We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cyclic parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

We demonstrate a technique to evaluate the aerodynamic robustness of a given blade profile which it is exposed to stochastic geometrical variation. The technique is based on random fields, with geometrical deviations continuously defined over the entire structure, with a prescribed statistical distribution function and a given correlation between these deviations. Control points are defined on the blade surface to model the blade geometry disturbances. At each control point a stochastic deviation is defined, which acts in the normal direction of the blade. By modeling disturbances in the normal direction instead of in the separate Cartesian directions, we automatically reduce the number of stochastic variables by a factor two. The perturbation variables are transformed via Karhunen-Loève eigenvalue decomposition, giving stochastically independent variables. The robustness is finally estimated by a Monte Carlo simulation, where computational fluid dynamic simulations are performed to evaluate the resulting change in blade performance for given geometrical perturbations.