Bayesian updating with adaptive, uncertainty-informed subset simulations: High-fidelity updating with multiple observations

The well-known BUS algorithm (i.e., Bayesian Updating with Structural reliability) transforms Bayesian updating problems into structural reliability to address challenges of updating with equality information and improve computational efficiency. However, as the number of observations increases, the resulting failure probability or acceptance ratio becomes exceedingly small, requiring a formidable number of evaluations of the likelihood function. To overcome this limitation especially for complex computational models, this paper presents a new approach where the probability estimation problem of the very rare event associated with updating is decomposed into a set of sub-reliability problems with uncertain failure thresholds. Two concepts of Conditional Acceptance Rate Curve (CARC) and Dynamic Learning Function (DLF) are proposed to enable precise identification of the intermediate failure thresholds and to train Kriging surrogate models for the established limit state functions. Two benchmark numerical examples and a practical corrosion problem in marine environments are investigated to analyze the efficiency of the proposed method relative to BUS and other state-of-the-art methods. Results indicate that the proposed method can reduce computational costs by about an order of magnitude while maintaining high accuracy; therefore, enabling Bayesian updating of complex computational models.