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In recent decades, the integration of solar energy sources has gradually become the main challenge for global energy consumption. Therefore, it is essential to predict global solar radiation in an accurate and efficient way when estimating outputs of the solar system. Inaccurate predictions either cause load overestimation that results in increased cost or failure to gather adequate supplies. However, accurate forecasting is a challenging task because solar resources are intermittent and uncontrollable. To tackle this difficulty, several machine learning models have been established; however, the forecasting outcomes of these models are not sufficiently accurate. Therefore, in this study, we investigate ensemble learning with square root regularization and intelligent optimization to forecast hourly global solar radiation. The main structure of the proposed method is constructed based on ensemble learning with a random subspace (RS) method that divides the original data into several covariate subspaces. A novel covariate-selection method called square root smoothly clipped absolute deviation (SRSCAD) is proposed and is applied to each subspace with efficient extraction of relevant covariates. To combine the forecasts obtained using RS and SRSCAD, a firefly algorithm (FA) is used to estimate the weights assigned to individual forecasts. To handle the complexity of the proposed ensemble system, a simple and efficient algorithm is derived based on a thresholding rule and accelerated gradient method. To illustrate the validity and effectiveness of the proposed method, global solar radiation datasets of eight locations of Xinjiang province in China are considered. The experimental results show that the proposed RS-SRSCAD-FA achieves the best performances with a mean absolute percentage error, root-mean-square error, Theil inequality coefficient, and correlation coefficient of 0.066, 20.21 W/ , 0.016, 3.40 s, and 0.98 in site 1, respectively. For the other seven datasets, RS-SRSCAD-FA still outperforms other approaches. Finally, a nonparametric Friedman test is applied to perform statistical comparisons of results over eight datasets.

Global Solar Radiation Forecasting Using Square Root Regularization-Based Ensemble