Two novel criteria for model-based design of experiments in ill-conditioned systems

Model-based design of experiments (MBDoE) for parameter precision is an emerging technique for designing informative experiments that improve the precision of estimated parameters while reducing experimental effort. However, complex mechanistic models often exhibit numerical instability or estimability issues when the associated information structure becomes ill-conditioned. Besides, classical MBDoE criteria frequently concentrate information in a few parameter directions, causing unbalanced precision across the parameter space. To address these shortcomings, this work introduces two complementary criteria, named Orthogonal Residual Balancing (ORB), and Spectral Entropy Maximisation (SEM). The former prioritises weakly excited directions by maximising their independent information contribution; whereas the latter promotes uniform information distribution across the Fisher Information Matrix eigenspectrum. Two in silico case studies representing ill-conditioned systems are used to evaluate their performance and compare them to classical alphabetical criteria in a critical way. Results demonstrate that both ORB and SEM allow improving conditioning, reducing collinearity, balancing parameter-space information, and eventually leading to the satisfactory estimation of a larger number of parameters.