Identification of effective machine learning models for predicting the compressive strength of cold-formed steel Z-shaped profiles

The excellent strength-to-weight ratio, ease of manufacturing, and cost-effectiveness of cold-formed steel (CFS) sections make them popular in structural applications. The Direct Strength Method (DSM) is widely used to predict CFS member strength; previous studies have mostly focused on analytical, numerical, and experimental investigations, and data-driven prediction frameworks for DSM-based CFS Z-section strength estimation are limited. This study develops machine learning models to predict DSM-based compressive strength of cold-formed steel Z-section columns and assess the influence of geometric and material parameters. A database of 1664 DSM-generated samples was created using CUFSM software by altering the flange, web, lip, thickness, and yield strength. Three Shuffled Frog Leaping Algorithm (SFLA)-optimized hybrid models and a total of nine predictive models were tested using five-fold cross-validation. Statistical measures, uncertainty analysis, REC curves, and SHAP-based interpretability were used to evaluate model performance. Ensemble learning models outperform conventional approaches, with GBM achieving the highest accuracy (R2 = 0.9652, RMSE = 0.0315, MAE = 0.0197), followed by RF and GRU. SFLA optimization improves the predictive ability of conventional models, especially SVR and RBFNs. SHAP analysis revealed that flange width, yield strength, and bending moment capability were most important.