Contributed Session Fri.1.MA 415

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

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

Reduced order model based optimization


Chair: Jane Ghiglieri



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

Andreas Schmidt
POD reduced-order modeling in the context of direct-approach optimization

Coauthors: Hans-Georg Bock, Stefan K├Ârkel


To solve optimization problems that involve PDE constraints in general two approaches are distinguished, namely the direct and the indirect approach where we either `first discretize - then optimize' or `first optimize - then discretize'. If Proper Orthogonal Decomposition (POD) is used to reduce the size of the optimization problem in most of
the applications this takes place in the indirect setting.
We will consider the use of POD in a direct-approach setting together with time-dependent PDEs. We can see that a naive application of POD will result in a reduced-order model that lacks the essential property to reflect derivative information of the original high-fidelity model. A remedy to overcome this is the inclusion of necessary derivative information obtained from the high-fidelity model. We will see that
the resulting `enriched' reduced-order model has very beneficial properties. More specifically we obtain accurate approximations to the original problem of either forward derivatives or adjoint derivatives. Furthermore the derivatives will always be consistent even for changing
parameter configurations.



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

Jane Ghiglieri
Optimal flow control based on POD and MPC for the cancellation of Tollmien-Schlichting waves by plasma actuators

Coauthor: Stefan Ulbrich


The occurrence of a transition in a flat plate boundary layer is characterized by the formation of growing disturbances inside the boundary layer, the Tollmien-Schlichting waves. Successful damping of these waves can delay transition for a significant distance downstream, lowering the skin friction drag of the body.
We consider plasma actuators which induce a body force for active flow control. By optimal control of the plasma actuator parameters it is possible to reduce or even cancel the Tollmien-Schlichting waves and delay the turbulence transition.
We present a Model predictive control (MPC) approach for the cancellation of Tollmien-Schlichting waves in the boundary layer of a flat plate. We use proper orthogonal decomposition (POD) for the low-order description of the flow model and the optimization of the control parameters is performed within the reduced system.
Furthermore, we will show methods for improving the reduced model whose quality is verified in comparison to the results of a finite element based simulation for the considered problem.
Finally, we present our cancellation results with this MPC approach in a numerical simulation.



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

Daniela Koller
Optimal control of hydroforming processes based on POD

Coauthor: Stefan Ulbrich


The sheet metal hydroforming process is a complex forming process, which
involves contact, friction and plasticity to manufacture curved
sheet metals with bifurcated cross section. These sheet metal products
are examined within the Collaborative Research Centre (CRC) 666.
Mathematically, the sheet metal hydroforming process leads to an evolution
quasi-variational inequality. We seek for optimal controls of the process
relevant control variables, e.g., the time dependent blank holder force and
the fluid pressure.
Since the resulting VI-constrained optimization problem is very complex and
computationally intensive, we apply model reduction techniques. We use
Proper Orthogonal Decomposition (POD) to obtain a low-order model of the
hydroforming process.
Based on a Galerkin approximation and a semismooth reformulation we will
discuss the derivation of a reduced model for the evolution variational
Numerical results of a simplified engineering application for the optimal
control of hydroforming processes will be presented.


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