Reduced-order hybrid modelling for powder compaction: Predicting density and classifying diametrical hardness

Maia Trower, Joe Emerson, Mingzhe Yu, Vincenzino Vivacqua, Timothy Johnson, Hugh Stitt, Goncalo dos Reis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
12 Downloads (Pure)


Drawing on machine learning (ML) techniques and physics-based modelling, two feature-based reduced-order models are presented: one for the quantitative prediction of density and another for the classification of the diametrical hardness of pellets from a powder compaction process (pelleting). For interpretability, the models use as input only the parameters from a modified Drucker–Prager Cap (DPC) model calculated from process data monitoring and the applied maximal compression force. For quantitative density prediction, 8 features linked to first-principles models of powder compaction are generated, and the final model uses only 2. A critical part of the modelling, and also one of the main contributions, is a data augmentation step for the primary data set of this study by leveraging much smaller supplementary data sets that have measurements not present in the primary data set.

The final results imply a significant reduction in the quantity of data needed for model input and cut down the cost of data acquisition, storage, and computational time. Additionally provided is a detailed analysis of the impact and relevance of the generated features on the model performance.

The density prediction model, using only 2 features, reaches a mean absolute scaled error (MASE) of 12.9% and a mean absolute error (MAE) of 0.10 (where r2= 0.975). The scaled (diametrical) hardness classifier has an F1 score of 0.915 using 4 features.
Original languageEnglish
Article number118745
JournalPowder Technology
Early online date20 Jun 2023
Publication statusPublished - 1 Sept 2023


  • Density modelling
  • Drucker–Prager Cap model
  • Hardness modelling
  • Machine learning
  • Powder compaction

ASJC Scopus subject areas

  • Chemical Engineering(all)


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