Predicting Buckling Load of Slender Hollow Rods Using Machine Learning: Model Comparison and Input Sensitivity Analysis

Abstract

Predicting the critical buckling load of slender structural rods is essential for reliable and weight-efficient design of automotive steering and suspension linkages such as tie rods. This study evaluates the performance of four machine learning models such as artificial neural network (ANN), support vector regression (SVR), Gaussian process regression (GPR), and random forest (RF) in predicting the critical buckling load (Pcr) from geometric and material design parameters which are rod length (L), diameter (D), wall thickness (t), Young’s modulus (E), and initial geometric imperfection (δ₀). A dataset was generated using a parametric MATLAB code, and models were trained on an 80/20 train-test split with min-max normalized inputs. ANN and GPR achieved near-perfect predictive accuracy (R²=1.000), outperforming SVR and RF (R² = 0.92-0.96). Input sensitivity was assessed using permutation importance across all four models, complemented by Garson’s algorithm and the connection weight method. Rod length and diameter were consistently identified as the dominant parameters governing buckling resistance, jointly accounting for the majority of predictive importance; when length was held constant, diameter alone emerged as the leading parameter, followed by comparable contributions from wall thickness and Young’s modulus. Initial imperfection showed negligible influence according to all permutation-based methods, although the connection weight method disagreed sharply, illustrating a key limitation of weight-based sensitivity analysis relative to permutation-based approaches.