Proper orthogonal decomposition-based data mining of aerodynamic shape for design optimization

Abstract

Global optimization methods are becoming more and more important in aerodynamic shape optimization. A large number of proceeding data will be generated during design optimization, from which the implicit but valuable design knowledge can be extracted. The design knowledge can then be used to help the designers to acquire the effects of geometric variations on the aerodynamic performance changes. In this paper, we strive to extract the implicit design knowledge from proceeding data by a data mining method based on proper orthogonal decomposition (POD), by which the design knowledge more enriched and more visualized than those obtained from other data mining methods can be obtained. Proceeding data for data mining are ingathered from aerodynamic shape optimization of a transonic compressor rotor blade, NASA Rotor 37. The design optimization attempts to maximize the adiabatic efficiency of Rotor 37 under the operation condition near peak efficiency with the constrains of mass flow rate and total pressure ratio. The parallel synchronous particle swarm optimization method is employed to search for the optimization in the design space. The particles with improved adiabatic efficiency, while within the optimization constrain tolerances are picked up from the design optimization, which are then used for data mining. The geometric coordinates of the aerodynamic shape with respect to the ingathered particles are regarded as the snapshots. Then the POD modes of the aerodynamic shape can be obtained by singular value decomposition on the snapshots. The results show that the universal rules of geometry variations for the optimization maximizing the adiabatic efficiency of Rotor 37 can be directly visualized by the design knowledge extracted from the proceeding data by POD-based data mining technique. Furthermore, the optimization results are also verified by the design knowledge extracted by data mining.