PCA Combined Model-Based Design of Experiments (DOE) Criteria for Differential and Algebraic System Parameter Estimation

Design of experiments (DOE) for parameter estimation in dynamic systems is receiving more attention from process system engineers. In this paper, a principal component analysis (PCA)-based optimal criterion (P-optimal) for model-based DOE is proposed that combines PCA with information matrix analysis. The P-optimal criterion is a general form that encompasses most widely used optimal design criteria such as D-, E-, and SV-optimal, and it can automatically choose the optimal objective function (criterion) to use for a specific differential and algebraic (DAE) system. Two engineering examples are used to validate the algorithms and assumptions. The advantages of P-optimal DOE include ease of reducing the scale of the optimization process by choosing parameter subsets to increase estimation accuracy of specific parameters and avoid an ill-conditioned information matrix.