INTEGRATED PHYSICS-BASED STATISTICAL MODELING, PARAMETER IDENTIFICATION, AND ROBUST MULTI-OBJECTIVE OPTIMIZATION OF LASER SURFACE HARDENING OF CYLINDRICAL SPECIMENS USING THE LUX-2000 SYSTEM

Abstract

The objective of this study is to develop a locally valid, physically interpretable, and statistically verifiable framework for parameter identification, comparative evaluation, and robust selection of processing conditions for the laser surface hardening of cylindrical specimens with a diameter of 30 mm and a thickness of 10 mm. The analysis is based on a balanced (2\times2\times3) factorial subset comprising twelve comparable processing conditions at laser power (P\in{200,300}) W, laser-beam width (b\in{1,2}) mm, and scanning speed (V\in{176,245,314}) mm/min. The methodology includes the formulation of kinematic, energy-based, and dimensionless indicators; identification of a log-linear power-law model; and application of the corrected Akaike information criterion (AICc), leave-one-out cross-validation, residual diagnostics, local sensitivity analysis, Pareto dominance, and chance-constrained optimization. The resulting model, ^u​=55,5407(P/200)4,1960(2/b)0,7932(314/V)0,7982 explains (R^2=0.9766) of the variation in (\ln(h_u)), with a leave-one-out root-mean-square error (LOO-RMSE) of 0.222. The maximum experimentally measured hardened-zone depth, (h_u=848\ \mu\text{m}), was obtained at a laser power of 300 W, a beam width of 1 mm, and a scanning speed of 176 mm/min. At the same time, processing condition 4/314 provided a hardened-zone depth of (h_u=648\ \mu\text{m}), with a 43.95% lower relative areal energy input and a 78.41% higher scanning speed than the condition producing the absolute maximum. The scientific novelty and principal methodological contribution of the study lie in the proposed unified hierarchy of evidence, which formally distinguishes direct experimental observation, empirical identification, physical hypothesis, and scenario-based probability. The resulting probabilistic estimates should be regarded as conditional because of the absence of replicated trials and an independent estimate of pure experimental error. The validity of the derived model is restricted to the investigated processing-parameter domain; therefore, extrapolation of the results to the nominal maximum laser-system power of 2000 W is not permissible.