A new reliability method combining adaptive Kriging and active variance reduction using multiple importance sampling

authored by

Augustin Persoons, Pengfei Wei, Matteo Broggi, Michael Beer

Abstract

This article describes a new adaptive Kriging method combined with adaptive importance sampling approximating the optimal auxiliary by iteratively building a Gaussian mixture distribution. The aim is to iteratively reduce both the modeling and sampling errors simultaneously, thus avoiding limitations in cases of very rare failure events. At each iteration, a near optimal auxiliary Gaussian distribution is defined and new samples are drawn from it following the scheme of adaptive multiple importance sampling (MIS). The corresponding estimator is provided as well as its variance. A new learning function is developed as a generalization of the U learning function for MIS populations. A stopping criterion is proposed based on both the modeling error and the variance of the estimator. Results on benchmark problems show that the method exhibits very good performances on both efficiency and accuracy.

Organisation(s)

Institute for Risk and Reliability

External Organisation(s)

KU Leuven
Northwestern Polytechnical University

Type

Article

Journal

Structural and Multidisciplinary Optimization

Volume

66

ISSN

1615-147X

Publication date

2023

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Software, Control and Systems Engineering, Computer Science Applications, Computer Graphics and Computer-Aided Design, Control and Optimization

Electronic version(s)

https://doi.org/10.1007/s00158-023-03598-6 (Access: Closed)