Improving aerodynamic optimization design of transonic airfoils with response surface methodology for design variables as many as about sixteen

Response Surface Methodology (RSM) has been used to improve successfully model precision for design variables as many as about ten^[1]. But if design variables higher than ten, say about sixteen, are needed, the quadratic polynomials can no longer satisfy precision requirement; higher polynomials are needed for design variables as many as about sixteen but they will bring almost prohibitive computational burden. We aim to solve this dilemma with using quadratic polynomials twice or thrice. In the full paper, we explain how to use quadratic polynomials repeatedly. Here we just give a briefing. First, we can divide the design space into several smaller design spaces. Then each design can be performed in a smaller design space until the results are good enough. In general two smaller design spaces are enough for transonic airfoil design with about sixteen design variables. For sixteen design variables, the design results obtained with using quadratic polynomials twice are; (1) the fitting errors are less than one percent; (2) the drag coefficient is reduced by 19.34 percent in drag-reducing design.