Proceedings of the
6
th International
Conference o
n Process Systems Engineering
(PSE ASIA)
25

27
Ju
ne 2013
,
Kuala Lumpur.
Machine Learning Based
Modeling
for
Solid Oxide
Fuel Cells Power Performance Prediction
M
.
N. Fuad
,
a
M
.
A
.
Hussain
,
b
a
Chemical Engineering Department, Faculty of Engineering, UCSI University, 56000
Cheras, Kuala Lumpur
Department of Chemical
Engineering, Faculty of Engineering, University of Malaya,
50603, Kuala Lumpur
Abstract
This study applies four different types of machine learning methods to model th
e power
performance behaviour of
a tubular solid oxide fuel cells (SOFC) under different
operating conditions. The corresponding machine learning
methods
are: artificial neural
network (ANN), fuzzy inference system (FIS), support vector machine (SVM), and
genetic programming (GP). By using four
types of
inputs of the SOFC operation: i.e.
load
current, fuel utilization, inlet air temperature, and air molar flow rate, the
task of
the
corresponding machine learning
methods
is to
predict the stack voltage and outlet
temperature values of the corresponding SOFC operation. 1000 input

output data
pai
rings that were generated from the simulations of a physical tubular SOFC model
under various operating conditions were used to train the corresponding machine
learning models. It was found out from this study that ANN
method
has
slightly
better
performanc
e in
modelling
the power performance
behaviour
of the corresponding SOFC
system under various operating conditions.
Keywords
:
Solid oxide fuel cells;
Machine
l
earning
m
ethods;
Power performance
pre
diction
1.
Introduction
Solid oxide fuel cells (SOFC) are expected to play a significant role in helping to meet
the ever

increasing demands for
cleaner
supply energy in the near future
(
Stambouli,
2011
)
. Already, SOFCs have been proposed as a potential power source for distributed
and
stationary power plants and
also
mobile applications. The advantages of SOFCs are
their high efficiency, modularity, low noise and low environmental pollution. Howe
ver,
certain challenges, including the optimum operation of the SOFC stacks, need to be
resolved before the technology can be adopted for
the
real

world applications.
Moreover,
this
issue will also take into considerations
the unique nature of the SOFC
ope
rating
phenomena
.
Clearly, the requirement to satisfy all these
challenges
will
require
the development of an
effective
control
strategy that is specifically tailored to
the SOFC
operation
. Model

based control strategies that rely on the availability of go
od
modeling description
s
of the SOFC phenomena are expected to play a crucial role in
this
regard
.
Machine
learning
has shown its great utility
in
modeling
complex phenomena in
chemical processes.
This utility
has brought
forward its
potential
for
applications
in
advanced process control
strategies
such as real

time optimization and model

based
20
M. N. Fuad et al.
predictive control
s
. Although first

principle ba
sed modeling is very useful for
design
purpose
and
as an aid for
the
understanding
, black

boxed modeling that
employs
machine learning principle
s
such as neural network and support vector machine
is
very
useful
for
real

time application
s that demand
fast
er
and robust computation
s
.
Moreover,
the developments of the corresponding
machine learning
model
s
are less de
manding as
long as sufficient collections of input

output data samples are available for training
purpose.
Once trained, the corresponding model
s
can be used
effectively and efficiently
to achieve various
objectives
such as operation point optimization or
model

based
controls.
Therefore,
driven by these motivations
, this paper seek
s
to study the
application of several machine learning
methods
to model the
power performance
behavior
of
a
solid oxide fuel cell
s
operation. Specifically, four types of machine
learning
methods
i.e. artificial neural network, fuzzy inference system, support vector
machines
and genetic programming
are
applied in this study
in order
to observe their
performances in modeling the
operat
ing behavior of the
corresponding
SOFC
system
.
2.
Brief Description
s
of the
Corresponding
Machine Learning
Methods
2.1.
Artificial Neural Network
s
Artificial neural networks (ANN) are a computational tool modeled on the
interconnection of the neurons in the ne
rvous systems of the human brain and that of
other
animals
(
Bishop, 1995
)
.
The structure of
a
feed

forward
multilayer
ANN is
displayed in Fig
ure
1
.
In this structure,
the
information
is passed
from the input layer
to
the hidden layer
via various network connections
and finally to the output layer. The
training phase
of ANN consists of submitting
samples of input

output data (called the
training data
)
to the network and
adjusting
the connection weights
until the measure of
difference between the target data and ANN output is minimized.
Past study
has proven
that the standard multilayer
feed

forward
network with a single hidden layer can be
used to approximate continuous function of arbitrary complexity (
i.e.
universal
approximation theorem
).
Figure 1
.
Feed

forward multilayer neural network
2.2.
Fuzzy Inference System
s
Fuzzy inference system
s
(FIS)
are simply the applications
of fuzzy logic and fuzzy set
theory
for
data classification, decision analysis, and pattern recognition
(
Takagi &
Sugeno, 1985
)
.
The general architecture of FIS consists of three parts (see Fig
ure
2
).
The first part i.e.
the
fuzzifier
, convert
the crisp input to
linguistic variable
s
by
using the
Machine Learning Based Modeling for Solid Oxide
Fuel Cells Power Performance
Prediction
21
membership functions stored in the fuzzy knowledge base. In the next
p
art
i.e.
inference
engine
, a collections of IF

THEN type fuzzy rules
will
convert the fuzzy input to the
fuzzy output. Finally in the
defuzzifier
part, the fuzzy output of the inference engine will
be converted to crisp output by using the membership funct
ion analogous to the ones
employed
by the fuzzifier.
Currently, two types of
fuzzy inference
system
s
are widely
employed
, i.e.
Mamdani and Takagi

Sugeno.
Moreover
, the Takagi

Sugeno
fuzzy
inference
system can be
‘trained’
by
an adaptive technique
in which
the parameters of
the membership functions
are
optimized
with respect to the given
samples of
input

output data
.
Figure 2.
Components of a fuzzy system
2.3.
Support Vector Machines
Support vector machines (SVM) are among kernel

based techniques that
are very
popular for data classification and regression
(
Ivanciuc, 2007
)
. More formally, a support
vector machines constructs
a hyperplane or set of hyperplanes in a high

or infinite

dimensional space from several points in training examples (called
support vectors
)
which can be used for classification or regression. Formerly developed as
a
linear data
classifier, the extension
to nonlinear classification was made possible by using
kernel
trick
that maps input space into a higher dimensional feature space. The training phase
of SVM amounts to
solving
an optimization problem that seeks
to find the largest
margin
hyperplane that re
presents the best separation of data into
its
proper categories.
The extension
of SVM
to nonlinear regression was
made possible
by using an ε

insensitive loss function. Generally, the goal of SVM regression (SVMR) is to identify a
function
f
(
x
) that for al
l training patterns
x
has a maximum deviation ε from the target
values
y
and has a maximum margin
(
Ivanciuc, 2007
)
.
2.4.
Genetic Programming
Genetic programming (GP) is an evolutionary algorithm

based methodology inspired by
biological evolution to find computer programs that
can
better
perform a user

defined
task
(
Koza, 1992
)
. It is a specialization of genetic algorithms where each individual is a
computer program
(see Figure
3
)
that
will be
evolved according to evolu
tionary
principle
s
that seek
s
the fittest individuals among the population of the candidate
solutions.
T
he fittest individuals represent computer programs that can perform the user

defined task optimally.
The principle
of GP use
s
various analog
s
of the nat
urally
occurring
evolutionary
operations, including crossover (sexual recombination),
mutation, gene duplication, and gene deletion.
Among the numerous applications
of GP
,
it
has been
used
successfully
for
symbolic regression
s
.
Specifically, i
n symbolic
re
gression
s
, the task of GP is to find both structure and parameters of
a
nonlinear model
that minimizes the error
criterion between
predictions and observed data
.
22
M. N. Fuad et al.
Figure 3.
A
computer program (e.g. mathematical function)
represented as a tree
structure
in
genetic programming
3.
Modeling SOFC Power Performance via Machine Learning
Methods
T
he
corresponding machine learning
methods
(i.e. ANN, FIS, GP and SVM)
are
used in
this study
to model the
power performance
behavior
of a tubular
SOFC
under various
operati
ng conditions.
In this study, e
ach
of the
corresponding machine learning
model
s
will receive
four inputs
of
the SOFC
operation
i.e.
load current
(
20

158 A
)
, fuel
utilization
(
50

90%
)
, inlet
air
temperature
(
973

1173 K
)
, and air molar flow rate
(
0.01

0.02 m
ol/s
)
.
In turn,
the model
s
will predict the
stack
voltage and
outlet
temperature
values
from the corresponding input
s
. The database
of
the SOFC operation is generated
from
the
simulations of a physical model
of a tubular SOFC
for 1000 input data
set
.
These
input

output data
pairings
are further partitioned into
800
dataset
for
t
raining/validation and 200 dataset
for testing.
Furthermore, the dataset for the
training/validation are corrupted by
±
5
%
measurement errors while the testing dataset
are
left intact
.
All the
input

output
dataset in this study are normalized
to [

1, 1] in order
to facilitate the training
phase
.
Finally, the
training
parameters
for
each
of the
machine
learning
models
are tabulated in Table
1
.
4.
Results and Discussions
Figure
4
shows the
parity plot
s
that were generated from
the testing data
and the
corresponding
machine learning model
predictions
at the conclusion of the trainings.
Although ANN method yield the
slightly
highest prediction accuracy with correlation
coefficient R = 0.99922, the other machine learning methods also exhibit satisfactory
performance in modeling the
operating
behavior of the corresponding SOFC system. It
should be noted that the corresponding pa
rity plots were generated from the uncorrupted
testing data that was not used in the training phase of the
corresponding
machine
learning
models
. As such, the corresponding testing data
(i.e.
unseen data
)
can provide
information to evaluate the performance
of the corresponding machine learning methods
in learning the
behavior
of the training/validation dataset
that was corrupted by
measurement errors.
Moreover, the prediction capabilities of the trained machine
learning models were also investigated further
by reproducing the power performance
curves of the corresponding SOFC system
at
various
fuel utilization and inlet air
temperature conditions as shown in Figure 5. As can be seen from the corresponding
figures, all the machine learning
methods
can
reprodu
ce the power performance curve
including the location of the maximum power point satisfactorily.
Machine Learning Based Modeling for Solid Oxide
Fuel Cells Power Performance
Prediction
23
Table 1.
Machine learning methods and their associated training parameters
Machine learning
Training parameters
Artificial neural network (ANN)
Multilayer
feed

forward neural network with one hidden
layer and 10 neurons in the hidden layer
Training algorithm: Backpropagation algorithm with early
stopping
(as implemented by neural network toolbox in
Matlab
®
software)
Fuzzy inference system (FIS)
The
training is based on the a
daptive network based fuzzy
inference system (ANFIS)
as implemented by fuzzy logic
toolbox in Matlab
®
software
2 membership functions of generalized bell type
are
implemented
for the input later and linear type
membership function
is implemented
for the output layer
Training algorithm: hybrid training method (i.e.
backpropagation algorithm with least

squares estimation
method)
Support vector machine (SVM)
SVM type: ν

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Figure 4.
Parity plots for the testing data predictions
24
M. N. Fuad et al.
Figure 5.
Comparisons of actual and predicted power performance curves
(air molar flowrate =
0.012 mol/s)
5.
Conclusions
In this study
,
we have
compare
d
different types of machine learning
methods
to model
t
he power performance behavior of a tubular
SOFC operation
. Among the different
types of machine learning
methods
that
were
covered in this study, it was found out that
ANN
method
has
slighlty
better performance in predicting the power performance
behavior
of the corresponding
SOFC
system
under various operating conditions.
Th
e
result
from this study
open
s
the possibility
for
applying the corresponding
machine
learning
method
for SOFC performance maps constructions and operation point
optimization.
References
Bishop, C. M. (1995).
Neural Networks for Pattern Recognition
. Oxford: Oxford University
Press.
Chang, C. C., & Lin, C. J. (2002). Training nu

support vector regression: theory and algorithms.
Neural Computation, 14
(8), 1959

19
77.
Ivanciuc, O. (2007). Applications of support vector machines in chemistry. In K. B. Lipkowitz &
T. R. Cundari (Eds.),
Reviews in Computational Chemistry
(Vol. 23, pp. 291

400). Weinheim:
Wiley

VCH.
Koza, J. (1992).
Genetic Programming: On the Programm
ing of Computers by Means of Natural
Selection
. Cambridge, MA: MIT Press.
Searson, D. P., Leahy, D. E., & Willis, M. J. (2010).
GPTIPS: An open source genetic
programming toolbox for multigene symbolic regression.
Paper presented at the International
Multi
Conference of Engineers and Computer Scientists Hong Kong.
Stambouli, A. B. (2011). Fuel cells: The expectations for an environmental

friendly and
sustainable source of energy.
Renewable and Sustainable Energy Reviews, 15
, 4507

4520.
Takagi, T., & Sugeno,
M. (1985). Fuzzy identification of systems and its applications to modeling
and control.
IEEE Transactions on Systems, Man and Cybernetics, 15
, 116

132.
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