Adaptive Kriging-assisted multi-fidelity subset simulation for reliability analysis

Accurate estimation of rare event probabilities with reasonable computational demands is crucial in reliability analysis. However, with increasing complexity of engineering problems, traditional methods are facing rising challenges in terms of computational efficiency and accuracy. In this work, an effective multi-fidelity framework is provided for assessing rare event probabilities. We firstly define the multi-fidelity failure domains by introducing a series of intermediate failure events associated with performance functions at various fidelity levels. Subset simulation is then employed to decompose the rare event probability into a series of conditional probabilities associated with these multi-fidelity failure domains. In this context, we demonstrate that the estimation accuracy of failure probability only depends on that of the conditional probability of a critical failure domain, rather than on those of the rest of multi-fidelity failure domains. With aid of this fact, the rest of failure domains is approximated by a series of Kriging models constructed with the computationally cheap low-fidelity performance functions. Thus, the computational demand for estimating the conditional probabilities of the rest failure domains is significantly decreased in reliability analysis. Since these approximated failure domains, which gradually approach the critical failure domain, allow for sufficiently sampling deep into the critical one, the Kriging model of the high-fidelity performance function can be accurately constructed with the sufficient number of candidate samples. As a result, the conditional probability of the critical failure domain, and thus the rare event probability, are finally estimated with high precision. Three illustrative examples, including a concrete arch dam subject to both hydrostatic and sediment accumulation loads, are investigated to validate the proposed method.