An Efficient White Shark Optimizer for Enhancing the Performance of Proton Exchange Membrane Fuel Cells
Abstract
:1. Introduction
2. Description of PEMFC
3. Materials and Methods
4. White Shark Optimizer (WSO)
5. The Proposed WSO-Based Approach
Algorithm 1. Pseudocode of the proposed WSO. |
1: Define the electrical specifications of the FC and operating conditions. 2: Input the measured data for stack voltage and current. 3: Define the parameters of WSO approach (K, n, and nrun) and the search space bounds (ubj, lbj). 4: Initialize the population matrix with probable solutions using Equation (16). 5: Generate the initial estimated voltage of PEMFC and calculate the RMSE using Equation (23) (). 6: While l < nrun do 7: While k < K do 8: While i < n do 9: Calculate the velocity of initial population (. 10: Update the values of parameters v, p1, p2, μ, a, b, wo, f, mv, and Ss. 11: Calculate the updated velocity of ith white shark using Equation (17). 12: Compute the new position of ith white shark toward the prey using Equation (21). 13: if rand < Ss then 14: Calculate the distance between the prey and ith white shark. 15: Update the movement of ith white shark towards the best one using Equation (22). 16: end if 17: Generate the estimated voltage of PEMFC and calculate the new RMSE using Equation (23) (). 18: if < then 19: Update the FC circuit parameters and fitness value. 20: end if 21: i = i + 1 22: end while 23: k = k + 1 24: end while 25: l = l + 1 26: end while 27: Plot the polarization curves of the estimated and measured data 28: Print the optimal parameters of PEMFC |
6. Results and Discussion
7. Conclusions and Future Recommendations
- (a)
- The RMSE values varied between minimum and maximum values of 0.009095329 and 0.028663611, respectively.
- (b)
- The mean RMSE value recorded for the PEMFC 250 W stack was 0.020057775.
- (c)
- The minimum RMSE rate was obtained through the WSO in which the operating temperature was 353.15 K, while the working anode and cathode pressures were 3 and 5 bar, respectively.
- (d)
- The proposed WSO attained the best optimization results in terms of absolute error compared to the other considered algorithms.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Category | Voltage Potential of the PEMFC | |
---|---|---|
250 W | 500 W | |
n | 24 | 32 |
A | 27 cm2 | 64 cm2 |
imax | 0.86 A.cm2 | 0.469 A.cm2 |
l (μm) | 127 | 178 |
Panode | 1.0 to 3.0 | 1 |
Pcathode | 1.0 to 5.0 | 0.209 |
TK | 343.15–353.15 K | 333 K |
RHanode | 1.0 | 1.0 |
RHcathode | 1.0 | 1.0 |
Category | Anode Pressure (Bar) | Cathode Pressure (Bar) | Temperature (°C) |
---|---|---|---|
A | 1.0 | 1.0 | 343.15 |
B | 1.5 | 1.5 | 343.15 |
C | 2.5 | 3.0 | 343.15 |
D | 3.0 | 5.0 | 353.15 |
Pressure | Algorithm | λ | b | RM (Ω) | RMSE | ||||
---|---|---|---|---|---|---|---|---|---|
Range 1 (1.5 bar) | WSO | −0.9474 | 0.0017 | 0.0001 | −0.0001 | 17.2769 | 0.0005 | 0.0381 | 0.0065650106 |
SSA | −0.9491 | 0.0017 | 0.0001 | −0.0001 | 18.9082 | 0.0004 | 0.0381 | 0.0065651050 | |
HHO | −0.9520 | 0.0017 | 0.0001 | −0.0001 | 18.8258 | 0.0003 | 0.0381 | 0.0065651729 | |
ASO | −0.9478 | 0.0017 | 0.0001 | −0.0001 | 17.7105 | 0.0004 | 0.0383 | 0.0066070152 | |
DBO | −0.9488 | 0.0017 | 0.0001 | −0.0001 | 20.3586 | 0.0003 | 0.0381 | 0.0065650549 | |
SPO | −0.9504 | 0.0017 | 0.0001 | −0.0001 | 19.4000 | 0.0007 | 0.0381 | 0.0065650829 | |
HCLAOA [23] | −0.9475 | 0.00302 | 7.42 × 10−5 | −0.0002 | 23.00 | 0.03198 | 0.0001 | 0.097700 | |
Range 2 (1 bar) | WSO | −0.983 | 0.002 | 0.000 | 0.000 | 17.765 | 0.000 | 0.038 | 0.0065635861 |
SSA | −0.960 | 0.002 | 0.000 | 0.000 | 18.685 | 0.000 | 0.038 | 0.0065645703 | |
HHO | −0.783 | 0.001 | 0.000 | 0.000 | 10.411 | 0.000 | 0.038 | 0.0066489707 | |
ASO | −0.943 | 0.002 | 0.000 | 0.000 | 17.075 | 0.000 | 0.036 | 0.0092132971 | |
DBO | −1.150 | 0.002 | 0.000 | 0.000 | 19.432 | 0.000 | 0.033 | 0.0635611941 | |
SPO | −0.890 | 0.001 | 0.000 | 0.000 | 15.698 | 0.000 | 0.038 | 0.0065642882 | |
HCLAOA [23] | −0.55692 | 0.00190 | 7.487 × 10−5 | 0.00018 | 22.9945 | 0.00010 | 0.02913 | 0.000200 |
Pressure | Model | λ | b | RM (Ω) | RMSE | ||||
---|---|---|---|---|---|---|---|---|---|
Scenario #1 T = 353.15 K, Pa = 3.0 bar, and Pc = 5.0 bar Range 1 (3.0 bar) | WSO | −0.9488 | 0.00222 | 0.000078 | −0.00018 | 18.7717 | 0.00062 | 0.0390 | 0.0091000650 |
SSA | −0.9475 | 0.00219 | 0.000076 | −0.00018 | 18.7223 | 0.00055 | 0.0390 | 0.0091005106 | |
HHO | −0.9517 | 0.00217 | 0.000074 | −0.00018 | 14.0023 | 0.00025 | 0.0391 | 0.0091063988 | |
ASO | −0.9468 | 0.00218 | 0.000076 | −0.00017 | 19.7275 | 0.00049 | 0.0397 | 0.0095256586 | |
DBO | −0.9467 | 0.00220 | 0.000077 | −0.00018 | 23.0000 | 0.00062 | 0.0390 | 0.0091002545 | |
SPO | −0.9487 | 0.00221 | 0.000077 | −0.00018 | 21.1909 | 0.00050 | 0.0380 | 0.0128255120 | |
Scenario #1 T = 353.15 K, Pa = 3.0 bar, and Pc = 5.0 bar Range 2 (5.0 bar) | WSO | −0.8280 | 0.00213 | 0.000098 | −0.00018 | 15.4846 | 0.00055 | 0.0390 | 0.0090953285 |
SSA | −0.8528 | 0.00188 | 0.000073 | −0.00018 | 19.2722 | 0.00047 | 0.0390 | 0.0091012427 | |
HHO | −0.9029 | 0.00200 | 0.000071 | −0.00018 | 19.5538 | 0.00021 | 0.0383 | 0.0097840723 | |
ASO | −0.8974 | 0.00196 | 0.000069 | −0.00018 | 16.1847 | 0.00033 | 0.0389 | 0.0091527368 | |
DBO | −1.0955 | 0.00273 | 0.000086 | −0.00018 | 15.6000 | 0.00021 | 0.0390 | 0.0090982661 | |
SPO | −0.8691 | 0.00222 | 0.000096 | −0.00018 | 18.3978 | 0.00014 | 0.0390 | 0.0090958449 | |
Scenario #2 T = 343.15 K, Pa = Pc = 1.5 bar Range 1 (1.5 bar) | WSO | −0.9465 | 0.0015 | 0.0001 | −0.0001 | 17.8703 | 0.0004 | 0.0410 | 0.0227666199 |
SSA | −0.9471 | 0.0015 | 0.0001 | −0.0001 | 19.6157 | 0.0005 | 0.0410 | 0.0227668628 | |
HHO | −0.9520 | 0.0015 | 0.0001 | −0.0001 | 21.8297 | 0.0005 | 0.0410 | 0.0227670591 | |
ASO | −0.9470 | 0.0015 | 0.0001 | −0.0001 | 18.6012 | 0.0005 | 0.0417 | 0.0232013235 | |
DBO | −0.9483 | 0.0016 | 0.0001 | −0.0001 | 19.4000 | 0.0007 | 0.0310 | 0.1257577650 | |
SPO | −0.9511 | 0.0016 | 0.0001 | −0.0001 | 17.6000 | 0.0007 | 0.0410 | 0.0227669952 | |
Scenario #2 T = 343.15 K, Pa = Pc = 1.5 bar Range 2 (1.0 bar) | WSO | −1.0247 | 0.0016 | 0.0000 | −0.0001 | 16.5426 | 0.0005 | 0.0410 | 0.0227613902 |
SSA | −0.9263 | 0.0014 | 0.0000 | −0.0001 | 16.8599 | 0.0004 | 0.0410 | 0.0227632963 | |
HHO | −0.8245 | 0.0010 | 0.0000 | −0.0001 | 10.0002 | 0.0001 | 0.0408 | 0.0228019166 | |
ASO | −1.0575 | 0.0017 | 0.0000 | −0.0001 | 17.4957 | 0.0005 | 0.0396 | 0.0253098813 | |
DBO | −1.0031 | 0.0016 | 0.0001 | −0.0001 | 18.4000 | 0.0004 | 0.0355 | 0.0846345710 | |
SPO | −1.0694 | 0.0018 | 0.0001 | −0.0001 | 21.2000 | 0.0006 | 0.0391 | 0.0368668305 | |
Scenario #2 T = 343.15 K, Pa = 2.5 bar, and Pc = 3.0 bar Range 1 (2.5 bar) | WSO | −0.9485 | 0.00210 | 0.000078 | −0.000186 | 17.3302 | 0.0004 | 0.0355 | 0.0275072010 |
SSA | −0.9464 | 0.00209 | 0.000077 | −0.000186 | 17.7727 | 0.0004 | 0.0355 | 0.0275086017 | |
HHO | −0.9514 | 0.00207 | 0.000074 | −0.000186 | 16.0098 | 0.0001 | 0.0355 | 0.0275140895 | |
ASO | −0.9498 | 0.00209 | 0.000077 | −0.000185 | 17.6659 | 0.0005 | 0.0360 | 0.0286636106 | |
DBO | −0.9483 | 0.00208 | 0.000076 | −0.000186 | 21.2000 | 0.0004 | 0.0355 | 0.0275095344 | |
SPO | −0.9491 | 0.00211 | 0.000078 | −0.000186 | 18.1953 | 0.0007 | 0.0355 | 0.0275072010 | |
Scenario #2 T = 343.15 K, Pa = 2.5 bar, and Pc = 3.0 bar Range 2 (3.0 bar) | WSO | −0.7016 | 0.00162 | 0.000098 | −0.000186 | 18.1117 | 0.0004 | 0.0355 | 0.0274780458 |
SSA | −0.8611 | 0.00158 | 0.000056 | −0.000186 | 15.3901 | 0.0005 | 0.0355 | 0.0275397490 | |
HHO | −1.1997 | 0.00267 | 0.000064 | −0.000186 | 17.8024 | 0.0002 | 0.0355 | 0.0275291018 | |
ASO | −0.9528 | 0.00201 | 0.000069 | −0.000184 | 16.7298 | 0.0005 | 0.0363 | 0.0285418356 | |
DBO | −0.8913 | 0.00203 | 0.000086 | −0.000186 | 15.6000 | 0.0004 | 0.0355 | 0.0274961351 | |
SPO | −1.0980 | 0.00246 | 0.000071 | −0.000186 | 20.0920 | 0.0004 | 0.0355 | 0.0275175448 |
Type of 500-W PEMFC | Number of Cells in the PEMFC | |
---|---|---|
1 | NedStack PS6 | 65 |
2 | BCS 500 W | 32 |
3 | SR-12PEM 500 W | 48 |
Algorithm | λ | b | RM (Ω) | RMSE | ||||
---|---|---|---|---|---|---|---|---|
WSO | −1.1997 | 0.003349 | 0.000046 | −0.000095 | 19.477 | 0.0008 | 0.493 | 0.7105894058 |
SSA | −1.1997 | 0.003349 | 0.000046 | −0.000095 | 19.180 | 0.0005 | 0.493 | 0.7106572465 |
HHO | −1.1881 | 0.003349 | 0.000048 | −0.000095 | 13.063 | 0.0001 | 0.491 | 0.7168685693 |
ASO | −1.0550 | 0.003349 | 0.000070 | −0.000096 | 17.821 | 0.0005 | 0.463 | 0.9128205567 |
DBO | −1.1997 | 0.003349 | 0.000046 | −0.000095 | 15.517 | 0.0007 | 0.493 | 0.7106178878 |
SPO | −1.1888 | 0.003349 | 0.000046 | −0.000095 | 15.487 | 0.0008 | 0.493 | 0.7105993421 |
Algorithm | λ | b | RM (Ω) | RMSE | ||||
---|---|---|---|---|---|---|---|---|
WSO | −1.1997 | 0.003349 | 0.000098 | −0.00026 | 14.817 | 0.0008 | 0.130 | 0.6340822405 |
SSA | −1.1997 | 0.003349 | 0.000098 | −0.00026 | 19.144 | 0.0008 | 0.130 | 0.6340822405 |
HHO | −1.1997 | 0.003349 | 0.000098 | −0.00026 | 21.631 | 0.0004 | 0.130 | 0.6376846297 |
ASO | −1.1899 | 0.003349 | 0.000098 | −0.00026 | 18.104 | 0.0005 | 0.165 | 0.9544281558 |
DBO | −1.1997 | 0.003349 | 0.000098 | −0.00026 | 18.032 | 0.0008 | 0.130 | 0.6361632411 |
SPO | −1.1997 | 0.003349 | 0.000098 | −0.00026 | 22.319 | 0.0008 | 0.130 | 0.6374624567 |
Algorithm | λ | b | RM (Ω) | RMSE | ||||
---|---|---|---|---|---|---|---|---|
WSO | −1.1997 | 0.003349 | 0.000083 | −0.000104 | 19.509 | 0.0008 | 0.500 | 0.2846999039 |
SSA | −1.1647 | 0.003349 | 0.000089 | −0.000104 | 18.872 | 0.0004 | 0.500 | 0.2847029141 |
HHO | −1.1200 | 0.003349 | 0.000098 | −0.000105 | 23.000 | 0.0008 | 0.500 | 0.2847886848 |
ASO | −1.1442 | 0.003349 | 0.000093 | −0.000117 | 19.158 | 0.0005 | 0.489 | 0.3344408484 |
DBO | −1.1997 | 0.003349 | 0.000083 | −0.000104 | 21.000 | 0.0007 | 0.500 | 0.2846999158 |
SPO | −1.1710 | 0.003349 | 0.000088 | −0.000104 | 21.050 | 0.0004 | 0.500 | 0.2847023839 |
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Fathy, A.; Alanazi, A. An Efficient White Shark Optimizer for Enhancing the Performance of Proton Exchange Membrane Fuel Cells. Sustainability 2023, 15, 11741. https://doi.org/10.3390/su151511741
Fathy A, Alanazi A. An Efficient White Shark Optimizer for Enhancing the Performance of Proton Exchange Membrane Fuel Cells. Sustainability. 2023; 15(15):11741. https://doi.org/10.3390/su151511741
Chicago/Turabian StyleFathy, Ahmed, and Abdulmohsen Alanazi. 2023. "An Efficient White Shark Optimizer for Enhancing the Performance of Proton Exchange Membrane Fuel Cells" Sustainability 15, no. 15: 11741. https://doi.org/10.3390/su151511741
APA StyleFathy, A., & Alanazi, A. (2023). An Efficient White Shark Optimizer for Enhancing the Performance of Proton Exchange Membrane Fuel Cells. Sustainability, 15(15), 11741. https://doi.org/10.3390/su151511741