Deterministic and robust optimisation strategies for metal forming proceesses


Bonte, M.H.A. and Boogaard, A.H. van den and Huetink, J. (2007) Deterministic and robust optimisation strategies for metal forming proceesses. In: Forming Technology Forum 2007 – Application of Stochastics and Optimization Methods, 14th – 15th March 2007, ETH Zurich, Switzerland.

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Abstract:Product improvement and cost reduction have always been important goals in the metal forming industry. The rise of
Finite Element simulations for metal forming processes has contributed to these goals in a major way. More recently, coupling
FEM simulations to mathematical optimisation techniques has shown the potential to make a further contribution to product
improvement and cost reduction.
Mathematical optimisation consists of the modelling and solving of optimisation problems. Although both the
modelling and the solving are essential for successfully optimising metal forming problems, much of the research published until
now has focussed on the solving part, i.e. the development of a specific optimisation algorithm and its application to a specific
optimisation problem for a specific metal forming process.
In this paper, we propose a generally applicable optimisation strategy which makes use of FEM simulations of metal
forming processes. It consists of a structured methodology for modelling optimisation problems related to metal forming.
Subsequently, screening is applied to reduce the size of the optimisation problem by selecting only the most important design
variables. Screening is also utilised to select the best level of discrete variables, which are in such a way removed from the
optimisation problem. Finally, the reduced optimisation problem is solved by an efficient optimisation algorithm. The strategy is
generally applicable in a sense that it is not constrained to a certain type of metal forming problems, products or processes. Also
any FEM code may be included in the strategy.
However, the above strategy is deterministic, which implies that the robustness of the optimum solution is not taken
into account. Robustness is a major item in the metal forming industry, hence we extended the deterministic optimisation
strategy in order to be able to include noise variables (e.g. material variation) during optimisation. This yielded a robust
optimisation strategy that enables to optimise to a robust solution of the problem, which contributes significantly to the industrial
demand to design robust metal forming processes. Just as the deterministic optimisation strategy, it consists of a modelling,
screening and solving stage.
The deterministic and robust optimisation strategies are compared to each other by application to an analytical test
function. This application emphasises the need to take robustness into account during optimisation, especially in case of
constrained optimisation. Finally, both the deterministic and the robust optimisation strategies are demonstrated by application to
an industrial hydroforming example.
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