Evaluation of the effectiveness of the hyperplane method in the problem of partial identification of an unknown substances

V. G. Nazarov

Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 2, pp. 222-239

Résumé

The problem of partial identification of a homogeneous medium of unknown chemical composition is investigated. The medium is subjected to repeated transillumination by X-ray fluxes collimated in energy and direction. According to the results of measuring the flux density of radiation entering and leaving the medium, it is necessary to establish the difference in the chemical composition of the medium from some in advance given substances. It is assumed that the measurements of radiation fluxes contain errors for which their maximum relative values are known. As a mathematical basis for the study the method of hyperplanes proposed earlier by the author is taken. The results of numerical calculations performed for problems of various dimensions and for a number of groups of specific chemical elements. Numerical estimates have been obtained for several groups of organic substances, under which any two substances will be successfully distinguished from each other by the results one single measurement experiment on transillumination. Using the hyperplane method in the identification problem for groups of organic substances showed enough high efficiency. As a result of computer calculations, it is shown that that any of the 1287 considered pairs of organic substances is well distinguishable if the total relative measurement error of the probing radiation flux does not exceed 9.726 %. The analysis of the dependence of the mass attenuation coefficients of radiation from the atomic number for all chemical elements of the periodic system has been carried out and conclusions about the behavior of the identification accuracy with an increase in the dimension of the problem were done. A justification is given that the hyperplane method will be effective in solving the problem of identification for other groups of chemical elements and identification accuracy does not get worse as the dimension of the problem increases.