In this paper, an adaptive approach has been developed for automatic initialization of the thickening curve using machine vision technology, which makes it possible to determine with high accuracy the material parameters necessary for the design of thickening and clarification apparatuses. Software has been developed that made it possible to search for the coordinates of the condensation critical point in automatic mode. Studies on two samples of materials (tailings of apatite-containing ores and gold-bearing concentrate) were carried out and made it possible to statistically prove the reproducibility of the results obtained using the parametric criteria of Fisher and Bartlett. It has been established that the deposition curves are approximated with high accuracy by the Weibull model, which, together with the piecewise linear approximation, makes it possible to formalize the method for determining the critical point coordinates. The empirical coefficients of the Weibull model for two samples are found, and the final liquefaction and settling rates of the studied materials are determined.

This study is dedicated to the application of neural network technologies for determining aeration parameters in order to predict the efficiency of flotation separation. Within the framework of the research, digital technology solutions were actively employed, including a neural network for segmentation at the stage of determining the granulometric characteristics of bubbles and a convolutional neural network module for determining the froth layer height. An analysis was conducted to examine the variation in the statistical parameter d₃₂, which characterizes the bubble size distribution, as a function of flotation time and measurement height. The analysis revealed that the d₃₂ values determined by neural network processing remained within the range of acceptable dispersion and are therefore suitable for subsequent analytical procedures. Furthermore, a comparative evaluation of the obtained size distributions indicated the absence of statistically significant differences between the neural network measurements and manually labelled data with a p-value equal to 0.64. A neural network for object detection was used to record the height of the froth layer during the experiment to obtain a time series, that were subsequently processed with data processing approaches including Savitzky–Golay and Singular Spectra Analysis. Based on the analysis of the sum of the obtained dependences, a criterion is proposed and modeled for evaluating the selectivity of frother by connecting the diameter of bubble in pulp and bubble in froth. Based on the modeling results, it was determined that the optimal range of bubble sizes and froth size ratios for MIBC is constrained to d₃₂ values ranging from 1.058 to 1.089 mm, with the ratio of froth bubble radius to d₃₂ ranging from 1.302 to 2.098, depending on the floatability ratios of the respective fractions. When employing OPF, the values for d₃₂ fall within the interval of 0.868 to 1.113 mm, while the Dₓ parameter ranges from 0.559 to 0.931.