Библиографическое описание:

Чукарина Ю. А., Сопова О. Н., Зуева С. Б., Филимонова О. Н., Вельо Ф. Mathematical Simulation of Industrial Waste Processing // Молодой ученый. — 2012. — №2. — С. 91-94.

The article is devoted to technological and environmental problems in the food industry. Authors suggested a cluster model to serve as a basis for the software, useful at the initial design stage, when it is important to determine the optimal set and sequence of technological operations of organic waste processing.

Key words: cluster model, software, organic waste, food industry, technological scheme.

The problems concerning optimal design of complexes to process organic wastes from food industry have become of the utmost importance in the modern world.

Complexity and controversy of the problem account for the immense diversity of industrial technologies. The choice of the most effective technological line involves a total evaluation of production conditions: waste processing equipment, production areas for modernization of the existing and installation of new equipment, entering and demanding on entering concentrations of contaminants (for example, for industrial effluents), etc. Indeed, technological parameters are calculated according to the optimality criteria: either the most profound effect or the lowest volume. The traditional manual methods of calculation are the main disadvantage of such an approach. As a result, when comparing different options for equipment to install at treatment plants according to technical-economic indicators, only several options out of the substantial amount of the available ones are to be chosen.

The primary purpose of the cluster analysis is to divide a multitude of the researched objects and properties into homogeneous groups and clusters understood as such.

The most considerable advantage of the cluster anaysis lies in the fact that the objects are divided not according to a single parameter but according to the whole set of properties. Such an analysis enables examination of quite a significant amount of information, its abrupt reduction and compression, thus ensuring its transformation into more compact and visual.

The task which the cluster analysis is to perform is the following: on the basis of the data contained in the X multitude the cluster analysis is to divide a multitude of G objects into n (n – the whole) clusters (subset) F1, F2 … so that each Gi object could belong to the only one cluster and be similar, while the objects belonging to different clusters were heterogeneous.

For example, let X be technological schemes that ensure processing of organic waste from food and agriculture industry. Then G (technological scheme ensuring processing of the given form of waste from food and agriculture industry) includes n methods (clusters), any of which is characterized by:

  • Environmental aspect (F2), which includes waste “quality” indicators (COD, content of suspended matters, metal content),

  • Technological aspect (F2), which includes such indicators as duration of treatment process, volumes of secondary wastes product, etc.),

  • Economic aspect (F3), which evaluates the cost of treatment, expected revenues when selling products obtained from the secondary raw materials, etc.

Any technological schemes of treatment is comprised of a certain set (n) of consecutive procedures (methods, equipment) – clusters. Thus, target setting is to determine an optimum set and cluster sequence necessary to select a technological line on the processing in order to minimize the process cost, receive revenues from waste processing and reduce an impact on the environment.

Mathematical model of the clustering problem is to consist of two components:

  1. Mathematical model of the clustering problem concerning a multitude of methods to process waste from food industry.

  2. Mathematical model of creating an optimum processing scheme.

When selecting a processing scheme for waste treatment, which is most suitable under the conditions of production, it is essential to take into account qualitative and quantitative indicators.

Solution algorithm of technological schemes for processing of organic waste from food and agriculture industry is peformed in the Picture 1.

To solve the algorithm a method for calculation of PQ quality index according to the quantitative evaluation of an object [2] is applied.

In order to receive a qualitative evaluation the most significant properties describing the given object are selected, and these properties are provided, for instance, in relation to a dimensionless number. For each property we define a method to adjust its value according to the range from 0 to 1. The above mentioned process is called definition of the PQ quality index value for the given propety.

In order to adjust properties according to the range from 0 to 1 it is necessary to specify an interval of the property values for the situation studied, the best and the worst values from the specified interval, which are later proved. Then normalized value 1 is correlated with the best value, 0 – with the worst one, and any value in the open range from 0 to 1 is correlated to any value from the interval, that is – 0<x<1. This range form 0 to 1 is called range of PQ indicators and a corresponding value – quality index of PQ quality. In the given research 1 was understood as conditionally clean water without any contaminants, 0 – influent wastewater.

To determine PQ value a linear function is arranged for two possible options:

  1. the best quality value is to the left (that is, the less the quality value is, the better it is);

  2. the best quality value is to the right (that is, the bigger the quality value is, the better it is).

Function motion from the best value to the worst one is called quality loss of the fucntion.

Let us analyze formation of cluster model of milk industry wastewater treatment process as an example (Picture 2).



As shown above, Mathematical model of the clustering problem could be as a principle for software, which select optimal treatment process (Picture 3).


Suggested cluster model can be recommended for application during the initial phase of design process, when it is necessary to choose the most effective waste treatment technological line for any industry out of a multitude of options. The model is characterized by modularity. As soon the rules are changed or updated, or when the new equipment is used, these rules and equipment are included into the data bank without any changes made in the structure on the whole.


  1. Cluster analysis. [Electronic resource] : Moscow, 2010. – Access mode: http://www.statsoft.ru/home/textbook/modules/stcluan.html - Title from the screen.

  2. Svatovskaya, L.B. New eco-protective technologies and their evaluation. PQ index [Text] / L. B. Svatovskaya, Т. S. Titova, А. V. Khitrova and others. – StP.: Petersburg State Transport University.


Основные термины: waste processing, cluster model, organic waste, PQ quality index, technological line, technological schemes, cluster analysis, food industry, effective technological line, agriculture industry, Industrial Waste Processing, technological scheme, organic waste processing, waste processing equipment, treatment technological line, Вельо Ф. Mathematical, Чукарина Ю. А., // Молодой ученый, Зуева С. Б., process organic wastes


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