The article contains a mathematical description of the process of mixing bulk materials in a drum aggregate using elements of mathematical statistics, theory of probability and averaging models. A random stationary process is a flow that is formed by means of dispensers in this case. The correlation function is used as its parameter. It is a measure of the stability of the process. The relationship between the variances of the input and output signals is established by means of a correlation analysis. It allows predicting the degree of homogeneity of the material flow (smoothing ability of the mixer) at the output for the given parameters of the input signal: the coefficients of recycling, the time of its presence in the mixer and the dispersion of the input signal. The correlation analysis of the flow of material allowed the development of a new design of a continuous drum mixer. As a result, we found that the organization of external and internal recycling circuits greatly affects the reduction of fluctuations in the input signal. This reduces the variance of components and increases homogeneity of the mixture.

The results of a study of the flowability of finely divided dry materials and mixtures depending on the diameter of the particles and their density are presented, the influence of the mechanical effect and the physicomechanical properties of the materials on the flowability are determined. A mathematical model is constructed that allows one to functionally evaluate the dependence of flowability on the physicomechanical characteristics of the material under study by the method of multiple regression analysis. Polynomial equations are obtained that describe the influence of the flow area, physical and mechanical properties on the flowability of various materials and mixtures. A flowability criterion is proposed that describes the motion of various materials under the action of inertia forces. Partial and universal criteria equations are obtained that describe the energy expenditures for mixing bulk materials

Introduction. Artificial neural networks are a popular tool of contemporary research and technology, including food science, where they can be used to model various technological processes. The present research objective was to develop an artificial neural network capable of predicting the content of isogumulone in a hop extract at given technological parameters of the rotary pulse generator. Study objects and methods. The mathematical modeling was based on experimental data. The isogumulone content in the hop extract I (mg/dm3) served as an output parameter. The input variables included: processing temperature t (°C), rotor speed n (rpm), processing time  (min), and the gap between the rotor teeth and stator s (mm). Results and discussion. The resulting model had the following parameters: two hidden layers, 30 neurons each; neuron activation function – GELU; loss function – MSELoss; learning step – 0.001; optimizer – Adam; L2 regularization at 0.00001; training set of four batches, 16 records each; 9,801 epochs. The accuracy of the artificial neural network (1.67%) was defined as the mean relative error. The error of the regression model was also low (2.85%). The neural network proved to be more accurate than the regression model and had a better ability to predict the value of the output variable. The accuracy of the artificial neural network was higher because it used test data not included in the training. The regression model when tested on test data showed much worse results. Conclusion. Artificial neural networks proved extremely useful as a means of technological modeling and require further research and application.