Evaluating uncertainties in electrochemical impedance spectra of solid oxide fuel cells

Electrochemical impedance spectroscopy (EIS) is a widely used tool for characterization of fuel cells and other electrochemical conversion systems. When applied to the on-line monitoring in the 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 ignore the random effects can result in misinterpreted spectra and, consequently, in misleading diagnostic reasoning. This fact has not been often addressed in the research so far. In this paper, we propose an approach to the quantification of the spectral uncertainty, which relies on evaluating the uncertainty of the equivalent circuit model (ECM). We apply the computationally efficient variational Bayes (VB) method and compare the quality of the results with those obtained with the Markov chain Monte Carlo (MCMC) algorithm. Namely, MCMC algorithm returns accurate distributions of the estimated model parameters, while VB approach provides the approximate distributions. By using simulated and real data we show that approximate results provided by VB approach, although slightly over-optimistic, are still 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 lower compared to MCMC. The performance of VB algorithm is demonstrated on a case of ECM parameters estimation in a 6 cell solid oxide fuel cell (SOFC) stack. The complete numerical implementation for recreating the results can be found at https://repo.ijs.si/lznidaric/variational-bayes-supplementary-material.