Degradation trajectories prognosis for PEM fuel cell systems based on Gaussian process regression

The aging trajectory prognosis is an effective tool to prolong the lifespan and lower the cost of proton exchange membrane fuel cell (PEMFC) systems. In this paper, Gaussian process regression modeling frameworks based on sparse pseudo-input Gaussian process (SPGP) and variational auto-encoded deep Gaussian process (VAE-DGP) are proposed to predict the degradation trend and cope with model uncertainty for PEMFCs. The optimal hyper parameters and pseudo-input locations are obtained with conjugate gradient by maximizing the marginal likelihood. Besides, the variational parameters and closed-form variational lower bound are optimized through variable inference, radial basis function (RBF) kernel is utilized to determine the priori distribution of Gaussian process. Then stack voltage and output power are extracted as health indicators (HIs). To fully demonstrate the prediction performance, long-term experimental validation with static and dynamic aging tests are performed, single-input and multi-input structures are respectively constructed in SPGP and VAE-DGP for comparison with the existing models. The results show that the proposed methods outperform other data-driven methods, moreover, SPGP is more suitable for large data regime and VAE-DGP operates better with small data regime. Finally, the performance evolution is presented with 95% confidence interval to validate the mapping accuracy and reliability further.