Integrated Response Surface Methodology and Gaussian Process Regression for Multi-Objective Particle Swarm Optimization of Tribological Performance in AZ91/ZrO₂ Composites

Abstract

The tribological performance of magnesium-based metal matrix composites under elevated-temperature sliding conditions is governed by complex interactions among operating parameters and ceramic reinforcement. This investigation examines the dry sliding wear and friction characteristics of AZ91 magnesium alloy reinforced with ZrO₂ particles using Box–Behnken design (BBD), response surface methodology (RSM), Gaussian process regression (GPR), and multi-objective particle swarm optimization (MOPSO). A 29-run BBD framework incorporated four independent variables: temperature (60–200 °C), sliding speed (0.75–1.95 m/s), normal load (15–55 N), and ZrO₂ concentration (1.5–7.5 wt.%). Specific wear rate (SWR) and coefficient of friction (COF) were selected as performance responses. Quadratic RSM models achieved determination coefficients of 0.9985 and 0.9984 for SWR and COF, respectively, while five-fold cross-validation yielded R² values of 0.9913 and 0.9882. Corresponding GPR models attained cross-validated R² values of 0.9863 and 0.9868, demonstrating close predictive agreement. Multi-objective optimization identified a compromise condition comprising 60°C, 1.9499 m/s sliding speed, 15.00 N normal load, and 4.6901 wt.% ZrO₂, with predicted SWR and COF values of 0.21003 × 10⁻³ mm³/(N·m) and 0.29220, respectively. Cross-model verification revealed prediction differences below 1% for both responses at the selected operating conditions. The findings demonstrate the applicability of integrated statistical modelling, machine learning, and Pareto-based optimization for examining wear–friction relationships and identifying favourable parameter combinations within the investigated design domain.