A mechanistic and data-driven approach for real-time online determination of ilmenite grade in pulp by X-ray fluorescence

This article addresses the issues of low accuracy and time-consuming processes associated with traditional correction methods for matrix effect in the quantitative analysis of ilmenite grade by proposing a novel correction method based on a combination of mechanistic and data-driven approaches using X-ray fluorescence. By analyzing the modeling features of ilmenite grade, linear known terms and nonlinear unknown terms are identified. A comprehensive recognition of ilmenite grade is achieved by combining the least-squares method with a stochastic configuration network algorithm with block increments. Additionally, the Fisher information matrix is introduced to eliminate redundant nodes during the model establishment of block incremental, thereby reducing the network’s scale and achieving a lightweight model architecture. The practical industrial application demonstrates that the proposed method for estimating ilmenite grade achieves lower mean absolute error and root-mean-square error values, a coefficient of determination closer to 1, and a higher proportion of samples within an acceptable margin of error. These results are superior to other comparative algorithms, significantly enhancing the effectiveness of the ilmenite grade detection model.