Simple Method for Incorporating Prior Parameter Information during Model-Based D-Optimal Design of Experiments for Multi-Response Chemical Process Models

Fundamental models are important for design, control, and optimization of chemical systems but often contain many unknown parameters that require estimation from experimental data. Model-based design of experiments (MBDoE) can be used to plan experiments, leading to accurate parameter estimates and improved model predictions. Computation of MBDoE objective functions is challenging for nonlinear models with many parameters due to a singular Fisher information matrix. Bayesian approaches can be used to overcome this problem. We propose a simplified Bayesian D-optimal objective function and minimum volume ellipsoid (MVE) calculation to test the effectiveness of the Bayesian approach. A pharmaceutical case study is used to show estimates obtained from sequential D-optimal experiments that occupy a smaller MVE than estimates from old data or corner-point experiments, confirming that the proposed approach leads to improved parameter estimates. Estimates from A-optimal and D-optimal experiments are compared, confirming that estimates from D-optimal experiments are better in a D-optimal sense.