Reliability updating with equality information using adaptive kriging-based importance sampling

Reliability updating can be interpreted by the process of reevaluating structural reliability with data stemming from structural health monitoring sensors or platforms. In virtue of the power of Bayesian statistics, reliability updating incorporates the up-to-date information within the framework of uncertainty quantification, which facilitates more reasonable and strategic decision-making. However, the associated computational cost for quantifying uncertainty can be also increasingly challenging due to the iterative simulation of sophisticated models (e.g., Finite Element Model). To expedite reliability updating with complex models, reliability updating with surrogate model has been proposed to overcome aforementioned limitations. However, the past work merely integrates reliability updating with Kriging-based crude Monte Carlo Simulation, thereby, still exists many computational limitations. For example, parameters such as the coefficient of variation of posterior failure probability, the batch size of samples, and active learning stopping criterion are not well defined or devised, which can lead to computational pitfalls. Therefore, this paper proposes RUAK-IS (Reliability Updating with Adaptive Kriging using Importance Sampling) to address the aforementioned limitations. Specifically, importance sampling is incorporated with Kriging to enable updating of small failure probability with robust estimate and error quantification. Two numerical and one practical finite element examples are investigated to explore the computational efficiency and accuracy of the proposed method. Results demonstrate the computational superiority of RUAK-IS in terms of robustness and accuracy.