Reliability calibration of knowledge informed machine learning for global buckling capacity of built up cold formed steel columns

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Accurate prediction of the global buckling resistance of built up cold formed steel (CFS) columns is complicated by partial interaction, connection detailing, and the transferability limits of models calibrated on heterogeneous experimental data. This study develops a knowledge informed discrepancy learning framework in which Direct Strength Method (DSM) resistance is retained as a mechanics based prior and machine learning is used to estimate a multiplicative model discrepancy. The analysed subset contains 148 global buckling tests drawn from 15 experimental source identifiers and 13 built up section families. A conventional random 80/20 split provides strong within database interpolation, with test mean absolute percentage errors of approximately 13–16% and coefficients of determination above 0.96 for the original kiML benchmark. In contrast, nested leave one source out validation gives substantially weaker transfer to unseen experimental programmes. The best source independent kiML result is obtained with Lasso regression ( R²=0.787 , RMSE $$=68.5$$ kN, MAPE $$=73.0%$$ ), and 49–57% of kiML predictions are unconservative depending on the algorithm. A matched direct machine learning baseline shows that discrepancy learning improves transfer for some model classes but not uniformly. Spearman correlation analysis identifies strong dependence among several mechanics derived predictors, and SHAP results are therefore interpreted as associative rather than causal; grouped resampling further shows variability in feature rankings. Reliability calibration based exclusively on out of source predictions produces LRFD resistance factors φ c=0.191 –0.399 and ASD safety factors Ω c=4.01 –8.38 for the kiML models, while the prescribed lower bound CoVΘ=0.065 is inactive. These findings support the value of integrating DSM discrepancy learning, explainability diagnostics, source grouped validation, and code oriented reliability calibration within one framework, while also showing that the present database does not justify unrestricted design use across unseen experimental programmes.