Gregor Kriwet

Methods for Model Calibration and Design of Optimal Experiments for Partial Differential Equation Models


Front	Back

ISBN:

978-3-8440-4749-3

Series:

Industriemathematik und Angewandte Mathematik

Keywords:

Parameter Estimation; Optimum Experimental Design; Model Validation of PDE; Gauß-Newton Method in Function Space; Hessian Approximation; Adjoint Computation of Derivatives; PDE Constrained Optimization

Type of publication:

Thesis

Language:

English

Pages:

188 pages

Figures:

4 figures

Weight:

332 g

Format:

24,0 x 17,0 cm

Binding:

Paperback

Price:

48,80 € / 61,10 SFr

Published:

September 2016

Buy:

Download:

Available PDF-Files for this title:

You need the Adobe Reader, to open the files. Here you get help and information, for the download.

These files are not printable.


	Document		Document
	Type		PDF
	Costs		36,60 EUR
	Action		Purchase in obligation and display of file - 1,2 MB (1243348 Byte)
	Action		Purchase in obligation and download of file - 1,2 MB (1243348 Byte)


	Document		Table of contents
	Type		PDF
	Costs		free
	Action		Display of file - 119 kB (121910 Byte)
	Action		Download of file - 119 kB (121910 Byte)

User settings for registered users

You can change your address here or download your paid documents again.

User:	Not logged in.
Actions:	Login / Register Forgotten your password?

Recommendation:

You want to recommend this title?

Review copy:

Here you can order a review copy.

Link:

You want to link this page? Click here.

Export citations:

Text
BibTex
RIS

Abstract:

Mathematical models are of great importance in manufacturing and engineering. Besides providing a scientific insight into processes, the mathematical models are used in process optimization and control. However, the results from simulation and optimization are only reliable if the underlying model precisely describes the underlying process. This implies a model validated by experimental data with sufficiently good estimates for model parameters.

In recent decades, powerful and efficient methods for model calibration and design of optimal experiments for ordinary differential equation (ODE) models have been developed. First steps towards model validation of partial differential equations (PDE) have been made by semi discretization in space, which transforms the PDE into a huge system of ODEs. In this case, it is not possible to use modern methods for PDE constrained optimization. Consequently, it is hardly possible to solve the problem on standard computers.

To cope with this problem, this dissertation combines modern methods for PDE constrained optimization with established approaches for model validation. The optimum experimental design problem is not of standard type. In order to consider the finite measurement time points, the problem is formulated as a multistage optimization problem. Furthermore, the evaluation of the objective function requires the computation of derivatives. Despite these problems, this dissertation successfully adapts the adjoint approach for the computation of the reduced gradient. Furthermore, the thesis presents a positive definite approximation of the second order derivatives, which can be computed very efficiently by adjoint PDEs.