GPR-Based Surrogate Model for Probabilistic Fatigue Safety Factor Prediction in Stepped Shafts

Abstract

This study develops a Gaussian Process Regression (GPR) surrogate model to predict the fatigue safety factor of stepped shafts, addressing the computational expense and meshing constraints of traditional Finite Element Analysis. A dataset of 314 high-fidelity ANSYS simulations was generated using Latin Hypercube and custom sampling across five parameters: minor diameter (d), major diameter (D), fillet radius (r), bending moment (M), and loading ratio (R). Trained with a Matern ν = 2.5 kernel, the model achieved exceptional accuracy (R2 = 0.9905, RMSE = 0.187) and robust generalization (5-fold CV, R2 = 0.971 ± 0.022). Permutation importance revealed a physically consistent parameter ranking (d > M > R > D > r) while predicted trends for R aligned with Goodman mean-stress correction theory. Beyond point predictions, GPR provides quantified uncertainty estimates, enabling risk-aware design decisions and targeted simulation refinement. This work demonstrates that Bayesian surrogate modeling can effectively replace repetitive FEA fatigue analyses, offering a computationally efficient, uncertainty-aware methodology that accelerates design exploration and enhances reliability assessment under constrained simulation environments.