Comparison of support vector machine and copula-based nonlinear quantile regression for estimating the daily diffuse solar radiation: A case study in China

In this paper, three kinds of models, including support vector machine-firefly algorithm (SVM-FFA), copula-base nonlinear quantile regression (CNQR) and empirical models were developed for daily diffuse radiation (H-d) estimation. The meteorological data during 1981-2000 and 2001-2010 of Lhasa, Urumqi, Beijing and Wuhan in China were used for model training and validation, respectively. Five combinations of meteorological data: (a) clearness index (K-t); (b) sunshine ratio (S); (c) K-t and S; (d) K-t, S and average temperature (T-a); (e) K-t, S, T-a and average relative humidity, were considered for simulation. The results showed that for the training phases, SVM-FFA outperformed the corresponding models while empirical models performed slightly better than corresponding CNQR models. For validation phases, CNQR and SVM-FFA models performed much better than empirical models. Compared CNQR and SVM-FFA, SVMFFA performed slightly better than CNQR models with average MABE decreased by 0.67% (0.01 MJm(-2)d(-1)) and average R-2 increased by 0.43% (0.004). For the training time, SVM-FFA (1.68 s) showed less computational costs than CNQR (6.68 s); but the parameter optimization time of SVM-FFA (4.9 x 10(5) ) were 10(5) times as much as CNQR. Thus, the overall computational costs of SVM-FFA during training phases were much higher than CNQR. Considering the trade-off between accuracy and computational costs, CNQR were highly recommended for the daily H-d estimation. (C) 2019 Elsevier Ltd. All rights reserved.