Predictive Modelling of Laser Hardening in EN25 Steel using Analytical Heat Source Theory, Response Surface Methodology, and Comparative Gaussian Process–Support Vector Regression

The present work investigates laser transformation hardening (LTH) of EN25 low-alloy steel (0.3 wt.% C) through an integrated analytical–statistical–predictive modelling framework combining analytical heat source theory, Response Surface Methodology (RSM), Gaussian Process Regression (GPR), and Support Vector Regression (SVR). A moving flat-top rectangular laser beam (10 × 30 mm) was employed to analytically estimate the case depth (CD), case hardness (HD), and residual stress (RS) developed within the hardened zone (HZ). Experiments were conducted according to a Box–Behnken design by varying laser power (1000–1500 W), scan speed (4–6 mm/s), and laser head stand-off distance (300–340 mm). The analytical model, incorporating austenitization-limited heat transfer, predicted case depths in the range of approximately 1.5–2.45 mm and reasonably captured the experimentally observed parametric trends. Experimental case depths ranged from ~0.68 to 2.52 mm, depending on the selected processing conditions. Experimental results showed case hardness values between ~500 and ~747 HV and compressive-type residual stresses ranging from ~-177 to ~-221 MPa. Quadratic RSM models were developed and validated using analysis of variance (ANOVA) to establish quantitative relationships between process parameters and responses; a composite desirability of 0.9623 identified an optimum process condition of 1500 W LP, 4 mm/s SS, and 320 mm SoD. To further investigate nonlinear process behaviour, GPR and SVR models employing a radial basis function kernel were developed and compared under a fold-safe leave-one-out cross-validation (LOOCV) protocol. Both models achieved strong predictive accuracy across all three responses, with SVR (R 2 = 0.991, 0.992, and 0.983 for CD, HD, and RS) slightly outperforming GPR (R 2 = 0.864, 0.977, and 0.982). GPR additionally provided posterior predictive uncertainty estimates unavailable from SVR. The proposed framework provides a practical tool for selecting suitable laser processing parameters within the investigated operating range, thereby reducing experimental trial-and-error effort and supporting efficient process planning for industrial laser transformation hardening applications.