Quantitative assessment of separation quality, using neural networks and multivariate stochastic modeling

The quality and behavior of application specific industrial materials, such as those used for the production of coatings, membranes and electrodes, are influenced by the properties of particles within the materials, for example, particle size, flatness and sphericity. To fabricate materials with desired properties, particle systems may undergo processes such as fractionation or magnetic separation for quality adjustment. X-ray computed tomography (CT) can image large volumes of given particle systems with a sufficiently good resolution to allow for the analysis of individual particles. However, methods to efficiently analyze such image data and model the observed particle properties are still an active field of research. When image data of particles exhibiting a wide range of shapes and sizes is considered, traditional image segmentation methods, such as the classic watershed algorithm, struggle to recognize particles with satisfying accuracy. Therefore, more advanced methods of machine learning can be utilized for such image segmentation tasks to improve the validity of further subsequent analyzes.

In this talk, experimentally measured three-dimensional CT images of a zinnwaldite-quartz composite material are considered before and after a magnetic separation process is applied to enrich valuable mineral ores. Therefore, an image segmentation method using a deep convolutional neural network (CNN), specifically an adaptation of the U-net architecture, is used. This has the advantage of requiring less hand-labeling than other machine learning methods, while also being more flexible with the possibility of transfer learning. In addition, a fully parametric vine copula based model is designed to determine multivariate probability distributions of particle size/shape/textural/composititional characteristics—allowing for the estimation and interpretable characterization of highly-dimensional interdependencies of particle characteristics. The described methodology is then applied to describe image data of particle systems before and after magnetic separation, to quantitatively evaluate the separation success.