A combination of XGBoost and neural network in LIBS spectrum processing for precise determination of critical elements in 620 iron ore samples of various origins

China is the worldwide largest importer of iron ores for supplying its iron and steel industries. The necessary inspections of iron ores not only concern total iron content but also involve minor elements, such as silicium, aluminum, magnesium, and calcium. Laser-induced breakdown spectroscopy (LIBS) promises in situ and on-site detection and analysis capabilities, which is required for efficient, reliable, and large-scale impartation inspections. Such opportunity represents at the same time, a challenge for the technique in terms of the quantitative analysis ability. A fundamental issue corresponds to the matrix effect in LIBS analysis due to a large diversity of iron ores in terms of mineralogical and chemical compositions. Demonstrated as effective to deal with the matrix effect in LIBS analyses of geological materials, the machine learning approach needs to be implemented within an optimized data processing pipeline, combining algorithms carefully chosen and tested. In this work, we developed a sequentially connected combination of an extreme gradient boosting (XGBoost) model and a back propagation neural network (BPNN) model, to effectively fit the functional relation between the concentrations and the spectra. The specificity of the approach consists in fitting the linear, low-order nonlinear, and high-order nonlinear terms in a sequential way to substantially improve the model prediction performances. The method has been developed and tested with a significant set of 620 collected iron ore samples of eight production countries and 35 different commercial brands, with a wide range of matrices in terms of mineralogical and chemical compositions. The samples underwent prior characterization using conventional laboratory analysis methods to establish the reference elemental concentrations. The results from this necessary step of laboratory investigation, with root mean square error for prediction ($\mathrm{RMSEP}$) of 0.407 wt%, 0.372 wt%, 0.085 wt%, 0.131 wt%, and 0.114 wt%, respectively for total iron (TFe), SiO₂, Al₂O₃, MgO, and CaO, show the potential for on-site inspections.