An explainable hybrid RSM–SHAP framework for multi-parameter optimization of WEDM performance in D2 tool steel

Abstract Wire Electrical Discharge Machining (WEDM) of D2 tool steel is difficult to control because of the material’s high hardness (58–62 HRC) and strong work-hardening tendency. This study combines Response Surface Methodology (RSM) with machine learning to minimize surface roughness (Ra) in WEDM of D2 steel. Five parameters—peak current, pulse-on time, wire tension, wire feed rate, and cutting speed—were varied through a 32-run face-centred Central Composite Design. A second-order RSM model explained the data well (R 2 = 99.95%, adjusted R 2 = 99.86%, predicted R 2 = 98.58%; lack-of-fit F = 0.56, p = 0.752); its leave-one-out cross-validated (LOOCV) RMSE was 0.033 µm. Artificial Neural Network (ANN), Random Forest and Gradient Boosting models were compared with RSM on identical leave-one-out and repeated 8-fold cross-validation partitions with nested hyperparameter tuning; on this 32-run dataset they generalised less well than RSM (LOOCV R 2 = 0.67–0.83) and were therefore used in an exploratory, interpretive role. SHapley Additive exPlanations (SHAP), with bootstrap ranking uncertainty, identified wire feed rate and peak current as the dominant parameters (ranked first and second in 98% and 94% of resamples), followed by pulse-on time, which affects Ra non-monotonically with a maximum near 1.0 µs. Desirability-based optimization, verified by multi-start and grid searches, gave a constrained optimum at the upper bounds WF = 8 m/min and PoT = 1.2 µs, with WT ≈1.17 kg, PC ≈9.66 A and CS ≈2.82 mm/min, predicting Ra = 2.20 µm (95% prediction interval 2.17–2.23 µm). Confirmation runs gave a mean Ra of 2.04 µm, 12.3% below the lowest Ra in the design (2.320 µm) and ≈26% below the design mean (2.744 µm); the 8.1% prediction error lies outside the prediction interval and indicates that the model is conservative near the design boundary.