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Abstract

Hydrogen is a promising energy carrier in the emerging green energy landscape. It is
environmentally friendly, transportable, and storable. The Solid Oxide Cell (SOC) system
is a complex technology that enables the bidirectional conversion of hydrogen to energy.
The label SOC entails solid oxide fuel cell (SOFC) systems, which produce electrical energy
from hydrogen, and solid oxide electrolyzer cell (SOEC) systems, which produce hydrogen
from water and electricity.
Compared to other electrochemical energy conversion systems, a SOC system offers
some remarkable advantages, such as flexible use of reactants and no dependence on rare
materials and catalysts (since they operate at temperatures as high as 600 − 1000K).
Despite significant developments in the last two decades and rising needs for applications
in green transport and smart grids, their deployment is still relatively slow. Part of the
reason is still insufficient durability and reliability, which are inherently conditioned by the
inevitable degradation processes. Reliable condition monitoring, prognostics, and health
management contribute to better operability and durability of SOC devices. Diagnosis and
prognosis, as the key functionalities, help the operators gain insight into the two critical
questions: (i) What is the internal health status of the devices and components, and if
there is a problem, what exactly is it about, and (ii) how long is the system expected to
operate before facing the inevitable end? This thesis focuses on these two fundamental
questions.
The body of research dealing with fault diagnosis and prognosis of SOC systems is
relatively small compared to other electrochemical conversion systems (batteries in particular).
Most works concern SOFC systems while the methodology is still emerging for
SOEC systems. The approaches range from those based on first principles to entirely datadriven
ones. A common denominator of all of them is that they build on some form of the
deterministic model of the underlying processes running within the stack and the balance
of the plant. Hence, the impact of process disturbances and uncertainties on the final result
is largely overlooked. To the best of our knowledge, this thesis provides a rare attempt to
systematically quantify the influence of random noise and disturbances on the diagnostic
inference and prediction of the remaining useful life. Indeed, uncertainties in the process
cannot result in specific reasoning outcomes. Therefore, it is of considerable engineering
and scientific interest to quantify the level of uncertainty of the results of inference, which
contributes to cautious and more reliable decision-making.
The thesis first addresses the uncertainty in the deconvolution of the electrochemical
impedance spectroscopy (EIS) utilizing the equivalent circuit models. It is well known
that instrumentation and process noise during the EIS measurements affect the spectra,
particularly in the low-frequency region. In our approach, we pursue the variational Bayes
(VB) approach, which tends to be an approximation of the Bayesian approach but computationally
much less overwhelming. Hence, the VB algorithm results in a code suitable
for online implementation. To mitigate the inherent bias of the VB approach, mixture distributions
are used as prior-posterior distributions, significantly reducing bias. The results
obtained on data gathered from EIS sessions on SOFC and SOEC stacks indicate that the
serial connection of a resistance and RQ elements (parallel connection of a resistance and a
constant phase element) sufficiently accurately describes the experimental data with relatively
low uncertainty. That observation holds provided the EIS were taken under regular
conditions, although the results can fluctuate from one EIS session to another.
The ground for fault diagnosis is the equivalent circuit model (ECM) parameters and
their evaluated uncertainties. A fault is deduced from the dissimilarity between the evaluated
and nominal ECM parameters. For that purpose, we introduce the Wasserstein distance
(WD) between the distributions of the evaluated and the nominal ECM parameters.
The conventional approaches tacitly assume that nominal ECM parameters are constant.
However, nominal values of the ECM parameters vary with the operating conditions. In
practice, especially in SOEC applications, the operating conditions change frequently and
decisively influence the EIS spectra. Therefore, process parameters must be considered in
the EIS analysis if we want consistent diagnosis resistant to changes in the operating point.
To do so, we propose an innovative approach in which the nominal ECM parameters are
calculated relative to the operating conditions. The data-driven Gaussian processes (GP)
model relates the process variables with the ECM parameters. Based on that, each time a
new EIS session is performed, the GP model predicts the ECM parameters from process
variables. Then, the WD between the predicted and measured distributions of the ECM
parameters is evaluated.
The problem of fault isolation is solved using the Support Vector Machine (SVM)
classifier, which evaluates the probability that the system is at a specific faulty state.
Finally, the problem of predicting the remaining useful life (RUL) is approached within
an entirely data-driven probabilistic framework. It is applied to a health indicator, which
can be, for example, the stack voltage or the area specific resistance (ASR). The idea of
the approach is simple, i.e., anticipate the end of life based on the linear trend model of the
health indicator. A closed-form solution for the probability distribution of the stack’s RUL
emerges. That is a rather unusual result, which renders the required computational effort
doable in no time. Additionally, the approach can be implemented on target platforms like
industrial controllers. The idea has been validated through simulations and experimental
data from an SOFC system to demonstrate its applicability to online monitoring and
control of SOC systems.
In this thesis, we have been seeking solutions that will be operable and implementable
on industrial control systems, which have much less computational power than PCs. The
code is derived in Python and, as such, can be ported on the HW platforms developed
within the framework of EU projects REACTT and RUBY, to name some examples.
In both cases, the target processor is Raspberry Pi 4, which, thanks to the adequately
conceptualized firmware, can include the operational code realized in Python.
The study begins by exploring Bayesian inference and introducing the Variational Bayes
approach and its optimization methods. These techniques are applied to simulated and
experimental SOC system data, demonstrating significant improvements in parameter estimation
accuracy. The research further investigates passive diagnostic methods, employing
data-driven feature extraction with Gaussian Processes to detect and isolate faults in SOC
systems.