Geodesic
The method of processing information obtained from the investigation of the steel sample surface in the case of unrepresentative data
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 6 (2017) no. 4, pp. 20-27 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Keywords: information processing, crystallography, nonmetallic inclusions, stereology, optimization. 
@article{VYURV_2017_6_4_a1,
     author = {A. D. Drozin and N. M. Yaparova},
     title = {The method of processing information obtained from the investigation of the steel sample surface in the case of unrepresentative data},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
     pages = {20--27},
     year = {2017},
     volume = {6},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURV_2017_6_4_a1/}
}
TY  - JOUR
AU  - A. D. Drozin
AU  - N. M. Yaparova
TI  - The method of processing information obtained from the investigation of the steel sample surface in the case of unrepresentative data
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika
PY  - 2017
SP  - 20
EP  - 27
VL  - 6
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VYURV_2017_6_4_a1/
LA  - ru
ID  - VYURV_2017_6_4_a1
ER  - 
%0 Journal Article
%A A. D. Drozin
%A N. M. Yaparova
%T The method of processing information obtained from the investigation of the steel sample surface in the case of unrepresentative data
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika
%D 2017
%P 20-27
%V 6
%N 4
%U http://geodesic.mathdoc.fr/item/VYURV_2017_6_4_a1/
%G ru
%F VYURV_2017_6_4_a1
A. D. Drozin; N. M. Yaparova. The method of processing information obtained from the investigation of the steel sample surface in the case of unrepresentative data. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 6 (2017) no. 4, pp. 20-27. http://geodesic.mathdoc.fr/item/VYURV_2017_6_4_a1/

[1] T. Lipiński, A. Wach, “Size of Non-Metallic Inclusions High-Grade Medium Carbon Steel”, Archives of Foundry Engineering, 14:4 (2012), 55–60

[2] K. Lambrighs, L. Verpoest et al., “Influence of Non-Metallic Inclusions on the Fatigue properties of Heavily Cold Drawn Steel Wires”, Procedia Engineering, 2:1 (2010), 173–181 | DOI

[3] D. Zeng, G. Tian et al., “Fatigue Strength Prediction of Drilling Materials Based on the Maximum Non-Metallic Inclusion Size”, Journal of Materials Engineering and Performance, 24:12 (2015), 4664–4672 | DOI

[4] V. E. Roshchin, A. V. Roshchin, Electrometallurgy and Metallurgy of Steel, Publishing Center of SUSU, Chelyabinsk, 2013, 571 pp.

[5] A. D. Drozin, “The Method of Processing Information about Nonmetallic Inclusions Obtained from the Investigation of the Surface of Finished Steel Samples”, Bulletin of South Ural State University. Series: Computational Mathematics and Software Engineering, 6:4 (2017)

[6] Numerical Methods for Constrained Optimization, ed. P. E. Gill, W. Murray., Academic Press, London, 1974, 303 pp.