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The non-stationarity, nonlinearity and complexity of the PM 2.5  series have caused difficulties in PM 2.5  prediction. To improve prediction accuracy, many forecasting methods have been developed. However, these methods usually do not consider the importance of data preprocessing and have limitations only using a single forecasting model. Therefore, this paper proposed a new hybrid decomposition–ensemble learning paradigm based on variation mode decomposition (VMD) and improved whale-optimization algorithm (IWOA) to address complex nonlinear environmental data. First, the VMD is employed to decompose the PM 2.5  sequences into a set of variational modes (VMs) with different frequencies. Then, an ensemble method based on four individual forecasting approaches is applied to forecast all the VMs. With regard to ensemble weight coefficients, the IWOA is applied to optimize the weight coefficients, and the final forecasting results were obtained by reconstructing the refined sequences. To verify and validate the proposed learning paradigm, four daily PM 2.5  datasets collected from the Jing-Jin-Ji area of China are chosen as the test cases to conduct the empirical research. The experimental results indicated that the proposed learning paradigm has the best results in all cases and metrics.

Research on a Novel Hybrid Decomposition–Ensemble Learning Paradigm Based on VMD and IWOA for PM2.5 Forecasting