New input selection procedure for machine learning methods in estimating daily global solar radiation

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Selection of optimal model inputs is a challenging issue particularly for non-linear and dynamic systems. In this study, a new input selection method, procrustes analysis (PA), was implemented and compared with gamma test (GT) for estimating daily global solar radiation (Rs). The PA and GT were applied for modeling with the non-linear models of artificial neural networks (ANNs) and support vector machines (SVMs). Goodness-of-fit of the models was evaluated by the coefficient of correlation (CC), root-mean-square error (RMSE), and Nash-Sutcliffe model efficiency coefficient (NS). The uncertainty of the model outputs was determined using 95PPU% (p-factor) and d-factor. In this study, we used maximum wind speed, mean wind speed, maximum temperature, minimum temperature, mean temperature, maximum sea surface pressure, minimum sea surface pressure, mean sea surface pressure, mean vapor pressure, total rainfall, maximum cloudiness, mean cloudiness, maximum humidity, minimum humidity, mean humidity, sunshine hours, evaporation, mean dew point temperature, mean wet point temperature, maximum air pressure, minimum air pressure, mean air pressure, and mean vapor saturation as input variables. Maximum and mean temperature; maximum wind speed; maximum, minimum, and mean sea surface pressure; maximum, minimum, and mean air pressure; mean vapor pressure; mean cloudiness; mean humidity; sunshine hours; mean dew point temperature; mean wet point temperature; and mean vapor saturation pressure were identified as significant input variables by GT in five or more of the eight studied stations. Also, mean air pressure, mean cloudiness, and mean temperature were identified as significant input variables for Rs modeling by the PA method for more than four stations. Results indicated that although ANN-GT and SVM-GT showed better goodness-of-fit metrics, ANN-PA and SVM-PA had lower uncertainties for estimating Rs. According to the obtained results, almost all models showed that the higher the bandwidth (95PPU or P-factor), the greater the d-factor, and the lower the bandwidth, the lower the d-factor, SVM-PA has the lowest uncertainty among the four models. So, it can be seen that the lowest bandwidth also belonged to the SVM-PA model for Kiashahr with a P-factor of 0.8% and a d-factor of 0.06, although the Aliabad-E-Katoul had the lowest d-factor of 0.017 and a p-factor of 1%. The highest d-factor belonged to the ANN-GT model for a Bandar-E-Torkman with a d-factor of 0.817 and a p-factor of 76%. One reason for the high uncertainty in this model might be due to the number of input variables selected by the GT. Lower uncertainty is a major scale for choosing the optimal model for solving a given problem, suggesting results of the SVM-PA model with lower uncertainty are more reliable.