A Hybrid Air Quality Prediction Model Integrating KL-PV-CBGRU: Case Studies of Shijiazhuang and Beijing

Accurate prediction of the Air Quality Index (AQI) is crucial for protecting public health; however, the inherent instability and high volatility of AQI present significant challenges. To address this, the present study introduces a novel hybrid deep learning model, KL-PV-CBGRU, which utilizes Kalman filtering to decompose AQI data into features and residuals, effectively mitigating volatility at the initial stage. For residual components that continue to exhibit substantial fluctuations, a secondary decomposition is conducted using variational mode decomposition (VMD), further optimized by the particle swarm optimization (PSO) algorithm to enhance stability. To overcome the limited predictive capabilities of single models, this hybrid framework integrates bidirectional gated recurrent units (BiGRU) with convolutional neural networks (CNNs) and convolutional attention modules, thereby improving prediction accuracy and feature fusion. Experimental results demonstrate the superior performance of KL-PV-CBGRU, achieving R2 values of 0.993, 0.963, 0.935, and 0.940 and corresponding MAE values of 2.397, 8.668, 11.001, and 14.035 at 1 h, 8 h, 16 h, and 24 h intervals, respectively, in Shijiazhuang—surpassing all benchmark models. Ablation studies further confirm the critical roles of both the secondary decomposition process and the hybrid architecture in enhancing predictive accuracy. Additionally, comparative experiments conducted in Beijing validate the model’s strong transferability and consistent outperformance over competing models, highlighting its robust generalization capability. These findings underscore the potential of the KL-PV-CBGRU model as a powerful and reliable tool for air quality forecasting across varied urban settings.