Invited Session Thu.1.MA 415

Thursday, 10:30 - 12:00 h, Room: MA 415

Cluster 19: PDE-constrained optimization & multi-level/multi-grid methods [...]

Optimization applications in industry VI


Chair: Dietmar Hömberg



Thursday, 10:30 - 10:55 h, Room: MA 415, Talk 1

Ekaterina Kostina
Optimization methods for nonlinear model predictive control of non-stationary partial differential equations

Coauthors: H.-G. Bock, G. Kriwet, J.P Schloeder


Many spatio-temporal processes in the natural and life sciences, and engineering are described by the mathematical model of non-stationary
PDE. It would be of high practical relevance as well as a mathematical challenge to use such models for a process optimization subject to numerous important inequality restrictions. However in the presence of disturbances and modeling errors the real process will never follow
the off-line computed optimal solution. Thus the challenge is to compute feedback controls that take these perturbations into account. We present a new optimization method for the NMPC. The NMPC principle is to solve a complete optimal control problem whenever new information about perturbations is available and to apply the first instant of the optimal control as a feedback law. However the frequency of perturbation information is orders of magnitude higher than even a single optimization iteration. Therefore we discuss multi-level iterations strategy to make NMPC computations real-time feasible for PDE optimal control problems.
% Based on joint work with H.G. Bock, G. Kriwet and J.P.Schloeder.



Thursday, 11:00 - 11:25 h, Room: MA 415, Talk 2

Georg Vossen
Optimization and model reduction methods for heat source determination in welding

Coauthors: Axel Haeck, Andreas Pittner


The physical phenomena in welding can yet not completely be described by mathematical models. In industrial applications, it is therefore common to describe the effects of the heat energy by means of a parametrized volume source. Its parameters are obtained in several steps by a calibration of computed and experimental temperature data extracted out of transverse sections and thermo-elements. In each step, a time-dependent partial differential equation (PDE) on a three-dimensional domain has to be solved. The industrial standard practice is to use standard Finite Element methods for simulation of the PDE and to apply the calibration manually leading to overall times of up to several weeks for the procedure.
In this talk, we will formulate the procedure as an optimization problem with a finite-dimensional optimization variable and infinite-dimensional equality constraints, and we will discuss theoretical aspects of the problem. We will then develop and apply optimization strategies combined with model reduction methods such as Proper Orthogonal Decomposition, H2-norm model reduction and Balanced Truncation to solve the problem efficiently.



Thursday, 11:30 - 11:55 h, Room: MA 415, Talk 3

Dietmar Hömberg
Optimal control of multiphase steel production

Coauthors: Klaus Krumbiegel, Nataliya Togobytska


In this talk I will discuss an optimal control problem related to the production of multiphase steels. The state system consists of a parabolic equation for the evolution of temperature and a system of rate laws to describe occurring phase transitions, while a coefficient in the Robin boundary condition acts as the control. I will discuss necessary and sufficient optimality conditions, describe a SQP-approach for its numerical solution and conclude with some numerical results for a pilot hot-rolling mill situated in the lab of our partners from engineering sciences at Bergakademie Freiberg.


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