Estimating magnetic susceptibilities of mineral phases from noisy magnetic and mineralogical particle data

Abstract

Magnetic separation is an important technique in primary and secondary resource processing, yet the magnetic susceptibilities of individual phases in complex particle feeds remain poorly characterized. Direct measurement at the phase or particle level is often infeasible due to the composite nature of particles, while indirect inference is challenged by the reliance on bulk magnetic measurements and by stereological variability inherent in two-dimensional mineralogical analyses. This paper presents a statistical estimation framework, Virtual Particle Clustering (VPC), for inferring phase-specific magnetic susceptibilities from noisy and incomplete process data. The framework applies to mineral phases exhibiting linear magnetic behavior, including paramagnetic and diamagnetic materials. By aggregating particle information within magnetic susceptibility classes, VPC reduces quantization effects in bulk magnetic measurements and stereological variability in automated mineralogy, enabling robust estimation via Huber regression. Experiments on synthetic datasets demonstrate that VPC consistently outperforms conventional estimation approaches. Application to a natural rare-earth-bearing ore from the Norra Kärr deposit yields physically plausible estimates that align with mineralogical expectations. We demonstrate how the inferred phase properties can be used to optimize magnetic separation thresholds for extraction efficiency, supporting predictive modeling and data-driven optimization of magnetic separation processes across a broad range of resources.