Optimization methods
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Date |
15/01/2007 |
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Author |
T.
V. Tran, S. Brisset, P. Brochet |
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Affiliation |
L2EP
– EC Lille – France |
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Email |
tran.tuan-vu@ec-lille.fr, stephane.brisset@ec-lille.fr, pascal.brochet@ec-lille.fr |
|
Method |
Output-mapping
technique |
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References |
Lagarias, J.C., J. A. Reeds, M. H.
Wright, and P. E. Wright, "Convergence Properties of the Nelder-Mead
Simplex Method in Low Dimensions," SIAM
Journal of Optimization, Vol. 9 Number 1, pp. 112-147, 1998. |
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Description of the method |
The
output-mapping technique is considered as another type of space mapping
technique. The idea of the output-mapping algorithm is to modify easily the
analytical coarse model by adding some estimators θi in order to align the responses of FEA and
analytical models. Here, least-squares function is used to minimize the
errors between both models. It is solved by the Nelder-Mead Simplex method
(Lagarias, 1998) to update θi
at each iteration. The
algorithm starts by setting all estimators equal to 1 and solving the SQP
optimization on analytical model. Then the constraints of the fine model are
checked by 3D FEA simulation with the geometric parameter zopt. The process of the
mapping of both models is a modification of the coefficients in order to
minimize the responses of two models. Actually, the estimators are computed
with the least-squares function where the input variables are constant and
equal to xi. |
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Publication of the method |
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