  Reliability updating refers to a problem that integrates Bayesian updating
technique with structural reliability analysis and cannot be directly solved by
structural reliability methods (SRMs) when it involves equality information.
The state-of-the-art approaches transform equality information into inequality
information by introducing an auxiliary standard normal parameter. These
methods, however, encounter the loss of computational efficiency due to the
difficulty in finding the maximum of the likelihood function, the large
coefficient of variation (COV) associated with the posterior failure
probability and the inapplicability to dynamic updating problems where new
information is constantly available. To overcome these limitations, this paper
proposes an innovative method called RU-SAIS (reliability updating using
sequential adaptive importance sampling), which combines elements of sequential
importance sampling and K-means clustering to construct a series of important
sampling densities (ISDs) using Gaussian mixture. The last ISD of the sequence
is further adaptively modified through application of the cross entropy method.
The performance of RU-SAIS is demonstrated by three examples. Results show that
RU-SAIS achieves a more accurate and robust estimator of the posterior failure
probability than the existing methods such as subset simulation.
