The limited durability is one of the key barriers of Proton Exchange Membrane Fuel Cell (PEMFC) to large-scale commercial applications. The data-driven prognostic method aims to estimate the Remaining Useful Life (RUL) without the need for complete knowledge about the system’s physical phenomena. As an improved structure of the recurrent neural network, the Echo State Network (ESN) has demonstrated better performances, especially in reducing the computational complexity and accelerating the convergence rate. The traditional prognostic methods utilize only the previous state, e.g. stack voltage, for prediction. Nevertheless, the current operating conditions, such as stack current, stack temperature and the pressures of the reactants (i.e. oxygen and hydrogen) can also contain important degradation information in practice. Especially, the stack current is a crucial operating parameter, since it is normally taken as the scheduling variable and it could reflect the operating conditions. Compared with the single-input and single-output (SISO-ESN) structure, the ESN with multiple inputs and multiple outputs (MIMO-ESN) is proposed in this paper to improve the RUL prediction accuracy. Stack voltage, stack current, stack temperature and the pressures of the reactants are combinedly used to predict the RUL. After the mathematical modeling and the parameter designing, the prediction performance of SISO-ESN and MIMO-ESN are verified and compared on a 1 kW electrical power test bench developed in the laboratory. Results show that the MIMO-ESN method has a better performance than the SISO-ESN method under both static and quasi-dynamic operating conditions.

有限的耐用性是质子交换膜燃料电池（PEMFC）进入大规模商业应用的主要障碍之一。数据驱动的预测方法旨在估计剩余的使用寿命（RUL），而无需完全了解系统的物理现象。作为递归神经网络的一种改进结构，回声状态网络（ESN）表现出更好的性能，尤其是在降低计算复杂性和加快收敛速度​​方面。传统的预后方法仅利用先前的状态（例如堆电压）进行预测。然而，当前的操作条件，例如堆电流，堆温度和反应物的压力（即氧气和氢气）在实践中也可能包含重要的降解信息。特别，堆电流是关键的工作参数，因为通常将其作为调度变量，并且它可以反映工作条件。与单输入单输出（SISO-ESN）结构相比，本文提出了一种多输入多输出的ESN（MIMO-ESN），以提高RUL的预测精度。堆电压，堆电流，堆温度和反应物的压力结合起来用于预测RUL。经过数学建模和参数设计，在实验室开发的1 kW电力测试台上验证并比较了SISO-ESN和MIMO-ESN的预测性能。结果表明，在静态和准动态工作条件下，MIMO-ESN方法均具有比SISO-ESN方法更好的性能。