Biannual Report - Fachbereich Mathematik - Technische Universität ...

Project: Simulation-based optimization methods for the hydro-forming of branched
structures
This project is part of the Collaborative Research Centre (SFB) 666 (Integral sheet metal
design with higher order bifurcations - development, production, evaluation) and is concerned
with the optimal control of the sheet metal hydro-forming. The sheet metal hydroforming
process is a complex forming process, which involves contact, friction, and plasticity
to manufacture complexly curved sheet metals with bifurcated cross-section. Mathematically,
this leads to a quasi-variational inequality. We want to find optimal controls
for typical control variables, e.g., the time dependent blank holder force and the fluid
pressure, by the use of simulation-based optimization methods. Our goal is to obtain a desired
final configuration, taking into consideration relevant parameters for the production.
On the one hand, we use derivative free optimization methods to solve the optimal control
problem, where the commercial FEM-software ABAQUS is invoked for the simulations
and, on the other hand, instantaneous optimization methods are under investigation. In
this context model reduction techniques, e.g. Proper Orthogonal Decomposition, will be
employed to achieve a suboptimal solution for the optimal control problem.
Partner: Collaborative Research Centre (SFB) 666: “Integral sheet metal design with
higher order bifurcations - development, production, evaluation”; speaker P. Groche (Department
of Mechanical Engineering, TU Darmstadt)
Support: German Research Foundation (DFG)
Contact: D. Koller, S. Ulbrich
References
[1] D. Koller and S. Ulbrich. Optimal control of hydroforming processes. Proceedings in Applied
Mathematics and Mechanics, 11:795 –796, 2011.
[2] D. Koller and S. Ulbrich. Ableitungsfreie Optimierungsverfahren für die optimale Steuerung
von wirkmedienbasierten Tiefziehprozessen. Tagungsband 4. Zwischenkolloquium Sonderforschungsbereich
666, Hrsg. Peter Groche, pages 41 – 48, 2012.
1.2.8 Stochastics
Research in the stochastics group is focused on mathematical statistics (i.e., on the mathematical
analysis of randomly disturbed data) and on statistical mechanics with connections
to the phsyical sciences.
We are interested in the theoretical analysis of methods of mathematical statistics, the
study of interacting particle systems, interacting Brownian motions, phase transitions and
critical phenomena. Furthermore we investigate applications in various fields of physics,
science and engineering.
Specifically, we work on curve estimation (in particular nonparametric regression and nonparametric
density estimation), spatial random permutations, and probabilistic methods
in quantum theory. Furthermore, we study Monte Carlo methods for financial engineering,
and applications of probability theory to the theory of Bose-Einstein condensation.
The members of the research group stochastics are involved in joint projects with colleagues
working in probability and statistics, as well as from neighboring disciplines like
econometrics, engineering sciences, physics, and psychology. Furthermore, we are carrying
out research projects in applied stochastics with well-known industrial partners.
84 1 Research