Details
Original language | English |
---|---|
Article number | 117705 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 436 |
Early online date | 1 Jan 2025 |
Publication status | E-pub ahead of print - 1 Jan 2025 |
Abstract
Accurate estimation of rare event probabilities with reasonable computational demands is crucial in reliability analysis. However, with increasing complexity of engineering problems, traditional methods are facing rising challenges in terms of computational efficiency and accuracy. In this work, an effective multi-fidelity framework is provided for assessing rare event probabilities. We firstly define the multi-fidelity failure domains by introducing a series of intermediate failure events associated with performance functions at various fidelity levels. Subset simulation is then employed to decompose the rare event probability into a series of conditional probabilities associated with these multi-fidelity failure domains. In this context, we demonstrate that the estimation accuracy of failure probability only depends on that of the conditional probability of a critical failure domain, rather than on those of the rest of multi-fidelity failure domains. With aid of this fact, the rest of failure domains is approximated by a series of Kriging models constructed with the computationally cheap low-fidelity performance functions. Thus, the computational demand for estimating the conditional probabilities of the rest failure domains is significantly decreased in reliability analysis. Since these approximated failure domains, which gradually approach the critical failure domain, allow for sufficiently sampling deep into the critical one, the Kriging model of the high-fidelity performance function can be accurately constructed with the sufficient number of candidate samples. As a result, the conditional probability of the critical failure domain, and thus the rare event probability, are finally estimated with high precision. Three illustrative examples, including a concrete arch dam subject to both hydrostatic and sediment accumulation loads, are investigated to validate the proposed method.
Keywords
- Active learning, Kriging, Multi-fidelity, Reliability, Subset simulation
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
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Computer Methods in Applied Mechanics and Engineering, Vol. 436, 117705, 01.03.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Adaptive Kriging-assisted multi-fidelity subset simulation for reliability analysis
AU - Dai, Hongzhe
AU - Li, Dashuai
AU - Beer, Michael
N1 - Publisher Copyright: © 2024 Elsevier B.V.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - Accurate estimation of rare event probabilities with reasonable computational demands is crucial in reliability analysis. However, with increasing complexity of engineering problems, traditional methods are facing rising challenges in terms of computational efficiency and accuracy. In this work, an effective multi-fidelity framework is provided for assessing rare event probabilities. We firstly define the multi-fidelity failure domains by introducing a series of intermediate failure events associated with performance functions at various fidelity levels. Subset simulation is then employed to decompose the rare event probability into a series of conditional probabilities associated with these multi-fidelity failure domains. In this context, we demonstrate that the estimation accuracy of failure probability only depends on that of the conditional probability of a critical failure domain, rather than on those of the rest of multi-fidelity failure domains. With aid of this fact, the rest of failure domains is approximated by a series of Kriging models constructed with the computationally cheap low-fidelity performance functions. Thus, the computational demand for estimating the conditional probabilities of the rest failure domains is significantly decreased in reliability analysis. Since these approximated failure domains, which gradually approach the critical failure domain, allow for sufficiently sampling deep into the critical one, the Kriging model of the high-fidelity performance function can be accurately constructed with the sufficient number of candidate samples. As a result, the conditional probability of the critical failure domain, and thus the rare event probability, are finally estimated with high precision. Three illustrative examples, including a concrete arch dam subject to both hydrostatic and sediment accumulation loads, are investigated to validate the proposed method.
AB - Accurate estimation of rare event probabilities with reasonable computational demands is crucial in reliability analysis. However, with increasing complexity of engineering problems, traditional methods are facing rising challenges in terms of computational efficiency and accuracy. In this work, an effective multi-fidelity framework is provided for assessing rare event probabilities. We firstly define the multi-fidelity failure domains by introducing a series of intermediate failure events associated with performance functions at various fidelity levels. Subset simulation is then employed to decompose the rare event probability into a series of conditional probabilities associated with these multi-fidelity failure domains. In this context, we demonstrate that the estimation accuracy of failure probability only depends on that of the conditional probability of a critical failure domain, rather than on those of the rest of multi-fidelity failure domains. With aid of this fact, the rest of failure domains is approximated by a series of Kriging models constructed with the computationally cheap low-fidelity performance functions. Thus, the computational demand for estimating the conditional probabilities of the rest failure domains is significantly decreased in reliability analysis. Since these approximated failure domains, which gradually approach the critical failure domain, allow for sufficiently sampling deep into the critical one, the Kriging model of the high-fidelity performance function can be accurately constructed with the sufficient number of candidate samples. As a result, the conditional probability of the critical failure domain, and thus the rare event probability, are finally estimated with high precision. Three illustrative examples, including a concrete arch dam subject to both hydrostatic and sediment accumulation loads, are investigated to validate the proposed method.
KW - Active learning
KW - Kriging
KW - Multi-fidelity
KW - Reliability
KW - Subset simulation
UR - http://www.scopus.com/inward/record.url?scp=85213542105&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2024.117705
DO - 10.1016/j.cma.2024.117705
M3 - Article
AN - SCOPUS:85213542105
VL - 436
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 117705
ER -