Synthesis of Markov chain theory and digital twins of vibrating screens for controlling the fractional composition of bulk building materials

The development of effective methods for controlling the fractional composition of bulk building materials is a critical challenge, upon which the strength and durability of concrete and other building composites depend. This paper proposes a hybrid methodology combining two approaches: digital simulation of material transport across the vibrating screen based on the discrete element method (first digital twin) and stochastic description of the separation process using Markov chains (second digital twin). The first twin determines macroparameters: the velocity of material movement across the screen, residence time, and layer height. The second twin, built on a probabilistic approach, describes the particle distribution across the height of the vibro-fluidized layer, diffusion, segregation, and screening kinetics. The combined use of the twins makes it possible to compensate for the shortcomings of each approach individually: DEM modeling provides a physically accurate picture of bulk material transport across the screen; Markov chains provide a fast prediction but require calibration. As a result of the synthesis, a tool suitable for use in process control systems is created. It is shown that the proposed hybrid model makes it possible to predict the particle size distribution of screening products with high accuracy, replacing expensive and labor-intensive full-scale experiments on industrial and laboratory equipment. The assumptions adopted in this work (spherical particle shape and a two-fraction mixture composition) do not reduce the value of the methodological approach, since a recalibration procedure is provided for real materials, and the extension to polydisperse systems does not change the structure of the Markov chains.