Details
| Original language | English |
|---|---|
| Article number | 144 |
| Journal | Structural and Multidisciplinary Optimization |
| Volume | 66 |
| Issue number | 6 |
| Early online date | 12 Jun 2023 |
| Publication status | Published - 23 Jun 2023 |
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.
Keywords
- Adaptive Kriging, Extremely rare failure events, Multiple importance sampling, Reliability method, Variance reduction
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Computer Science Applications
- Computer Science(all)
- Computer Graphics and Computer-Aided Design
- Mathematics(all)
- Control and Optimization
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In: Structural and Multidisciplinary Optimization, Vol. 66, No. 6, 144, 23.06.2023.
Research output: Contribution to journal › Article › Research › peer review
}
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 -