Particle size distribution reconstruction using a finite number of its moments through artificial neural networks: a practical application

An artificial neural network (ANN) approach to reconstruct the particle size distribution (PSD) is proposed in this paper. This novel technique has been applied for acetaminophen crystallization in ethanol. Several experimental PSDs taken in different operating conditions, such as temperature and agitation degree, at different stages of the process have been considered, in order to ensure a wide range of different distributions for the system taken into account. The first stage of the ANN modeling is represented by the structure definition and the network training through a backpropagation algorithm in which the experimental PSDs and their associated vector of moments have been used. The second stage is represented by the feedforward application and validations of the proposed model estimating the PSDs using a finite set of experimental moments compared with their associated PSDs and then, using a set of time-dependent moments, obtaining the transitory PSD. The proposed approach represents a more suitable way to reconstruct the PSD in full, for the first time without assuming any reference distribution or knowing in advance the shape of the experimental PSD, leading to a generalized characterization of the PSDs with possible implementations in other multiphase unit operations.