TY - JOUR

T1 - A new reliability method combining adaptive Kriging and active variance reduction using multiple importance sampling

AU - Persoons, Augustin

AU - Wei, Pengfei

AU - Broggi, Matteo

AU - Beer, Michael

N1 - Funding Information: The authors gratefully acknowledge the support of the Research Foundation Flanders (FWO) under Grant GOC2218N (A. Persoons). In addition, we acknowledge the European Union’s Horizon 2020 Research and Innovation Program GREYDIENT under Grant Agreement n° 955393.

PY - 2023/6/23

Y1 - 2023/6/23

N2 - 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.

AB - 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.

KW - Adaptive Kriging

KW - Extremely rare failure events

KW - Multiple importance sampling

KW - Reliability method

KW - Variance reduction

UR - http://www.scopus.com/inward/record.url?scp=85161868435&partnerID=8YFLogxK

U2 - 10.1007/s00158-023-03598-6

DO - 10.1007/s00158-023-03598-6

M3 - Article

AN - SCOPUS:85161868435

VL - 66

JO - Structural and Multidisciplinary Optimization

JF - Structural and Multidisciplinary Optimization

SN - 1615-147X

IS - 6

M1 - 144

ER -