An Innovative Approach to the Mathematical Modelling of Filtration Systems for Industrial Pollutants

This study presents a comprehensive framework for the mathematical modelling and optimisation of industrial pollutant filtration systems. By integrating differential-equation-based physical models with deep neural networks (CNNs and RNNs) and distributed sensor networks, the framework enables real-time, adaptive adjustment of filtration parameters, ensuring optimal performance under dynamic industrial conditions. The methodology was applied to datasets capturing fine particulate matter (PM₂.₅, PM₁₀), sulphur dioxide (SO₂), nitrogen oxides (NOₓ), and local meteorological variables, allowing the evaluation of both pollutant concentrations and filtration efficiency. Results demonstrate significantly improved particulate capture, reduced emissions of toxic gases, and enhanced operational efficiency compared with conventional filtration systems. Experimental validation using field-deployed sensors confirmed the model’s predictive accuracy, robustness, and capacity to generalise to unseen conditions. Sensitivity analyses highlighted the dominant influence of filter efficiency and airflow on pollutant removal, supporting targeted optimisation strategies. The proposed framework offers a scalable, data-driven tool for intelligent industrial filtration, enabling adaptive control, compliance with environmental regulations, and mitigation of public health risks. By combining rigorous modelling, machine learning, and real-time sensor data, this approach provides actionable insights for sustainable industrial practices and informs policy-making for effective air quality management.