  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.

Computation;Machine Learning;Applications;Machine Learning