title: An algorithm combining neural networks with fundamental parameters
abstract: An algorithm combining neural networks with the fundamental parameters equations (NNFP) is proposed for making corrections for non-linear matrix effects in x-ray fluorescence analysis. In the algorithm, neural networks were applied to relate the concentrations of components to both the measured intensities and the relative theoretical intensities calculated by the fundamental parameter equations. The NNFP algorithm is compared with the classical theoretical correction models, including the fundamental parameters approach, the Lachance-Traill model, a hyperbolic function model and the COLA algorithm. For an alloy system with 15 measured elements, in most cases, the prediction errors of the NNFP algorithm are lower than those of the fundamental parameters approach, the Lachance-Traill model, the hyperbolic function model and the COLA algorithm separately. If there are the serious matrix effects, such as matrix effects among Cr, Fe and Ni, the NNFP algorithm generally decreased predictive errors as compared with the classical models, except for the case of Cr by the fundamental parameters approach. The main reason why the NNFP algorithm has generally a better predictive ability than the classical theoretical correction models might be that neural networks can better calibrate the non-linear matrix effects in a complex multivariate system
keyphrases: algorithm neural networks fundamental parameters fundamental parameters equations Fe x-ray fluorescence analysis intensities NNFP algorithm theoretical correction models Lachance-Traill model hyperbolic function model COLA algorithm alloy system Cr Ni complex multivariate system nonlinear matrix effects