Measurement method for angle of repose and particle size distribution of bulk materials on belt conveyor based on point cloud segmentation

The angle of repose (the dynamic angle of repose under actual conveying conditions) and particle size distribution of bulk materials on the conveyor belt are important parameters for characterizing the state of materials transported by belt conveyors. To address difficulties in three-dimensional point cloud segmentation caused by complex troughing and sagging deformation of the conveyor belt, as well as measurement inaccuracies caused by particle occlusion and adhesion, a method for measuring the angle of repose and particle size distribution of bulk materials on the conveyor belt based on point cloud segmentation with adaptive surface fitting was proposed. To achieve high-fidelity segmentation of bulk materials, a bicubic polynomial surface model was constructed, and weighted least squares were used to adaptively fit the actual deformed belt surface and accurately extract clean bulk material point clouds. For angle of repose measurement, equally spaced point cloud slicing was combined with the Hough transform to extract linear contour features, effectively eliminating interference from local protrusions of large particles and enabling accurate measurement of local angles of repose. For particle size distribution measurement, a three-dimensional depth field representing the bulk material pile morphology was constructed and combined with a three-dimensional watershed algorithm to accurately segment individual particles, determine the median particle size, and obtain particle size distribution statistics. Experimental results showed that the proposed adaptive surface fitting algorithm achieved an intersection over union of 95.84% for point cloud segmentation. The absolute errors in local angle of repose measurements were within 1.35°, with a mean absolute error of only 0.66°. Particle size distribution measurement effectively reduced statistical bias caused by occlusion in stacked bulk materials, and the corrected median particle size fell within the reference interval obtained by standard mechanical sieving. These results demonstrate that the proposed method can significantly improve the accuracy and robustness of bulk material state parameter measurements under complex operating conditions.