Deep learning hybrid models with multivariate variational mode decomposition for estimating daily solar radiation

Solar energy is one of the renewable and clean energy sources. Accurate solar radiation (SR) estimates are therefore needed in solar energy applications. Firstly, two deep learning models, including gated recurrent unit (GRU) and long short-term memory (LSTM), were developed in this study. Next, a data pre-processing technique named multivariate variational mode decomposition (MVMD) was used to construct the MVMD-GRU and MVMD-LSTM hybrid models. To better test the performance of proposed simple and hybrid models, four stations located in the Illinois State of the USA (i.e., Dixon Springs, Fairfield, Rend Lake, and Carbondale) were considered as the study sites. Whole the simple and hybrid models were established under two different strategies, i.e., local and external. In the local strategy, SR of each location was estimated using the minimum and maximum air temperatures from the same station. While, minimum and maximum air temperatures as well as SR data from the nearby station were utilized in external strategy to estimate SR time series of any target site. Root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R2) metrics were used when evaluating the models performances. The overall results revealed that the proposed MVMD-GRU and MVMD-LSTM hybrid models illustrated better SR estimates compared to the simple GRU and LSTM in both the local and external strategies. The values of error metrics obtained for the superior hybrid models (i.e., MVMD-LSTM) during the testing period were as: RMSE = 2.532 MJ/m2.day, MAE = 1.921 MJ/m2.day, R2 = 0.916 at Dixon Springs; RMSE = 2.476 MJ/m2.day, MAE = 1.878 MJ/m2.day, R2 = 0.921 at Fairfield; RMSE = 2.359 MJ/m2.day, MAE = 1.780 MJ/m2.day, R2 = 0.924 at Rend Lake; RMSE = 2.576 MJ/m2.day, MAE = 1.941 MJ/m2.day, R2 = 0.914 at Carbondale. Therefore, the coupled models proposed in this study can be possibly recommended as suitable alternatives to the simple deep learning models with a reliable precision in estimating SR time series.