Inverse airfoil design algorithm based on multi-output least-squares support vector regression machines

Inverse airfoil design algorithm can obtain the airfoil geometry according to the target pressure coefficient (Cp) distribution. Recently, the rapid development of machine learning method provides new idea to solve engineering problem. Multi-output least-squares support vector regression machines (MLS-SVR) is a multi-output regression machine learning method which can make prediction for several outputs simultaneously through learning a mapping from a multivariate input feature space to a multivariate output space. In this paper, MLS-SVR is used to learn the mapping from the Cp distribution to the geometry, which can be seen as a multi-output regression problem. Through iteratively adding the predicted airfoil geometry and its pressure coefficient distribution into the sample database, the precision of MLS-SVR to predict the right airfoil geometry corresponding to the target Cp distribution is improved. A low speed, transonic and supersonic airfoil inverse design problem are used to validate the efficiency of the proposed algorithm, and the experimental results show that the proposed algorithm can save 34.1% and 58.6% CFD evaluations for low speed and transonic cases respectively to obtain satisfactory airfoil.