Aerodynamic shape optimization in transonic conditions through parametric model embedding

The paper presents a novel approach for aerodynamic shape optimization problems using the parametric model embedding (PME) method. PME reduces the design-space dimensionality while maintaining a connection to the original design parameters, addressing the curse of dimensionality. The optimization of an airfoil's drag in transonic conditions demonstrates the method, using the RAE-2822 airfoil at Mach 0.734 and a Reynolds number of 6.5 million. Employing the covariance matrix adaptation evolution strategy, the process is performed with 1,000 function evaluations in both original and PME-reduced design spaces. Moreover, statistical criteria based on advanced risk function are introduced to characterize and study the evolution of the optimization process. Results show that PME effectively retains essential design space characteristics, capturing at least 95% of the geometric variance associated with the original design space. This leads to significant aerodynamic improvements, including reduced drag and smoother pressure distributions. Additionally, the statistical analysis helps to understand the advantages and disadvantages of different levels of parameter space compression.