A comprehensive framework for model evaluation and refinement using MBDoE estimability and structural identifiability: application to a crystallization process

Abstract

• A novel framework combining structural identifiability, estimability, and MBDoE. • A set of model candidates is systematically constructed from plausible crystallization kinetics. • Models are discriminated based on the structural identifiability and prediction performance. • A new MBDoE approach combining estimability analysis and D-optimal criterion. • A novel operational protocol ensures rich data from a single experiment. This paper presents a novel framework for the systematic evaluation, discrimination, and calibration of mathematical models. A diverse set of model candidates is first constructed to capture a broad range of underlying physical and kinetic phenomena. Structural identifiability analysis is then employed to determine whether unique parameter estimates can be derived from ideal, noise-free data, enabling early-stage model screening. A single model is then selected based on a rigorous model discrimination criterion. To calibrate and refine the selected model, parameter estimability analysis is integrated with Model-Based Design of Experiments (MBDoE), ensuring optimal sampling strategies, data-rich experiments, and reduced prediction uncertainty. To maximize the effectiveness of MBDoE, a novel temperature cycling protocol is introduced, enabling a single, well-designed, information-rich experiment that minimizes experimental effort. This methodology is demonstrated through a cooling crystallization case study using paracetamol. The results show that the proposed framework significantly enhances model discrimination, parameter precision, and estimability resulting in a model with superior predictive performance, as proven by the additional post-MBDoE validation experiment operated under different conditions and designed independently from the MBDoE framework. The proposed framework bridges the gaps between the different modeling pillars, reduces experimental efforts, and lays the foundation for more effective modeling and optimal design of experiments for the crystallization systems and beyond.

Topics & Concepts