Extracting Quantitative Insights from Electrochemical Impedance
Spectra Using Statistical Methods
Pavle Boškoski
1
, Benjamin Königshofer
3
, Gjorgji Nusev
1
, Aljaž Ostrež
2
, and Vanja Suboti
´
c
3
1
Jožef Stefan Institute, Jamova cesta 39, Ljubljana, Slovenia
pavle.boskoski@ijs.si
gjorgji.nusev@gmail.com
2
Faculty of Information Studies in Novo mesto, Ljubljanska cesta 31a, Novo mesto, Slovenia
aljaz.ostrez@student.fis.unm.si
3
Institute of Thermal Engineering, Graz University of Technology, Infeldgasse 25b/5, 8010 Graz, Austria
ben.konigshofer@gmail.com
vanja.subotic@tug.at
ABSTRACT
Statistical analysis of electrochemical impedance spec-
troscopy data provides a systematic way of detecting changes
in electrochemical energy systems. Applying concepts of
divergence measures directly on electrochemical impedance
spectroscopy data, one can reliably detect and quantify
statistically significant changes. The result is a set of high-
lighted frequency bands where the measured impedance
characteristics differ statistically significantly from a ref-
erence curve. The approach is evaluated on a solid-oxide
electrolyser cell operated under different conditions and
proves to be sensitive to even the smallest changes. The
complete numerical implementation and corresponding
experimental data are available as supplementary mate-
rial at https://portal .ijs .si/nextcloud /s/
xTa2cmtfxXn2jSz.
1. INTRODUCTION
In characterizing and online monitoring of electrochemi-
cal energy systems, electrochemical impedance spectroscopy
(EIS) is the primary source of information (Yang et al., 2020).
However, direct analysis of impedance curves for detect-
ing small changes is often challenging. Consequently, vari-
ous post-processing techniques have been developed, for in-
stance, distribution of relaxation times (DRT) and equivalent
circuit model (ECM). As a result, the changes of the EIS
Pavle Boškoski et al. This is an open-access article distributed under the
terms of the Creative Commons Attribution 3.0 United States License, which
permits unrestricted use, distribution, and reproduction in any medium, pro-
vided the original author and source are credited.
curves are quantified through changes in the model param-
eters. Despite the effectiveness of these approaches, a logical
question arises: Can the analysis of impedance data be per-
formed in a more direct approach without introducing addi-
tional models?
There are two main challenges with the current approaches
for analyzing EIS curves. The first is the limited number
of measured data points. EIS is typically performed using
(multi-)sine excitation that results in no more than a dozen
points per decade. With such a low cardinality data set, any
task of model fitting almost always becomes ill-posed, i.e.,
the number of the model parameters is comparable to the
size of the data set. This is usually resolved by introducing
regularisation parameters (Papurello, Menichini, & Lanzini,
2017; Wan, Saccoccio, Chen, & Ciucci, 2015; Effat & Ciucci,
2017).
The second challenge is that electrochemical energy sys-
tems belong to a particular group of linear systems called
fractional-order systems (Sadli et al., 2010). These linear sys-
tems include a concept of non-integer derivation order, hence
the name. The biggest challenge when performing identifica-
tion of such systems is the still-open issue of structural iden-
tification, i.e., determining the most suitable model based on
the available information in the acquired signals. In the con-
text of integer-order linear systems, structural identification
determines the number of poles of the system or, in terms
of ECM, the number of RC elements (Overschee & Moor,
1993). For fractional-order systems, in addition to the num-
ber of poles, one also needs the power of the pole, i.e., the
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