Abstract Accurate modelling of fuel cells (FC) is essential to better control their operation. In this article, we applied the butterfly flame optimization algorithm (MFO) taking into account the measurement uncertainty to estimate the parameters of the proton exchange membrane fuel cell (PEMFC) for their electrical equations based on current-voltage characteristics (I-V). To evaluate the performance of the proposed algorithm, three commercial PEMFCs with their experimental data (I-V) are considered such as 250 W, NedSstack PS6 and BCS 500-W. The cases of the models with 6, 7 and 11 parameters unknown and the learning technique have been treated. The performance analysis of the proposed method is carried out by applying the two sum squared errors (SSE) and root mean square error (RMSE) between the estimated and experimental data, the proposed approach is affirmed by its great superiority compared to the other methods recently published in Literature.

中文翻译：

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基于飞蛾火焰优化的PEM燃料电池模型参数提取

摘要 燃料电池 (FC) 的准确建模对于更好地控制其运行至关重要。在本文中，我们应用蝴蝶火焰优化算法 (MFO) 考虑测量不确定性，以基于电流-电压特性 (IV) 来估计质子交换膜燃料电池 (PEMFC) 的电方程参数。为了评估所提出算法的性能，考虑了三个商业 PEMFC 及其实验数据 (IV)，例如 250 W、NedSstack PS6 和 BCS 500-W。6、7和11个参数未知的模型和学习技术的情况已经得到处理。通过在估计和实验数据之间应用两个平方和误差（SSE）和均方根误差（RMSE），对所提出的方法进行性能分析，