Predicting steel column stability with uncertain initial defects using bayesian deep learning

Abstract

The stability of steel columns is difficult to predict accurately due to uncertain initial defects such as geometric imperfections and residual stress. To address this issue, we propose a probabilistic model that uses variational autoencoder (VAE) and transfer learning to estimate the loading capacities of steel columns. Our model can predict the confidence intervals of buckling loads without knowing the exact distribution of initial defects, providing more comprehensive information for engineering applications than traditional deterministic strength index. We establish a dataset of 1500 load-displacement curves of steel columns using four data augmentation approaches, and analyze the data distribution to validate the model's assumptions. Various criterions, including the mean squared error (MSE), the prediction interval coverage probability (PICP), and the prediction interval normalized average width (PINAW), are adopted to comprehensively measure the performance of confidence interval prediction. The numerical experiment validates that the trained model accurately predicts the confidence intervals for load-displacement responses, which perfectly cover the true curves with reasonable PINAW. Finally, we conduct a case study with a practical experiment to illustrate the model's potential application in failure probability calculation and reliability design. Our proposed model provides a promising probabilistic solution for quantifying the impact of uncertain parameters on structural analysis and significantly simplifies probability-based reliability design and optimal design processes.