Table 5.
A summary of the studies regarding the prediction of solar radiation data using hybrid methods.
| Location | Model | Input parameters | Output parameter | Data scale | Statistical benchmarks | Key findings | References |
|---|---|---|---|---|---|---|---|
| Gurgaon, India | ANN, ANFIS, and HMM-GFM | 15 different combinations of inputs | Global solar radiation | 2009 to 2011 | r-value, RMSE, and MAPE | For the best prediction accuracy, the combination of input parameters is as follows: relative humidity, atmospheric pressure, sunshine, day number, and temperature. The proposed HMM-GFM method achieved the best estimation accuracy with 7.9124 MJ/m2 of RMSE, 3.0083% of MAPE, and 0.9921 of r-value. | [92] |
| Murcia, Spain | CRO–ELM, ELM, and SVR |
Meteorological variables | Global solar radiation | January 1, 2010, to December 31, 2011 | RMSE and MAE | The prediction accuracy of the CRO-ELM is higher than the conventional SVR and ELM algorithms. | [93] |
| Singapore | GAMMF, TDNN, ARMA (1,1), and ARMA-TDNN |
Historical global solar radiation | 5 min ahead solar radiation | 2009 to 2010 | SMAPE and RMSE | GAMMF achieved higher predictive accuracy compared to other methods. | [94] |
| Six locations in the USA | CS-OP-ELM, OP-ELM, ARMA, and BPNN |
Eight input variables | Hourly clear and real sky global horizontal radiation | Hourly data from 2008 to 2010 | MRE and RMSE | CS-OP-ELM had better prediction results of solar irradiation as compared to conventional OP-ELM, ARMA, and BPNN. | [95] |
| Four sites in the USA | RBF, Hard-ridge-RBF, DE-hard-ridge-RBF, and CS-hard-ridge-RBF | 12 meteorological parameters | Monthly average global solar radiation | 1998 to 2010 | RMSE and MAPE | The RMSE and MAPE metric results showed that the hybrid methods (DE-hard-ridge-RBF and CS-hard-ridge-RBF) predict solar radiation with higher accuracy than conventional RBF and hard-ridge-RBF models. | [96] |
| USA (Colorado) and Singapore | SOM- SVR-PSO, ARIMA, SES, LES, and RW | Past 8-hour data | Hourly global solar radiation | USA (1997–2013) Singapore (2010–2013) | nRMSE and nMBE | The mean nRMSE value of the proposed hybrid model for USA data is on average 4% better than the ARIMA, LES, SES, and RW methods. For the Singapore data, the nMBE value of all models is usually less than 3%. | [97] |
| Three provinces (Maiduguri, Jos, and Iseyin) in Nigeria | GP, ANN, and SVM–FFA | Sunshine duration, min and max temperatures | Monthly mean horizontal global solar radiation | 1987 to 2007 | r, R2, RMSE, and MAPE | The proposed SVM-FFA gave the best prediction results with r, R2, RMSE, and MAPE of 0.8532, 0.7280, 1.8661 MJ/m2, and 11.5192%, respectively. | [98] |
| Four sites in the USA | SVM, SVM-HARD, GSO-SVM-HARD, and HARD-RIDGE-SVM |
Meteorological variables | 30 daily global solar radiations | One year | MSE, MAPE, and RMSE | It was observed that the hybrid GSO-SVM-HARD method achieved the best estimation accuracy in all regions. Also, the MAPE values of the hybrid method were between 5% and 15%. | [99] |
| Klang Valley, Malaysia | RFs–FFA, ANN-FFA, ANN, and RFs |
Number of hours per day, humidity, day and month number ambient temperature, and sunshine ratio | Hourly global solar radiation | Hourly meteorological data for one year | MBE, MAPE, and RMSE |
The proposed RFs-FA method is more successful in terms of prediction accuracy with 2.86% MBE, 6.38% MAPE, and 18.98% RMSE compared to hybrid ANN-FFA, ANN, and RFs models. | [100] |
| Four locations in India | DCGSO-LASSO, LASSO, SVM, and GRESH |
Relative humidity, wind direction, wind speed, pressure, solar zenith angle, temperature, and precipitation | 5 days global horizontal radiation | January 1, 2014 to December 31, 2014 | RMSE, MAPE, and RMSE/Avg |
The proposed DCGSO-LASSO achieved the best prediction accuracy for the four locations respectively with 16.815/23.02/22.354/11.437 of RMSE, 7.148%/13.101%/7.756%/1.782% of MAPE, and 2.991%/4.939%/4.423%/2.302% of RMSE/Avg. | [101] |
| Türkiye (65 locations) | FRF-SVM, ANFIS, and GenProg |
Relative humidity, mean air temperature, altitude, latitude, and longitude | Horizontal global solar radiation | 2000 to 2013 | MAE, RMSE, IQR-AE, and MaxAE |
In the training set, it was determined that the most suitable model was Gaussian kernel-based FRF-SVM with 0.531 of MAE and 1.571 of RMSE. In the testing, the error value of FRF-SVM-Gauss is slightly higher compared to the GenProg approach. | [102] |
| USA | NSMOBA, BPNN, GABPNN, GRNN, and CSAWNN |
12 meteorological variables | Global solar radiation | 1991 to 2010 | MAE, MSE, and MAPE | The developed NSMOBA algorithm gave lower error values compared to other individual and hybrid prediction algorithms. | [103] |
| The Mashhad province of Iran | ANN-SA, ANN, SVM, MLSR, and GP |
Relative humidity, atmospheric pressure, earth skin temperature, wind speed, minimum, average, and maximum air temperatures | Daily solar radiation | 1995 to 2014 | R2, MAE, and RMSE | The prediction results demonstrated that integrating the SA algorithm into the ANN modeling process increased prediction accuracy. | [104] |
| Malaysia (Kuala Terengganu) | ANFIS, ANFIS-DE, ANFIS-GA, and ANFIS-PSO | Clearness index, minimum and maximum temperature, monthly rainfall, and sunshine duration | Monthly global solar radiation | January 2006 to December 2014 | r, R2, MABE, MAPE, RMSE, and RRMSE |
ANFIS-PSO gave the best prediction results with 0.9963 of r, 0.9921 of R2, 0.2482 MJ/m2 of MABE, 1.4097% of MAPE, 0.3065 MJ/m2 of RMSE, and 1.7933% of RRMSE. | [105] |
| Eight provinces (Isfahan, Tabriz, Tehran, Zabol, Kermanshah, Bandar Abbas, Ahvaz, and Mashhad) of Iran | SVR-KHA and SVR | Historical global solar radiation data | Global solar radiation | 1979 to 2014 | MAE, MAPE, RMSE, R2 and RRMSE |
SVR-KHA model gave low error compared to classical SVR with 0.93 of R2, 7.4% of MAPE, and 1.98 MJ/m2 of RMSE. | [106] |
| North Dakota, USA | ANFIS-muSG, ANFIS-GA ANFIS-GWO ANFIS-GOA, ANFIS-DA, ANFIS-SSA, ANFIS-PSO, and ANFIS |
Minimum, mean, and maximum air temperatures | Global solar radiation | 2010 to 2018 | R2, MAE, RMSE, MARE, MRE, AAPRE, and RMSRE |
Hybrid ANFIS-muSG performed 25.7%–54.8% better than its competitors in terms of RMSE metric for different locations of the studied region. | [107] |
| Three provinces (Dhahran, Riyadh, and Jeddah) in Saudi Arabia | SVR-GOA-BAK, ANN, DT, KNN, and RF | 14 input variables | Global horizontal irradiance (at the 1-h ahead time horizon) | June 1, 2013, to May 31, 2017 | R2, MAE, nMAE, MAPE, RMSE, and nRMSE |
The hybrid SVR-GOA-BAK, achieved 32.15–39.69% better prediction accuracy in terms of MAPE performance criterion compared to the individual SVR methods. | [108] |
| China (Station of longitude 124.181 W and latitude 44.382 N) | Hybrid WT-CEEMDAN-IASO-ORELM, and nine competitive models | Historical solar radiation data | Short-term (10 min ahead) solar radiation | Different months of 2020 year: March, June, September, and December | MAPE, MAE, RMSE, and r-value | It has been observed that the proposed hybrid WT-CEEMDAN-IASO-ORELM model gives excellent results for short-term solar radiation prediction and is a prospective technology. | [109] |
| Queensland, Australia (Six solar farms) | CNN-REGST, CNN, LSTM, DNN, ELM, REGST, RFR, GBM, and MARS | Meteorological parameters | Daily global solar radiation | 54 years of data | r-value, RMSE, MAE, RMSEr, RRMSE, RMAE, WI, NSE, LM, KGE, DS, APB, EVar | Given all metric results, it has been seen that the proposed hybrid CNN-REGST model exhibits a successful forecasting performance in daily GSR forecasting compared to deep learning and ML methods. | [110] |
| Four stations (Dori, Po, Gaoua and Boromo) in Burkina Faso | XGB-CMAES, adn MARS-CMAES | Minimum and maximum values of both weather temperature and humidity, wind velocity, evaporation, and vapor pressure deficit | Daily global solar radiation | January 1, 1998, to December 31, 2012 | NSE, RMSE, MAE, R, and VAF | MARS-CMAES method gave better prediction performance compared to XGB-CMAES. | [111] |