Data-driven modeling of product crystal size distribution and optimal input design for batch cooling crystallization processes

In this paper, a novel data-driven model building method is proposed for predicting one-dimensional product crystal size distribution (CSD) or chord length distribution (CLD) of batch cooling crystallization processes, based on only batch run data. The proposed model relating the manipulated variable of cooling rate to the product CSD are constructed by two classes of basis functions, one is the wavelet basis function for reshaping the CSD and the other is the polynomial basis function for weighting the chosen wavelet basis functions to reflect the nonlinear relationship between the input and the density of individual crystal size among the product crystals. Correspondingly, a double-layer least-squares algorithm is established to estimate the model parameters, along with an adaptive strategy to determine the location and number of wavelet basis functions. By introducing an objective function that combines the information entropy of product CSD and the sample deviation of product crystals in each batch with respect to the target crystal size, the optimal input design of cooling rate for the desired product CSD is carried out by using a particle swarm optimization (PSO) algorithm to solve the non-convex optimization problem with the established CSD model. Simulation tests on the hen-egg-white lysozyme crystallization process along with experiments on the L-glutamic acid cooling crystallization process are performed to demonstrate the effectiveness and advantage of the proposed method.