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

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• 作者：Lamia Benabbas ; Steven P. Asprey ; and Sandro Macchietto
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：2005
• 出版时间：August 31, 2005
• 年：2005
• 卷：44
• 期：18
• 页码：7120 - 7131
• 全文大小：391K
• 年卷期：v.44,no.18(August 31, 2005)
• ISSN：1520-5045

文摘

It is common practice in nonlinear regression situations to use asymptotic linear approximationsof the model functions to construct parameter inference regions; such approximations may turnout to be a poor representation of the true underlying surfaces, especially for highly nonlinearsituations and small sample sizes. For this reason, experimental designs based on theseapproximations could well be moderately noninformative. We present a new method for optimalexperimental design for improving parametric precision while taking account of curvature inmultiresponse nonlinear structured dynamic models. We base the curvature measures in themultiresponse case on the Box-Draper estimation criterion through use of the generalized least-squares model conditioned on the maximum likelihood estimate of the variance-covariancematrix for the responses. Curvature measures commensurate with those found in the literatureare used for the generalized least-squares model in the neighborhood of the parameter pointestimates. The problem of designing dynamic experiments is cast as an optimal control problemthat 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 subjectto general constraints on inputs and outputs. We illustrate the experimental design conceptswith a relatively simple but pedagogical example of the dynamic modeling of the fermentationof baker's yeast.