Evaluating uncertainties in electrochemical impedance spectra of solid oxide fuel cells

Electrochemical impedance spectra is a widely used tool for characterization of fuel cells and electrochemical conversion systems in general. When applied to the on-line monitoring in context of in-field applications, the disturbances, drifts and sensor noise may cause severe distortions in the evaluated spectra, especially in the low-frequency part. Failure to account for the random effects can implicate difficulties in interpreting the spectra and misleading diagnostic reasoning. In the literature, this fact has been largely ignored. In this paper, we propose a computationally efficient approach to the quantification of the spectral uncertainty by quantifying the uncertainty of the equivalent circuit model (ECM) parameters by means of the Variational Bayes (VB) approach. To assess the quality of the VB posterior estimates, we compare the results of VB approach with those obtained with the Markov Chain Monte Carlo (MCMC) algorithm. Namely, MCMC algorithm is expected to return accurate posterior distributions, while VB approach provides the approximative distributions. By using simulated and real data we show that VB approach generates approximations, which although slightly over-optimistic, are still pretty close to the more realistic MCMC estimates. A great advantage of the VB method for online monitoring is low computational load, which is several orders of magnitude lighter than that of MCMC. The performance of VB algorithm is demonstrated on a case of ECM parameters estimation in a 6 cell solid-oxide fuel cell stack. The complete numerical implementation for recreating the results can be found at https://repo.ijs.si/lznidaric/variational-bayes-supplementary-material.