A Novel Framework Based on the Stacking Ensemble Machine Learning (SEML) Method: Application in Wind Speed Modeling
Abstract
:1. Introduction
2. Materials and Methods
2.1. Present Work Steps
- Level 1 (base algorithms): All algorithms perform their operations separately at this level. The outputs of this level’s algorithms are used as input into the meta-algorithm.
- Level 2 (meta-algorithm): At this level, the meta-algorithm produces high-precision outputs by combining the results of the level 1 algorithms.
Algorithm1. Pseudo-code of the proposed framework based on the SEML method. |
|
- Level 1: WS was modeled using eleven ML algorithms, including ANN, MLR, MNLR, GRNN, MARS, M5, GBR, RBFNN, LSBoost, LSSVM-GS, and LSSVM-HHO, at sixteen stations.
- Level 2: Due to the simple structure and high speed of the LSBoost, this algorithm was used as a meta-algorithm to combine the results of the base algorithms.
2.2. Artificial Neural Network (ANN)
2.3. Multiple Linear Regression (MLR)
2.4. Multiple Nonlinear Regression (MNLR)
2.5. General Regression Neural Network (GRNN)
2.6. Multivariate Adaptive Regression Splines (MARS)
2.7. M5 Model Tree (M5)
2.8. Gradient Boosted Regression (GBR)
2.9. Radial Basis Function Neural Network (RBFNN)
2.10. Least Squares Boost (LSBoost)
2.11. Least Squares Support Vector Machine-Grid Search (LSSVM-GS)
2.12. Harris Hawks Optimization (HHO)
2.13. LSSVM-HHO
2.14. Performance Evaluation of the Algorithms
2.15. Case Study and Data Sources
3. Results and Discussion
3.1. Modeling WS using the SEML Method (Level 1—Base Algorithms)
3.2. Modeling WS using the SEML Method (Level 2—Meta-Algorithm)
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix B
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
ANN | 1.10 | 1.50 | 0.89 | 0.46 | 1.11 | 1.52 | 0.91 | 0.42 |
MLR | 1.18 | 1.58 | 0.94 | 0.34 | 1.17 | 1.58 | 0.95 | 0.32 |
MNLR | 1.16 | 1.56 | 0.93 | 0.37 | 1.15 | 1.56 | 0.94 | 0.35 |
GRNN | 0.86 | 1.21 | 0.72 | 0.74 | 1.13 | 1.56 | 0.93 | 0.36 |
MARS | 1.14 | 1.54 | 0.91 | 0.41 | 1.13 | 1.54 | 0.92 | 0.40 |
M5 | 1.13 | 1.53 | 0.91 | 0.41 | 1.13 | 1.56 | 0.93 | 0.37 |
GBR | 1.03 | 1.39 | 0.83 | 0.59 | 1.11 | 1.52 | 0.91 | 0.42 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 1.43 | 1.81 | 1.08 | −0.01 |
LSBoost | 1.06 | 1.41 | 0.84 | 0.57 | 1.12 | 1.54 | 0.92 | 0.40 |
LSSVM-GS | 0.95 | 1.28 | 0.76 | 0.68 | 1.11 | 1.52 | 0.91 | 0.42 |
LSSVM-HHO | 1.03 | 1.39 | 0.82 | 0.59 | 1.11 | 1.52 | 0.91 | 0.42 |
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
ANN | 0.92 | 1.23 | 0.86 | 0.51 | 0.98 | 1.29 | 0.88 | 0.47 |
MLR | 0.93 | 1.25 | 0.87 | 0.49 | 0.98 | 1.30 | 0.89 | 0.46 |
MNLR | 0.93 | 1.24 | 0.86 | 0.50 | 0.98 | 1.29 | 0.88 | 0.47 |
GRNN | 0.69 | 0.97 | 0.68 | 0.75 | 0.98 | 1.30 | 0.89 | 0.47 |
MARS | 0.92 | 1.23 | 0.86 | 0.51 | 0.98 | 1.29 | 0.88 | 0.47 |
M5 | 0.91 | 1.22 | 0.85 | 0.53 | 0.99 | 1.30 | 0.89 | 0.46 |
GBR | 0.78 | 1.05 | 0.73 | 0.70 | 0.97 | 1.28 | 0.87 | 0.49 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 1.71 | 1.95 | 1.33 | 0.00 |
LSBoost | 0.89 | 1.18 | 0.83 | 0.57 | 0.97 | 1.29 | 0.88 | 0.48 |
LSSVM-GS | 0.78 | 1.04 | 0.73 | 0.70 | 0.97 | 1.28 | 0.87 | 0.49 |
LSSVM-HHO | 0.78 | 1.05 | 0.73 | 0.70 | 0.97 | 1.28 | 0.87 | 0.49 |
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
ANN | 1.35 | 1.92 | 0.97 | 0.25 | 1.45 | 2.07 | 0.98 | 0.20 |
MLR | 1.38 | 1.96 | 0.99 | 0.16 | 1.46 | 2.08 | 0.99 | 0.17 |
MNLR | 1.37 | 1.95 | 0.98 | 0.19 | 1.45 | 2.07 | 0.98 | 0.18 |
GRNN | 0.99 | 1.44 | 0.73 | 0.75 | 1.48 | 2.12 | 1.01 | 0.11 |
MARS | 1.37 | 1.94 | 0.98 | 0.21 | 1.45 | 2.07 | 0.98 | 0.19 |
M5 | 1.35 | 1.92 | 0.97 | 0.25 | 1.47 | 2.09 | 0.99 | 0.16 |
GBR | 1.29 | 1.84 | 0.93 | 0.43 | 1.45 | 2.07 | 0.98 | 0.20 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 1.48 | 2.11 | 1.00 | 0.01 |
LSBoost | 1.33 | 1.88 | 0.95 | 0.35 | 1.45 | 2.07 | 0.98 | 0.18 |
LSSVM-GS | 1.15 | 1.63 | 0.82 | 0.69 | 1.45 | 2.07 | 0.98 | 0.19 |
LSSVM-HHO | 1.29 | 1.84 | 0.93 | 0.43 | 1.45 | 2.07 | 0.98 | 0.20 |
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
ANN | 0.77 | 1.02 | 0.87 | 0.49 | 0.80 | 1.04 | 0.89 | 0.46 |
MLR | 0.79 | 1.05 | 0.90 | 0.43 | 0.81 | 1.06 | 0.91 | 0.42 |
MNLR | 0.79 | 1.05 | 0.90 | 0.44 | 0.81 | 1.06 | 0.90 | 0.43 |
GRNN | 0.58 | 0.79 | 0.67 | 0.77 | 0.80 | 1.07 | 0.91 | 0.42 |
MARS | 0.79 | 1.04 | 0.89 | 0.45 | 0.81 | 1.05 | 0.90 | 0.43 |
M5 | 0.78 | 1.04 | 0.89 | 0.45 | 0.81 | 1.07 | 0.91 | 0.41 |
GBR | 0.72 | 0.95 | 0.82 | 0.59 | 0.80 | 1.05 | 0.89 | 0.45 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 2.20 | 2.49 | 2.13 | 0.00 |
LSBoost | 0.76 | 1.00 | 0.86 | 0.52 | 0.80 | 1.05 | 0.90 | 0.44 |
LSSVM-GS | 0.66 | 0.87 | 0.75 | 0.69 | 0.80 | 1.05 | 0.90 | 0.44 |
LSSVM-HHO | 0.72 | 0.95 | 0.82 | 0.59 | 0.80 | 1.05 | 0.89 | 0.45 |
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
ANN | 0.59 | 0.79 | 0.86 | 0.51 | 0.59 | 0.80 | 0.88 | 0.48 |
MLR | 0.61 | 0.81 | 0.89 | 0.46 | 0.61 | 0.82 | 0.90 | 0.44 |
MNLR | 0.60 | 0.80 | 0.88 | 0.47 | 0.61 | 0.81 | 0.89 | 0.45 |
GRNN | 0.45 | 0.63 | 0.70 | 0.74 | 0.61 | 0.82 | 0.90 | 0.44 |
MARS | 0.59 | 0.79 | 0.87 | 0.50 | 0.59 | 0.80 | 0.88 | 0.48 |
M5 | 0.59 | 0.79 | 0.87 | 0.49 | 0.60 | 0.81 | 0.89 | 0.46 |
GBR | 0.51 | 0.69 | 0.76 | 0.67 | 0.59 | 0.79 | 0.87 | 0.49 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 0.71 | 0.91 | 1.00 | 0.00 |
LSBoost | 0.57 | 0.76 | 0.83 | 0.56 | 0.60 | 0.80 | 0.88 | 0.47 |
LSSVM-GS | 0.50 | 0.67 | 0.74 | 0.70 | 0.59 | 0.79 | 0.87 | 0.49 |
LSSVM-HHO | 0.51 | 0.69 | 0.76 | 0.67 | 0.59 | 0.79 | 0.87 | 0.49 |
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
ANN | 0.75 | 1.01 | 0.91 | 0.42 | 0.75 | 1.01 | 0.90 | 0.45 |
MLR | 0.77 | 1.04 | 0.93 | 0.37 | 0.76 | 1.03 | 0.91 | 0.41 |
MNLR | 0.77 | 1.03 | 0.92 | 0.38 | 0.76 | 1.03 | 0.91 | 0.42 |
GRNN | 0.58 | 0.81 | 0.72 | 0.72 | 0.77 | 1.04 | 0.92 | 0.39 |
MARS | 0.75 | 1.02 | 0.91 | 0.41 | 0.75 | 1.02 | 0.90 | 0.44 |
M5 | 0.75 | 1.02 | 0.91 | 0.41 | 0.75 | 1.02 | 0.90 | 0.44 |
GBR | 0.68 | 0.93 | 0.83 | 0.58 | 0.75 | 1.01 | 0.90 | 0.45 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 0.84 | 1.11 | 0.98 | 0.22 |
LSBoost | 0.71 | 0.95 | 0.85 | 0.54 | 0.75 | 1.02 | 0.90 | 0.43 |
LSSVM-GS | 0.64 | 0.87 | 0.78 | 0.67 | 0.75 | 1.02 | 0.90 | 0.44 |
LSSVM-HHO | 0.64 | 0.87 | 0.78 | 0.67 | 0.75 | 1.02 | 0.90 | 0.44 |
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
ANN | 0.77 | 1.03 | 0.88 | 0.47 | 0.80 | 1.08 | 0.90 | 0.44 |
MLR | 0.79 | 1.07 | 0.91 | 0.42 | 0.81 | 1.09 | 0.91 | 0.41 |
MNLR | 0.79 | 1.06 | 0.90 | 0.43 | 0.81 | 1.09 | 0.91 | 0.42 |
GRNN | 0.57 | 0.80 | 0.68 | 0.76 | 0.81 | 1.10 | 0.92 | 0.40 |
MARS | 0.79 | 1.05 | 0.90 | 0.44 | 0.80 | 1.08 | 0.90 | 0.43 |
M5 | 0.78 | 1.05 | 0.89 | 0.46 | 0.82 | 1.11 | 0.92 | 0.39 |
GBR | 0.72 | 0.97 | 0.82 | 0.58 | 0.80 | 1.07 | 0.90 | 0.44 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 0.94 | 1.21 | 1.01 | 0.03 |
LSBoost | 0.73 | 0.97 | 0.83 | 0.58 | 0.80 | 1.08 | 0.90 | 0.43 |
LSSVM-GS | 0.66 | 0.89 | 0.76 | 0.69 | 0.80 | 1.07 | 0.90 | 0.44 |
LSSVM-HHO | 0.72 | 0.97 | 0.82 | 0.58 | 0.80 | 1.07 | 0.90 | 0.44 |
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
ANN | 0.90 | 1.21 | 0.80 | 0.61 | 0.94 | 1.26 | 0.83 | 0.56 |
MLR | 0.96 | 1.28 | 0.84 | 0.54 | 0.99 | 1.32 | 0.87 | 0.50 |
MNLR | 0.94 | 1.26 | 0.83 | 0.56 | 0.97 | 1.30 | 0.85 | 0.53 |
GRNN | 0.70 | 0.98 | 0.64 | 0.78 | 0.96 | 1.30 | 0.85 | 0.53 |
MARS | 0.92 | 1.23 | 0.81 | 0.59 | 0.94 | 1.27 | 0.83 | 0.55 |
M5 | 0.92 | 1.24 | 0.82 | 0.58 | 0.95 | 1.27 | 0.84 | 0.55 |
GBR | 0.83 | 1.12 | 0.73 | 0.69 | 0.94 | 1.26 | 0.83 | 0.56 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 1.36 | 1.74 | 1.14 | 0.00 |
LSBoost | 0.86 | 1.15 | 0.76 | 0.66 | 0.95 | 1.27 | 0.84 | 0.55 |
LSSVM-GS | 0.77 | 1.04 | 0.68 | 0.74 | 0.94 | 1.27 | 0.83 | 0.56 |
LSSVM-HHO | 0.83 | 1.12 | 0.73 | 0.69 | 0.94 | 1.26 | 0.83 | 0.56 |
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
ANN | 0.87 | 1.17 | 0.87 | 0.49 | 0.90 | 1.20 | 0.88 | 0.47 |
MLR | 0.92 | 1.23 | 0.91 | 0.41 | 0.92 | 1.23 | 0.90 | 0.43 |
MNLR | 0.90 | 1.21 | 0.90 | 0.44 | 0.91 | 1.21 | 0.89 | 0.46 |
GRNN | 0.68 | 0.96 | 0.71 | 0.72 | 0.91 | 1.21 | 0.89 | 0.45 |
MARS | 0.89 | 1.19 | 0.88 | 0.47 | 0.90 | 1.20 | 0.88 | 0.47 |
M5 | 0.88 | 1.19 | 0.88 | 0.48 | 0.90 | 1.21 | 0.89 | 0.46 |
GBR | 0.75 | 1.00 | 0.74 | 0.69 | 0.89 | 1.19 | 0.87 | 0.49 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 1.03 | 1.36 | 1.00 | 0.02 |
LSBoost | 0.77 | 1.02 | 0.76 | 0.68 | 0.90 | 1.19 | 0.88 | 0.48 |
LSSVM-GS | 0.73 | 0.98 | 0.73 | 0.72 | 0.89 | 1.19 | 0.87 | 0.49 |
LSSVM-HHO | 0.75 | 1.00 | 0.74 | 0.69 | 0.89 | 1.19 | 0.87 | 0.49 |
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
ANN | 1.23 | 1.72 | 0.77 | 0.64 | 1.28 | 1.80 | 0.79 | 0.62 |
MLR | 1.35 | 1.85 | 0.83 | 0.56 | 1.36 | 1.89 | 0.83 | 0.56 |
MNLR | 1.29 | 1.78 | 0.79 | 0.61 | 1.30 | 1.82 | 0.80 | 0.60 |
GRNN | 1.01 | 1.49 | 0.67 | 0.75 | 1.29 | 1.81 | 0.79 | 0.61 |
MARS | 1.27 | 1.76 | 0.78 | 0.62 | 1.28 | 1.80 | 0.79 | 0.62 |
M5 | 1.25 | 1.75 | 0.78 | 0.63 | 1.29 | 1.82 | 0.80 | 0.60 |
GBR | 1.17 | 1.63 | 0.73 | 0.69 | 1.27 | 1.78 | 0.78 | 0.62 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 1.54 | 2.21 | 0.97 | 0.36 |
LSBoost | 1.22 | 1.68 | 0.75 | 0.66 | 1.29 | 1.81 | 0.79 | 0.61 |
LSSVM-GS | 1.07 | 1.50 | 0.67 | 0.75 | 1.27 | 1.79 | 0.78 | 0.62 |
LSSVM-HHO | 1.17 | 1.63 | 0.73 | 0.69 | 1.27 | 1.78 | 0.78 | 0.62 |
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
ANN | 0.78 | 1.08 | 0.90 | 0.43 | 0.77 | 1.08 | 0.90 | 0.43 |
MLR | 0.82 | 1.12 | 0.94 | 0.35 | 0.81 | 1.10 | 0.92 | 0.38 |
MNLR | 0.82 | 1.12 | 0.94 | 0.35 | 0.80 | 1.10 | 0.92 | 0.39 |
GRNN | 0.60 | 0.86 | 0.72 | 0.73 | 0.80 | 1.11 | 0.93 | 0.37 |
MARS | 0.80 | 1.11 | 0.93 | 0.38 | 0.79 | 1.09 | 0.91 | 0.41 |
M5 | 0.80 | 1.10 | 0.92 | 0.39 | 0.80 | 1.09 | 0.92 | 0.40 |
GBR | 0.68 | 0.94 | 0.78 | 0.66 | 0.78 | 1.07 | 0.90 | 0.43 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 0.93 | 1.19 | 1.00 | 0.00 |
LSBoost | 0.75 | 1.02 | 0.85 | 0.54 | 0.79 | 1.08 | 0.91 | 0.41 |
LSSVM-GS | 0.68 | 0.93 | 0.78 | 0.67 | 0.78 | 1.07 | 0.90 | 0.43 |
LSSVM-HHO | 0.68 | 0.93 | 0.78 | 0.67 | 0.78 | 1.07 | 0.90 | 0.43 |
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
ANN | 1.69 | 2.23 | 0.86 | 0.51 | 1.70 | 2.23 | 0.86 | 0.50 |
MLR | 1.74 | 2.29 | 0.88 | 0.47 | 1.75 | 2.29 | 0.89 | 0.46 |
MNLR | 1.71 | 2.26 | 0.87 | 0.50 | 1.72 | 2.26 | 0.87 | 0.48 |
GRNN | 1.29 | 1.78 | 0.68 | 0.75 | 1.74 | 2.28 | 0.88 | 0.47 |
MARS | 1.69 | 2.23 | 0.86 | 0.52 | 1.71 | 2.24 | 0.87 | 0.50 |
M5 | 1.68 | 2.22 | 0.85 | 0.53 | 1.74 | 2.28 | 0.88 | 0.48 |
GBR | 1.59 | 2.10 | 0.80 | 0.60 | 1.71 | 2.24 | 0.87 | 0.50 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 1.89 | 2.49 | 0.96 | 0.31 |
LSBoost | 1.58 | 2.07 | 0.80 | 0.61 | 1.71 | 2.24 | 0.87 | 0.49 |
LSSVM-GS | 1.44 | 1.90 | 0.73 | 0.70 | 1.72 | 2.24 | 0.87 | 0.50 |
LSSVM-HHO | 1.59 | 2.10 | 0.80 | 0.60 | 1.71 | 2.24 | 0.87 | 0.50 |
Appendix C
Appendix D
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Input | Output | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Station | Parameter | Tmin (°C) | Tmean (°C) | Tmax (°C) | Hmin (%) | Hmean (%) | Hmax (%) | SH (hr) | WS (m/s) | Longitude | Latitude |
Quchan | Average | 7.86 | 74.64 | 55.11 | 36.83 | 19.65 | 12.84 | 6.10 | 2.06 | 58.51 | 37.11 |
Std a | 3.39 | 18.34 | 19.70 | 20.12 | 10.46 | 9.63 | 8.07 | 1.37 | |||
Sarakhs | Average | 8.20 | 65.78 | 48.87 | 33.60 | 23.97 | 18.02 | 10.26 | 2.20 | 61.16 | 36.53 |
Std a | 3.63 | 19.26 | 19.55 | 18.97 | 10.22 | 9.37 | 7.47 | 1.4 | |||
Sabzevar | Average | 8.44 | 58.95 | 42.02 | 26.81 | 24.52 | 17.44 | 11.56 | 2.54 | 57.68 | 36.21 |
Std a | 2.69 | 19.29 | 16.56 | 13.94 | 9.45 | 8.79 | 8.03 | 1.20 | |||
Golmakan | Average | 7.87 | 65.94 | 48.91 | 34.44 | 20.14 | 15.07 | 6.57 | 2.91 | 59.15 | 36.48 |
Std a | 2.76 | 17.72 | 17.69 | 17.25 | 9.31 | 8.79 | 6.71 | 1.65 | |||
Mashhad | Average | 8.29 | 71.57 | 52.28 | 33.93 | 21.44 | 14.76 | 8.50 | 2.17 | 59.61 | 36.3 |
Std a | 3.05 | 19.75 | 18.45 | 17.13 | 9.50 | 8.51 | 7.36 | 0.97 | |||
Neyshabur | Average | 8.75 | 66.05 | 49.80 | 32.20 | 22.40 | 15.59 | 6.75 | 1.34 | 58.45 | 36.45 |
Std a | 2.75 | 17.90 | 17.73 | 16.36 | 9.16 | 8.65 | 6.57 | 0.79 | |||
Torbat Heydarieh | Average | 9.06 | 63.81 | 45.69 | 29.63 | 21.23 | 14.80 | 8.41 | 2.38 | 59.22 | 35.28 |
Std a | 3.11 | 21.00 | 17.71 | 14.61 | 8.88 | 8.52 | 7.84 | 1.45 | |||
Kashmar | Average | 9.08 | 53.66 | 39.46 | 27.69 | 24.13 | 18.59 | 11.50 | 1.56 | 58.47 | 35.33 |
Std a | 2.69 | 21.17 | 16.70 | 13.15 | 9.09 | 8.72 | 7.59 | 0.94 | |||
Gonabad | Average | 9.21 | 54.58 | 38.54 | 27.06 | 24.56 | 19.25 | 10.66 | 2.15 | 58.56 | 34.27 |
Std a | 2.50 | 20.10 | 16.80 | 14.17 | 8.85 | 8.57 | 7.36 | 1.32 | |||
Tabas | Average | 9.11 | 45.34 | 31.43 | 19.97 | 28.44 | 21.73 | 15.16 | 2.05 | 56.92 | 33.58 |
Std a | 2.68 | 20.17 | 15.50 | 11.48 | 9.37 | 9.11 | 8.45 | 1.38 | |||
Ferdows | Average | 9.29 | 52.91 | 36.37 | 24.24 | 24.57 | 18.66 | 10.00 | 2.20 | 58.17 | 34.01 |
Std a | 2.52 | 19.32 | 16.18 | 13.34 | 8.76 | 8.61 | 7.43 | 1.00 | |||
Qaen | Average | 9.22 | 55.83 | 36.89 | 24.54 | 22.24 | 16.62 | 6.92 | 2.65 | 59.2 | 33.73 |
Std a | 2.50 | 19.00 | 15.28 | 12.73 | 7.91 | 7.90 | 6.86 | 1.30 | |||
Birjand | Average | 9.13 | 53.85 | 35.99 | 20.21 | 24.13 | 16.56 | 8.79 | 2.38 | 59.13 | 32.53 |
Std a | 2.46 | 20.83 | 16.15 | 12.21 | 8.18 | 7.92 | 7.44 | 1.17 | |||
Nehbandan | Average | 8.57 | 48.13 | 30.63 | 19.88 | 26.21 | 20.76 | 12.51 | 3.17 | 60.03 | 31.53 |
Std a | 2.73 | 21.86 | 15.52 | 11.99 | 8.42 | 8.43 | 8.03 | 1.98 | |||
Boshruyeh | Average | 8.43 | 52.82 | 36.59 | 24.69 | 27.16 | 20.90 | 11.43 | 1.39 | 57.45 | 33.87 |
Std a | 2.61 | 18.39 | 15.65 | 13.10 | 9.33 | 9.10 | 7.81 | 1.00 | |||
Khor Birjand | Average | 9.18 | 44.91 | 28.46 | 19.32 | 26.00 | 20.57 | 12.49 | 4.93 | 58.26 | 32.56 |
Std a | 2.51 | 18.27 | 13.21 | 10.76 | 8.53 | 8.77 | 8.10 | 2.26 |
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
Quchan | ||||||||
ANN | 0.95 | 1.23 | 0.79 | 0.61 | 0.96 | 1.23 | 0.80 | 0.61 |
MLR | 1.00 | 1.30 | 0.83 | 0.55 | 0.98 | 1.27 | 0.82 | 0.57 |
MNLR | 0.98 | 1.27 | 0.82 | 0.58 | 0.97 | 1.26 | 0.81 | 0.59 |
GRNN | 0.76 | 1.05 | 0.68 | 0.74 | 0.97 | 1.24 | 0.80 | 0.60 |
MARS | 0.96 | 1.24 | 0.80 | 0.61 | 0.95 | 1.23 | 0.80 | 0.61 |
M5 | 0.95 | 1.24 | 0.79 | 0.61 | 0.96 | 1.24 | 0.80 | 0.60 |
GBR | 0.87 | 1.13 | 0.73 | 0.69 | 0.95 | 1.22 | 0.79 | 0.61 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 1.08 | 1.42 | 0.92 | 0.43 |
LSBoost | 0.93 | 1.20 | 0.77 | 0.63 | 0.95 | 1.23 | 0.79 | 0.61 |
LSSVM-GS | 0.82 | 1.07 | 0.68 | 0.74 | 0.95 | 1.22 | 0.79 | 0.61 |
LSSVM-HHO | 0.87 | 1.13 | 0.73 | 0.69 | 0.95 | 1.22 | 0.79 | 0.61 |
Torbat Heydarieh | ||||||||
ANN | 0.95 | 1.29 | 0.78 | 0.63 | 0.97 | 1.32 | 0.79 | 0.62 |
MLR | 1.00 | 1.35 | 0.81 | 0.58 | 1.01 | 1.38 | 0.82 | 0.57 |
MNLR | 0.98 | 1.34 | 0.80 | 0.59 | 1.00 | 1.36 | 0.81 | 0.59 |
GRNN | 0.75 | 1.07 | 0.65 | 0.77 | 1.00 | 1.36 | 0.81 | 0.59 |
MARS | 0.96 | 1.30 | 0.78 | 0.62 | 0.97 | 1.33 | 0.79 | 0.61 |
M5 | 0.96 | 1.30 | 0.79 | 0.62 | 0.99 | 1.35 | 0.81 | 0.59 |
GBR | 0.82 | 1.11 | 0.67 | 0.75 | 0.97 | 1.32 | 0.79 | 0.62 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 1.34 | 1.80 | 1.07 | 0.34 |
LSBoost | 0.84 | 1.14 | 0.68 | 0.74 | 0.97 | 1.33 | 0.79 | 0.61 |
LSSVM-GS | 0.82 | 1.11 | 0.67 | 0.75 | 0.97 | 1.32 | 0.79 | 0.61 |
LSSVM-HHO | 0.82 | 1.11 | 0.67 | 0.75 | 0.97 | 1.32 | 0.79 | 0.62 |
Gonabad | ||||||||
ANN | 0.95 | 1.31 | 0.85 | 0.53 | 0.96 | 1.32 | 0.85 | 0.52 |
MLR | 1.00 | 1.36 | 0.88 | 0.48 | 1.00 | 1.36 | 0.88 | 0.48 |
MNLR | 0.99 | 1.35 | 0.87 | 0.49 | 1.00 | 1.35 | 0.87 | 0.48 |
GRNN | 0.75 | 1.08 | 0.70 | 0.73 | 0.98 | 1.35 | 0.87 | 0.49 |
MARS | 0.97 | 1.33 | 0.86 | 0.51 | 0.97 | 1.33 | 0.86 | 0.51 |
M5 | 0.96 | 1.32 | 0.85 | 0.52 | 0.97 | 1.33 | 0.86 | 0.51 |
GBR | 0.87 | 1.19 | 0.77 | 0.65 | 0.96 | 1.32 | 0.85 | 0.52 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 1.15 | 1.49 | 0.97 | 0.27 |
LSBoost | 0.86 | 1.16 | 0.75 | 0.67 | 0.97 | 1.33 | 0.86 | 0.51 |
LSSVM-GS | 0.83 | 1.13 | 0.73 | 0.70 | 0.96 | 1.32 | 0.85 | 0.52 |
LSSVM-HHO | 0.87 | 1.19 | 0.77 | 0.65 | 0.96 | 1.32 | 0.85 | 0.52 |
Tabas | ||||||||
ANN | 0.82 | 1.11 | 0.87 | 0.49 | 0.84 | 1.14 | 0.88 | 0.48 |
MLR | 0.85 | 1.14 | 0.89 | 0.45 | 0.86 | 1.16 | 0.89 | 0.45 |
MNLR | 0.85 | 1.14 | 0.89 | 0.45 | 0.86 | 1.16 | 0.89 | 0.46 |
GRNN | 0.63 | 0.89 | 0.69 | 0.74 | 0.86 | 1.16 | 0.89 | 0.45 |
MARS | 0.83 | 1.12 | 0.88 | 0.48 | 0.85 | 1.15 | 0.88 | 0.48 |
M5 | 0.83 | 1.12 | 0.87 | 0.49 | 0.86 | 1.17 | 0.90 | 0.45 |
GBR | 0.40 | 0.71 | 0.45 | 0.89 | 0.40 | 0.71 | 0.47 | 0.62 |
RBFNN | 0.00 | 0.00 | 0.00 | 1.00 | 1.01 | 1.31 | 1.00 | 0.00 |
LSBoost | 0.77 | 1.04 | 0.81 | 0.59 | 0.84 | 1.15 | 0.88 | 0.48 |
LSSVM-GS | 0.70 | 0.95 | 0.74 | 0.70 | 0.84 | 1.14 | 0.88 | 0.48 |
LSSVM-HHO | 0.76 | 1.03 | 0.80 | 0.61 | 0.84 | 1.14 | 0.87 | 0.48 |
MAE | RMSE | RRMSE | R | |
---|---|---|---|---|
ANN | 0.99 | 1.34 | 0.87 | 0.48 |
MLR | 1.02 | 1.37 | 0.89 | 0.44 |
MNLR | 1.01 | 1.36 | 0.88 | 0.46 |
GRNN | 1.01 | 1.36 | 0.89 | 0.45 |
MARS | 0.99 | 1.34 | 0.87 | 0.47 |
M5 | 1.00 | 1.36 | 0.88 | 0.46 |
GBR | 0.96 | 1.31 | 0.84 | 0.51 |
RBFNN | 1.29 | 1.66 | 1.10 | 0.12 |
LSBoost | 0.99 | 1.34 | 0.87 | 0.47 |
LSSVM-GS | 0.99 | 1.34 | 0.87 | 0.48 |
LSSVM-HHO | 0.99 | 1.33 | 0.87 | 0.49 |
Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE | R | MAE | RMSE | RRMSE | R | |
Quchan | 0.41 | 0.71 | 0.46 | 0.89 | 0.41 | 0.71 | 0.46 | 0.89 |
Sarakhs | 0.45 | 0.77 | 0.46 | 0.89 | 0.50 | 0.93 | 0.53 | 0.85 |
Sabzevar | 0.42 | 0.72 | 0.50 | 0.87 | 0.45 | 0.78 | 0.54 | 0.84 |
Golmakan | 0.56 | 1.11 | 0.55 | 0.84 | 0.57 | 1.20 | 0.60 | 0.80 |
Mashhad | 0.30 | 0.56 | 0.48 | 0.88 | 0.35 | 0.64 | 0.54 | 0.84 |
Neyshabur | 0.24 | 0.44 | 0.49 | 0.87 | 0.26 | 0.44 | 0.49 | 0.87 |
Torbat Heydarieh | 0.43 | 0.77 | 0.46 | 0.89 | 0.44 | 0.78 | 0.47 | 0.88 |
Kashmar | 0.30 | 0.55 | 0.49 | 0.87 | 0.32 | 0.60 | 0.53 | 0.85 |
Gonabad | 0.41 | 0.73 | 0.47 | 0.88 | 0.42 | 0.73 | 0.48 | 0.88 |
Tabas | 0.39 | 0.67 | 0.43 | 0.90 | 0.42 | 0.71 | 0.46 | 0.89 |
Ferdows | 0.33 | 0.60 | 0.51 | 0.86 | 0.34 | 0.61 | 0.51 | 0.86 |
Qaen | 0.41 | 0.72 | 0.47 | 0.88 | 0.42 | 0.76 | 0.50 | 0.87 |
Birjand | 0.30 | 0.55 | 0.40 | 0.92 | 0.37 | 0.69 | 0.52 | 0.86 |
Nehbandan | 0.56 | 1.04 | 0.46 | 0.89 | 0.58 | 1.06 | 0.48 | 0.88 |
Boshruyeh | 0.33 | 0.61 | 0.51 | 0.86 | 0.34 | 0.60 | 0.51 | 0.86 |
Khor Birjand | 0.69 | 1.23 | 0.48 | 0.88 | 0.71 | 1.29 | 0.49 | 0.87 |
Average | 0.41 | 0.74 | 0.48 | 0.88 | 0.43 | 0.78 | 0.51 | 0.86 |
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Morshed-Bozorgdel, A.; Kadkhodazadeh, M.; Valikhan Anaraki, M.; Farzin, S. A Novel Framework Based on the Stacking Ensemble Machine Learning (SEML) Method: Application in Wind Speed Modeling. Atmosphere 2022, 13, 758. https://doi.org/10.3390/atmos13050758
Morshed-Bozorgdel A, Kadkhodazadeh M, Valikhan Anaraki M, Farzin S. A Novel Framework Based on the Stacking Ensemble Machine Learning (SEML) Method: Application in Wind Speed Modeling. Atmosphere. 2022; 13(5):758. https://doi.org/10.3390/atmos13050758
Chicago/Turabian StyleMorshed-Bozorgdel, Amirreza, Mojtaba Kadkhodazadeh, Mahdi Valikhan Anaraki, and Saeed Farzin. 2022. "A Novel Framework Based on the Stacking Ensemble Machine Learning (SEML) Method: Application in Wind Speed Modeling" Atmosphere 13, no. 5: 758. https://doi.org/10.3390/atmos13050758
APA StyleMorshed-Bozorgdel, A., Kadkhodazadeh, M., Valikhan Anaraki, M., & Farzin, S. (2022). A Novel Framework Based on the Stacking Ensemble Machine Learning (SEML) Method: Application in Wind Speed Modeling. Atmosphere, 13(5), 758. https://doi.org/10.3390/atmos13050758