The Effect of Multiple Additional Sampling with Multi-Fidelity, Multi-Objective Efficient Global Optimization Applied to an Airfoil Design

Abstract

The multiple additional sampling point method has become popular for use in Efficient Global Optimization (EGO) to obtain aerodynamically shaped designs in recent years. It is a challenging task to study the influence of adding multi-sampling points, especially when multi-objective and multi-fidelity requirements are applied in the EGO process, because its factors have not been revealed yet in the research. In this study, the addition of two (multi-) sampling points (2-MAs) and four (multi-) sampling points (4-MAs) in each iteration are used to study the proposed techniques and compare them against results obtained from a single additional sampling point (1-SA); this is the approach that is conventionally used for updating the hybrid surrogate model. The multi-fidelity multi-objective method is included in EGO. The performance of the system, the computational convergence rate, and the model accuracy of the hybrid surrogate are the main elements for comparison. Each technique is verified by mathematical test functions and is applied to the airfoil design. Class Shape Function Transformation is used to create the airfoil shapes. The design objectives are to minimize drag and to maximize lift at designated conditions for a Reynolds number of one million. Computational Fluid Dynamics is used for ensuring high fidelity, whereas the panel method is employed when ensuring low fidelity. The Kriging method and the Radial Basis Function were utilized to construct high-fidelity and low-fidelity functions, respectively. The Genetic Algorithm was employed to maximize the Expected Hypervolume Improvement. Similar results were observed from the proposed techniques with a slight reduction in drag and a significant rise in lift compared to the initial design. Among the different techniques, the 4-MAs were found to converge at the greatest rate, with the best accuracy. Moreover, all multiple additional sampling point techniques are shown to improve the model accuracy of the hybrid surrogate and increase the diversity of the data compared to the single additional point technique. Hence, the addition of four sampling points can enhance the overall performance of multi-fidelity, multi-objective EGO and can be utilized in highly sophisticated aerodynamic design problems.

Keywords

• multi-additional sampling
• multi-fidelity
• multi-objective
• efficient global optimization
• airfoil design