Modeling the Maximum Magnetic Entropy Change of Doped Manganite Using a Grid Search-Based Extreme Learning Machine and Hybrid Gravitational Search-Based Support Vector Regression
Abstract
:1. Introduction
2. Mathematical Formulation of the Proposed Models
2.1. Description of the Support Vector Regression Algorithm
2.2. Physical Principles of the Gravitational Search Algorithm
2.3. Mathematical Background of the Extreme Learning Machine
3. Dataset Description and Computational Implementation of the Proposed Models
3.1. Dataset Description and Chemical Formula of the Doped Manganite that Can be Incorporated into the Developed Models
3.2. Computational Hybridization of the Gravitational Search and Support Vector Regression Algorithms
3.3. Computational Implementation of the Grid Search-Based Extreme Learning Machine
4. Results and Discussion
4.1. Searching for the Optimum Hyperparameters of the Developed Models
4.2. Generalization and Predictive Strength Comparison Between the SVR- and ELM-Based Models
4.3. Superiority of the Present Models as Compared to the Existing Models in the Literature
4.4. Investigating the Doping Effect of Fe on the Value of the MMEC of the Pr0.6Ca 0.1Sr 0.3Mn 1-xFexO3 Manganite Compound Using the Developed GSA-SVR-Crystal Model
4.5. Implementation of the Developed Model for Determining the Maximum Magnetic Entropy Change of Different Classes of Doped Manganite
5. Conclusions and Recommendations
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Quantity | Minimum | Maximum | Mean | Standard Deviation | Correlation Coefficient |
---|---|---|---|---|---|
R(pm) | 109.8 | 143 | 115.696 | 4.652 | −0.272 |
A(pm) | 0 | 152 | 103.83 | 51.2 | 0.389 |
B(pm) | 0 | 152 | 79.92 | 66.139 | 0.334 |
C(pm) | 0 | 100 | 23.07 | 38.523 | 0.14 |
a | 0 | 0.45 | 0.162 | 0.126 | 0.261 |
b | 0 | 0.45 | 0.161 | 0.169 | 0.441 |
c | 0 | 0.3 | 0.029 | 0.048 | −0.189 |
Distortion along a-axis | 5.429 | 5.553 | 5.488 | 0.033 | −0.557 |
Distortion along b-axis | 5.438 | 13.467 | 6.483 | 1.307 | 0.102 |
Distortion along c-axis | 5.419 | 359.95 | 12.036 | 35.311 | 0.105 |
Applied field (T) | 0.05 | 6 | 3.483 | 1.758 | 0.583 |
MMEC | 0.003 | 7.14 | 2.117 | 1.567 |
GSA-SVR-Radii | GSA-SVR-Crystal | ELM-GS-Radii | ELM-GS-Crystal | |
---|---|---|---|---|
Penalty factor | 944.3013 | 592.9928 | ---- | --- |
Epsilon | 0.1003 | 0.3758 | ---- | --- |
Kernel option | 0.8198 | 0.2516 | ----- | ---- |
Number in the population | 70 | 30 | ---- | --- |
Activation function | --- | --- | Hardlim | Sin |
Number of hidden nodes | --- | --- | 58 | 24 |
Parameters | GSA-SVR-Radii | GSA-SVR-Crystal | ELM-GS-Radii | ELM-GS-Crystal | ||||
---|---|---|---|---|---|---|---|---|
Training Testing | Training Testing | Training Testing | Training Testing | |||||
CC | 0.9545 | 0.958 | 0.9317 | 0.9044 | 0.83777 | 0.961358 | 0.88462 | 0.914984 |
RMSE (J/Kg K) | 0.4655 | 0.462 | 0.577 | 0.767 | 0.85233 | 0.285445 | 0.715575 | 0.46994 |
MAE (J/Kg K) | 0.1766 | 0.376 | 0.4094 | 0.5299 | 0.586574 | 0.426137 | 0.51419 | 0.670479 |
GA-SVR_Ionic (Existing) [38] | GA-SVR-Lattice (Existing) [38] | GSA-SVR-Radii (This Work) | GSA-SVR-Crystal (This Work) | ELM-GS-Radii (This Work) | ELM-GS-Crystal (This Work) | |
---|---|---|---|---|---|---|
MAE (J/Kg K) | 0.304311 | 0.578056 | 0.216517 | 0.433503 | 0.526348 | 0.50534 |
RMSE (J/Kg K) | 0.590673 | 0.890676 | 0.464783 | 0.619666 | 0.785806 | 0.706786 |
Doped Manganite-Based Compounds | Measured MMEC (J/KgK) | Estimated MMEC Using GSA-SVR-Crystal (J/KgK) | Absolute Error |
---|---|---|---|
La0.7Ca0.25Sr0.05MnO3 | 1.65 [73] | 1.5601 | 0.0899 |
La0.67Ca0.13 Ba0.2Mn0.9Co 0.1O3 | 1.93 [74] | 1.5141 | 0.4159 |
La0.6Bi0.1Sr0.3Mn0.9Cu 0.1O3 | 3.39 [75] | 3.9562 | 0.5662 |
La0.8Na0.2Mn0.94Ni 0.06O3 | 3.70 [76] | 4.1572 | 0.4572 |
La0.065Nd0.05Ba0.3Mn0.85Cr0.15O3 | 3.55 [77] | 3.1356 | 0.4144 |
Pr0.6Ca 0.1Sr 0.3MnO3 | 3.64 [70] | 3.8108 | 0.1708 |
Pr0.6Ca 0.1Sr 0.3Mn0.975 Fe0.025O3 | 3.53 [70] | 3.9058 | 0.3758 |
Pr0.6Ca 0.1Sr 0.3Mn0.95 Fe0.05O3 | 3.7 [70] | 3.845 | 0.145 |
Pr0.6Ca 0.1Sr 0.3Mn0.925 Fe0.075O3 | 3.12 [70] | 3.5018 | 0.3818 |
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Shamsah, S.M.I.; Owolabi, T.O. Modeling the Maximum Magnetic Entropy Change of Doped Manganite Using a Grid Search-Based Extreme Learning Machine and Hybrid Gravitational Search-Based Support Vector Regression. Crystals 2020, 10, 310. https://doi.org/10.3390/cryst10040310
Shamsah SMI, Owolabi TO. Modeling the Maximum Magnetic Entropy Change of Doped Manganite Using a Grid Search-Based Extreme Learning Machine and Hybrid Gravitational Search-Based Support Vector Regression. Crystals. 2020; 10(4):310. https://doi.org/10.3390/cryst10040310
Chicago/Turabian StyleShamsah, Sami M. Ibn, and Taoreed O. Owolabi. 2020. "Modeling the Maximum Magnetic Entropy Change of Doped Manganite Using a Grid Search-Based Extreme Learning Machine and Hybrid Gravitational Search-Based Support Vector Regression" Crystals 10, no. 4: 310. https://doi.org/10.3390/cryst10040310