An integrated BLS-Net optimized with dual PCA and improved PSO-CARS variable selection strategy to determine heavy...

Combining machine learning with X-ray fluorescence (XRF) spectroscopy is a promising solution for quantitatively analyzing heavy metal elements in soil. However, the implied linear and nonlinear interferences between spectral intensities and elemental concentrations are difficult to quantify by a single model, thus degrading the prediction performance for low-concentration elements. This paper presents a novel combined spectral variable selection and fusion modeling framework for quantitative analysis of heavy metal elements in soil XRF, which consists of the proposed Particle Swarm Optimization-based Competitive Adaptive Re-weighted Sampling (PSO-CARS) by adaptive decay strategy and Dual Principal Component Analysis-based broad learning system (BLS-Net). The proposed method is compared with advanced machine learning methods by predicting the concentrations of Cr, Cd, Cu, and Pb. The results show that PSO-CARS provides more efficient characteristic and auxiliary spectral variables for BLS-Net. BLS-Net precisely quantified concentrations of heavy metal elements by distinguishing between linear and nonlinear responses in spectra, resulting in average predictive coefficients of determination (R²) exceeding 0.995 of the different elements. The proposed method is a competitive spectral quantitative fusion modeling solution, offering a more precise and reliable analysis of heavy metal elements.