Robustness criterion for the optimization scheme based on kriging metamodel

International audienceIn the context of robust shape optimization, the estimation cost of some physical models is reduce with the use of a response surface. A procedure that requires the estimation of moment 1 and 2 is set up for the robust optimization. The step of the optimization procedure and the partitioning of Pareto front are already developed in the literature. However, the research of a criteria to estimate the robustness of each solution at each iteration is not much explored. The function, the first and second derivatives is given by the majority of industrial code. We propose a robust optimization procedure that based on the prediction of the function and its derivatives predicted by a kriging with a Matern 5/2 covariance kernel. The modeling of the second derivative and consequently the prediction of first and the second derivatives are possible with this kernel. In this context we propose to consider the Taylor theorem calculated in each point of the conception space to approximate the variation around these points. This criterion is used as the replacement of the moment 2 usually employed. A Pareto front of the robust solutions (minimization of the function and the robustness criteria) is generated by a genetic algorithm named NSGA-II. This algorithm gives a Pareto front in an reasonable time of calculation. We show the motivations of this method with an academic example