating conditions defined as optimal for each stack design by its manufacturer, the gains from the optimization procedure were up to over 12% and up to over 7% for the stack voltage and efficiency, respectively. The validation of the procedure involved 5 stack specimens and four laboratories and consistent results were obtained.     

Optimization of a solid oxide fuel cell and micro gas turbine hybrid system

For a solid oxide fuel cell (SOFC) and micro gas turbine (MGT) hybrid system, optimal control of load changes requires optimal dynamic scheduling of set points for the system's controllers. Thus, this paper proposes an improved iterative particle swarm optimization (PSO) algorithm to optimize the operating parameters under various loads. This method combines the iteration method and the PSO algorithm together, which can execute the discrete PSO iteratively until the control profile would converge to an optimal one. In MATLAB environment, the simulation results show that the SOFC/MGT hybrid model with the optimized parameters can effectively track the output power with high efficiency. Hence, the improved iterative PSO algorithm can be helpful for system analysis, optimization design, and real‐time control of the SOFC/MGT hybrid system. Copyright © 2011 John Wiley & Sons, Ltd.     

基于ALMBO算法的PEMFC分数阶时域子空间模型研究

针对质子交换膜燃料电池（PEMFC）发电过程复杂难以建模的问题,考虑PEMFC系统的分数阶特性,提出一种基于优化的分数阶时域子空间辨识方法,并建立PEMFC的分数阶状态空间模型。首先,将分数阶微分理论与子空间时域辨识方法相结合,采用Poisson滤波器对输入输出信号进行滤波处理,并引入权重矩阵提高辨识的精度;其次,对Poisson滤波器以及辨识的分数阶阶次寻优,提出一种变异反向学习的自适应帝王蝶优化算法（ALMBO）,在迁移算子中引入变异反向学习策略、并融入自适应权重来提高寻优的精度,防止陷入局部最优解。最后,通过仿真结果验证算法的有效性,所得的PEMFC辨识模型能准确描述PEMFC的动态过程。     

Channel geometry optimization using a 2D fuel cell model and its verification for a polymer electrolyte membrane fuel cell

This paper studies the optimization method of channel geometries for a proton exchange membrane fuel cell (PEMFC) using a genetic algorithm (GA). The channel and rib widths and channel height are selected as geometry variables. The fuel cell output power is chosen as the cost function for the optimization. In this paper, an in-house genetic algorithm is constructed, and the fuel cell output power is obtained using an interfacing program connected to a commercial computational fluid dynamics (CFD) tool, COMSOL, in a Matlab environment. The 2D PEMFC is used to calculate the performance cost function for computational time and cost. The calculated output power of the PEMFC is delivered to the in-house GA program to check for optimality. After the optimality is checked, the new geometry data is fed back to the COMSOL to calculate the PEMFC output power until the optimization process is finished. Experiments are conducted to support the optimized results using three different channel geometries: channel-to-rib width ratios of 0.5:1, 1:1, and 2:1. A full 3D PEMFC CFD model is constructed using COMSOL to support the 2D CFD optimization results. This paper shows the possibility of applying the geometry optimization process to sophisticated electrochemical reaction systems, such as a PEMFC, using a GA and a commercial CFD tool on the Matlab platform. The geometries and materials can be optimized using this approach to obtain the most efficient performance of an electrochemical system.     

The parameter identification of the Nexa 1.2 kW PEMFC's model using particle swarm optimization

People's extensive and ignorant lifestyles impose an increasing amount of destruction on the environment, which lead to an increased governmental and research interest towards the development and use of green technology such as fuel cells. Fuel cells are recently receiving a major share of research interest due to their promising features. This paper presents an offline parameter identification approach based on particle swarm optimization (PSO) to identify the mathematical modeling parameters of the Nexa 1.2 kW proton exchange membrane fuel cell (PEMFC) system. The goal of this work is not to get a new technique in modeling, but rather to obtain a very good model of the PEMFC system using a simple and fast heuristic approach that requires minimal mathematical effort. This model can then be utilized to perform further analysis and fault diagnosis studies on PEMFCs. The proposed approach uses basic fitting to determine some of the initial values for the PSO, while the rest of the initial values are set to be chosen randomly. The developed model is then successfully validated using actual experimental data sets.     

Multi-objective topology optimization of end plates of proton exchange membrane fuel cell stacks

End plates of the proton exchange membrane fuel cell (PEMFC) need to be well designed because their strength and rigidity directly affect the clamping pressure distribution and thus affect the performance and lifetime of fuel cell stacks. In this paper, a multi-objective topology optimization model of the end plates in a PEMFC stack with nonlinear contact boundary conditions was established to obtain an optimized structural design. It was found that the design improved with topology optimization is not only light but also meets manufacturability requirements. This provides good guidance for the design of a high-performance end plate.     

基于改进粒子群优化支持向量机的汽轮机组故障诊断

基于支持向量机（SVM）在核函数参数和惩罚因子人为选取的盲目性以及传统粒子群算法（PSO）后期易陷于局部最小值的不足,提出了一种改进的粒子群算法（MPSO）,建立了汽轮机组振动故障诊断模型并且利用故障数据进行了模式识别.结果表明：模型能够对SVM相关参数自动寻优,并且能达到较为理想的全局最优解;与PSO-SVM和GA-SVM算法相比,MPSO-SVM算法在收敛速度和准确率方面都有所提高.     

Energy consumption reduction of a PEM fuel cell motor-compressor group thanks to efficient control laws

This paper deals with the energy optimization of an embedded fuel cell generator. To reach this aim, experimentally validated models of a low power 5 kW proton exchange membrane fuel cell (PEMFC) and its most power hungry ancillary (motor-compressor group) are described. All simulation results have been performed using Matlab/Simulink^® environment. Moreover, a control strategy of the air supply circuit integrated in an embedded fuel cell system is proposed. The air flow control of the air supply circuit is built around a fuzzy PD + I controller and for the air supply set point determination, a fuzzy supervision is proposed. The parameters of this fuzzy supervision have been optimized thanks to particle swarm optimization (PSO) method.     

Exergy analysis and optimization of a HT-PEMFC using developed Manta Ray Foraging Optimization Algorithm

This paper analyzes the efficiency of a high-temperature proton exchange membrane fuel cell (HT-PEMFC) by calculating the output voltage of the cell in different working conditions, using the semi-experimental relationships. The irreversibility and the exergy efficiency of the fuel cell is calculated under different working conditions and the effect of temperature and pressure has been studied. To achieve optimal design for the PEMFC, its parameters are optimized based on irreversibility, exergy efficiency, and its work. The system optimization is applied by a modified version of the Manta Ray Foraging Optimization Algorithm. The suggested algorithm is then compared with other algorithms from the literature and also simulation results and showed a high agreement between the suggested algorithm and the simulation results.     

Degradation prediction model of PEMFC based on multi-reservoir echo state network with mini reservoir

The durability of the proton exchange membrane fuel cell (PEMFC) has always been a major obstacle in its commercialization process and effective degradation prediction can improve this problem to a certain extent. Data-driven degradation prediction model is one of the most effective prediction methods available, which is able to ignore the structure of the PEMFC itself and rely solely on the data to make predictions, greatly simplifying the prediction process. Echo state network (ESN), as one of the data-driven methods, has received much attention for its low computational complexity and fast convergence in the degradation prediction of PEMFC. In this paper, the multi-reservoir echo state network with mini reservoir (MRM) degradation prediction model of PEMFC is proposed. The structure of MRM is that the main reservoirs are stacked in a layer and the mini reservoir is in the next level to collect and organize the main reservoir states. In addition, in order to improve the prediction accuracy, this paper firstly uses Savitzky-Golay (SG) filter to process the original data, and then investigates the influence of two important parameters, the number of main reservoirs and the number of main reservoir neurons, on the prediction accuracy and finds the optimal number of main reservoirs and main reservoir neurons for this model using particle swarm optimization (PSO) algorithm. Finally, the effectiveness of the model is verified on different lengths of training sets under both static and dynamic conditions. The results show that the model has higher accuracy and better robustness in the PEMFC degradation prediction compared with other models.     

粒子群算法惯性权重策略对参数反分析优化性能的影响

以某混凝土重力坝挡水坝段为例,针对惯性权重为粒子群算法中平衡全局搜索能力和局部搜索能力的关键参数,分析了不同的惯性权重策略影响粒子群算法在材料参数反分析领域的优化性能,并比较了四种惯性权重策略。结果表明,线性微分递减惯性权重策略最优,可使材料参数反分析过程收敛速度更快、稳定性更强。     

Influences of assembly pressure and flow channel size on performances of proton exchange membrane fuel cells based on a multi-model

In this work, assembly pressure and flow channel size on proton exchange membrane fuel cell performance are optimized by means of a multi-model. Based on stress-strain data of the SGL-22BB GDL obtained from its initial compression experiments, Young's modulus with different ranges of assembly pressure fits well through modeling. A mechanical model is established to analyze influences of assembly pressure on various gas diffusion layer parameters. Moreover, a CFD calculation model with different assembly pressures, channel width, and channel depth are established to calculate PEMFC performances. Furthermore, a BP neural network model is utilized to explore optimal combination of assembly pressure, channel width and channel depth. Finally, the CFD model is used to validate effect of size optimization on PEMFC performance. Results indicate that gap change of GDL below bipolar ribs is more remarkable than that below channels under action of the assembly pressure, making liquid water easily transported under high porosity, which is conducive to liquid water to the channels, reduces the accumulation of liquid water under the ribs, and enhances water removal in the PEMFC. Affected by the assembly force, change of GDL porosity affects its diffusion rate, permeability and other parameters, which is not conducive to mass transfer in GDL. Optimizing the depth and different dimensions through width of the flow field can effectively compensate for this effect. Therefore, the PEMFC performance can be enhanced through the comprehensive optimization of the assembly force, flow channel width and flow channel depth. The optimal parameter is obtained when assembly pressure, channel width and channel depth are set as 0.6 MPa, 0.8 mm, and 0.8 mm, respectively. The parameter optimization enhances the mass transfer, impedance, and electrochemical characteristics of PEMFC. Besides, it effectively enhances the quality transfer efficiency inside GDL, prevents flooding, and reduces concentration loss and ohmic loss.     

Performance improvement of proton exchange membrane fuel cells with compressed nickel foam as flow field structure

In order to improve the performance of proton exchange membrane fuel cell (PEMFC), the compressed nickel foam as flow field structure was applied to the fuel cell. The fuel cell test system was built and the performance of fuel cells with nickel foam flow field with different thicknesses were tested and analyzed by electrochemical active surface area (EASA), electrochemical impedance and polarization curve. And its operating parameters were optimized to improve the performance of PEMFC. Our results show that the membrane electrode assembly (MEA) can show a larger catalytic active area and uniformity of gas diffusion can be improved by using the nickel foam flow field instead of the conventional graphite serpentine flow field, and the impedance characteristic of 110PPI nickel foam can be improved by increasing the compression ratio of the original material. What's more, the polarization characteristic and power output performance of PEMFC with nickel foam flow field were improved by optimizing the operating parameters. Using the optimized operating parameters (cell temperature = 80 °C; humidification temperature = 75 °C; stoichiometric ratio = 2; back pressure = 0.23 Map), a peak power density of 1.89 W cm⁻² was obtained with an output voltage of 0.46 V.     

Parameters extraction of PEMFC's model using manta rays foraging optimizer

In this article, a recently developed bio-inspired based manta rays foraging optimizer (MRFO) is attempted for reliable and accurate extraction of the model uncertain parameters of proton exchange membrane fuel cells (PEMFCs). The parameter estimation is formulated as a non-linear optimization problem subject to set of restrictions. The great development and tremendous revolution of computation heuristic-based algorithms are the impetus of the authors to apply the MRFO to solve this constrained optimization problem resulting in a precise PEMFC model. Three case studies of typical field PEMFC stacks namely Ballard type Mark V, NedStack type PS6, and Horizon type H-12. Various I to V datasets are demonstrated to appraise the performance of MRFO among other recent optimizers available in the literature. To be objective and for sake of quantifications, the best scores of minimum fitness values are 0.8533, 2.1360, and 0.0966 for the later said PEMFC stacks, correspondingly. At a later stage, production of various characteristics under varying operating conditions such as changeable cell temperature and regulating pressures are established using the generated best values of PEMFCs model. Further calculations of statistical indices are performed to validate the robustness of obtained results by the MRFO. Through comprehensive performance assessments, it can be confirmed that MRFO is very promising tool for the effective extraction of PEMFCs' model and suggested to be applied for solving other engineering problems.     

Modelling the performance of an SOEC by optimization of neural network with MPSO algorithm

This paper studies the Solid Oxide Electrolyzer Cell as a promising system in the sustainable development for the hydrogen economy and energy systems as a robust system. The Solid Oxide Electrolyzer Cell converts the steam and carbon-dioxide directly to functional fuels through consumption of the additional electrical power of green power sources or off-peak network powers. The present paper evaluates the static efficiency of the SOEC under four various gas mixtures. Modeling of this system is performed using Elman neural network (ENN) and modified particle swarm optimization (MPSO) algorithm. The MPSO algorithm is utilized to determine the optimal values for ENN adjustable parameters. It's known from the empirical results that the steam and carbon-dioxide concentrations can affect the SOEC efficiency. The operational potential and volume share of the hydrogen, carbon dioxide and steam are considered as the system inputs, and efficiency (current) is remarked as its output. The correlation factors of the achieved model are greater than 0.999, and its MSE (mean squared error) is lower than 0.017. It reveals that the forecasted values are almost equal to the empirical data. Subsequently, the efficiency of the SOEC is studied using the achieved model of the MPSO-based ENN in various feedstock concentrations. Thus, this dataset that is used for ENN model can be desirable for different applications of fast-modeling in a standalone group. It as well can be useful for cost, computing-time, and computing burden reduction in a model construction in the efficiency analyzing and system-level designing processes.