Sensitivity-Based Parameterization for Aerodynamic Shape Global Optimization

Abstract

For aerodynamic shape design using gradient-free searching algorithms, which can be applied more flexibly than gradient-based ones, computing costs increase dramatically with dimensionality. Rational design variables are considered vital to elevate design performance in gradient-free optimization. In this paper, the Bèzier surface free-form deformation (FFD) parameterization based on adjoint surface sensitivity analysis is proposed for aerodynamic shape global optimization. Specifically, FFD point lattice is located where a wide variation is identified in adjoint surface sensitivity. In addition, input space has been adjusted accordingly to enhance space coverage due to the smoothness feature of Bernstein polynomial basis in Bèzier surface FFD. The proposed parameterization was applied to a transonic inviscid drag reduction problem for NACA 0012 with thickness constraints in dimensionality from 5 to 11, and 360.5 counts reduction in drag was achieved. In general, compared with the regularly spaced control lattice, the proposed parameterization effectively weakens the strong shock wave, and drag is decreased considerably using a small-scale sample database.