Optimized ensemble deep random vector functional link with nature inspired algorithm and boruta feature selection: Multi-site intelligent model for air quality index forecasting

Air quality index (AQI) forecasting is complex due to its variability, instability, and inconsistent trends resulting from dynamic atmospheric conditions, various contaminants, and interactions between environmental factors. Advanced modeling techniques are needed to accurately forecast AQI values to capture subtle patterns and variations in air quality data. Thus, a new forecasting model is suggested in this study to improve the accuracy of AQI forecasting. The model integrates three-phase decomposition technique, a feature selection approach, and ensemble Deep Random Vector Functional Link (EDRVFL), optimized using adaptive teaching-learning-based optimization and differential evolution (ATLDE). The AQI series was first broken down into a group of intrinsic mode functions (IMFs) with different frequencies using multivariate variational mode decomposition (MVMD). Subsequently, a feature selection method based on the Boruta technique was applied to identify the most significant input variables. Finally, for daily AQI levels forecasting, ATLDE optimized the EDRVFL model (EDRVFL-ATLDE). Three daily AQI series gathered from Chengdu, Wuhan, and Taiyuan in China from January 1, 2018, to December 30, 2022, were used to test and confirm the proposed model via empirical research. Based on the results, the proposed model can yield the superior results for three cities (Chengdu: correlation coefficient (R = 0.987), root mean square error (RMSE = 5.583), Wuhan: (R = 0.987), (RMSE = 3.299), and Taiyuan: (R = 0.996), (RMSE = 4.521)) in China. The experimental findings demonstrated the feasibility of the three-phase hybrid methodology, outperforming all other models regarding forecast accuracy.