Machine Learning Based Modeling for Solid Oxide Fuel Cells Power Performance Prediction

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Oct 14, 2013 (3 years and 10 months ago)

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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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-
来g攠sym扯汩挠牥杲敳獩潮e
(
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㈰㄰
)

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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.