Assessment of the possibility of modeling nonlinear multivariable calibration function using artificial neural networks

Abstract

The use of artificial neural networks (ANNs) is considered justified when studying the problems that do not have a generally accepted solution algorithm. One of such problems in X-ray fluorescence analysis (XRF) is a control of the metal content in atmospheric air and air of the working area. Determination of the calibration characteristics is raveled by the lack of standard samples of the composition of aerosols collected on the filter. To solve this problem, synthetic calibration samples (CS) were manufactured as a thin organic film containing a powder material of the known chemical composition. The weight of the film samples varied within a range of 40 – 155 mg to simulate different aerosol loading of the filters and the content of components in them changed 20 – 200 times which corresponds to the samples of real aerosols. The possibility of modeling a nonlinear calibration multivariable function using artificial neural networks was evaluated in analysis of 38 film calibration samples (from 40 to 100 mg). The structure of the neural network, activation functions, learning algorithms have been investigated. Modeling was performed using an academic version of the BaseGroup Deductor analytical platform. It is shown that implementation of the back propagation of errors leads to much higher values of the error of analysis compared to the error of the regression calibration functions, whereas the Resilient Propagation algorithm provides the smallest values of the error of vanadium determination (Sr) in the calibration samples of aerosols. The range of low content of the elements in the training set is determined with a greater error compared to high content range, and therefore, the sigmoid activation function leads to unsatisfactory accuracy of the analysis results, and preference should be given to hyperbolic tangent (tanh).