### Система керування процесом заключного очищення дифузійного соку з використанням методів тензорного аналізу

#### Анотація

**THE METHOD OF TENSOR ANALYSIS FOR USING IN PROCESS CONTROL SYSTEM FINAL EXTRACT PURIFICATION**

*V. Sidletskyy,**N. Fedorych*

To one of the main stages of the final juice purification section includes a second saturation - a stage of purification of juice with lime and carbon dioxide from netsukriv (juice purifying section). Scheme juice purification at the site of the second carbonation consists of the following operations: heating; hot defecator; second carbonation device.

That is, depending on the quality of the processed beet production process and technology mode will be selected to achieve the appropriate quality indicators juice output apparatus of the second carbonation and technical and economic performance of the enterprise.

Changes in the process also impose requirements for control systems that site.

For juice purification process characterized by a significant variation, but given the variability related to the process. The same situation is in relation to the control system.

For the second saturation characteristic are several approaches to control most widespread scheme of control supply lime milk the ratio of costs to supply juice and carbonation gas called pH deviation at the output of the saturator. The best indicators of regulation when carbonation gas is fed by the ratio of juice to the amount of gas for pH correction and output the content of CO2 carbonation gas.

To select a method of controlling and setting regulators need clear understanding of the process: physical and chemical composition, the time of its passage, inertia, transportation delays the process. That is why the control process is widely used simulation of the process and process control. Using models makes understanding the causes and effect relationships, and facilitates the selection of management approaches. Now for modeling widely used methods of differential and algebraic equations, but developed a model should consider all input and output parameters of the process; able structural changes (ie able to include or exclude certain elements of the model are associated with the work of some technological devices); to respond to changing range of control actions; consider previous processes and be able to integrate into the following model calculations or control actions. That is the model of juice purification process and control the process should take into account all the possible work and provide the opportunity for analysis and solutions.

Therefore, in this paper the methods of the tensor analysis to develop a model components and perform calculations management system juice purification process. Tensor analysis simplifies the modeling process virtually any area by introducing categories multidimensional space. Developed tensor model allows to describe all tasks regardless of their complexity.

Tensor generalizes the notion of scalar, vector and matrix. This transformation rules tensor components are arranged so that we can design new tensors available on some simple rules.

Tensor analysis and tensor decomposition have been used for the development of neural networks, artificial vision systems design, signal processing, data processing and analysis.

First tensor - a mathematical object that does not depend on changing the system of coordinates, but its components by changing the coordinate system transformed by certain mathematical laws. From tensor closely related to its rank and it can be: zero, first, second and so on rank. Tensor of zero rank - a scalar and is the result of direct measurement parameters such as temperature, density, flow, pressure, etc. More sophisticated measurements such as spectroscopy provides a set of parameters that can be set as a vector - a tensor of the first rank. In two-dimensional space tensor of the second rank easiest represented as a matrix describing the heterogeneity of a given space, and operates on the input vector, changing its direction and scale. Generally, for the analysis of complex data n-th order tensor formed n-th rank is used to simulate the functions of a large number of variables.

The theory of tensor analysis simplifies modeling laws for almost any area by introducing categories multidimensional space. It allows you to describe all surfaces regardless of their complexity. Tensor analysis and tensor decomposition have been used in many fields, such as neural networks, artificial vision systems design, signal processing and data processing and analysis. Tensor analysis is a generalization of the concepts of vector analysis and allows you to combine data sets and complex nature of physical quantities that can not be described or presented in a scalar or vector. Therefore, the use of tensor method for constructing a model of the production process is the most appropriate.

To work with tensors widely used software packages for computers. They can solve the problem of representation and processing of data in a tensor. These software packages are used for signal processing, control systems, neural networks, fuzzy logic, statistical analysis and modeling.

The aim - using tensor analysis techniques to develop components of the model and perform calculations in the control system juice purification process.

Control systems 2nd saturation share on juice pH stabilization system and system optimization for minimum calcium salts. The simplest and most common control scheme 2nd saturation involves stabilizing the pH by changing the gas flow in the unit, but this scheme does not include lime supply device, which significantly affects the quality of regulation. Therefore, this scheme is complemented by regulation ratio "juice - milk of lime", which are used by the regulator divider lime.

Vector output variables to plot defecosaturation have the following components: temperature juice, juice alkalinity, pH, content netsukriv, color juice, juice purity. Like all models, the model will perform tensor transformation vector input parameters in the vector output parameters.

But tensor describes only the process, because in this case you must also specify and control steps for the process, so you need to add vector control, and therefore the basis vectors: limestone milk and carbonation gas flow.

During carbonation juice content of calcium in the solution is maintained minimal, which is suitable for pH juice. That pH is selected based on the content netsukriv juice and its color, but these figures depend on the need and the amount of supply in the second saturation lime milk.

That is, the process of the second saturation values of milk and the pH may be selected within the range of values that vary greatly depending on the juice, which in turn causes the change process and regime change as a result of the control system. Changing the mode will change the basis for the tensor model.

When you change the base change and tensor components. So tensor components to list in accordance with the new base and, consequently, we investigate the results, namely, or creates a new set of numbers tensor.

To use tensor formed as a model process for the automated control systems, in particular for the calculation of management actions or projected value reduction is made tensor dimension to dimension input. For this purpose mathematical device tensor dimensionality reduction, namely tensor decomposition. This allows the spread of space tensor with the necessary ingredients for further analysis. It is thus possible to combine in a single array of data from different areas of the company.

**Conclusions**

A unique feature tensor use in the control system portion of the second carbonation is tensors that can be both scalar and vectors as tensor analysis can be viewed as an extension and generalization of vector analysis of three-dimensional space to n-. Moreover, if there tensors for process or machine line, the need for models of area businesses or entire production tensors can add and multiply. This new tensors will be formed, that will be developed a new tensor model for the site, and the entire enterprise, which can be used for calculation of system automation across the enterprise.

#### Повний текст:

PDF#### Посилання

Sidletskiy, V. M., Kushkov, V.M., Shved, S.M. (2008). ASU stantsiyami sokodobyivaniya i sokoochistki [ACS for juice production and juice cleaning stations]. Avtomatizatsiya v promyishlennosti. 2, 26-29.

L.J. Vega Montoto. (2005) Maximum Likelihood Methods for Three-Way Analysis in Chemistry., Ph.D. dissertations, Dalhousie University, Halifax, Nova Scotia,. 217.

Cichocki, A., Zdunek, R., Phan, A.-H., Amari, S. (2009) Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. Chichester. U.K.: John Wiley&Sons Ltd. 407.

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