Experimental Design Tools for Ordinary and Algebraic Differential Equations

Abstract

The purpose of this paper is to present practical tools to facilitate the interpretation of parameter estimation results and to optimize experimental designs, where the underlying dynamical model consists of systems of ordinary or algebraic differential equations. We present a heuristic procedure to compute significance levels of model parameters and allow successive elimination of redundant ones. To compute the optimal experimental designs, we choose the A-criterion to evaluate the performance of the system, i.e., the identifiability of model parameters to be computed after getting the experimental data. Pseudo-weights are introduced and treated as design variables, to reduce the number of experiments and determine those time values at which experiments should be taken. A couple of practically relevant case studies from chemical engineering are included, which have been investigated previously by other authors.

Experiment-driven electrochemical modeling and systematic parameterization for a lithium-ion battery cell

“…In this section, an algorithm for the analysis of the identifiability of the parameters [17,31] is introduced. It is applied to the parameter estimation problem of secondary lithium-ion cells for the first time.…”

Dynamic modeling of an industrial diesel hydroprocessing plant by the method of continuous lumping

“…In order to have reliable estimates, the most sensitive and reliable set of parameters have to be tuned and the other parameters should be fixed at some nominal values. Fisher Information matrix is used for this purpose (Sildir et al, 2012;Goodwin and Payne, 1977;Schittkowski, 2007). First, parameter estimation is done without fixing any of the parameters and an initial parameter set is obtained.…”

“…First, parameter estimation is done without fixing any of the parameters and an initial parameter set is obtained. Next, following the algorithm given in Schittkowski (2007), the number of parameters is reduced by specifying a minimum threshold for the eigenvalues of Fisher information matrix. Parameter selection is finalized with the four parameters listed in Table 5 since adding more adjustable parameters increased the 95% confidence limits.…”

Detailed kinetic model describing new oligosaccharides synthesis using different β-galactosidases

“…Calibration of nonlinear models is usually a very challenging task due to nonconvexity that may be overcome by the use of global optimization techniques. However, the key question when trying to identify the parameters of a model is not only whether the model fits the experimental data but also whether the computed parameters are uniquely determined (Schittkowski, 2002(Schittkowski, , 2007. This question is often neglected leading to models that are able to accurately fit the data but with meaningless parameters due to their huge confidence intervals that are not always computed.…”