Optimization-based framework for kernel parameter identification in multi-material population balance models

This study presents a robust, parallelized optimization framework for kernel parameter identification that is adaptable to any population balance equation (PBE) formulation and process type. The framework addresses the challenge of incomplete 2D particle size distribution (PSD) measurements in multi-material systems by combining a reduced 2D PSD with complementary 1D datasets. The framework was validated by using noisy synthetic PSD data and evaluating both the error in PSD and kernel values across eight kernel parameters. Hyperparameter and sensitivity analyses provided configuration recommendations and insights into the influence of individual parameters, thus guiding kernel model selection. Incorporating prior knowledge of one kernel parameter (e.g., through multi-scale simulations) mitigated non-unique solutions and enhanced noise tolerance, ultimately improving the framework’s robustness and reliability. A case study based on experimental data from a dispersion process demonstrated the framework’s flexibility and practical relevance.