This application discloses a method for assessing small failure probabilities based on prior constraint integration and hierarchical correction sampling, relating to the field of
uncertainty quantification technology. The method includes: first, constructing an integrated
surrogate model incorporating multiple types of prior constraints and performing residual correction using high-fidelity anchor samples; then, calculating soft failure weights based on the corrected
surrogate model, and using this weights to perform
hierarchical search of candidate samples to obtain a failure sample set; next, clustering the failure samples to identify
multiple failure sample clusters and constructing a multi-scale
hybrid proposal distribution; then, performing effective sample size-driven bridging sampling, adaptively controlling the transition step size to obtain a stable initial
failure probability estimate; finally, using inverse probability weighted unbiased correction, performing high-fidelity
verification of the bridging samples prioritizing false negative risk and correcting the initial estimate, outputting the final
failure probability. Under the condition of strictly limited high-fidelity evaluation times, this method achieves high-precision, high-stability, and statistically unbiased
estimation of small failure probabilities.