Main content area

Sequential Model-Based A-Optimal Design of Experiments When the Fisher Information Matrix Is Noninvertible

Shahmohammadi, Ali, McAuley, Kimberley B.
Industrial & engineering chemistry process design and development 2018 v.58 no.3 pp. 1244-1261
Monte Carlo method, dynamic models, experimental design, process design, regression analysis
The sequential model-based optimal design of experiments (e.g., A-, D-, and E-optimal design) is a well-known technique for selecting experimental conditions that lead to informative data for obtaining reliable parameter estimates and model predictions. An important computational step for selecting new model-based experiments is to compute the inverse of the Fisher information matrix (FIM) which may not be invertible. In this study, three different methodologies for selecting new experiments are compared for situations where the FIM is noninvertible. The first approach finds and leaves out problematic parameters that make FIM noninvertible and then designs experiments using a reduced FIM (LO approach). The second approach uses a Moore-Penrose pseudoinverse of the FIM in A-optimal design calculations (PI approach). The third methodology is an ad hoc approach which does not require optimization. In this MS approach, the modeler selects settings at corners of the specified design space. Comparisons are made using two linear regression models and a nonlinear dynamic model for production of a pharmaceutical agent. Monte Carlo simulation results show that experimental settings obtained by LO and PI approaches give better parameter estimates on average than the MS approach, with the LO approach giving the best estimates in 20 of 24 linear situations studied. The LO approach also gives the best parameter estimates on average for the nonlinear pharmaceutical model.