Air Quality Index Forecasting Based on Quadratic Decomposition and Transformer-BiLSTM—A Case Study of Beijing

Accurate Air Quality Index (AQI) forecasting is crucial for environmental pollution control. However, the strong nonlinearity and pronounced non-stationarity of AQI time series limit the precision of single-model predictions. This paper therefore proposes an efficient new AQI forecasting model. First, the raw AQI sequence is decomposed using Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). This is combined with Sample Entropy (SE) and K-means clustering to reconstruct high-, medium-, and low-frequency sub-sequences. For the high-frequency component, a second decomposition is performed using Variational Mode Decomposition (VMD) optimised by the Crested Porcupine Optimizer (CPO). This forms the basis for constructing a hybrid forecasting model: the CEEMDAN–SE–CPO–VMD–Transformer-BiLSTM model. Finally, the prediction error is corrected via Least Squares Support Vector Machine (LSSVM). Empirical analysis based on AQI data of Beijing in summer 2023 demonstrates that this model significantly outperforms traditional models and single-decomposition models in terms of MAE, RMSE, MAPE, and R² metrics. Cross-seasonal experiments further confirm its excellent predictive performance and robustness across the spring, autumn, and winter. This model provides a new, efficient, and reliable approach for AQI forecasting.