HDMR-based surrogate model for high dimensional aerodynamic design problems

Conventional surrogate models will break down in dealing with high dimensional design problems which is known as the “curse-of-dimensionality”. The purpose of the current work is to develop a more accurate surrogate model for high dimensional problems. In this paper, the High Dimensional Model Representation (HDMR) is studied. The basic idea of HDMR is that for most well-defined physical systems, only relatively low-order correlations of the input variables are expected to have an impact upon the output. The superiority of HDMR-based surrogate model over conventional LHS-based surrogate models is shown through mathematical test functions with a wide scope of dimensionalities. Further, the HDMR-based surrogate model is applied to aerodynamic design of wing with high dimensional design variables. Aerodynamic data of a transonic wing and a supersonic wing are utilized to build the surrogate models and results show that the HDMR-based surrogate model is much better than conventional LHS-based surrogate model.