Abstract
Solar radiation is an important parameter that affects the atmosphere-earth thermal balance and many water and soil processes such as evapotranspiration and plant growth. The modeling of the daily and monthly solar radiation by Gaussian process regression (GPR) with K-fold cross-validation model has been discussed recently. This study evaluated different neural models such as artificial neural network (ANN), support vector machine (SVM), adaptive network-based fuzzy inference system (ANFIS), and multiple linear regression (MLR) for estimating the global solar radiation (daily and monthly) with K-fold cross-validation method. For the appropriate comparison of the models, the randomized complete block (RCB) design applied in the training and test phases. Also, different data sets were evaluated by K-fold cross-validation in each model. The results showed that radial basis function (RBF) model has the lowest error for estimating the monthly and daily solar radiation. In this study, the result of RBF was compared with the GPR models. The conclusion indicated that RBF methodology can predict solar radiation with higher accuracy relative to the GPR model. The results of yearly solar radiation estimation (2009–2014) showed that the RBF model can estimate solar radiation with the MAPE and RMSE of 5.1% and 0.29, respectively. Also, the coefficient of correlation (R2) between actual and estimated values throughout the year is 98% and can be used by the engineers and other researchers for solar and thermal applications.
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Abbreviations
- ANFIS:
-
Adaptive Network-Based Fuzzy Inference System
- BP:
-
Back-propagation
- G oH :
-
Daily extraterrestrial radiation (W m−2)
- H :
-
Daily global solar radiation (W m−2)
- N :
-
Day length
- R h :
-
Daily average relative humidity (%)
- T max :
-
Daily maximum temperature (K)
- T ave :
-
Daily average temperature (K)
- P :
-
Daily total rainfall
- EF:
-
Efficiency model
- f(T ave):
-
Function based on the daily mean temperature
- FIS:
-
Fuzzy Inference System
- GPR:
-
Gaussian process regression
- GSR:
-
Global solar radiation
- QVNN:
-
Quaternion-valued neural network
- GD:
-
Gradient descent
- LSE:
-
Least-squares error
- LM:
-
Levenberg–Marquardt
- MLR:
-
Multiple linear regression
- MAPE:
-
Mean absolute percentage error
- MLP:
-
Multilayer perceptron
- RBF:
-
Radial bias function
- RMSE:
-
Root mean square error
- Φ:
-
Site latitude
- I sc :
-
Solar constant
- Δ:
-
Solar declination
- SC:
-
Subtractive clustering
- ω s :
-
Sunset hour angle
- n :
-
Sunshine hours
- SVM:
-
Support vector machine
- WT:
-
Wavelet transform
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Acknowledgments
The authors would like to thank the editor in chief and the anonymous referees for their valuable suggestions and useful comments that improved the paper content substantially. Also special thanks to the Meteorological Office Data Center in Khorasan Razavi, Iran, for providing data related to this study. This study was supported by Agricultural Sciences and Natural Resources University of Khuzestan, Iran. The authors are grateful for the support provided by this university.
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Morteza Taki: conceptualization, methodology, software, investigation, writing—original draft. Abbas Rohani: software, resources, data curation. Hasan Yildizhan: review and editing.
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Appendix
Appendix
Extraterrestrial solar radiation (GoH)
In this study, daily total extraterrestrial radiation (GoH W m−2) was calculated based on Kalogirou (2014):
where n is the day of the year, φ is the site latitude, δ is the solar angle, and ω is the hour angle.
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Taki, M., Rohani, A. & Yildizhan, H. Application of machine learning for solar radiation modeling. Theor Appl Climatol 143, 1599–1613 (2021). https://doi.org/10.1007/s00704-020-03484-x
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DOI: https://doi.org/10.1007/s00704-020-03484-x