The method of processing information obtained from the investigation of the steel sample surface in the case of unrepresentative data

To study nonmetallic inclusions – harmful impurities formed during melting and crystallization of steel, a polished section plain is prepared from the sample of the metal being studied. The sections of the inclusions by the section plain are examined by a microscope. The possible sizes of the inclusion sections are divided into intervals and the number of the inclusion sections falls into each such interval is calculated. The dependence of the number of the inclusion sections on the size must be a monotonically decreasing function. However, the researcher may encounter a case where this is not performed. For example, in some size ranges, there are no sections at all (although there are sections in the higher ranges). If such data are applied known techniques for determining the numbers and sizes of inclusions (which formed these sections), then in some ranges negative amounts of inclusions will be obtained. This can happen when the numbers of the inclusions are small and the unlikely case of a cut is realized. In this paper, a technique is proposed that allows, despite this, with some error, to estimate the true quantities and the sizes of the nonmetallic inclusions in the metal volume. A numerical method of conditional optimization is applied.