Hybrid Linear–Nonlinear Model with Adaptive Regularization for Accurate X-Ray Fluorescence Determination of Total Iron Ore Grade

In mineral processing and metallurgy, total iron grade serves as a critical indicator guiding the entire production chain from crushing to smelting, directly influencing the quality and yield of steel products. To address the limitations of conventional matrix effect correction methods in X-ray fluorescence (XRF) analysis—such as low accuracy, high time consumption, and labor-intensive procedures—this study proposes a novel hybrid model (DSCN-LS) integrating least squares (LS) with dynamically regularized stochastic configuration networks (DSCNs) for total iron ore grade quantification. Through feature analysis, we decompose the grade modeling problem into a linear structural component and nonlinear residual terms. The linear component is resolved by means of LS, while the nonlinear terms are processed by the DSCN with a dynamic regularization strategy. This strategy implements node-specific weighted regularization: weak constraints preserve salient features in high-weight-norm nodes, while strong regularization suppresses redundant information in low-weight-norm nodes, collectively enhancing model generalizability and robustness. Notably, the model was trained and validated using datasets collected directly from industrial sites, ensuring that the results reflect real-world production scenarios. Industrial validation demonstrates that the proposed method achieves an average absolute error of 0.3092, a root mean square error of 0.5561, and a coefficient of determination (R2) of 99.91% in total iron grade estimation. All metrics surpass existing benchmarks, confirming significant improvements in accuracy and operational practicality for XRF detection under complex industrial conditions.