Random splits flattered machine-learned steel column corrections; holding out whole test programmes drops the safety factor to 4.01–8.38

Evaluation of built-up column capacity prediction moved from a random split to holding out whole experimental sources, so no test programme appears in both training and testing. Under the random 80/20 split, the knowledge-informed models showed test mean absolute percentage errors of roughly 13–16% and coefficients of determination above 0.96, but specimens sharing a source could land in both subsets. In nested leave-one-source-out validation, each of the 148 specimens is predicted once by a model that never saw its source; the best result, Lasso, gives $R^2=0.787$, RMSE 68.5 kN and MAPE 73.0%.

The learned quantity is the ratio of measured to Direct Strength Method resistance, so machine learning estimates a multiplicative discrepancy rather than replacing the design equation. The Direct Strength Method was calibrated for single cold-formed steel members, and applying it to built-up columns requires simplifying assumptions about partial interaction between connected elements. Six regression algorithms share the same source partitions and are compared against a direct machine-learning baseline given identical mechanics information plus the Direct Strength Method resistance; discrepancy learning improves transfer for Ridge, Lasso, Elastic Net and the decision tree but not for kNN or AdaBoost.

Reliability calibration uses only out-of-source predictions, so the resulting resistance and safety factors carry cross-programme transfer uncertainty. Calibration on a random holdout understates dispersion because held-out specimens come from the same experimental programmes as the training data. Across the six models, out-of-source dispersion ranges from 0.552 to 0.898, leaving the prescribed 0.065 lower bound inactive, and 49.3–57.4% of predictions exceed the measured resistance depending on algorithm.

The scope covers the 13 built-up section families, yield strengths of about 288–615 MPa, lengths of 503–3500 mm, thicknesses of 1–3 mm, fastener-spacing records of 0–1906.7 mm, and the represented pinned, semi-fixed and fixed boundary conditions and flexural/global buckling cases recorded in the analysed database. Local buckling, distortional buckling and local–global or distortional–global interaction lie outside the present model and would need their own mode-specific critical loads, slenderness measures and Direct Strength Method branches. The source proposes expanding source diversity, building explicit mode-aware datasets, investigating physically constrained or monotonic learning formulations, and repeating grouped reliability calibration before extending the method to general built-up column design.

Only 15 source groups are available and they differ widely in size and response range, so cluster-bootstrap intervals are wide: the Lasso out-of-source $R^2$ of 0.787 has a 95% interval of about -1.79 to 0.89, and its MAPE interval is about 18.7–147.6%. Across 30 repeated grouped holdouts, mean $R^2$ is negative for every knowledge-informed model and mean MAPE ranges from 67.7% to 111.1%, so results depend on which programmes are withheld. Mechanics-derived features are strongly correlated, for example global slenderness and the yield-to-elastic-critical-load ratio have a Spearman coefficient of 0.9998, so SHAP results are read as associations, and grouped resampling shows the ranking of several variables is unstable.