Interpretable machine learning models for predicting probabilistic axial buckling strength of steel circular hollow section members considering discreteness of geometries and material

Steel circular hollow section (CHS) members are widely utilized as axial force-resisting structural members in civil engineering structures. The buckling strength under axial loads is one of the critical parameters to determine the performance of the steel CHS members, which is significantly affected by the discreteness introduced by geometries, material, and initial imperfections. However, the reduction factor employed in the modern design codes (i.e. Chinese codes and EC3) only accounts for the reduction caused by all kinds of discreteness and does not reflect the impacts of every single discreteness and imperfection. To fill the gap, this paper proposed an interpretable machine-learning method to provide the probabilistic axial buckling strength of steel CHS members prediction result in a distribution form with the consideration of detailed discreteness. The model to predict the nominal axial buckling strength of steel CHS members was first developed utilizing ten machine learning algorithms after sufficient numerical simulations, where the numerical model was verified using test results. The artificial neural network (ANN) was selected for developing the prediction model due to its highly reliable performance in testing. The developed ANN models were further interpreted utilizing Shapley Additive exPlanations (SHAP) to determine the interrelationship of different parameters. Then, the probabilistic axial bucking strength prediction model was established based on the developed ANN models, where the Latin hypercube sampling method was applied to address the discreteness of geometries, material, and initial imperfections. The generated probabilistic axial bucking strength prediction model’s effectiveness was verified by the evidence that the machine learning prediction results can highly match the numerical results' probability density function and the result from codes while significantly reducing the computation time. Finally, the design parameters’ impact on the axial buckling strength’s discreteness was evaluated using the global sensitivity analysis (GSA) method. The result shows that the discreteness of design parameters substantially influences the distribution of the axial buckling strength of the steel CHS members and the proposed prediction model can provide an accurate probabilistic distribution prediction.