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

Particle properties such as size, shape and composition are key for many products and in many processes. For example, in order to enrich minerals in a targeted manner, an ore must be crushed, classified and sorted so that high grades are achieved with a high recovery at the same time. To describe and optimize the processes, the influence of particle properties on the process result must be determined. 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 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 minerals. Therefore, an image segmentation method using a deep convolutional neural network (CNN), specifically an adaptation of the 3D 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 characterize the particle systems before and after
magnetic separation, to quantitatively evaluate the separation success.