Remaining useful life prediction of PEMFC systems based on the multi-input echo state network

•Data-driven method is used to predict the remaining useful life of fuel cell.•Multi-input and multi-output based echo state network is deployed for the prognostic.•Aging experimental tests of static and quasi-dynamic are conducted.•Validation results denote the improvement in the prediction accuracy. 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.