Red-Billed Blue Magpie Optimizer for Electrical Characterization of Fuel Cells with Prioritizing Estimated Parameters
<p>Procedures of the RBMO framework.</p> "> Figure 2
<p>Convergence patterns of all studied test cases.</p> "> Figure 3
<p>The principal performance of Ballard Mark V.</p> "> Figure 4
<p>Principal performance of Temasek 1 kW.</p> "> Figure 5
<p>Principal performance of Horizon H-12 unit.</p> "> Figure 6
<p>Percentage of biased voltage.</p> "> Figure 6 Cont.
<p>Percentage of biased voltage.</p> ">
Abstract
:1. Introduction
2. Mathematical Formulation of PEMFCs’ Modeling
3. Problem Formulation and Constraints
4. Procedures of the RBMO
5. Numerical Simulations, Demonstrations, and Validations
5.1. Test Cases and Their Associated Results
5.1.1. Test Case 1: Ballard Mark V
5.1.2. Test Case 2: Temasek 1 kW
5.1.3. Test Case 3: Horizon H-12
5.2. Validations by Some Measures
5.3. Sensitivity Analysis of Extracted Parameters
6. Conclusions and Suggestions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
FCs | Fuel cells. |
PEMFCs | Proton exchange membrane FCs. |
SSD | Sum of squared deviations. |
DOA | Dandelion optimization algorithm. |
RBMO | Red-billed blue magpie optimizer. |
SSO | Shark smell optimizer. |
CHHO | Chaotic Harris hawks optimizer. |
QOBO | Quasi oppositional bonobo optimizer. |
MFFO | Modified farmland fertility optimizer. |
MAEO | Modified artificial ecosystem optimizer. |
CSA | Circle search algorithm. |
NNO | Neural network optimizer. |
MRFO | Manta rays foraging optimizer. |
WOA | Whale optimization algorithm. |
GhO | Grasshopper optimizer. |
TSO | Transient search optimizer. |
ARO | Artificial rabbits optimizer. |
HBO | Honey badger optimizer. |
DE | Differential evolution. |
ABDEO | Artificial bee colony DE optimizer. |
AEO | Artificial ecosystem-based optimizer. |
ELBO | Enhanced Lévy flight bat optimizer. |
SCE | Shuffled complex evolution. |
PFA | Pathfinder algorithm. |
ASSA | Adaptive sparrow search algorithm. |
PSO | Particle swarm optimizer. |
GA | Genetic algorithm. |
IAHA | Improved artificial hummingbird algorithm. |
FF | Fitness function. |
SCHO | Sinh cosh optimizer. |
GO | Growth optimizer. |
ann | Artificial neural network. |
GPR | Gaussian process regression. |
Nomenclature
Concentration voltage. | |
Ohmic or resistive voltage. | |
Activation voltage. | |
and | Partial pressures of and , respectively. |
Cell temperature (K). | |
Drawn load current from the FCs. | |
Parametric Coefficients. | |
Concentration of oxygen (mol/). | |
and | Contact and the membrane resistances, respectively. |
Active area of the cell (). | |
Actual current density (mA/). | |
Membrane water content. | |
Resistivity of the membrane (Ω.cm). | |
Constant number. | |
Ultimate current density (A/cm2). | |
Number of series-n fuel cells. | |
Measured voltage value of reading. | |
Estimated voltage value of reading. | |
Measured voltage value of reading. | |
Number of readings taken from the experimental setup. | |
Lower limits of the uncertain PEMFCs parameters. | |
Higher limits of the uncertain PEMFCs parameters. | |
, | Min/max range of parametric coefficients . |
, | Min/max range of water content, parameter. |
, | Min/max range of contact resistance. |
, | Min/max range of constant. |
Average of experimental voltage points. | |
Average of estimated voltage points. | |
Standard deviation of experimental voltage points. | |
Standard deviation of estimated voltage points. | |
, , | Random variables in the range [0, 1]. |
Population size. | |
Iteration counter. | |
Maximum iterations. | |
Number of design variables. | |
Position of the candidate in iteration. | |
New position of the agent. | |
Number of agents in small groups. | |
Number of agents in clusters. | |
Agent chosen randomly. | |
Randomly selected agents. | |
Position of the food. | |
Fitness value before the position updated for ith agent. | |
Fitness value after the position updated for ith agent. |
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PEMFCs’ Unit | Specs | ||||||
---|---|---|---|---|---|---|---|
Ballard Mark V | 35 | 50.6 | 178 | 1500 | 343 | 1.0 | 1.0 |
Temasek 1 kW | 20 | 150 | 51 | 1500 | 323 | 0.5 | 0.5 |
Horizon H-12 | 13 | 8.1 | 25 | 246.9 | 302.15 | 0.4935 | 1.0 |
Limits | ( | (V/K) | (V/K) | (V) | |||
---|---|---|---|---|---|---|---|
−1.1997 | 0.8000 | 3.6000 | −26.0000 | 0.1000 | 13.0000 | 0.0136 | |
−0.8532 | 6.0000 | 9.8000 | −9.5400 | 0.8000 | 23.0000 | 0.5000 |
Parameter | |||||||||
---|---|---|---|---|---|---|---|---|---|
Optimizer | |||||||||
CSA [35] | 1.18130 | 3.569096 | 3.9929 | −16.2830 | 23.00 | 0.1000 | 0.0136 | 0.853601 | |
MRFO [41] | 1.08980 | 3.8249 | 7.7306 | −16.2830 | 23.00 | 0.1000 | 0.0136 | 0.853661 | |
NNO [76] | 0.97997 | 3.6940 | 9.0870 | −16.2800 | 23.00 | 0.1000 | 0.0136 | 0.863697 | |
WOA [41] | 1.197800 | 4.4183 | 9.7214 | −16.2730 | 23.00 | 0.1002 | 0.0136 | 0.853766 | |
GhO [40] | 0.85300 | 3.4170 | 9.8000 | −15.9500 | 22.84 | 0.1000 | 0.0136 | 0.853661 | |
ETSO [36] | −0.85340 | 2.5591 | 3.6100 | −16.2870 | 23.00 | 0.1000 | 0.0136 | 0.853600 | |
ARO [3] | −1.158859 | 3.5208 | 4.0526 | −16.7251 | 23.99 * | 0.1000 | 0.015884 | 0.813912 | |
IAHA [4] | −1.0130 | 4.0000 | 8.9800 | −16.3000 | 23.0000 | 0.1000 | 0.0136 | 0.853608 | |
HBO [54] | −1.1997 | 4.33453 | 9.20688 | −16.283 | 23.0000 | 0.1000 | 0.0136 | 0.853608 | |
TSO [54] | −0.8552 | 2.72227 | 4.86143 | −16.2831 | 23.0000 | 0.1000 | 0.0136 | 0.853608 | |
ESMO [54] | −0.8532 | 2.54055 | 3.60422 | −16.2824 | 23.0000 | 0.1000 | 0.0136 | 0.853608 | |
GO | −1.19263 | 3.52557 | 3.61898 | −16.00296 | 22.99967 | 0.12442 | 0.01368 | 0.865333 | |
SCHO | −1.19392 | 3.98211 | 7.07842 | −14.80570 | 22.42048 | 0.12154 | 0.01463 | 0.957596 | |
DOA | −0.85745 | 2.93264 | 6.31831 | −16.28304 | 23.00000 | 0.10000 | 0.01360 | 0.853608 | |
RBMO | −1.000618 | 3.83643 | 9.79532 | −16.28296 | 22.99999 | 0.10000 | 0.01360 | 0.853608 |
Parameter | |||||||||
---|---|---|---|---|---|---|---|---|---|
Optimizer | |||||||||
SSO [51] | −1.0299 | 2.4105 | 4.00000 | −9.5400 | 10.0005 | 0.10870 | 0.1274 | 1.6481 | |
CHHO [33] | −1.0944 | 4.4282 | 8.76560 | −21.4650 | 18.6392 | 0.18910 | 0.1016 | 0.80234 | |
MFFO [53] | −0.9035 | 3.8267 | 8.47510 | −22.9347 | 13.3251 | 0.10010 | 0.0705 | 0.791000 | |
QOBO [77] | −1.1997 | 3.8220 | 3.60000 | −22.9500 | 13.0000 | 0.10000 | 0.0680 | 0.783040 | |
MAEA [78] | −0.8544 | 3.5766 | 7.88880 | −22.9258 | 13.0017 | 0.10000 | 0.0683 | 0.79096 | |
MAEO [78] | −1.11706 | 3.8290 | 4.56767 | −2.26309 | 22.5232 | 0.10192 | 0.11019 | 0.79243 | |
HHO [78] | −0.85320 | 3.49910 | 7.21118 | −2.44049 | 22.9963 | 0.18265 | 0.07124 | 0.80553 | |
GO | −0.91402 | 3.41643 | 9.73056 | −9.54000 | 13.03231 | 0.10076 | 0.16117 | 0.597749 | |
SCHO | −0.87344 | 2.80162 | 6.26615 | −10.09827 | 18.00000 | 0.10000 | 0.18541 | 0.731239 | |
DOA | −1.16873 | 3.61233 | 5.66745 | −9.54000 | 22.29625 | 0.10000 | 0.19962 | 0.601922 | |
RBMO | −0.91921 | 3.33183 | 9.04072 | −9.54000 | 13.00000 | 0.10000 | 0.16105 | 0.597504 |
Parameter | |||||||||
---|---|---|---|---|---|---|---|---|---|
Optimizer | |||||||||
WOA [41] | −1.1870 | 2.66970 | 3.6000 | −9.5400 | 13.8240 | 0.8000 | 0.1598 | 0.1160 | |
MRFO [43] | −1.0630 | 2.36410 | 4.3272 | −9.5400 | 19.8150 | 0.2853 | 0.1829 | 0.0966 | |
ASSA [79] | −1.1300 | 2.44000 | 3.5700 | −9.5400 | 18.7900 | 0.7140 | 18.1700 | 0.0970 | |
PFA [23] | −1.1113 | 2.05730 | 3.6000 | −9.5400 | 22.9999 | 0.1058 | 0.1868 | 0.0965 | |
ETSO [36] | −1.032285 | 2.729677 | 7.7200 | −9.5400 | 22.99898 | 0.112417 | 0.186888 | 0.09653 | |
TSO [36] | −10.8532 | 1.571852 | 3.6100 | −9.5400 | 13.02437 | 0.327874 | 0.175274 | 0.09685 | |
HHO [36] | −0.861488 | 1.93210 | 6.0300 | −9.5400 | 13.54238 | 0.1974 | 0.174067 | 0.09657 | |
PSO [36] | −1.034754 | 2.54490 | 6.3200 | −9.5400 | 23.0000 | 0.8000 | 0.182704 | 0.09658 | |
ABDEO [42] | −0.85435 | 20.09613 | 6.76763 | −9.54000 | 23.00000 | 0.10000 | 0.18685 | 0.096536 | |
AEO [42] | −1.00278 | 27.44907 | 8.53668 | −9.54000 | 18.13900 | 0.10000 | 0.18230 | 0.096536 | |
SCE [42] | −0.85575 | 15.77536 | 3.60145 | −9.54000 | 23.00000 | 0.10000 | 0.18685 | 0.096536 | |
ELBO [42] | −0.97712 | 23.73787 | 6.46218 | −9.54000 | 23.00000 | 0.10000 | 0.18685 | 0.096536 | |
GO | −1.18668 | 3.38134 | 8.80335 | −9.54000 | 22.57700 | 0.10186 | 0.03510 | 0.0616502 | |
SCHO | −1.04862 | 2.50321 | 5.75161 | −9.75943 | 14.80501 | 0.46664 | 0.03153 | 0.0672907 | |
DOA | −0.86428 | 1.75798 | 4.76938 | −9.54000 | 21.80941 | 0.13155 | 0.034797 | 0.601255 | |
RBMO | −0.97738 | 1.98296 | 3.68744 | −9.54000 | 22.99970 | 0.10000 | 0.03505 | 0.0616371 |
Ballard Mark V | Temasek 1 kW | Horizon H-12 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
5.0600 | 33.2500 | 32.9392 | 0.3108 | 0.8322 | 18.2517 | 18.5784 | −0.3267 | 0.1040 | 9.5800 | 9.7198 | −0.1398 |
10.6260 | 30.8000 | 31.0698 | −0.2698 | 3.7448 | 17.5222 | 17.5809 | −0.0587 | 0.2000 | 9.4200 | 9.4477 | −0.0277 |
16.1920 | 29.7500 | 29.8076 | −0.0576 | 6.3800 | 17.1493 | 17.1880 | −0.0387 | 0.3090 | 9.2500 | 9.2524 | −0.0024 |
20.2400 | 28.7000 | 29.0379 | −0.3379 | 9.5700 | 16.8575 | 16.8590 | −0.0015 | 0.4030 | 9.2000 | 9.1235 | 0.0765 |
27.8300 | 28.0000 | 27.7503 | 0.2497 | 14.1470 | 16.4684 | 16.5030 | −0.0345 | 0.5100 | 9.0900 | 8.9999 | 0.0901 |
34.4080 | 26.6000 | 26.7082 | −0.1082 | 19.0014 | 16.1928 | 16.1966 | −0.0038 | 0.6140 | 8.9500 | 8.8938 | 0.0562 |
37.4440 | 26.2500 | 26.2340 | 0.0160 | 24.2718 | 15.8848 | 15.9076 | −0.0228 | 0.7030 | 8.8500 | 8.8097 | 0.0403 |
43.0100 | 25.2000 | 25.3594 | −0.1594 | 28.9875 | 15.6903 | 15.6720 | 0.0183 | 0.8060 | 8.7400 | 8.7171 | 0.0229 |
48.0700 | 24.5000 | 24.5439 | −0.0439 | 33.1484 | 15.4957 | 15.4757 | 0.0200 | 0.9080 | 8.6500 | 8.6281 | 0.0219 |
56.1660 | 23.8000 | 23.1583 | 0.6417 | 38.0028 | 15.3174 | 15.2563 | 0.0611 | 1.0760 | 8.4500 | 8.4823 | −0.0323 |
61.2260 | 22.0500 | 22.2109 | −0.1609 | 43.6893 | 15.1391 | 15.0080 | 0.1311 | 1.1270 | 8.4100 | 8.4373 | −0.0273 |
67.2980 | 21.0000 | 20.9302 | 0.0698 | 48.8211 | 14.9445 | 14.7892 | 0.1554 | 1.2880 | 8.2000 | 8.2885 | −0.0885 |
71.8520 | 19.6000 | 19.7503 | −0.1503 | 53.6754 | 14.7824 | 14.5850 | 0.1974 | 1.3900 | 8.1200 | 8.1858 | −0.0658 |
, V | 0.1982 | 58.5298 | 14.5879 | 14.3822 | 0.2057 | 1.4500 | 8.1100 | 8.1206 | −0.0106 | ||
63.3842 | 14.3771 | 14.1798 | 0.1973 | 1.5780 | 8.0500 | 7.9635 | 0.0865 | ||||
68.6547 | 14.1015 | 13.9596 | 0.1420 | , V | 0.0526 | ||||||
73.2316 | 13.8422 | 13.7671 | 0.0750 | ||||||||
78.0860 | 13.5341 | 13.5612 | −0.0271 | ||||||||
81.6921 | 13.2261 | 13.4067 | −0.1806 | ||||||||
, V | 0.1095 |
PEMFCs Unit | Index | |||||||
---|---|---|---|---|---|---|---|---|
Ballard Mark 5 | −0.02011 | 0.14612 | −0.04515 | −0.02258 | −0.02196 | −0.02004 | −0.01996 | |
0.73694 | 0.89428 | 0.12701 | 0.05336 | 0.01640 | 0.00002 | 0.00023 | ||
Rank | 2 | 1 | 3 | 4 | 5 | 7 | 6 | |
0.05374 | 0.19968 | 0.07201 | 0.09620 | 0.09291 | 0.08687 | 0.08374 | ||
0.80768 | 0.91263 | 0.13991 | 0.05326 | 0.01662 | 0.00002 | 0.00028 | ||
Rank | 2 | 1 | 3 | 4 | 5 | 7 | 6 | |
Temasek 1 kW | −0.01186 | 0.12336 | −0.04709 | −0.02796 | −0.02626 | −0.02619 | −0.02688 | |
0.72454 | 0.87072 | 0.20621 | 0.01315 | 0.00056 | 0.00002 | 0.00143 | ||
Rank | 2 | 1 | 3 | 4 | 6 | 7 | 5 | |
0.04619 | 0.20495 | 0.07647 | 0.08417 | 0.08768 | 0.08673 | 0.07861 | ||
0.79104 | 0.88583 | 0.22618 | 0.01296 | 0.00056 | 0.00002 | 0.00164 | ||
Rank | 2 | 1 | 3 | 4 | 6 | 7 | 5 | |
Horizon H−12 | 0.25405 | 0.03101 | −0.04507 | −0.03886 | −0.03850 | −0.03864 | −0.03890 | |
0.97969 | 0.67889 | 0.05194 | 0.00034 | 0.00001 | 0.00000 | 0.00107 | ||
Rank | 1 | 2 | 3 | 5 | 6 | 7 | 4 | |
0.29141 | 0.07841 | 0.10773 | 0.10332 | 0.10458 | 0.10452 | 0.09923 | ||
1.00166 | 0.72235 | 0.05722 | 0.00032 | 0.00001 | 0.00000 | 0.00121 | ||
Rank | 1 | 2 | 3 | 5 | 6 | 7 | 4 |
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Share and Cite
El-Fergany, A.A.; Agwa, A.M. Red-Billed Blue Magpie Optimizer for Electrical Characterization of Fuel Cells with Prioritizing Estimated Parameters. Technologies 2024, 12, 156. https://doi.org/10.3390/technologies12090156
El-Fergany AA, Agwa AM. Red-Billed Blue Magpie Optimizer for Electrical Characterization of Fuel Cells with Prioritizing Estimated Parameters. Technologies. 2024; 12(9):156. https://doi.org/10.3390/technologies12090156
Chicago/Turabian StyleEl-Fergany, Attia A., and Ahmed M. Agwa. 2024. "Red-Billed Blue Magpie Optimizer for Electrical Characterization of Fuel Cells with Prioritizing Estimated Parameters" Technologies 12, no. 9: 156. https://doi.org/10.3390/technologies12090156