Quantitative Determination of Cd Using Energy Dispersion XRF Based on Gaussian Mixture Clustering-Multilevel Model Recalibration

Energy dispersive X-ray fluorescence (EDXRF) is an efficient, nondestructive, and cost-effective analytical method for the detection of multiple heavy metal elements in soil via X-rays. This method has been extensively applied in rapid on-site screening of soil, indicating a promising market outlook. The analysis accuracy of energy dispersion X-ray fluorescence spectrometry (XRF) for detecting heavy metal in agricultural soils is severely depending on complex matrix effect（such as soil organic matter, soil type, parent material, and texture），thereby posing a challenge in fast and precise monitoring soil contamination. To calibrate the XRF detection, this study proposes a Gaussian mixture clustering-multilevel model (GMC-MLM) to enhance XRF accuracy for Cd in agricultural soils，which considers the interactive effects of organic matter, soil type, parent material, and texture during XRF detection. Using a Gaussian Mixture Clustering Model (GMC) to pre-classify the sample detection results, we adopt laboratory measurements as the true values and employ a multi-level modeling (MLM) approach for integrated modeling. This approach aims to further eliminate residual errors in the quantitative analysis of instrumental detection. Additionally, to address the complexity of soil matrices in different regions, we propose a technical method for constructing XRF detection corrections localized knowledge bases to address the inconsistency of modeling parameters across regions. Hilly cultivated land was designated as the experimental area in Hubei Province, China. A total of 350 soil samples were collected to ensure uniform spatial distribution across the region, which covers approximately 3,855 km². These samples encompass 4 categories of parent materials, 7 soil types, and 3 texture types. To verify the effectiveness, a comparative analysis was conducted with conventional calibration methods, including linear regression, random forest and support vector machine. The results demonstrate that the Gaussian Mixture Clustering-Multilevel Model (GMC-MLM) can effectively disentangle the nested distribution characteristics of XRF detection errors. The correlation coefficient between the XRF detection results and ICP-MS test results for the corrected samples can reach 0.9085, with 74% of the corrected samples having a relative error of less than 30%. When the number of knowledge base sample points is 50, the RMSE (Root Mean Squared Error), and REM (Relative Error of Mean) are 0.7347, 3.7014%, respectively. It can be observed that the model has good extrapolation capability, and with the increase in the number of knowledge base sample points, the correction effect based on the knowledge base gradually stabilizes. This knowledge base-based GMC-MLM calibration method not only can be embedded into XRF detection instruments to correct XRF detection results in different regions of China but also provides theoretical support for the establishment of a nationwide soil sample knowledge base. This study also provides technical references for the popularization and application of EDXRF in on-site detection of farmland soils.