A novel four-stage hybrid intelligent model for particulate matter prediction

The ubiquitous and deleterious nature of particulate matter (PM) calls for accurate forecasting models to enhance control and management. Accordingly, this study proposed four-stage hybrid intelligent models based on empirical wavelet transform (EWT), variational mode decomposition (VMD), phase space reconstruction (PSR), and multivariate adaptive regression spline (MARS) for PM 10 forecasting. The proposed models, including EWT-VMD-PSR-BPNN, EWT-VMD-PSR-MARS, EWT-VMD-PSR-RBFNN and EWT-VMD-PSR-GMDH, were tested in five different communities using accuracy assessors such as correlation coefficient ( r ), root mean square error (RMSE), normalised root mean square error (NRMSE), the variance accounted for (VAF), performance index (PI) and Taylor diagram. The results showed that the proposed models could predict the PM 10 concentrations to various acceptable accuracies for the five mining communities considered. However, model inter-comparison revealed the supremacy of EWT-VMD-PSR-MARS by producing the best r, RMSE, NRMSE, VAF and PI values in the range of 0.91–0.99, 1.34–4.56, 0.06–0.14, 73.66–97.84%, and 1.5–1.90 respectively for the five studied mining communities. The Taylor diagram also showed the EWT-VMD-PSR-MARS model’s prediction superiority, making it a promising tool for complex time series forecasting.