Shapley Additive Explanations of Multigeometrical Variable Coupling Effect in Transonic Compressor

Abstract Optimization algorithms in the compressor detailed design stage generate big data of geometries and corresponding performances, but these data are often not exploited efficiently to unveil hidden compressor design guidance. In this work, the Shapley additive explanations (SHAP) method from game theory is proposed as an efficient methodology to extract design guidelines from databases. A database was generated when optimizing the blade features (sweep, lean, and end-bend) of Rotor 37. Based on this, a neural network is trained to predict compressor efficiency. The SHAP method is then applied to explain the neural network behavior, which provides information on the sensitivity of single geometrical variables and the coupling effect between multiple geometrical variables. Results show that the near-tip sweep and midspan lean angles are most influential on efficiency. Within the same group of variables, the adjacent variables tend to present strong positive coupling effects on efficiency. Among different groups, evident coupling effects are observed between sweep and lean and between lean and end-bend, but the coupling effect between sweep and end-bend is negligible. Flow mechanisms behind the coupling effects are discussed. For near-tip lean angles L3 and L4, the positive coupling effect is due to the change of the passage shock. For near-tip lean angle L4 and sweep angle S4, the change of detached shock leads to a negative coupling effect. The proposed data mining method based on the neural network and SHAP is promising and transferable to other turbomachinery optimization databases in the future.