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A modified farmland fertility optimizer for parameters estimation of fuel cell models

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Abstract

This paper proposes a modified version of a well-known optimization technique called Farmland Fertility Optimization algorithm (FFA). The modified FFA (MFFA) is developed in order to improve the performance of conventional FFA. It is mainly based on two stages. Firstly, the Levy flights are used to enhance the local searching capability in the exploitation phase and the global searching capability in the exploration phase. Secondly sine–cosine functions are used to create different solutions which fluctuate outwards or towards the best possible solution. The developed algorithm has been validated using ten benchmark functions and three mechanical engineering benchmark optimization problems. After that, the newly developed algorithm MFFA is used for extracting the effective unknown parameters of Proton Exchange Membrane Fuel Cells (PEMFCs) models. The optimal extraction of these parameters is essential to determine an accurate semi-empirical mathematical model for PEMFC. The sum of squared errors between the experimental data and the corresponding calculated ones is adopted as the objective function. Four different commercial PEMFC stacks are used to validate the effectiveness of the developed algorithm. The results obtained by MFFA are compared with those obtained by the conventional FFA and other well-known optimization techniques. Moreover, a comprehensive statistical analysis is performed to determine the accuracy and efficiency of the developed algorithm. The results prove the reliability and superiority of the developed algorithm compared with the conventional FFA and other state-of-the-art optimizers.

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Abbreviations

FC:

Fuel cell

PEMFC:

Proton exchange membrane fuel cell

SSE:

Sum of squared errors

V stack :

PEMFC stack voltage (V)

E Nernst :

Nernst voltage of a single FC (V)

N cells :

Number of cells in the stack

v act, v ohm , and v con :

Activation, ohmic, and concentration over potential, respectively (V)

T :

FC operating temperature (K)

P H2 and P O2 :

Hydrogen and oxygen partial pressures, respectively (atm)

ζ 1, ζ 2, ζ 3, and ζ 4 :

Parametric adjustable parameters for a particular FC

I fc :

PEMFC stack current (A)

R c and R M :

Resistance due to concentration and transfer of proton, respectively (Ω)

ρ M :

Specific resistance of the membrane (Ω cm)

l :

Membrane thickness (μm)

A :

Effective electrode area (cm2)

λ :

Adjustable parameter describes the water content in the membrane

b :

Parametric coefficient (V)

J and J max :

Actual and maximum current density of the FC stack, respectively (A cm−2)

N :

Population size

k :

Number of sections

n :

Number of solutions available in each section

maxiter :

Maximum number of iterations

L j and U j :

Lower and upper limits of the design variable, respectively

Fit_Sections:

Average quality of the solutions in each section

M local and M Global :

Number of solutions in local and global memories, respectively

t :

Constant between 0.1 and 1

h :

Decimal number

α :

A number in the range of (0,1)

X MGlobal :

A randomly selected solution from the global memory

X new :

A new solution that obtained by applied changes

β :

An arbitrary number in the range of (0,1)

Best Local :

The best available solution in the local memory

Best Global :

The best solution ever found

Q :

A parameter between (0,1)

w 1 :

A parameter of the FFA reduced as the optimization process progresses

R v :

A constant number between 0 to 1

rr 1 and rr 2 :

Two randomly distributed numbers between [0,1]

MaxIt :

Maximum number of iterations

rand :

A random number between (0,1)

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Acknowledgment

The authors thank the support of the National Research and Development Agency of Chile (ANID), ANID/Fondap/15110019.

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Authors and Affiliations

  1. Electrical Engineering Department, Faculty of Engineering, Minia University, Minia, 61111, Egypt

    Ahmed S. Menesy & Hamdy M. Sultan

  2. Electrical Power Systems Department, Moscow Power Engineering Institute “MPEI”, Moscow, Russia, 111250

    Hamdy M. Sultan

  3. Electrical Engineering Department, Faculty of Engineering, Aswan University, Aswan, 81542, Egypt

    Ahmed Korashy & Salah Kamel

  4. Department of Electrical Engineering, University of Jaén, EPS, 23700, Linares, Jaén, Spain

    Ahmed Korashy & Francisco Jurado

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  1. Ahmed S. Menesy
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Correspondence to Francisco Jurado.

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Menesy, A.S., Sultan, H.M., Korashy, A. et al. A modified farmland fertility optimizer for parameters estimation of fuel cell models. Neural Comput & Applic 33, 12169–12190 (2021). https://doi.org/10.1007/s00521-021-05821-1

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