A multi-fidelity stochastic simulation scheme for estimation of small failure probabilities

Computing small failure probabilities is often of interest in the reliability analysis of engineering systems. However, this task can be computationally demanding since many evaluations of expensive high-fidelity models are often required. To address this, a multi-fidelity approach is proposed in this work within the setting of stratified sampling. The overall idea is to reduce the required number of high-fidelity model runs by integrating the information provided by different levels of model fidelity while maintaining accuracy in estimating the failure probabilities. More specifically, strata-wise multi-fidelity models are established based on Gaussian process models to efficiently predict the high-fidelity response and the system collapse from the low-fidelity response. Due to the reduced computational cost of the low-fidelity models, the multi-fidelity approach can achieve a significant speedup in estimating small failure probabilities associated with high-fidelity models. The effectiveness and efficiency of the proposed multi-fidelity stochastic simulation scheme are validated through an application to a two-story two-bay steel building under extreme winds.