The functioning and the achievable power of a proton exchange membrane fuel cell (PEMFC) are determined by several parameters simultaneously. Part of these cannot be measured directly. They must be estimated with parameter fitting techniques. In order to give reliable estimations for the unknown parameters, we first set up an adequate finite difference numerical solution of the mathematical model of the fuel cell. Then the values of the unknown parameters are calculated by fitting the model results to measurements. In this paper our primary aim is to compare several parameter fitting tools on the model of a PEMFC and give a prescription for the use of these methods. We test three methods together with their variants: the Levenberg–Marquardt method, the trust region method, and the simulated annealing method, among which the Levenberg–Marquardt method turns to be the most efficient one.

References

References
1.
Pukrushpan
,
J. T.
,
Stefanopoulou
,
A. G.
, and
Peng
,
H.
,
2004
,
Equation of State Calculations by Fast Computing Machines. Principles, Modeling, Analysis and Feedback Design
,
Springer
,
New York
.
2.
Subramanian
,
V. R.
,
Devan
,
S.
, and
White
,
R. E.
,
2004
, “
An Approximate Solution for a Pseudocapacitor
,”
J. Power Sources
,
135
, pp.
361
367
.10.1016/j.jpowsour.2004.03.069
3.
Kriston
,
Á.
,
Inzelt
,
G.
,
Faragó
,
I.
, and
Szabó
,
T.
,
2010
, “
Simulation of the Transient Behavior of Fuel Cells by Using Operator Splitting Techniques for Real-Time Applications
,”
Comput. Chem. Eng.
,
34
, pp.
339
348
.10.1016/j.compchemeng.2009.11.006
4.
Levenberg
,
K.
,
1944
, “
A Method for the Solution of Certain Non-Linear Problems in Least Squares
,”
Q. Appl. Math.
,
2
, pp.
164
168
.
5.
Marquardt
,
D.
,
1963
, “
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
,”
SIM J. Appl. Math.
,
11
, pp.
431
441
.10.1137/0111030
6.
Nocedal
,
J.
, and
Wright
,
S. J.
,
1999
,
Numerical Optimization. Series in Operations Research
,
Springer
,
New York
.
7.
Cerny
,
V.
,
1985
, “
Thermodynamical Approach to the Traveling Salesman Problem: An Efficient Simulation Algorithm
,”
J. Opt. Theory Appl.
,
45
, pp.
41
45
.10.1007/BF00940812
8.
Kirkpatrick
,
S.
,
Geddat
,
C. D.
, and
Vecchi
,
M. P.
,
1983
, “
Optimization by Simulated Annealing
,”
Science
,
220
, pp.
671
680
.10.1126/science.220.4598.671
9.
Litster
,
S.
, and
Djilali
,
N.
,
2007
, “
Performance Analysis of Microstructured Fuel Cells for Portable Devices
,”
Electrochimica Acta
,
52
(
11
), pp.
3849
3862
.10.1016/j.electacta.2006.11.002
10.
Kulikovsky
,
A. A.
,
2002
, “
The Voltage-Current Curve of a Polymer Electrolyte Fuel Cell: ‘Exact’ and Fitting Equations
,”
Electrochem. Commun.
,
4
, pp.
845
852
.10.1016/S1388-2481(02)00466-6
11.
Weber
,
A. Z.
, and
Newman
,
J.
,
2004
, “
Transport in Polymer-Electrolyte Membranes
,”
J. Electrochem. Soc.
,
151
, p.
A311
.10.1149/1.1639157
12.
Faragó
,
I.
,
Izsák
,
F.
,
Szabó
,
T.
, and
Kriston
,
A.
,
2013
, “
An IMEX Scheme for Reaction-Diffusion Equations: Application for a PEM Fuel Cell Model
,”
Cent. Eur. J. Math.
,
11
(
4
), pp.
746
759
.10.2478/s11533-012-0157-9
13.
Guo
,
Q.
,
Sethuraman
,
V. A.
, and
White
,
R. E.
,
2004
, “
Parameter Estimates for a PEMFC Cathode
,”
J. Electrochem. Soc.
,
151
(
7
), pp.
A983
A993
.10.1149/1.1747850
14.
Ma
,
C.
, and
Jiang
,
L.
,
2007
, “
Some Research on Levenberg–Marquardt Method for the Nonlinear Equations
,”
Appl. Math. Comput.
,
184
, pp.
1032
1040
.10.1016/j.amc.2006.07.004
15.
Fan
,
J.
, and
Pan
,
J.
,
2009
, “
A Note on the Levenberg–Marquardt Parameter
,”
Appl. Math. Comput.
,
207
, pp.
351
359
.10.1016/j.amc.2008.10.056
16.
Conn
,
A. R.
,
Gould
,
N. I. M.
, and
Toint
,
P. L.
,
2000
,
Trust-Region Methods
(MPS-SIAM Series on Optimization),
SIAM
,
Philadelphia, PA
.
17.
Metropolis
,
N.
,
Rosenbluth
,
A. W.
,
Rosenbluth
,
M. N.
, and
Teller
,
A. H.
,
1953
, “
Equation of State Calculations by Fast Computing Machines
,”
J. Chem. Phys.
,
21
(
6
), pp. 1087–1092.10.1063/1.1699114
18.
Yang
,
W. Y.
,
Cao
,
W.
,
Chung
,
T.-S.
, and
Morris
,
J.
,
2007
,
Applied Numerical Methods Using MATLAB
,
John Wiley and Sons
,
New York
.
You do not currently have access to this content.