Surrogate Modeling with Sensitivity-Based Experiment Design and Process Optimization of Seeded Cooling Crystallization: A Case Study on β-Form LGA

Abstract

To facilitate quality-by-design (QbD) of seeded cooling crystallization, a novel surrogate modeling and process optimization method is proposed in this paper, based on the design of experiments (DoE) with sensitivity analysis on the process operating conditions. To overcome the deficiency of the crystal growth kinetic model related to the population balance equation, which could not reflect the explicit relationship between the process operating conditions (e.g., initial solution supersaturation and cooling rate) and product crystal size distribution (CSD), a surrogate model is established by using the Gaussian process regression (GPR) approach, based on experimental data from a permitted range of operating conditions. Correspondingly, a swarm-based metaheuristic algorithm named beluga whale optimization (BWO) is adopted to determine proper hyperparameters in the surrogate model. By analyzing the global sensitivity analysis (GSA) of product CSD with respect to these operation conditions, a sensitivity-based DoE is developed to reduce the number of batch experiments required for implementation. Based on the established surrogate model, a comprehensive quality criterion is introduced to optimize these operating conditions, which takes into account the information entropy of product CSD together with the desired product yield and size range. The seeded cooling crystallization process of the β-form l-glutamic acid is tested to verify the effectiveness and merits of the proposed modeling and optimization method.