Adaptive Kriging-assisted multi-fidelity subset simulation for reliability analysis

authored by: Hongzhe Dai, Dashuai Li, Michael Beer
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.
Organisation(s): Institute for Risk and Reliability
External Organisation(s): Harbin Institute of Technology
University of Liverpool
Tongji University
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 436
ISSN: 0045-7825
Publication date: 01.03.2025
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2024.117705 (Access: Closed)

BibTeX

@article{d3ba31f62af8479683fcab64e4d2d941,
title = "Adaptive Kriging-assisted multi-fidelity subset simulation for reliability analysis",
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",
author = "Hongzhe Dai and Dashuai Li and Michael Beer",
note = "Publisher Copyright: {\textcopyright} 2024 Elsevier B.V.",
year = "2025",
month = mar,
day = "1",
doi = "10.1016/j.cma.2024.117705",
language = "English",
volume = "436",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}