The Development and Adaptation of a Predictive Model of Full-Factor Optimisation of the Basic Probiotic Fermented Dairy Product Technological Process
Authors: Zobkova Zinaida Semyonovna , Kondratenko Vladimir Vladimirovich , Pryanichnikova Natalia Sergeevna , Zenina Daria Vyacheslavovna , Korovina Natalia Sergeevna 
Published: January 2024

Introduction: In the conditions of rapidly developing markets and the increasing needs of the population for new types of products with long shelf life, there is a need to expand their range, further improve their quality and biological value, and modernize traditional technologies. The main means of achieving these goals is to increase the efficiency and quality of scientific research and accelerate the introduction of scientific achievements in industry. The latter will make adjustments to accelerate the development of effective technologies of whole-milk products. The use of new methods of experiment planning in order to optimize technological processes will reduce the duration of research on the creation of new types of products.

Purpose: The article is devoted to the research related to the development and adaptation of a predictive (mathematical) model for optimization of the technological process of probiotic fermented dairy product production. This approach will allow to ensure the design of a certain set of formulations for probiotic fermented dairy product, in which the relative biological value (RBV) will correspond to the maximum value at satisfactory given process parameters.

Materials and Methods: The objects of research were: probiotic fermented dairy product manufactured in accordance with the developed mathematical model of the process. The search of specialized literature was carried out using electronic databases: E-library, Scopus, MDPI, Science Direct. Mathematical processing of experimental data for the development of the probiotic fermented dairy product model was carried out using Microsoft Excel 2010 (Microsoft Corporation, Ink.) with the "Solution Search" add-in, as well as specialized software packages TableCurve 2D v.5.01 (SYSTAT Software, Ink.) and Wolfram Mathematica 10.2 (Wolfram Research, Ink.).

Results: A mathematical model for optimization of the technological process of probiotic fermented dairy product production was developed. A full-factor experiment (FFE) was conducted, in which the mass fraction of sucrose ( , %) and fat-protein index (r) - the ratio of the mass fraction of fat to the mass fraction of protein in the normalized mixture in the intervals from 0 to 10 and from 0 to 1.5%, respectively, were taken as independent factors. RBV was taken as the resultant factor. Based on the results of the research, a refined mathematical description of the dependence of RBV indicator on the mass fraction of sucrose and fat-protein index was obtained. The set of data on the influence of the mass fraction of sucrose on the dynamics of local maximum of RBV and the dynamics of the corresponding values of the mass fraction of fat showed that the maximum of RBV equal to 244.866% corresponded to the mass fraction of sucrose equal to 7.31%. The latter corresponded to the optimum fat-protein index of 1.241. In order to ensure maximum RBV, the lower limit of the mass fraction of fat had to correspond to 3.475%. The analysis of the FFE data showed the presence of additional corrective factors of RBV indicator dependence on fat and protein mass fraction indices. To refine the developed model taking into account additional factors, a correction factor (Q) was introduced into it.

Conclusion: Approbation of the optimization model of the technological process of probiotic fermented dairy product production and the obtained mathematical dependencies can serve as a criterion for the formation of a set of formulations for the production of sugar-containing fermented dairy products with a high potential of relative biological value. It should be taken into account that the definition area of this approach is limited in terms of mass fraction of fat in the range from 0.06 to 4.84% and mass fraction of protein - from 2.8 to 3.9%. With this approach (model development) it is possible to analyze promising modes for the studied process, which in real conditions at the experimental stage are not always possible to obtain. The development of this model will significantly reduce the duration of research on the optimization of the technological process.