Project Details
Projekt
Kernel Methods for Confidence Regions in Optimal Experimental Design and Parameter Estimation
Applicants
Professor Dr. Michael Bortz; Dr.-Ing. Erik Esche
Subject Area
Chemical and Thermal Process Engineering
Mathematics
Mathematics
Term
since 2021
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 466397921
Reliable models are the prerequisite for virtual process design and process optimization. For this purpose, models are calibrated on measurement data, resulting in uncertainties due to inaccuracies in the measurements and in the models. A measure of reliability are confidence regions in the space of the model parameters and prediction errors for the model functions. For nonlinear models, these have so far been obtained from linearizations leading to elliptical confidence regions and the corresponding prediction errors. Due to the linearization, these do not adequately represent the real uncertainties. As a result, overly optimistic or overly pessimistic assumptions about the uncertainties may be made. In this project, kernel-based classification methods, the Kernel Minimal Enclosing Balls (KMEB), combined with adaptive Bayes-like data generation, will be used and further developed to arrive at a realistic quantification of the uncertainties. The core trick allows arbitrarily shaped confidence regions by mapping them to an abstract feature space in which the elliptical shape (even spherical) is again assumed. With these resulting uncertainty measures ideally fitted to the model nonlinearities, methods for parameter estimation and optimal experimental design should be numerically much more robust and efficient, and more reliable in terms of results. The feasibility and usefulness of this method for chemical engineering is exemplified for a reactive multiphase system. Such systems are known for strong nonlinearities with discontinuous and non-differentiable behavior; parameter estimation and experimental design for them are correspondingly challenging. The KMEB-based technique, initially demonstrated here with simple examples, is developed and used to obtain promising new methods for parameter estimation and optimal experimental design. Data from the model are collected from adaptive Bayesian sampling strategies; measurement data come from experiments conducted in the project.
DFG Programme
Priority Programmes
