Open Access
 Issue BIO Web Conf. Volume 27, 2020 International Scientific-Practical Conference “Agriculture and Food Security: Technology, Innovation, Markets, Human Resources” (FIES 2020) 00017 6 https://doi.org/10.1051/bioconf/20202700017 25 November 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 [1-7]. 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 [8-11].

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 two-factor experiment (n = 2) equals N=13. To the full factor experiment 22 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 two-dimensional sections of response surface allows preliminarily determining areas of factor space, where we achieved an optimal value of output parameters. Figures 1-16 show a graphic picture of regression models as paraboloids and a two-dimensional 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(n0 -1)=16 (tm=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 FT = 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 X1, X2 – 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 X1, X2 – coded values of factors, related with natural values xi by ratios:

The task of multi-criteria optimization by the target programming method transformation into a mono-criteria task of minimization of the number of deviations with some indicator p:(2)

where wk- 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.

Table 1.

Planning matrix and results of the experiment «Grain bars»

Table 2.

Dependences of response function of input factors «Grain bars»

 Fig. 1.General form of response surface Y1
 Fig. 2.Two-dimensional section of response Y1
 Fig. 3.General form of response surface Y2
 Fig. 4.Two-dimensional section of response surface Y2
 Fig. 5.General form of response surface Y3
 Fig. 6.Two-dimensional section of response surface Y3
 Fig. 7.General form of response surface Y4
 Fig. 8.Two-dimensional section of response surface Y4
Table 3.

Planning matrix and results of the experiment «Puff buns»

Table 4.

Results of coefficients significant check of models and the adequacy of the regression equation «Puff buns»

Table 5.

Dependences of the response function of input factors «Puff buns»

 Fig. 9.General form of response surface Y1
 Fig. 10.Two-dimensional section of response surface Y1
 Fig. 11.General form of response surface Y2
 Fig. 12.Two-dimensional section of response surface Y2
 Fig. 13.General form of response surface Y3
 Fig. 14.Two-dimensional section of response surface
 Fig. 15.General form of response surface Y4
 Fig. 16.Two-dimensional section of response surface Y4

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.

References

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All Tables

Table 1.

Planning matrix and results of the experiment «Grain bars»

Table 2.

Dependences of response function of input factors «Grain bars»

Table 3.

Planning matrix and results of the experiment «Puff buns»

Table 4.

Results of coefficients significant check of models and the adequacy of the regression equation «Puff buns»

Table 5.

Dependences of the response function of input factors «Puff buns»

All Figures

 Fig. 1.General form of response surface Y1 In the text
 Fig. 2.Two-dimensional section of response Y1 In the text
 Fig. 3.General form of response surface Y2 In the text
 Fig. 4.Two-dimensional section of response surface Y2 In the text
 Fig. 5.General form of response surface Y3 In the text
 Fig. 6.Two-dimensional section of response surface Y3 In the text
 Fig. 7.General form of response surface Y4 In the text
 Fig. 8.Two-dimensional section of response surface Y4 In the text
 Fig. 9.General form of response surface Y1 In the text
 Fig. 10.Two-dimensional section of response surface Y1 In the text
 Fig. 11.General form of response surface Y2 In the text
 Fig. 12.Two-dimensional section of response surface Y2 In the text
 Fig. 13.General form of response surface Y3 In the text
 Fig. 14.Two-dimensional section of response surface In the text
 Fig. 15.General form of response surface Y4 In the text
 Fig. 16.Two-dimensional section of response surface Y4 In the text

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