Machine learning shadowgraphy for simultaneous monitoring of particle size distribution and solids concentration of slurries

• An in-focus criterion was proposed. • Unfocused particles were effectively screened out by using a machine learning model. • The model reduced the overall analysis time by six times while maintaining measurement accuracy. The present study introduces an effective tool integrating volumetric shadowgraph and the celebrated UNET architecture for simultaneously characterizing the particle size distribution (PSD) and solids concentration of slurries, important for process monitoring and control in a broad range of industrial operations. To address the intrinsic limitations of field depth in shadowgraphy, we propose a straightforward in-focus criterion, the ratio of the width of the halo (the blurred outer ring) to the diameter of the core (the sharply defined center) of the particle image. Applying the in-focus criterion allowed for shape-independent analysis for particle size. A case study was conducted using coal particles of irregular shape, and the results showed that with the classical image analysis approach, when the in-focus criterion was set to 0.20, calibrating the system with circular graticules would enable accurate analysis of the PSDs and solids concentrations of various coal slurries. The monitoring system, equipped with a 5× lens, successfully and consistently measures the size of coal particles within the range of 10–150 μm, but this approach requires evaluating the in-focus criterion for every particle identified in the image, which is time-consuming. To resolve this issue, unfocused particles were effectively screened out by using a UNET-based machine learning model in the shadowgraphy system through training the model on a slurry image dataset paired with the corresponding masked image dataset. The trained UNET significantly reduced the overall analysis time by up to six times without compromising the diagnostic accuracy. The present work enhances classical image analysis in shadowgraphy by refining the in-focus criterion, making it more effective for slurry monitoring. Additionally, integration with the machine learning technique enables real-time shadowgraphy applications, significantly boosting image processing speed while maintaining measurement accuracy, even with a small image dataset.