Machine learning-based prediction formulas for buckling resistance of welding-strengthened circular steel tubes

Welding curved cover plates is commonly used to strengthen circular hollow section (CHS) members under service loads, but welding heat input can induce lateral deflection and complex post-strengthening stress states that reduce the buckling resistance. This study develops machine-learning (ML)-based prediction models and a practical buckling-resistance prediction formula for such members. A database of 800 finite-element (FE) samples, derived from 400 structural configurations, was generated using validated sequentially coupled thermo-mechanical analyses covering service loading, welding, cooling, and post-strengthening loading. K-nearest neighbours (KNN), adaptive boosting (AdaBoost), artificial neural networks (ANN), and deep and cross networks (DCN) were trained to predict the stability factor, welding-induced deflection amplification factor, and post-strengthening compressive stress level. Among them, DCN showed the best overall performance, with test-set R 2 values exceeding 0.992 for all three targets. SHapley Additive exPlanations (SHAP) identified post-strengthening normalised slenderness ( λ ns ), service load level ( α p ), the diameter-to-cover-plate-thickness ratio (2 γ s ), and original-member yield strength ( f y0 ) as the governing features. Higher α p and lower 2 γ s and f y0 increased deformation and compressive stress, thereby reducing buckling resistance. Based on these relationships, an explicit resistance prediction formula was established by combining a service-load-induced resistance reduction factor with column-curve selection criteria. The proposed formula achieved a mean predicted-to-FE resistance ratio of 0.952 and a MAPE of 6.03%, outperforming an existing semi-empirical model and code provisions.