Classification of particle height in a hopper bin from limited discharge data using convolutional neural network models

Hopper bin discharge processes are ubiquitous in many industrial applications. The preponderance of previous studies of this system has been focused on the forward discharge process given an initial particle packing configuration. Motivated by the needs in reaction design and optimization, we develop here an inverse reconstruction procedure that enables one to obtain the particle height information in the initial packing configuration in the hopper bin from limited discharge dynamics data and particle characteristics. Our procedure is based on convolutional neural network (CNN) models, which take experimentally measurable particle residence time, diameter and density as input, and provide a classification of particle height in the initial packing as output. Using MFIX-DEM simulations with enhanced physical modeling capabilities, we generate extensive discharge data for hoppers containing two distinct solid phase particles with four distinct classes of initial packing geometries. The CNN reconstruction models are subsequently trained and tested using the discharge data. We find that the reconstruction (i.e., particle height classification) accuracy strongly depends on the initial packing geometry. For hopper-specific CNN models exclusively trained using discharge data from a single hopper, the classification can attain an accuracy up to almost 90%. The accuracy decreases for generic reconstruction models trained using a collection of discharge data for multiple hoppers. Finally, we apply the CNN model to accurately reconstruct a hopper containing four distinct solid phases with a layered configuration to further demonstrate its utility.