Iterative response surface based optimization scheme for transonic airfoil design

An improved response surface based optimization technique is presented for two-dimensional airfoil design at transonic speed. The method is based on an iterative scheme where least-square fitted quadratic polynomials of objective function and constraints are repeatedly corrected locally, about the current minimum, by adding the actual function value to the data set used to construct the polynomials. When no further cost function reduction is achieved, the design domain upon which the optimization is initially performed is changed, preserving its initial size, by updating the center point with the position of the last minimum found. The optimization is then conducted by using the same approximations built over the initial design space, which are again iteratively corrected until convergence to a given tolerance. To construct the response surfaces, the design space is explored by using a uniform Latin hypercube, aiming at reducing the bias error, in contrast with previous techniques based on D-optimality criterion. The geometry is modeled by using the PARSEC parameterization. The multiple tests conducted to validate the methodology, regarding a redesign of the outer wing of a blended wing body configuration and the optimization of the RAE2822 airfoil, suggest that the present technique can be more efficient and effective than some other published methods proposed for numerical aerodynamic optimization.