Optimal Experimental Design for Parameter Identification and Model Selection

Abstract

The main focus of this thesis lies on elementary steps of Optimal Experimental Design (OED). In general, OED aims to determine operating conditions which are expected to provide informative measurement data. Here, the term informative depends on the intended task. In case of parameter identification problems, informative data correlate with precise parameter estimates and reliable simulation results, respectively. On the other hand, another objective in the framework of modelling is to select the most plausible model candidate from a pool of various model candidates/hypotheses. In this field, informative data are associated with measurements which facilitate the actual model selection process. Indeed, these two strategies might be different in their outcomes, but both depend critically on the credibility of the applied algorithm for uncertainty propagation. Therefore, the Unscented Transformation (UT) approach as an alternative to standard approaches of uncertainty propagation is reviewed in detail. It is demonstrated that the UT method outperforms the linearisation concept in precision while utilising a low level of computational load compared to Monte Carlo simulations. In practice, when applied to OED problems for parameter identification the UT approach contributes to the overall performance beneficially. Moreover, in case of model selection issues the UT method as part of the Unscented Kalman Filter enables an online model selection routine. That means, in parallel to the experimental run the operating conditions are optimised simultaneously. In doing so, the process of model selection becomes more robust against a potential poor initial guess of initial conditions and/or estimates of model parameters. Finally, the concept of the flat input based parameter identification is introduced. It is shown, that by evaluating cost functions based on flat inputs instead of simulation results the parameter identification routine can be speeded up significantly. This effect is achieved by replacing the cpuintensive numerical integration algorithms for solving the underlying model equations by a less computationally cumbersome differentiation of surrogate functions. By analysing the associated cost functions it is illustrated that the flat input based expressions are likely to be more suitable candidates for a proper parameter identification, i.e., they may possess less local minima in comparison to the standard approach and, additionally, they are independent of the initial conditions. The general relation of the flat input concept to OED is given by a closer look at parameter sensitivities.