A study on constrained efficient global optimization method for noisy computational fluid dynamics data

Abstract

The efficient global optimization method is a global optimization technique that can select the next sample point automatically by infill sampling criteria and search for the global minimum with less samples than the conventional global optimization needs. Infill sampling criteria function consists of the predictor and mean square error provided from the kriging model, which is a stochastic metamodel. Also, the constrained efficient global optimization method can minimize the objective function when dealing with constraints under the efficient global optimization concept. In this study, the constrained efficient global optimization method was applied to the RAE2822 airfoil shape design formulated with constraint. But the noisy computational fluid dynamics data caused the kriging model to fail to depict the true function. The distorted kriging model would make the efficient global optimization deviate from the correct search. This distortion of kriging model can be handled with the interpolation (p = free) kriging model. With the interpolation (p = free) kriging model, however, the search for efficient global optimization solution was stalled in a narrow feasible region, so there were less chances to update the objective and constraint functions. Then the accuracy of the efficient global optimization solution may not be good enough, so the three-step search method is proposed to obtain an accurate global minimum as well as prevent the distortion of kriging model for the noisy constrained computational fluid dynamics problem.