Optimal experimental design for identification of transport coefficient models in convection–diffusion equations

Abstract

Methods for the careful design of optimal experiments for the identification of the structure and parameters of transport models often strongly depend on a-priori knowledge about the unknown model. However, this kind of knowledge is usually poor for complex systems. We propose a novel procedure that is less sensitive with respect to poor a-priori knowledge; it relies on an optimization problem to maximize the information content of the measurement data for the purpose of model identification. Specifically, based on existing model-based methods, optimal design of experiments is addressed in the context of three-dimensional, time-dependent transport problems by introducing experiment design variables and the transport coefficient as degrees of freedom of the optimization. The problem is solved by means of an iterative strategy that – by sequentially designing a series of experiments – strives to adjust the settings of the experimental conditions by exploiting the results from previous experiments.The key methodical ingredient of the novel procedure is the use of incremental model identification introduced previously. The suggested procedure is illustrated by means of an extensive numerical case study for a convection–diffusion equation originating from the modeling and simulation of energy transport in laminar wavy film flow.