Experimental Design Tools for Ordinary and Algebraic Differential Equations

K. Schittkowski: Industrial and Engineering Chemistry Research, Vol. 46, 9137-9147
Abstract: The purpose of this paper is to present practical tools to facilitate the interpretation of parameter estimation results and to optimize experimental designs. The underlying dynamical model consists of systems of ordinary or algebraic differential equations, where additional constraints are permitted to restrict the model or design parameter space, respectively. Besides of the well-known confidence intervals, we present a heuristic procedure to compute significance levels of model parameters. Particularly in case of overdetermined systems, these levels allow to identify redundant parameters to be treated as constants, or to outline the necessity for providing additional experimental data.
Experimental design helps to find suitable values for additional so-called design parameters, for example initial concentrations or input feeds, which have to be set before conducting experiments. We choose the A-criterion to evaluate the performance of the system, i.e., the identifiability of the model parameters to be computed after getting the experimental data. A simple procedure is proposed to approximate corresponding derivatives subject to the design parameters by forward differences. By introducing pseudo-weights subject to a given set of time values and by treating them as design variables, it is in addition possible to reduce the number of experiments and to figure out those times at which experiments should be taken. Derivatives subject to weights are easily obtained from available data.
A couple of practically relevant case studies are included, which have been investigated before by other authors. All test runs can be repeated and modified by downloading the test environment EASY-FIT.

To download a preprint, click here: expdes.pdf

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