Identification of the mass distributions of the milk fat phase using universal Pearson distributions

In this paper we consider the problem of approximating the experimental values ​​of the coefficient of attenuation of ultrasonic oscillations and the mass distribution of the fat globules in the milk and milk products. The analysis of experimental data in terms of the choice of the method of approximation was done. A approximating dependence is based on the solution of Pearson differential equations. The advantages of the proposed method for the type of approximation of the experimental data obtained. An algorithm for constructing a mathematical model describing the relaxation spectrum and mass distribution of the fat globules in the milk and milk products was implemented. As a result, a family of Pearson approximation curves of the experimental data shows the ability to qualitatively correctly describe the change in the distribution of the fat phase in the process of homogenization. It estimates the error of approximating dependence, which amounted to 18 %. It is shown that during of the process of homogenization of dairy products changes shape of the curve describing the distribution of the fat globules, in view of the fact that there is a local extremum, caused by the presence of the non-homogenized fat globules. The accuracy of the selected mathematical model is significantly reduced. At the same time, it loses its physical meaning and its parameters. To address the identified deviations in the proposed mass distribution of fat globules as a function with two modes. It is proved that the complexity of the model is not only doubles the number of its parameters, but also complicates the interpretation of measurement results in a control system, and makes it difficult to analyze the obtained parameters of approximation by decision-maker. As a result of approximation of experimental data suggested to use statistical moments of the distribution for problem decision.