Details
| Original language | English |
|---|---|
| Article number | 116902 |
| Number of pages | 35 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 424 |
| Early online date | 12 Mar 2024 |
| Publication status | Published - 1 May 2024 |
Abstract
A Bayesian reinforcement learning reliability method that combines Bayesian inference for the failure probability estimation and reinforcement learning-guided sequential experimental design is proposed. The reliability-oriented sequential experimental design is framed as a finite-horizon Markov decision process (MDP), with the associated utility function defined by a measure of epistemic uncertainty about Kriging-estimated failure probability, referred to as integrated probability of misclassification (IPM). On this basis, a one-step Bayes optimal learning function termed integrated probability of misclassification reduction (IPMR), along with a compatible convergence criterion, is defined. Three effective strategies are implemented to accelerate IPMR-informed sequential experimental design: (i) Analytical derivation of the inner expectation in IPMR, simplifying it to a single expectation. (ii) Substitution of IPMR with its upper bound IPMRU to avoid element-wise computation of its integrand. (iii) Rational pruning of both quadrature set and candidate pool in IPMRU to alleviate computer memory constraint. The efficacy of the proposed approach is demonstrated on two benchmark examples and two numerical examples. Results indicate that IPMRU facilitates a much more rapid reduction of IPM compared to other existing learning functions, while requiring much less computational time than IPMR itself. Therefore, the proposed reliability method offers a substantial advantage in both computational efficiency and accuracy, especially in complex dynamic reliability problems.
Keywords
- Bayesian inference, Integrated probability of misclassification reduction, One-step Bayes optimal learning function, Reinforcement learning, Reliability analysis
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 424, 116902, 01.05.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Bayesian reinforcement learning reliability analysis
AU - Zhou, Tong
AU - Guo, Tong
AU - Dang, Chao
AU - Beer, Michael
N1 - Funding Information: The support of the National Natural Science Foundation of China (Grant No. 52125802 ) is highly appreciated.
PY - 2024/5/1
Y1 - 2024/5/1
N2 - A Bayesian reinforcement learning reliability method that combines Bayesian inference for the failure probability estimation and reinforcement learning-guided sequential experimental design is proposed. The reliability-oriented sequential experimental design is framed as a finite-horizon Markov decision process (MDP), with the associated utility function defined by a measure of epistemic uncertainty about Kriging-estimated failure probability, referred to as integrated probability of misclassification (IPM). On this basis, a one-step Bayes optimal learning function termed integrated probability of misclassification reduction (IPMR), along with a compatible convergence criterion, is defined. Three effective strategies are implemented to accelerate IPMR-informed sequential experimental design: (i) Analytical derivation of the inner expectation in IPMR, simplifying it to a single expectation. (ii) Substitution of IPMR with its upper bound IPMRU to avoid element-wise computation of its integrand. (iii) Rational pruning of both quadrature set and candidate pool in IPMRU to alleviate computer memory constraint. The efficacy of the proposed approach is demonstrated on two benchmark examples and two numerical examples. Results indicate that IPMRU facilitates a much more rapid reduction of IPM compared to other existing learning functions, while requiring much less computational time than IPMR itself. Therefore, the proposed reliability method offers a substantial advantage in both computational efficiency and accuracy, especially in complex dynamic reliability problems.
AB - A Bayesian reinforcement learning reliability method that combines Bayesian inference for the failure probability estimation and reinforcement learning-guided sequential experimental design is proposed. The reliability-oriented sequential experimental design is framed as a finite-horizon Markov decision process (MDP), with the associated utility function defined by a measure of epistemic uncertainty about Kriging-estimated failure probability, referred to as integrated probability of misclassification (IPM). On this basis, a one-step Bayes optimal learning function termed integrated probability of misclassification reduction (IPMR), along with a compatible convergence criterion, is defined. Three effective strategies are implemented to accelerate IPMR-informed sequential experimental design: (i) Analytical derivation of the inner expectation in IPMR, simplifying it to a single expectation. (ii) Substitution of IPMR with its upper bound IPMRU to avoid element-wise computation of its integrand. (iii) Rational pruning of both quadrature set and candidate pool in IPMRU to alleviate computer memory constraint. The efficacy of the proposed approach is demonstrated on two benchmark examples and two numerical examples. Results indicate that IPMRU facilitates a much more rapid reduction of IPM compared to other existing learning functions, while requiring much less computational time than IPMR itself. Therefore, the proposed reliability method offers a substantial advantage in both computational efficiency and accuracy, especially in complex dynamic reliability problems.
KW - Bayesian inference
KW - Integrated probability of misclassification reduction
KW - One-step Bayes optimal learning function
KW - Reinforcement learning
KW - Reliability analysis
UR - http://www.scopus.com/inward/record.url?scp=85187206497&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2024.116902
DO - 10.1016/j.cma.2024.116902
M3 - Article
AN - SCOPUS:85187206497
VL - 424
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 116902
ER -