Multi fidelity Information Fusion for Efficient Estimation of Small Failure Probabilities Considering Multiple Limit States

Abstract

Stochastic simulation methods, such as Monte Carlo simulation (MCS), are typically used to estimate failure probabilities in reliability analysis, but they can be computationally intensive, often requiring many evaluations of an expensive high-fidelity numerical model. The computational burden is even greater when rare events are involved. Additional challenges can exist when multiple limit states are of interest. To overcome these difficulties, this work proposes an efficient stochastic simulation approach based on multi-fidelity information fusion. The basic idea is to reduce the required number of high-fidelity runs while maintaining the accuracy of the estimated failure probabilities by fusing information from the low- and high-fidelity models. More specifically, the proposed approach is developed within a stratified sampling framework where, within each stratum, a Gaussian process regression/classification based multi-fidelity model is established to predict the low- and high-fidelity response relationship using a small number of high-fidelity runs. To achieve sufficient prediction accuracy with minimal high-fidelity evaluations, an active learning strategy is developed to enable intelligent generation of training data. To address the potential challenge associated with multiple limit states (i.e., the need to build many multi-fidelity models and select training samples considering all limit states), this work proposes to project the multidimensional low-fidelity and high-fidelity response (corresponding to multiple limit states) into a low-dimensional latent space using principal component analysis (PCA). A strata-wise holistic multi-fidelity model is then built in the latent space and used to predict the high-fidelity response for each limit state along with the projection matrix. Finally, in computing the small failure probabilities, low-fidelity models are first evaluated for a large number of MCS samples of the uncertain input variables in each stratum, and the corresponding results are used to predict the high-fidelity response with rigorous confidence bounds based on the constructed multi-fidelity models, from which the relevant failure probabilities can be estimated. Since the low-fidelity models can be evaluated efficiently, the multi-fidelity approach can achieve significant speedups in estimating small failure probabilities compared to direct simulation using the high-fidelity models. In addition, the proposed approach can enable a simultaneous estimation of the failure probabilities for multiple limit states. To validate the effectiveness and efficiency of the proposed approach, it is applied to a 45-story steel building subjected to stochastic wind excitation to estimate the small failure probabilities associated with multiple limit states and extreme responses.