Geomaterials, 2012, 2, 24-27
http://dx.doi.org/10.4236/gm.2012.21004 Published Online January 2012 (http://www.SciRP.org/journal/gm)
Information Estimation on Extraction and Contents of
Technological Redistribution at Steel Production
Kazhikenova Saule
Karaganda State University, Karaganda, Kazakhstan
Received October 13, 2011; revised November 20, 2011; accepted December 19, 2011
ABSTRACT
The work suggests a formula for estimating complex indeterminancy of a group of technological operations undergoing
analyses before and after their improvement, as well as technological schemes as a whole in the information units. The
formula allows to estimate the complex indeterminancy of a group of technological operations undergoing analyses, as
well as technological schemes as a whole, which will result in determining predictability and technological reliability of
these operations.
Keywords: Entropy; Information; Hierarchical Systems; Technological Products; Technological Processes; Number of
Levels
1. Introduction
Technical and technological modernization of industry is
closely connected with the development of new and im-
provement of known technologies, reduction of the en-
ergy expenses on production of the product, increasing of
production efficiency. The world industry, having con-
centrated in itself enormous a great number of enterprise
on mining of ore, melting and conversion of black and
non-ferrous metals, chemical and machine-building com-
plexes, plants of precise mechanical engineering, appli-
ance-engineering and radio electronics must receive the
further development. To study the regularities of the pro-
cesses of enrichment, extraction, reception, refining of me-
tals, as well as processes, connected with the change in
contents, structure and characteristic of alloys and mate-
rials in metallurgy physic-chemical and mathematical
methods of the research are used. The Improvement of
the technological processes with considering of the raw
materials complex in structure is impossible on the only
base of traditional methods of the opening the causal
relationships in processes of the general technological sche-
me with analysis of their material and heat balances. The
additional analysis of these processes is necessary on
base of information entropy by Shannon; the reason for it
is to integrate disembodied hitherto factors on extraction
of valuable components and their contents in final prod-
ucts on redistribution and on technological scheme as a
whole with the following use of this method for analysis
and comparative estimation at chemist-metallurgical pro-
duction. In this connection using as a base the informa-
tion entropy by Shannon we designed a method of inte-
grating disembodied hitherto factors on extraction of
valuable components and their contents in final products
on redistribution and on technological scheme as a whole
with the following using of this method for analysis and
comparative estimation of chemist-metallurgical produc-
tion. As original data we used reference materials on con-
tents and extraction of elements, published in brief guide
to metallurgy of the non-ferrous metals by the authors
Gudima N. В., Shein I. P. [1] and the most recent refer-
ence book under editing by M. E. Dritza [2] on the char-
acteristics of elements in two volumes, where all the lat-
est data from foreign reference book, monograph and
scientific articles are taken into account. With the aim to
conduct the comparative analysis of the competitive sche-
mes or improving operations taken apart on united gen-
eralized criterion of complex completeness, as well as un-
certainty, we shall consider usage of the formula by Shan-
non for determination of the information balance of the
production processes by means of factors of the extrac-
tion and contents of copper. For entropy-information an-
alysis of any object the formula by Shannon for expres-
sion of the uncertainty of the system is broadly used [3]:
2
1
log
N
ii
i
pp



11
N
i
ip

H
(1)
where pi is a probability of the finding of any uniform
system element in their multitude N;

i
p
1, 2,...,iN
,
0,

.
2. Decision Problem
As a characteristic of probability of finding the main sys-
C
opyright © 2012 SciRes. GM

K. SAULE 25
tem element it is possible to take its contents expressed
in fractions of the unit. For instance, this is the contents
of extracted chemical element ferric in corresponding
products. The same is true for the process of the extrac-
tion of the element into one or another product, since in
this case factor of the extraction is identical to probability
of the transition of the given element from one state of
the system into another. Both these factors—contents and
extraction—can be used at equal degree for estimation of
the uncertainty in product quality or technological opera-
tion. Then for the single controlled system element we
use common mathematical calculations for expression of
the information uncertainty as follows. If p is a prob-
ability of finding of the controlled element in product or
transition at extraction, then uncertainty or unexpected-
ness of each of these events is a reciprocal from its de-
termined identification that is 1/p. In our variant of the
estimation of uncertainty in the behavior of the only one
system element this uncertainty is expressed by follow-
ing formula:
22
1ln
gln 2
p
plog loH
p
 (2)
Let’s define the quality of technological redistribution
and distributed products on the grounds of comparing
analysis of the competitive schemes on united general-
ized criterion of complex uncertainty and completeness
of the technological scheme of steel production by do-
main process and direct reception ferric. Since the extrac-
tion of any component is pro rata to its contents in source
material and back pro rata to its contents in product then
in the first approximation extraction of ferric from terres-
trial cortex in ore resources is possible to estimate on
correlation:
з..
..
100%
к
рм



0
 (3)
where 0

, a factor of the extraction at zero level of te-
chnological scheme,
з.к.
.рм.

, a factor of the contents in ore resources.
Since for ferric
0
n
ki
i

, a factor of the contents in terrestrial cortex;
H
H



(4)
оn the grounds of information formula by Shannon (2)
we shall conduct entropy-information analysis of each
technological redistribution for calculating the complex
uncertainty and completeness of the technological sche-
me as a whole on example of steel production. Having
received characteristic of complex uncertainty of the te-
chnological scheme it is possible by means of turned
formula


expln 22k
H
kk the parts of the unit
(p.u.). (5) find corresponding to it characteristics of com-
plex certainty of the technological scheme [4] steel pro-
duction.
pH  
The results of comparative calculations on redistribu-
tions and on technological scheme of steel production by
domain process as a whole are presented in Table 1, by
direct reception of ferric in Table 2. The Comparing of
calculating data on new model (2), (5) with practical data
(Tables 1 and 2) let’s illustrate graphically in coordinates
in accordance with (Figure 1). At comparison of refer-
ence data on extraction and contents of the target com-
ponent of technological organization of steel production
by domain process (Tab le 1 ) with new model (2), (5) we
revealed adequate correlation (R = 0,847942, tR =
6,035314 > 2) for system determination, much higher for
level determination (R = 0.991408, tR = 115.8812 > 2). At
comparison of reference data on extraction and contents
of the target component of technological organization of
steel production by direct reception of ferric (Table 2)
with new model (2), (5) we revealed identical correlation
(R = 0.733544, tR = 3.176112 > 2) for system determina-
tion and (R = 0.96213, tR = 25.89614 > 2) for level de-
termination. Calculations offered by us for information
analysis of steel quality and metallurgical redistribution
of the conversion of ferric already in the first approxima-
tion correlate with dynamics of raise of deterministic con-
stituting in abstract hierarchical system.
Table 1. Information estimation on extraction and contents of technological redistribution at steel production by domain
process.
Factors of the contents Factors of extraction
Technological redistributions α H
α bit β H β bit Hαβ pαβ
Mining 0.5000 1.0000 0.1020 3.2934 4.2934 0.0510
Enrichment 0.6550 0.6104 0.8700 0.2009 0.8113 0.5696
Domain melting 0.8830 0.1795 0.9910 0.0130 0.1925 0.8751
The Smelting 0.9550 0.0664 0.9980 0.0029 0.0693 0.9531
Re-melting 0.9950 0.0072 0.9990 0.0014 0.0086 0.9940
Refining 0.9999 0.0001 0.9999 0.0001 0.0002 0.9998
Hk bi t - 1.8636 - 3.5117 5.3753 -
pk p.u 0.2748 - 0.0877 - - 2.4087 × 10–2

K. SAULE
26
Table 2. Information estimation on extraction and contents of technological redistribution of steel production by direct re-
ception of ferric.
Factors of the contents Factors of extraction
Technological redistributions α Hα bit β Hβ bit Hαβ pαβ
Mining 0.5000 1.0000 0.1020 3.2934 4.2934 0.0510
Enrichment 0.7140 0.4860 0.8920 0.1649 0.6509 0.6368
Plating 0.9800 0.0291 0.9950 0.0072 0.0363 0.9751
The Smelting 0.9910 0.0130 0.9980 0.0029 0.0159 0.9890
Re-melting 0.9950 0.0072 0.9990 0.0014 0.0086 0.9940
Refining 0.9999 0.0001 0.9999 0.0001 0.0002 0.9998
Hk bi t - 1.5354 - 3.4699 5.0053 -
pk p.u 0.3449 - 0.0902 - - 3.1131 × 10–2
(a) (b)
Figure 1. Dependency of the information estimation of the factors on extraction and contents from level of the technological
scheme of steel production. a) Domain process; b) Direct reception of ferric; n: number of level; d- determination; 1: Sy stem
determination, 2: level determination; points: prac tic al data.
Thereby, intercoupling is set between technological
factors on extraction and contents of ferric with probabil-
ity of its transition and finding on every level and on te-
chnological scheme as a whole at steel production by
domain process and by direct reception of ferric on the
grounds of analysis of entropy-information characteris-
tics.
With the aim to improve steel-melting production spe-
cialists from many leading metallurgical companies of
the world continue to investigate ecological safe and che-
aper technology of steel melting. Last years in the world
steel branch they have been actively searching for prof-
itable technology, capable to substitute the traditional
process of steel production by means of domain stoves
and oxygen convertor. But, as we predict the domain pro-
cess of steel production will prevail on any other process
of steel reception. Such is information estimation of cer-
tainty at realization of the technological schemes which
can be used for comparison of their state before and after
the improvement alongside with base characteristics of
the complex uncertainty.
3. Conclusions
1) For the information analysis of quality of technolo-
gical products and processes of their reception quantita-
tive estimations of value of the information can be made
only after the preliminary arrangement what exactly in
each concrete case has value for considered metallurgical
processes [5-9].
2) Use of the measure of certainty and uncertainty of
the information allows to analyze the general mechani-
sms of entropy-information laws of the technological re-
partitions being a fundamental basis of all spontaneously
proceeding processes of accumulation of the information
which result in self-organizing technological processes,
namely, to hierarchical systems. For multilevel hierarchi-
cal system of technological repartition it is important to
describe the subordinate level as interaction of the inter-
connected subsystems, each of which possesses the in-
formation properties. Therefore at reception of an infor-
mation estimation main attention is inverted on into-level
and intra-level interactions. The considered approach, in
our opinion, fully complies with the basic requirements
of the system entropy-information analysis as while mo-
deling hierarchical system of technological processes it
provides integrity of its consideration due to the general-
theoretical and methodical concepts allowing to keep in
sight the system as a whole entirely for the solution of a

K. SAULE 27
task at all levels of hierarchical system.
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