Aerodynamics shape optimization with parameter reduced adjoint method

Shape optimization is important for improving the performance of industrial designs, but adjoint-based methods often require hundreds or thousands of design variables, which makes optimization costly and difficult. This study proposes a parameter reduction method that keeps the flexibility of the design space while reducing computational effort.
The method combines Inverse Distance Weighting (IDW) interpolation and Radial Basis Function (RBF) interpolation for mesh deformation. IDW, with a surface smoothing procedure, provides an explicit one-to-one mapping without solving additional linear systems, which ensures efficient deformation. However, IDW alone may result in poor smoothness in the aerodynamic surface and its gradients. To overcome this, RBF interpolation is introduced, so that parameter reduction acts on control points instead of dense mesh nodes, improving both smoothness and convergence. In this framework, adjoint sensitivities are used to rank and select the most important design parameters, allowing the optimizer to focus on the aerodynamic regions that matter most, without pre-defined topologies.
The approach was tested on a 2D aerofoil, a gas turbine blade tip, and a large wind turbine blade. In the aerofoil case, the reduced-parameter method achieved a 6.8% drag reduction, comparable to the full adjoint method, while using more than 70% fewer variables. For the turbine tip, the optimized design reduced leakage mass flow by 12%. In the wind turbine blade case, aerodynamic efficiency improved with 40% less computational time compared to the full design space. In all cases, the optimizer maintained or improved design quality at much lower cost.
The results show that combining IDW and RBF with sensitivity-based parameter reduction provides a robust and scalable strategy for high-dimensional aerodynamic optimization.