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