Application of Entropy Theory and Principal Component Analysis to Determine Input Variables for Estimating Solar Radiation using Machine Learning Algorithms

Solar radiation is crucial in energy balance models and plant growth simulations. This research investigates the performance of Principal Component Analysis (PCA) and Shannon Entropy Theory (ENT) in determining the input for machine learning models – Random Forest (RF), Linear Regression (LR), Support Vector Regression (SVR), K-Nearest Neighbors (KNN), Decision Tree (DT), and XGBoost (XGB) – for estimating solar radiation at the Yazd synoptic station between 2006 and 2023. Daily data for average temperature, minimum temperature, maximum temperature, sunshine hours, relative humidity, and solar radiation were obtained from the Meteorological Organization. Extraterrestrial radiation, the relative Earth-Sun distance, solar declination angle, and maximum sunshine hours were calculated using existing formulas and selected as inputs for the pre-processing methods. The results of machine learning algorithms indicated their acceptable accuracy in estimating solar radiation. By reducing the dimensionality of the input data to the machine learning algorithms, the results showed that the Principal Component Analysis (PCA) method increased the model's accuracy. Among the models used, the PCA-SVR model showed the best result at the Yazd station with a coefficient of determination of 0.923 and an accuracy of 92.84%. It is worth mentioning that the Shannon entropy theory method failed to improve the modeling results compared to the method without initial pre-processing. This analysis shows that using dimensionality reduction techniques and selecting appropriate models can lead to greater accuracy and less computational complexity in prediction problems. However, sufficient care should be taken when selecting a pre-processing model for the initial data.