Combining a physics-informed broad learning system and multimodal spectral fusion for accurate analysis of chromium speciation in tailings

Abstract

A novel analytical framework is presented that combines a physics-informed broad learning system network (PI-BLS-Net) with multimodal spectral fusion to enable rapid, low-cost, and interpretable chromium speciation in industrial tailings. The PI-BLS-Net integrates visible–near-infrared (vis-NIR) and X-ray fluorescence (XRF) spectral data, transforming one-dimensional spectra into two-dimensional images via Gramian Angular Field (GAF) techniques to enhance feature extraction. Discriminative features are learned from the fused spectral images using a Principal Component Analysis Network (PCANet), with key geochemical parameters (measured pH and Eh) and physicochemical constraints—such as redox equilibrium and mass balance based on the Nernst equation—explicitly embedded into both the model architecture and its loss function. This approach enables accurate quantification of Cr(III) and Cr(VI) concentrations in rare earth tailings, supporting scientific waste classification and risk assessment. Validation on 218 tailings samples demonstrates that the PI-BLS-Net achieves excellent performance in classifying tailings hazard based on chromium speciation, with an accuracy of 89.5%, F1-score of 89.0%, and area under the receiver operating characteristic curve (AUC) of 0.95 on an independent test set. Ablation studies further confirm the significant contributions of spectral-to-image transformation, multimodal fusion, PCANet feature extraction, and especially the physics-informed module to overall model performance. This work provides a rapid, interpretable, and robust approach for pollutant speciation analysis in complex matrices, offering valuable technical support for the scientific management and environmental risk assessment of Cr-bearing tailings.