Solving optimisation problems in metal forming using Finite Element simulation and metamodelling techniques


Bonte, M.H.A. and Boogaard, A.H. van den and Huetink, J. (2005) Solving optimisation problems in metal forming using Finite Element simulation and metamodelling techniques. In: Apomat conference, 2005, Morschach, Switzerland.

open access
Abstract:During the last decades, Finite Element (FEM) simulations
of metal forming processes have become important
tools for designing feasible production processes. In more
recent years, several authors recognised the potential of
coupling FEM simulations to mathematical optimisation
algorithms to design optimal metal forming processes instead
of only feasible ones.
Within the current project, an optimisation strategy is being
developed, which is capable of optimising metal forming
processes in general using time consuming nonlinear
FEM simulations. The expression “optimisation strategy”
is used to emphasise that the focus is not solely on solving
optimisation problems by an optimisation algorithm, but
the way these optimisation problems in metal forming are
modelled is also investigated. This modelling comprises
the quantification of objective functions and constraints
and the selection of design variables.
This paper, however, is concerned with the choice for
and the implementation of an optimisation algorithm for
solving optimisation problems in metal forming. Several
groups of optimisation algorithms can be encountered in
metal forming literature: classical iterative, genetic and
approximate optimisation algorithms are already applied
in the field. We propose a metamodel based optimisation
algorithm belonging to the latter group, since approximate
algorithms are relatively efficient in case of time consuming
function evaluations such as the nonlinear FEM calculations
we are considering. Additionally, approximate optimisation
algorithms strive for a global optimum and do
not need sensitivities, which are quite difficult to obtain
for FEM simulations. A final advantage of approximate
optimisation algorithms is the process knowledge, which
can be gained by visualising metamodels.
In this paper, we propose a sequential approximate optimisation
algorithm, which incorporates both Response
Surface Methodology (RSM) and Design and Analysis
of Computer Experiments (DACE) metamodelling techniques.
RSM is based on fitting lower order polynomials
by least squares regression, whereas DACE uses Kriging
interpolation functions as metamodels. Most authors in
the field of metal forming use RSM, although this metamodelling
technique was originally developed for physical
experiments that are known to have a stochastic na-
¤Faculty of Engineering Technology (Applied Mechanics group),
University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands,
ture due to measurement noise present. This measurement
noise is absent in case of deterministic computer experiments
such as FEM simulations. Hence, an interpolation
model fitted by DACE is thought to be more applicable in
combination with metal forming simulations. Nevertheless,
the proposed algorithm utilises both RSM and DACE
metamodelling techniques.
As a Design Of Experiments (DOE) strategy, a combination
of a maximin spacefilling Latin Hypercubes Design
and a full factorial design was implemented, which takes
into account explicit constraints. Additionally, the algorithm
incorporates cross validation as a metamodel validation
technique and uses a Sequential Quadratic Programming
algorithm for metamodel optimisation. To overcome
the problem of ending up in a local optimum, the
SQP algorithm is initialised from every DOE point, which
is very time efficient since evaluating the metamodels can
be done within a fraction of a second. The proposed algorithm
allows for sequential improvement of the metamodels
to obtain a more accurate optimum.
As an example case, the optimisation algorithm was applied
to obtain the optimised internal pressure and axial
feeding load paths to minimise wall thickness variations
in a simple hydroformed product. The results are satisfactory,
which shows the good applicability of metamodelling
techniques to optimise metal forming processes using
time consuming FEM simulations.
Item Type:Conference or Workshop Item
Engineering Technology (CTW)
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