Improved Bayesian parameters estimation with model-based design of experiments for over-parameterized systems

It is efficient to integrate Bayesian parameter estimation (BPE) with model-based design of experiments (MBDoE) to estimate process parameters. But for over-parameterized models, significant challenges are involved such as the singularity of the Fisher Information Matrix (FIM) and the non-convergence of Markov Chain Monte Carlo (MCMC) methods. To address these challenges, this study introduces a novel approach that integrates BPE and model transformation through singular value decomposition (SVD). Under the proposed structure, the noise distribution not only converges to a stable state but also consistently recovers the true noise variance. Good performance in achieving more accurate model and improved experimental efficiency is validated through two case studies on dynamic batch reactor systems.