🤖 AI Summary
For computationally expensive rare failure event analysis in nonlinear stochastic systems—such as tall steel frames subjected to stochastic wind excitation—this paper proposes an adaptive multi-fidelity hierarchical sampling method. The approach integrates high- and low-fidelity model data to construct an adaptive deep learning surrogate, embedded within a hierarchical importance sampling and multi-fidelity Monte Carlo framework, ensuring unbiased estimation while substantially improving computational efficiency. Key contributions include: (i) adaptive, data-driven updating of the surrogate training process; and (ii) fidelity-coordinated modeling to alleviate bottlenecks associated with high-accuracy finite element simulations. In predicting exceedance probabilities of wind-induced nonlinear structural responses, the proposed method reduces computational cost by over one order of magnitude compared to single-fidelity approaches, while preserving accuracy in failure probability estimation.
📝 Abstract
Existing variance reduction techniques used in stochastic simulations for rare event analysis still require a substantial number of model evaluations to estimate small failure probabilities. In the context of complex, nonlinear finite element modeling environments, this can become computationally challenging-particularly for systems subjected to stochastic excitation. To address this challenge, a multi-fidelity stratified sampling scheme with adaptive machine learning metamodels is introduced for efficiently propagating uncertainties and estimating small failure probabilities. In this approach, a high-fidelity dataset generated through stratified sampling is used to train a deep learning-based metamodel, which then serves as a cost-effective and highly correlated low-fidelity model. An adaptive training scheme is proposed to balance the trade-off between approximation quality and computational demand associated with the development of the low-fidelity model. By integrating the low-fidelity outputs with additional high-fidelity results, an unbiased estimate of the strata-wise failure probabilities is obtained using a multi-fidelity Monte Carlo framework. The overall probability of failure is then computed using the total probability theorem. Application to a full-scale high-rise steel building subjected to stochastic wind excitation demonstrates that the proposed scheme can accurately estimate exceedance probability curves for nonlinear responses of interest, while achieving significant computational savings compared to single-fidelity variance reduction approaches.