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Machine Learning Forecasting of Direct Solar Radiation: A Multi-Model Evaluation with Trigonometric Cyclical Encoding

Author

Listed:
  • Latif Bukari Rashid

    (Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran 31261, Saudi Arabia)

  • Shahzada Zaman Shuja

    (Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran 31261, Saudi Arabia
    Interdisciplinary Research Center for Sustainable Energy Systems (IRC-SES), King Fahd University of Petroleum and Minerals (KFUPM), Dhahran 31261, Saudi Arabia)

  • Shafiqur Rehman

    (Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran 31261, Saudi Arabia
    Interdisciplinary Research Center for Sustainable Energy Systems (IRC-SES), King Fahd University of Petroleum and Minerals (KFUPM), Dhahran 31261, Saudi Arabia)

Abstract

As the world is shifting toward cleaner energy sources, accurate forecasting of solar radiation is critical for optimizing the performance and integration of solar energy systems. In this study, we explore eight machine learning models, namely, Random Forest Regressor, Linear Regression Model, Artificial Neural Network, k-Nearest Neighbors, Support Vector Regression, Gradient Boosting Regressor, Gaussian Process Regression, and Deep Learning, as to their use in forecasting direct solar radiation across six climatically diverse regions in the Kingdom of Saudi Arabia. The models were evaluated using eight statistical metrics along with time-series and absolute error analyses. A key contribution of this work is the introduction of Trigonometric Cyclical Encoding, which has significantly improved temporal representation learning. Comparative SHAP-based feature-importance analysis revealed that Trigonometric Cyclical Encoding enhanced the explanatory power of temporal features by 49.26% for monthly cycles and 53.30% for daily cycles. The findings show that Deep Learning achieved the lowest root mean square error, as well as the highest coefficient of determination, while Artificial Neural Network demonstrated consistently high accuracy across the sites. Support Vector Regression performed optimally but was less reliable in some regions. Error and time-series analyses reveal that Artificial Neural Network and Deep Learning maintained stable prediction accuracy throughout high solar radiation seasons, whereas Linear Regression, Random Forest Regressor, and k-Nearest Neighbors showed greater fluctuations. The proposed Trigonometric Cyclical Encoding technique further enhanced model performance by maintaining the overall fitness of the models, which ranged between 81.79% and 94.36% in all scenarios. This paper supports the effective planning of solar energy and integration in challenging climatic conditions.

Suggested Citation

  • Latif Bukari Rashid & Shahzada Zaman Shuja & Shafiqur Rehman, 2025. "Machine Learning Forecasting of Direct Solar Radiation: A Multi-Model Evaluation with Trigonometric Cyclical Encoding," Forecasting, MDPI, vol. 7(4), pages 1-25, October.
    • Handle: RePEc:gam:jforec:v:7:y:2025:i:4:p:58-:d:1773709
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    References listed on IDEAS

    as
    1. Yang, Liu & Cao, Qimeng & Yu, Ying & Liu, Yan, 2020. "Comparison of daily diffuse radiation models in regions of China without solar radiation measurement," Energy, Elsevier, vol. 191(C).
    2. Hasna Hissou & Said Benkirane & Azidine Guezzaz & Mourade Azrour & Abderrahim Beni-Hssane, 2023. "A Novel Machine Learning Approach for Solar Radiation Estimation," Sustainability, MDPI, vol. 15(13), pages 1-21, July.
    3. Rehman, Shafiqur & Mohandes, Mohamed, 2008. "Artificial neural network estimation of global solar radiation using air temperature and relative humidity," Energy Policy, Elsevier, vol. 36(2), pages 571-576, February.
    4. Zang, Haixiang & Cheng, Lilin & Ding, Tao & Cheung, Kwok W. & Wang, Miaomiao & Wei, Zhinong & Sun, Guoqiang, 2020. "Application of functional deep belief network for estimating daily global solar radiation: A case study in China," Energy, Elsevier, vol. 191(C).
    5. Chao Chen & Jamie Twycross & Jonathan M Garibaldi, 2017. "A new accuracy measure based on bounded relative error for time series forecasting," PLOS ONE, Public Library of Science, vol. 12(3), pages 1-23, March.
    6. Wassila Tercha & Sid Ahmed Tadjer & Fathia Chekired & Laurent Canale, 2024. "Machine Learning-Based Forecasting of Temperature and Solar Irradiance for Photovoltaic Systems," Energies, MDPI, vol. 17(5), pages 1-20, February.
    7. Duan, Jikai & Zuo, Hongchao & Bai, Yulong & Chang, Mingheng & Chen, Xiangyue & Wang, Wenpeng & Ma, Lei & Chen, Bolong, 2023. "A multistep short-term solar radiation forecasting model using fully convolutional neural networks and chaotic aquila optimization combining WRF-Solar model results," Energy, Elsevier, vol. 271(C).
    8. Edna S. Solano & Carolina M. Affonso, 2023. "Solar Irradiation Forecasting Using Ensemble Voting Based on Machine Learning Algorithms," Sustainability, MDPI, vol. 15(10), pages 1-19, May.
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