Machine learning and hybrid modelling of particle breakage in a jet mill

This work aims to compare data-driven, first-principles and hybrid modelling approaches for the prediction of a zeolite product particle size distribution (PSD) in a jet mill process. A small dataset is collected from jet milling experiments with different process conditions and feed PSDs. A population balance model (PBM) serves as the first-principles model, while the machine learning model is an artificial neural network (ANN) using Monte Carlo dropout, predicting the final PSD directly from the process conditions and feed PSD. A serial hybrid model (SHM) is implemented using an ANN to predict two PBM parameters, and as well as a corrective hybrid model (CHM) using an ANN to predict the PBM error. All of the models are trained and evaluated in a leave-one-out cross-validation (LOOCV) procedure, and hyperparameters are optimised using Optuna. The SHM is found to be better than the PBM alone but worse than the other purely data-driven models, suggesting that the chosen PBM structure is too simple to capture the complexities of the jet milling process for the zeolite material, and thus constrain and limit the data-driven component of the serial model. The CHM is the best performing model, achieving a 34.5% reduction in cross-validation mean absolute error (MAECV) over the purely data-driven model. The CHM performance is explored on the two held-out test experiments, showing the effective corrective action on the PBM predictions with uncertainty estimates from Monte Carlo dropout. Explainable AI techniques (Shapley values) are implemented to understand the jet mill parameters which have significant influence on the magnitude and direction of the predicted corrective action. The work demonstrates the advantages of hybrid modelling, and highlights the importance of selecting an appropriate hybrid model structure with consideration of the underlying first-principles model’s capabilities and limitations. It demonstrates the application of explainable AI techniques with corrective hybrid modelling for development of the underlying first-principles model.