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Communication Dans Un Congrès Année : 2011

Multilevel Optimization Using Multiparametric Strategy and Cokriging Metamodel

Résumé

Optimization strategies on assembly design are often relatively time expensive because of the large numbers of non-linear calculations (due to contact or friction problems) required to localize the optimum of an objective function. The work presented here lies in reduction of the computational time. To attain this goal, a classical multilevel model optimization process and a specific strategy that allows to reduce the computational cost are introduced. Composed by two levels the optimization process consists in the building of kriging-based metamodel used to localize one or some areas where the optimum may be found. Then, an optimization using the mechanical model is achieved to find precisely the optimum. In this case, the mechanical model is used during two phases: to build the metamodel and to refine the optimum research. Developed by, multiparametric strategy associated to the mechanical model is based on a finite element method and an iterative scheme called the LaTin method. Associated to a set of design parameters this algorithm allows us to obtain an approximated solution on the whole loading path and on every points of the structure. On each iteration the approximated solution is enriched. If we search the solution associated to another set of parameters, the multiparametric strategy consists to reinitialize the LaTIn algorithm with an approximated solution obtained for another set of design parameters. The reuse of results provides faster convergence and allows one to reduce significantly the computational time. In this context, the use of this strategy enables one to obtain inexpensively the gradients of the objective function using finite difference method. Indeed the evaluations required to compute the gradients are obtained with very low variation of the design parameters and are time inexpensive. The gradients are often required in some optimization algorithms but another very interesting aspect is that they can also be used to build some richer kind of metamodels. One of them is called Cokriging and comes from the multivariate geostatistics. It has similar features of the spatial interpolation technique called Kriging. The prediction of the response of a function on any point of the space is made from the real deterministic evaluations and gradients of the quantity of interest. Thanks to the multiparametric strategy and the CoKriging, the metamodel obtained is less time expensive and more accurate than that is obtained with a classical strategy for the same number of calls to the full mechanical model. The first step of the strategy will be presented: building of Cokriging metamodel using multiparametric strategy. The gain in terms of computational cost will be demonstrated on several analytical and mechanical examples.
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Dates et versions

hal-01431908 , version 1 (11-01-2017)

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  • HAL Id : hal-01431908 , version 1

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Luc Laurent, Pierre-Alain Boucard, Bruno Soulier. Multilevel Optimization Using Multiparametric Strategy and Cokriging Metamodel. IRTG 1627 Workshop, Sep 2011, Porquerolles, France. ⟨hal-01431908⟩
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