Global Sensitivity Analysis in Aerodynamic Design Using Shapley Effects and Polynomial Chaos Regression

Quantifying the impact of design variables in aerodynamic design exploration can provide valuable insights to designers. Global sensitivity analysis (GSA) is a crucial tool in aerodynamic design exploration that enables designers to gain valuable insights by quantifying the impact of design variables. In the field of GSA, the Shapley effect is a powerful alternative to total Sobol indices due to several mathematical advantages of the former. However, computing the Shapley effect is computationally expensive due to the large number of permutations involved. To overcome this challenge, surrogate models are often used to accurately estimate Shapley effects while reducing the number of function calls. This paper aims to investigate the effectiveness of using PCE to compute Shapley effects for independent inputs in aerodynamic design exploration. The exact calculation from PCE also enables the rapid assessment of confidence intervals for Shapley effects, taking into account the randomness in the experimental design via bootstrap resampling. The usefulness of Shapley effects with PCE is then demonstrated and compared with total Sobol indices through a nonlinear test function and three engineering problems, including subsonic wing, transonic airfoil, and fan blade design. The results also show that the confidence intervals of the Shapley effects are narrower than those of total Sobol indices, allowing better interpretation and higher confidence on the estimated GSA metric.