Scale-independent solid fraction prediction in dry granulation process using a gray-box model integrating machine learning model and Johanson model

We propose a novel approach for predicting the solid fraction after roller compaction processes. It is crucial to predict and control the solid fraction, as it has a significant impact on the product quality. The solid fraction can be theoretically predicted by a first-principles model developed by Johanson. The Johanson model, however, cannot be directly used for solid fraction prediction after roller compaction because it requires the values of preconsolidation properties, i.e., pressure and solid fraction before compaction, which cannot be measured with standard equipment. In this work, we developed a statistical model that predicts the newly defined preconsolidation parameter, which reflects preconsolidation properties, from the powder's material properties and the process parameters. Then we integrated the statistical model with Johanson's first-principles model, resulting in a novel gray-box (hybrid) model for the solid fraction prediction. The preconsolidation parameter was universally available regardless of the roller compactor size. With past data on material properties, process parameters, and corresponding solid fraction, the statistical model predicted the preconsolidation parameter without roller compaction experiments for the target formulation. The gray-box model predicted the solid fraction across various roll speeds, including the high throughput conditions causing powder velocity gradients. This robustness results from satisfying the Johanson model's premise that the one-dimensional mass remains constant before and after compaction. These results demonstrate the advantage of the proposed gray-box model, which can be used across scales and formulations without introducing complex additional concepts to the roller compaction mechanism.