A robust method for reliability updating with equality information using sequential adaptive importance sampling

TL;DR

This paper introduces RU-SAIS, a novel sequential importance sampling method that efficiently updates reliability assessments with equality information, overcoming computational challenges of existing approaches.

Contribution

The paper presents RU-SAIS, combining sequential importance sampling, K-means clustering, and cross entropy to improve reliability updating with equality information.

Findings

RU-SAIS provides more accurate posterior failure probability estimates.

The method demonstrates robustness and efficiency over existing techniques.

Applications show improved performance in dynamic reliability updating.

Abstract

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.