DF-OSELM: a dynamic feedback feature learning model for air quality online prediction

Accurate and timely air quality forecasting is crucial for mitigating pollution risks and protecting public health. However, existing offline and online models face limitations in adaptability, computational efficiency, and interpretability. To address these issues, this study proposes a Dynamic Feedback Feature Learning Online Sequential Extreme Learning Machine (DF-OSELM) for real-time air quality prediction. The model integrates dual Extreme Learning Machine Autoencoders (ELM-AEs) for adaptive adjustment of input and hidden weights, a normalization layer to mitigate covariate shift, and a recurrent feedback mechanism to enhance memory of sequential dependencies. The dataset, comprising 10,000 hourly samples of PM₂.₅, PM₁₀, SO₂, and NO₂ collected from northern China. The model was trained in a fully online manner and evaluated using normalized root mean square error (NRMSE), mean absolute percentage error (MAPE), and coefficient of determination (R²). Experimental results demonstrate that DF-OSELM achieves superior predictive performance, with NRMSE consistently below 0.1 and R² above 0.99, outperforming baseline models. Ablation studies confirm the indispensable roles of normalization and dual autoencoder mechanisms, while uncertainty quantification (via Bayesian ELM and Monte Carlo Dropout) provides reliable confidence intervals. Moreover, SHAP-based interpretability analysis reveals that recent 0-24-h lags are the most influential for predictions, aligning with known air pollution dynamics. With an average online update time under 3 ms and memory usage below 1 GB, DF-OSELM balances accuracy, efficiency, and interpretability, making it highly suitable for real-time monitoring and risk assessment in large-scale environmental platforms.