A data-driven metric-based proper orthogonal decomposition method with Shapley Additive Explanations for aerodynamic shape inverse design optimization

Abstract

In the present study, an effective optimization framework of aerodynamic shape inverse design is established based on the data-driven metric-based proper orthogonal decomposition (DMPOD) method. This framework employs a DMPOD method that filters superior data sets and POD bases using a data-driven filtering strategy with Shapley Additive Explanations (SHAP) and a modified application criterion for bases. The efficiency of the framework is improved by reduced design variables and narrowed design space which both benefit from the DMPOD method. In the DMPOD method, the data-driven filtering strategy effectively filters superior data sets, addressing the limitations of traditional methods, while geometric approximation-based sample generation method enhances dynamic change capture during the optimization process. In addition, the modified application criterion for bases selects important bases based on their relevance to the objective function and determines the necessary quantity. The effectiveness, efficiency, and robustness of the optimization framework are validated by the inverse design case of the RAE2822 airfoil. The results show that the optimization framework with DMPOD effectively enhances optimization efficiency and robustness, with improvements of 31.32% and 84.89% for superior data set, respectively, compared to the MPOD method, and have a better optimization effect.