A physics-informed stacked ensemble learning framework for thrust force prediction in ultrasonic vibration-assisted micro-drilling of DD6 superalloy

Ultrasonic vibration-assisted micro-drilling (UVAMD) is an effective approach for producing high-integrity micro-holes in DD6 superalloy, but accurate prediction of thrust force remains difficult because of nonlinear interactions among machining and vibration parameters. This study proposes a physics-informed stacked ensemble regression (PISER) framework using spindle speed, feed rate, vibration amplitude, frequency, and derived physics-informed features. Six regression models, such as linear regression (LR), gradient boosting regression (GBR), Gaussian process regression (GPR), kernel ridge regression (KRR), support vector regression (SVR), and PISER, were optimized and evaluated through nested five-fold cross-validation. PISER achieved the lowest cross-validation RMSE of 1.287 N and the best testing performance, with R² = 0.962, RMSE = 1.543 N, RRMSE = 4.69%, MAE = 1.32 N, and MAPE = 4.53%. It also outperformed the best individual models, KRR and GPR. Permutation sensitivity analysis showed that feed rate and feed per revolution contributed 30.8% and 27.9%, respectively, accounting for 58.7% of the total predictive importance. Partial dependence and response-surface analyses showed that thrust force increased with feed rate but decreased with spindle speed and vibration amplitude. The proposed framework provides accurate prediction and interpretable guidance for UVAMD process optimization.