Curvature-Based Methods for Designing Optimally Informative Experiments in Multiresponse Nonlinear Dynamic Situations

It is common practice in nonlinear regression situations to use asymptotic linear approximations of the model functions to construct parameter inference regions; such approximations may turn out to be a poor representation of the true underlying surfaces, especially for highly nonlinear situations and small sample sizes. For this reason, experimental designs based on these approximations could well be moderately noninformative. We present a new method for optimal experimental design for improving parametric precision while taking account of curvature in multiresponse nonlinear structured dynamic models. We base the curvature measures in the multiresponse case on the Box-Draper estimation criterion through use of the generalized least-squares model conditioned on the maximum likelihood estimate of the variance-covariance matrix for the responses. Curvature measures commensurate with those found in the literature are used for the generalized least-squares model in the neighborhood of the parameter point estimates. The problem of designing dynamic experiments is cast as an optimal control problem that enables the calculation of a fixed number of optimal sampling points, experiment duration, fixed and variable external control profiles, and initial conditions of a dynamic experiment subject to general constraints on inputs and outputs. We illustrate the experimental design concepts with a relatively simple but pedagogical example of the dynamic modeling of the fermentation of bakerʹs yeast.