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ANALYSES OF MANUFACTURING PROCESS ON ZHEZKAZGAN AND BALKHASH COPPER-SMELTING PLANTS

Kazhikenova S.SH.

Perfection of manufacture of copper considering the growing poor and complex-structured raw material is impossible only on a basis of traditional methods of opening the relationships of cause and effect during the general technological circuit. These methods require additional probable aspects which are taking into account casual character of the valid transformations of substance during a course of realization of the technological circuit with relation to both the basic product, and to accompanying valuable or harmful impurity. For a multilevel hierarchical system of technological repartition it is important to describe a subordinate level as interaction of the interconnected subsystems each of which possesses the information properties. Therefore at reception of information estimation the basic attention is inverted on introlevel and interlevel interactions. The considered approach, in our opinion, fully complies with the basic requirements of the systematic entropy-information analysis as while modeling hierarchical system of technological processes it provides integrity of its consideration due to the general-theoretical and methodical concepts allowing entirely keeping in sight all system as a whole for the decision of a task at all levels. Besides, on the basis of the account of basic elements in system and connections between them it provides complete and multifold consideration. The suggested algorithm of simplification at modeling allows to reflect real technological repartition adequately and to take into account determining factors in hierarchical system.

Quantitative estimations of sense and value of the information can be made for the information analysis of quality of technological products and processes of their reception only after the preliminary agreement about what precisely in each concrete case has value and sense for the considered phenomena. Methods of calculation the information suggested by Shannon allow to reveal a ratio of quantity of the predicted information and quantities of the unexpected information which cannot be predicted beforehand, and thus to enable to define a qualitative and quantitative estimation of the certain technological circuit. As a probability of detection of the main element of technological system it is possible to accept its maintenance in a product, expressed in shares of unit.

Let's show how quality of technological products and the technological processes resulting in reception of these products is estimated by results of technological repartitions copper-liquating manufactures on Zhezkazgan and Balkhash copper-smelting plants (CSP) (table 1). So, the maintenance of copper in ore makes 0,5-1,2% (on the average 0,85%), and in concentrates 5,5-40% (on the average 22,75%). Stein of melting in a liquid bath contains 40-55% copper (on the average 47,5%). The basic result of the work carried out on a scientific, technological and technical substantiation of process of converting finally is reduced to an opportunity to increase the maintenance of copper in draft metal. This parameter varies within the limits of 98,6-98,9% (on the average 98,75%). As a result of technological process of anodic melting the parameters of the maintenance of copper in anodes are the following 99,2-99,5% (on the average 99,35%). In process of electrolyte refinements parameters of the maintenance of copper in cathodes make 99,9-99,99% (on the average 99,95%).

Table 1 - The maintenance of copper in products on Zhezkazgan and Balkhash CSP

Repartition	The name	Maintenance	Average value
Extraction	Ore	0,5-1,2%	0,85%
Enrichment	A concentrate	5,5-40%	22,75%
Melting	Stein	40-55%	47,5%
Converting	Draft copper	98,6-98,9%	98,75%
Fire refinement	Anodic copper	99,2-99,5%	99,35%
Electrolyte refinement	Cathode copper	99,9-99,99%	99,95%

For accounting of a various degree of unexpectedness (probability) of events C.Shannon has suggested to use probabilities' function of entropy borrowed from statistical physics, resulted as [1]:

, (1)

where – is a probability of detection in their set , , .

The mathematical description of development of any system is set by the formula:

,

where - weight of technological system; - number of elements of technological system.

The positive second derivative testifies the accelerated development of the system. The essence of this acceleration is that at transition to a higher structural level of technological process the law or a principle of progressive increase of variety comes into effect [2]. In mathematical understanding the principle of increase of variety means the following: with transition to higher structural levels the number of the elements forming the given structural level, having various attributes, increases under the law:

, (2)

where , - number of levels, - length of a code of elements at each level of hierarchical system.

Before the publication of K. Shannon's theory R.Hartly has suggested to define quantity of the information under the formula [3]:

, (3)

where , - number of levels, - length of a code of elements at each level of hierarchical system.

Let - number of elements of - level. - capacity of the information of a zero level of technological system. Then the capacity of the information of -level counting upon one element is expressed by the formula:

.

Information capacity of hierarchical system and n-level are defined by:

, , (4)

where - greatest possible entropy of a system.

Information capacity of technological system is defined by its stochastic part.

The limiting degrees of determination and of ineradicable stochasticity of technological system are defined under the formula:

, ,

where , - a system determined and stochastic componenst, - the system maximal information.

The sense of surplus information is connected to knowledge of technological system, at which the taken information is always less than the information objectively contained in it in the form of the determined ratio. The factor of stochasticity can change from zero to infinite and in more details reflects the stochastic and determined properties of technological system [2]. With the purpose of reception of analytical dependence of maximum stochastic information from the general conditions of formation of technological system from the formula (4) with a method of a mathematical induction we shall deduce the recurrent formula for a finding:

.

At substitution of equality (2) in (4) we shall receive formulas for definition of all kinds of the information of hierarchical system:

, , (5)

, , (6)

, . (7)

In the technological circuit considered by us there is a sample of set of elements - an element and not an element (in our case copper and all other elements in aggregate) then the equation (2) will become:

.

Essentially important advantage of an information estimation of quality of products or technological operations is that a suggested parameter , as well as any entropy-information sizes, can be added. The given property of additive is immanently inherent to entropy and information and is a basis for expression of the law of preservation of their sum. Hence, technological uncertainty of various operations within the limits of the unified circuit can be expressed by a system parameter of uncertainty:

, bit/el.

The determined component of the information on the basis of the theorem 2 is defined by:

bit/el.

As the information capacity of technological system is defined by its stochastic part on the basis (3) we shall receive:

bit/el.,

The system determined component is equal:

bit/el.,

Having defined degrees of determination and ineradicable stochasticity at each level of technological system under formulas [3]:

, ,

let's analyze the received results of the carried out calculations which are submitted in table 2.

Table 2 - Settlement information-entropy characteristics of technological repartitions in hierarchical system for ,

0	0	1,0	0	0	1,0	0
1	1,00	2,0	0,50	1,00	3,0	0,33
2	3,33	4,0	0,83	4,33	7,0	0,62
3	7,67	8,0	0,96	12,0	15,0	0,80
4	15,9	16,0	0,99	27,9	31,0	0,90
5	32,0	32,0	1,0	59,8	63,0	0,95
6	64,0	64,0	1,0	124,0	127,0	0,98
7	128,0	128,0	1,0	252,0	255,0	0,99
8	256,0	256,0	1,0	508,0	511,0	0,99
9	512,0	512,0	1,0	1020,0	1023,0	0,998
10	1024,0	1024,0	1,0	2044,0	2047,0	0,999

1,2 - dependence on new model, points - experimental data

Figure 1 - Dependence of a degree of determination on a level

We shall illustrate the comparison of these data with practical "know-how" of copper (tab. 1) graphically in coordinates (fig. 1). The factor of their correlation () has made 0,8614 at the importance 6,6744>2, and () has made 0,9479 at the importance 7,348>2, that testifies the adequacy of suggested model of an information estimation of quality of products in consecutive operations of the technological circuit.

The size in this case does not influence the solution of a problem as it is reduced at calculation of level and system determinations.

Influence of length of a code that is elements of system (target component and the basic impurity) can be revealed in the further researches. As a whole the improvement of quality of a product in process of its technological processing correlates with dynamics of growth of the determined component in abstract hierarchical system that proves the expediency of the further entropy-information analysis of similar systems.

The literature

1 Shannon C.E. A mathematical theory of communication. Bell System Technical Journal. V. 27, p. 379-423 (1948).

2 Malyshev V.P. Probability-determined display. 1994, Almaty: Fылым, 376p.

3 Kazhikenova S.Sh. A new interpretation of information analysis of quality of technological process and products // Nauka I Studia. Poland.–2009. - Vol. 18. No 6. – pp. 6–13.

4 Kazhikenova S.Sh. The information estimation of quality of metallurgical repartitions // Nauka I Studia. Poland. – 2009. - Vol. 23. No 11. – pp. 21-27.