Stochastic modeling of multidimensional particle properties with parametric copulas for the investigation of microstructure effects on the fractionation of fine particle system

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In this project, the mathematical analysis and modeling techniques developed in the first funding period of the SPP 2045 will be applied on image data and measurements of particle systems which are investigated by the partners within SPP 2045. In addition, the methods are further developed, which quantify the separation success and the relationship between multidimensional particle characteristics and separation-relevant physical parameters. Furthermore, a stereological prediction model is developed to characterize 3D particles from 2D sections through the particle systems. In particular, the following tasks will be addressed. The methods developed in the first funding period for extracting particles from CT image data, for parametric modeling of multivariate distributions of particle characteristics, for characterizing the materials within composite-particles from CT data, and for quantifying the separation success, are applied to further particle systems and modified if necessary. For this purpose, the workflow, consisting of the automated extraction of particles from CT data and the subsequent modeling of multivariate feature distributions of the particles, is applied to particle systems before and after the application of separation processes. This reduces the (difficult) direct comparison of CT image data to the comparison of distributions of particle characteristics of the feed material and the product. Subsequently, measures for the separation success, such as purity and yield, are determined to analyze and compare the quality of the separation methods. Another project goal is to quantify the relationship between particle properties and separation success using stochastic 3D particle models, i.e., by generating "digital twins" which describe the shape and internal structure of the particles. Furthermore, these models allow the generation of a wide range of virtual but realistic particles with different feature distributions. These virtual particles will be made available to the partner groups of SPP 2045 via a particle database, such that the partners can use them as input for numerical simulations of sedimentation and flow processes. By correlating the simulation results with multivariate distributions of characteristics of the feed particles, relationships between particle properties and separation success will be determined. In addition, a stereological prediction model is developed, which determines multivariate distributions of characteristics of 3D particles from 2D slices (gained e.g. by SEM measurements) through the particle system. For this purpose, the above-mentioned stochastic (single) particle models are extended to a model for spatially dispersed particle systems. By generating a large number of virtual 3D particle systems neural networks are trained, which can characterize the 3D particles from 2D sections of the considered particle system.