Issue 
BIO Web Conf.
Volume 27, 2020
International ScientificPractical Conference “Agriculture and Food Security: Technology, Innovation, Markets, Human Resources” (FIES 2020)



Article Number  00017  
Number of page(s)  6  
DOI  https://doi.org/10.1051/bioconf/20202700017  
Published online  25 November 2020 
Modeling of recipes of special purpose bakery products
^{1}
Аlmaty Technological University, 050012 Almaty, Kazakhstan
^{2}
KyrgyzTurkish Manas University, 720038 Bishkek, Kyrgyzstan
^{3}
Saratov State Agrarian University named after N.I. Vavilov, 410012 Saratov, Russia
^{*} Corresponding author: aist_2707@mail.ru
In this article the results of calculations of experimentalstatistical methods are given, using the optimized contents of components in “Puff buns” and “Grain bars” recipes. The proposed products are balanced in the content of nutrients (proteins, fats, carbohydrates), contain a wide range of vitamins and essential amino acids, which allows expanding the consumer food market and more efficiently using vegetable resources. In order to obtain the percentage ratio of the components in the flour products composition, the complete factor experiment – a central compositional rotatable planning experiment – was applied. According to the results of mathematical modeling for “Puff buns”, the optimal percentage ratio of rice bioflour and pumpkin was chosen as 20:20, for “Grain bar” the optimal dosage of mashed bananas and Jerusalem artichoke is 28:12 respectively.
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
Food products design is a process of creation rational recipes that can provide a high level of adequacy of the complex of properties of food products to the consumers’ requirements and to the standardized values of nutrients and energy content [17]. According to the modern views, the term design of products includes the development of models that describes steps of products creation using the given quality. It also represents mathematical dependence of changing one or several key parameters on which base they are being developed, including the optimization of choice and the ratio of components [811].
Purpose of the study – ingredients’ optimization in bakery products’ recipe – “Puff buns”, “Grain bars” which by quantitative content and quality composition will match the formula of balanced diet, as much as possible, meet biomedical requirements and own high consumer properties.
2 Materials and Research Methods
The optimization of the prescribed composition of “Puff buns”, “Cereal bars” was performed by experimental statistical methods. To construct the mathematical models of function dependency, the response of input factors, we used central compositional rotable planning of the experiment (CCRP).
The regression equation with two variables in central compositional rotable planning is presented as the second order equation:(1)
The number of experiments using CCRP in the twofactor experiment (n = 2) equals N=13. To the full factor experiment 2^{2} let us add 5 experiments in centre of the plan and four “star” points with coordinates (+a; 0); ( a;0); (0;+a); and (0; a).
Using CCRP for the regression equations coefficients (1) and relevant marks of dispersions, we use formulas from the tutorial [12].
3 Results and Discussion
The grafic interpritation of the regression equation is response surface. Analysis of twodimensional sections of response surface allows preliminarily determining areas of factor space, where we achieved an optimal value of output parameters. Figures 116 show a graphic picture of regression models as paraboloids and a twodimensional section of paraboloids.
The comparison of estimated values of the Student criterion with the table at a significance level of α = 0,05 and the number of degrees of freedom N(n_{0} 1)=16 (t_{m}=1.7459) allows choosing significant regression coefficients.
Table values of the Fisher criterion at a significance level of α = 0,05 and the number of degrees of freedom of numerator and denominator and equal F_{T} = 6.59. The comparison of the Fisher criterion estimated value and table shows that regression equations are adequate to experimental data.
Built regression models may be used for recipe optimization of «Cereal bars», «Puff buns».
For the ratio of components determination in the «Cereal bars» recipe, let`s build a mathematical model of optimization by four criteria:
here X_{1}, X_{2} – coded values of factors, related with natural values xi by ratios:
For determination of the components ratio in the recipe of «Puff buns» let`s build a mathematical model of optimization by four criteria:
here X_{1}, X_{2} – coded values of factors, related with natural values xi by ratios:
The task of multicriteria optimization by the target programming method transformation into a monocriteria task of minimization of the number of deviations with some indicator p:(2)
where w_{k} some weight coefficients that characterize the importance of one or other criterion, – values of target functions on the optimal plan for each criteria, p – parameter, k  number of target functions.
At p=2 and we get the following task of minimization of the amount and limitations:
where – maximum of the first criterion,  maximum of the second criterion. – maximum of the third criterion,  maximum of the fourth criterion.
According to the results of the calculations, experimental and statistical methods optimized the contents of the components in the formulation of the developed products, which are confirmed by the results of trial laboratory baking.
The optimal solution of the single criterion task is point .
The optimal dose of banana and Jerusalem artichoke puree is 28% and 12% respectively.
The optimal solution of the single criterion task is point .
The optimal dose of rice flour and pumpkin puree is 20% and 20% respectively.
Planning matrix and results of the experiment «Grain bars»
Dependences of response function of input factors «Grain bars»
Fig. 1. General form of response surface Y_{1} 
Fig. 2. Twodimensional section of response Y_{1} 
Fig. 3. General form of response surface Y_{2} 
Fig. 4. Twodimensional section of response surface Y_{2} 
Fig. 5. General form of response surface Y_{3} 
Fig. 6. Twodimensional section of response surface Y_{3} 
Fig. 7. General form of response surface Y_{4} 
Fig. 8. Twodimensional section of response surface Y_{4} 
Planning matrix and results of the experiment «Puff buns»
Results of coefficients significant check of models and the adequacy of the regression equation «Puff buns»
Dependences of the response function of input factors «Puff buns»
Fig. 9. General form of response surface Y_{1} 
Fig. 10. Twodimensional section of response surface Y_{1} 
Fig. 11. General form of response surface Y_{2} 
Fig. 12. Twodimensional section of response surface Y_{2} 
Fig. 13. General form of response surface Y_{3} 
Fig. 14. Twodimensional section of response surface 
Fig. 15. General form of response surface Y_{4} 
Fig. 16. Twodimensional section of response surface Y_{4} 
4 Conclusion
Thus, the presented results of mathematical modeling of recipes “Grain bars” and “Puff buns”, based on the use of raw materials with different chemical composition and functional and technological properties, make it possible to obtain the ratio of recipe components, providing high organoleptic and physicochemical indicators of specialized products.
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All Tables
Results of coefficients significant check of models and the adequacy of the regression equation «Puff buns»
All Figures
Fig. 1. General form of response surface Y_{1} 

In the text 
Fig. 2. Twodimensional section of response Y_{1} 

In the text 
Fig. 3. General form of response surface Y_{2} 

In the text 
Fig. 4. Twodimensional section of response surface Y_{2} 

In the text 
Fig. 5. General form of response surface Y_{3} 

In the text 
Fig. 6. Twodimensional section of response surface Y_{3} 

In the text 
Fig. 7. General form of response surface Y_{4} 

In the text 
Fig. 8. Twodimensional section of response surface Y_{4} 

In the text 
Fig. 9. General form of response surface Y_{1} 

In the text 
Fig. 10. Twodimensional section of response surface Y_{1} 

In the text 
Fig. 11. General form of response surface Y_{2} 

In the text 
Fig. 12. Twodimensional section of response surface Y_{2} 

In the text 
Fig. 13. General form of response surface Y_{3} 

In the text 
Fig. 14. Twodimensional section of response surface 

In the text 
Fig. 15. General form of response surface Y_{4} 

In the text 
Fig. 16. Twodimensional section of response surface Y_{4} 

In the text 
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