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GCOE Seminars
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
2013/02/27
10:00-11:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Dietmar Hoemberg (Weierstrass Institute)
Sufficient optimality conditions for a semi-linear parabolic system related to multiphase steel production (ENGLISH)
Dietmar Hoemberg (Weierstrass Institute)
Sufficient optimality conditions for a semi-linear parabolic system related to multiphase steel production (ENGLISH)
[ Abstract ]
Multiphase steels combine good formability properties with high strength and have therefore become important construction materials, especially in automotive industry. The standard process route is hot rolling with subsequent controlled cooling to adjust the desired phase mixture. In the first part of the talk a phenomenological model for the austenite ferrite phase transition is developed in terms of a nucleation and growth process, where the growth rate depends on the carbon concentration in austenite. The approach allows for further extensions, e.g., to account for a speed up of nucleation due to deformation of austenite grains. The model is coupled with an energy balance to describe the phase transitions on a run-out table after hot rolling. Here, the most important control parameters are the amount of water flowing per time and the feed velocity of the strip. The spatial flux profile of the water nozzles has been identified from experiments.
Since the process window for the adjustment of the phase composition is very tight the computation of optimal process parameters is an important task also in practice. This is discussed in the second part of the talk using a classical optimal control approach, where 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.
(joint work with K. Krumbiegel and N. Togobytska, WIAS)
Multiphase steels combine good formability properties with high strength and have therefore become important construction materials, especially in automotive industry. The standard process route is hot rolling with subsequent controlled cooling to adjust the desired phase mixture. In the first part of the talk a phenomenological model for the austenite ferrite phase transition is developed in terms of a nucleation and growth process, where the growth rate depends on the carbon concentration in austenite. The approach allows for further extensions, e.g., to account for a speed up of nucleation due to deformation of austenite grains. The model is coupled with an energy balance to describe the phase transitions on a run-out table after hot rolling. Here, the most important control parameters are the amount of water flowing per time and the feed velocity of the strip. The spatial flux profile of the water nozzles has been identified from experiments.
Since the process window for the adjustment of the phase composition is very tight the computation of optimal process parameters is an important task also in practice. This is discussed in the second part of the talk using a classical optimal control approach, where 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.
(joint work with K. Krumbiegel and N. Togobytska, WIAS)
