Improving Drought Modeling Using Hybrid Random Vector Functional Link Methods
Abstract
:1. Introduction
2. Materials and Methods
2.1. Case Study
2.2. Standard Precipitation Index (SPI)
2.3. Random Vector Functional Link Networks (RVFL)
2.4. Particle Swarm Optimization (PSO)
2.5. Genetic Algorithm (GA)
2.6. Grey Wolves Optimization (GWO)
2.7. Social Spider Optimization (SSO)
2.8. Salp SWARM Algorithm (SSA)
2.9. Hunger Games Search (HGS)
2.10. Model Performance Evaluation Matrices
3. Application and Results
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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RFVL | Activation function | radial basis |
Hidden neurons | 200 | |
PSO | ) | 2 |
) | 2 | |
inertia weight | 0.2–0.9 | |
GA | Crossover percentage | 0.9 |
Mutation percentage | 0.5 | |
Mutation rate | 0.1 | |
GWO | decreased from 2 to 0 | |
HGS | 0.03 | |
1000 | ||
SSO | 0.7 | |
SSA | 0 | |
All algorithms | Population | 40 |
Number of iterations | 100 | |
Number of runs for each algorithm | 20 |
Drought Indices | Input Comb. | Models | Training | Testing | ||||||
---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAE | R2 | NSE | RMSE | MAE | R2 | NSE | |||
SPI3 | SPI3t-1 | RFVL | 0.506 | 0.392 | 0.803 | 0.803 | 0.570 | 0.409 | 0.705 | 0.647 |
PSO | 0.495 | 0.381 | 0.814 | 0.814 | 0.547 | 0.374 | 0.740 | 0.688 | ||
GA | 0.493 | 0.380 | 0.817 | 0.817 | 0.537 | 0.363 | 0.748 | 0.706 | ||
GWO | 0.482 | 0.377 | 0.837 | 0.837 | 0.535 | 0.357 | 0.757 | 0.710 | ||
SSO | 0.472 | 0.368 | 0.865 | 0.865 | 0.523 | 0.351 | 0.765 | 0.730 | ||
SSA | 0.470 | 0.366 | 0.870 | 0.870 | 0.523 | 0.344 | 0.767 | 0.731 | ||
HGS | 0.454 | 0.351 | 0.883 | 0.883 | 0.511 | 0.340 | 0.769 | 0.734 | ||
SPI3t-1,SPI3t-2 | RFVL | 0.492 | 0.378 | 0.820 | 0.820 | 0.543 | 0.368 | 0.736 | 0.696 | |
PSO | 0.479 | 0.374 | 0.842 | 0.842 | 0.541 | 0.363 | 0.746 | 0.700 | ||
GA | 0.474 | 0.372 | 0.851 | 0.851 | 0.525 | 0.349 | 0.760 | 0.727 | ||
GWO | 0.465 | 0.359 | 0.865 | 0.865 | 0.522 | 0.346 | 0.764 | 0.733 | ||
SSO | 0.463 | 0.360 | 0.868 | 0.868 | 0.516 | 0.339 | 0.773 | 0.743 | ||
SSA | 0.444 | 0.344 | 0.898 | 0.898 | 0.507 | 0.331 | 0.781 | 0.748 | ||
HGS | 0.440 | 0.335 | 0.905 | 0.905 | 0.502 | 0.328 | 0.784 | 0.759 | ||
SPI6 | SPI6t-1,SP6t-2 | RFVL | 0.375 | 0.268 | 0.843 | 0.843 | 0.489 | 0.260 | 0.751 | 0.705 |
PSO | 0.365 | 0.253 | 0.858 | 0.858 | 0.446 | 0.229 | 0.788 | 0.740 | ||
GA | 0.364 | 0.258 | 0.858 | 0.858 | 0.440 | 0.218 | 0.791 | 0.749 | ||
GWO | 0.353 | 0.249 | 0.875 | 0.875 | 0.404 | 0.223 | 0.832 | 0.755 | ||
SSO | 0.329 | 0.229 | 0.858 | 0.858 | 0.389 | 0.212 | 0.824 | 0.778 | ||
SSA | 0.304 | 0.218 | 0.891 | 0.891 | 0.378 | 0.190 | 0.823 | 0.794 | ||
HGS | 0.304 | 0.218 | 0.891 | 0.891 | 0.372 | 0.190 | 0.831 | 0.802 | ||
SPI6t-1,SPI6t-2,SPI6t-3,SPI6t-4 | RFVL | 0.370 | 0.252 | 0.850 | 0.850 | 0.465 | 0.219 | 0.774 | 0.709 | |
PSO | 0.340 | 0.245 | 0.859 | 0.859 | 0.417 | 0.205 | 0.792 | 0.746 | ||
GA | 0.339 | 0.241 | 0.864 | 0.864 | 0.406 | 0.196 | 0.798 | 0.780 | ||
GWO | 0.332 | 0.238 | 0.871 | 0.871 | 0.377 | 0.192 | 0.810 | 0.785 | ||
SSO | 0.320 | 0.231 | 0.880 | 0.880 | 0.384 | 0.188 | 0.812 | 0.786 | ||
SSA | 0.299 | 0.214 | 0.898 | 0.898 | 0.355 | 0.175 | 0.840 | 0.798 | ||
HGS | 0.284 | 0.195 | 0.921 | 0.921 | 0.342 | 0.159 | 0.848 | 0.803 |
Drought Indices | Input Comb. | Models | Training | Testing | ||||||
---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAE | R2 | NSE | RMSE | MAE | R2 | NSE | |||
SPI9 | SPI9t-1,SPI9t-2, SPI9t-3, | RFVL | 0.395 | 0.242 | 0.796 | 0.796 | 0.430 | 0.291 | 0.788 | 0.760 |
PSO | 0.390 | 0.242 | 0.801 | 0.801 | 0.400 | 0.288 | 0.815 | 0.801 | ||
GA | 0.389 | 0.241 | 0.803 | 0.803 | 0.397 | 0.277 | 0.825 | 0.806 | ||
GWO | 0.379 | 0.239 | 0.816 | 0.815 | 0.386 | 0.267 | 0.830 | 0.810 | ||
SSO | 0.346 | 0.218 | 0.853 | 0.853 | 0.379 | 0.265 | 0.833 | 0.812 | ||
SSA | 0.313 | 0.190 | 0.878 | 0.878 | 0.374 | 0.262 | 0.835 | 0.816 | ||
HGS | 0.307 | 0.189 | 0.884 | 0.884 | 0.372 | 0.260 | 0.838 | 0.823 | ||
SPI9t-1,SPI9t-2,SPI9t-3,SPI9t-4,SPI9t-5 | RFVL | 0.416 | 0.273 | 0.770 | 0.769 | 0.490 | 0.315 | 0.733 | 0.709 | |
PSO | 0.396 | 0.244 | 0.794 | 0.794 | 0.427 | 0.293 | 0.793 | 0.765 | ||
GA | 0.395 | 0.241 | 0.795 | 0.795 | 0.420 | 0.288 | 0.806 | 0.778 | ||
GWO | 0.366 | 0.226 | 0.828 | 0.828 | 0.408 | 0.275 | 0.820 | 0.790 | ||
SSO | 0.355 | 0.220 | 0.842 | 0.842 | 0.401 | 0.270 | 0.827 | 0.804 | ||
SSA | 0.349 | 0.218 | 0.849 | 0.849 | 0.397 | 0.267 | 0.831 | 0.806 | ||
HGS | 0.340 | 0.210 | 0.860 | 0.860 | 0.395 | 0.264 | 0.834 | 0.810 | ||
SPI12 | SPI12t-1,SPI12t-2, SPI12t-3, | RFVL | 0.300 | 0.165 | 0.897 | 0.897 | 0.346 | 0.208 | 0.793 | 0.778 |
PSO | 0.298 | 0.162 | 0.900 | 0.900 | 0.337 | 0.213 | 0.804 | 0.789 | ||
GA | 0.295 | 0.163 | 0.902 | 0.902 | 0.327 | 0.203 | 0.814 | 0.801 | ||
GWO | 0.284 | 0.158 | 0.914 | 0.913 | 0.302 | 0.181 | 0.837 | 0.820 | ||
SSO | 0.247 | 0.140 | 0.947 | 0.947 | 0.287 | 0.163 | 0.874 | 0.851 | ||
SSA | 0.240 | 0.134 | 0.953 | 0.953 | 0.271 | 0.156 | 0.883 | 0.864 | ||
HGS | 0.225 | 0.118 | 0.966 | 0.966 | 0.260 | 0.151 | 0.888 | 0.875 | ||
SPI12t-1,SPI12t-2,SPI12t-3,SPI12t-4,SPI12t-5 | RFVL | 0.312 | 0.174 | 0.885 | 0.885 | 0.409 | 0.276 | 0.722 | 0.708 | |
PSO | 0.309 | 0.164 | 0.895 | 0.895 | 0.355 | 0.233 | 0.790 | 0.766 | ||
GA | 0.301 | 0.161 | 0.896 | 0.896 | 0.353 | 0.224 | 0.798 | 0.769 | ||
GWO | 0.293 | 0.157 | 0.907 | 0.907 | 0.329 | 0.194 | 0.826 | 0.816 | ||
SSO | 0.284 | 0.152 | 0.913 | 0.913 | 0.291 | 0.169 | 0.869 | 0.845 | ||
SSA | 0.272 | 0.145 | 0.925 | 0.925 | 0.287 | 0.159 | 0.875 | 0.856 | ||
HGS | 0.249 | 0.137 | 0.946 | 0.946 | 0.269 | 0.157 | 0.884 | 0.867 |
Station | Input Comb. | Models | Training | Testing | ||||||
---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAE | R2 | NSE | RMSE | MAE | R2 | NSE | |||
Station 1 | OPT SPI3+MN | RFVL | 0.493 | 0.343 | 0.788 | 0.788 | 0.519 | 0.361 | 0.764 | 0.678 |
PSO | 0.476 | 0.328 | 0.816 | 0.816 | 0.500 | 0.343 | 0.812 | 0.718 | ||
GA | 0.475 | 0.323 | 0.818 | 0.817 | 0.498 | 0.344 | 0.791 | 0.723 | ||
GWO | 0.473 | 0.318 | 0.821 | 0.821 | 0.496 | 0.343 | 0.796 | 0.727 | ||
SSO | 0.450 | 0.310 | 0.856 | 0.856 | 0.491 | 0.341 | 0.801 | 0.731 | ||
SSA | 0.439 | 0.303 | 0.873 | 0.873 | 0.487 | 0.338 | 0.810 | 0.746 | ||
HGS | 0.430 | 0.290 | 0.892 | 0.892 | 0.482 | 0.327 | 0.821 | 0.756 | ||
Station 2 | OPT SPI3+MN | RFVL | 0.467 | 0.321 | 0.782 | 0.782 | 0.541 | 0.367 | 0.768 | 0.730 |
PSO | 0.456 | 0.310 | 0.798 | 0.798 | 0.537 | 0.365 | 0.777 | 0.733 | ||
GA | 0.445 | 0.304 | 0.818 | 0.818 | 0.535 | 0.362 | 0.778 | 0.735 | ||
GWO | 0.442 | 0.301 | 0.823 | 0.823 | 0.526 | 0.356 | 0.802 | 0.762 | ||
SSO | 0.435 | 0.286 | 0.838 | 0.838 | 0.512 | 0.345 | 0.814 | 0.784 | ||
SSA | 0.431 | 0.283 | 0.845 | 0.845 | 0.509 | 0.343 | 0.817 | 0.784 | ||
HGS | 0.402 | 0.261 | 0.890 | 0.890 | 0.505 | 0.341 | 0.819 | 0.787 | ||
Station 3 | OPT SPI3+MN | RFVL | 0.489 | 0.376 | 0.823 | 0.823 | 0.541 | 0.365 | 0.739 | 0.700 |
PSO | 0.476 | 0.371 | 0.845 | 0.845 | 0.538 | 0.360 | 0.749 | 0.702 | ||
GA | 0.471 | 0.370 | 0.854 | 0.854 | 0.522 | 0.346 | 0.763 | 0.730 | ||
GWO | 0.463 | 0.357 | 0.869 | 0.869 | 0.517 | 0.343 | 0.767 | 0.735 | ||
SSO | 0.460 | 0.355 | 0.872 | 0.872 | 0.513 | 0.336 | 0.777 | 0.746 | ||
SSA | 0.440 | 0.340 | 0.902 | 0.902 | 0.504 | 0.328 | 0.782 | 0.750 | ||
HGS | 0.434 | 0.332 | 0.908 | 0.908 | 0.500 | 0.325 | 0.787 | 0.765 |
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Adnan, R.M.; Mostafa, R.R.; Islam, A.R.M.T.; Gorgij, A.D.; Kuriqi, A.; Kisi, O. Improving Drought Modeling Using Hybrid Random Vector Functional Link Methods. Water 2021, 13, 3379. https://doi.org/10.3390/w13233379
Adnan RM, Mostafa RR, Islam ARMT, Gorgij AD, Kuriqi A, Kisi O. Improving Drought Modeling Using Hybrid Random Vector Functional Link Methods. Water. 2021; 13(23):3379. https://doi.org/10.3390/w13233379
Chicago/Turabian StyleAdnan, Rana Muhammad, Reham R. Mostafa, Abu Reza Md. Towfiqul Islam, Alireza Docheshmeh Gorgij, Alban Kuriqi, and Ozgur Kisi. 2021. "Improving Drought Modeling Using Hybrid Random Vector Functional Link Methods" Water 13, no. 23: 3379. https://doi.org/10.3390/w13233379