Data-Driven Prediction of Anode Relative Humidity and Voltage in an Open-Cathode PEM Fuel Cell Stack Using the Koopman Operator

Control of anode relative humidity is crucial for optimal hydration and performance in proton exchange membrane (PEM) fuel cells. Accurate predictive models can be essential to enabling real-time control of humidity. This study applies the Koopman operator with radial basis function (RBF) and time-delay embeddings as observables in an extended dynamic mode decomposition (EDMD) framework, to predict anode relative humidity and stack voltage in a 5kW open-cathode PEM fuel cell stack. The performance of the Koopman approaches is compared to a NARX neural network. The Koopman model with time delay embeddings as the basis function consistently outperformed that with RBF across all prediction horizons investigated. Particularly at a 5-step prediction horizon, the RBF EDMD recorded RMSE of 0.61% and 1.17V for humidity and voltage respectively while the time-delay EDMD demonstrated exceptional performance, achieving RMSE on the order of 10-13 for both outputs. The NARX model with random data division showed competitive results (RMSE of 0.77% and 1.05V) but deteriorated in performance (RMSE of 2.97% and 2.01V) when tested on unseen data. These findings highlight the effectiveness of the Koopman operator, especially with time-delay embeddings as coordinate basis. Additionally, the linearity of the Koopman model enables easy integration with established linear control strategies.