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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 97
PROCEEDINGS OF THE SECOND INTERNATIONAL CONFERENCE ON SOFT COMPUTING TECHNOLOGY IN CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING
Edited by: Y. Tsompanakis, B.H.V. Topping
Paper 50

Fast Multilevel Optimization using a Multiparametric Strategy and a Cokriging Metamodel

L. Laurent, P.A. Boucard and B. Soulier

LMT-Cachan, (ENS Cachan/CNRS/Université Paris 6/PRES UniverSud Paris), Cachan, France

Full Bibliographic Reference for this paper
L. Laurent, P.A. Boucard, B. Soulier, "Fast Multilevel Optimization using a Multiparametric Strategy and a Cokriging Metamodel", in Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Second International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 50, 2011. doi:10.4203/ccp.97.50
Keywords: multilevel optimization, metamodel, cokriging, multiparametric strategy, LATIN method, assemblies.

Summary
Optimization processes on assembly design are often relatively time consuming. This kind of strategy requires a large number of calculations to localize the optimum of an objective function. Moreover, these calculations are often nonlinear as a result of the contact or friction problems. In this context our main purpose is therefore to reduce computation time. Therefore a multilevel model optimization process [1] and a dedicated mechanical solving strategy are used. Our multilevel model optimization uses two levels: the first is composed of a kriging-based metamodel and the second one of the full mechanical model. In the paper, the proposed study focused on the computation cost to build a metamodel using data obtained using the full mechanical model.

Firstly, a specific multiparametric strategy [2] is presented. It relies on the LaTIn method developed by Ladevèze [3] and using a reinitialization process, it allows the computation time to be significantly reduced. This strategy was applied on one two-variable example to illustrate the method. It appears that the multiparametric strategy is very efficient for the calculation of solutions on very close sample points.

This property is adapted to coupling the multiparametric strategy with a gradient-based metamodel in which the gradients are obtained with a finite difference method. Thus a cokriging metamodel [4] is presented and compared with a classical kriging metamodel [5]. The two kinds of metamodels were applied to one- and two-dimensional analytic functions. The main conclusions are that for a same number of sample points cokriging provides a better approximation than kriging and for a same number of evaluations both metamodels can provide a similar approximation.

Finally this specific feature was used on a real mechanical problem. Thus the coupling between the metamodel and the multiparametric strategy allows us to obtain a good quality of the approximation of the quantity of interest with an important gain in terms of computation cost.

These results are not only significant for the building of metamodels but also to decrease computation time in gradient-based optimization algorithm. This aspect will be crucial in the development of the direct optimization on the second level of our multilevel model optimization.

References
1
G.M. Robinson, A.J. Keane, "A case for multi-level optimisation in aeronautical design", Aeronautical Journal, 103(1028), 481-485, 1999.
2
P.A. Boucard, L. Champaney, "A suitable computational strategy for the parametric analysis of problems with multiple contact", International Journal for Numerical Methods in Engineering, 57(9), 1259-1281, 2003. doi:10.1002/nme.724
3
P. Ladevèze, "Nonlinear computational structural mechanics: new approaches and non-incremental methods of calculation", Springer Verlag, 1999.
4
N.A.C. Cressie, "Statistics for spatial data", John Wiley & Sons, New York, 1993.
5
G. Matheron, "Principles of geostatistics", Economic geology, 58(8), 1246, 1963. doi:10.2113/gsecongeo.58.8.1246

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