SORM, Design Points, Subset Simulation, and Markov Chain Monte Carlo
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 4
Abstract
The calculation of failure probabilities is one of the basic problems in structural reliability. But to understand the causes of failure, the pure calculation of probabilities is not sufficient. It is attempted to explain that this can be done using the concept of design points. Some important mathematical aspects of the subset simulation method are studied in detail. In this context, it is outlined that this approach is merely a Monte Carlo (MC) style numerical approximation attempt for finding the neighborhoods of the design points, i.e., a disguised importance sampling method. New methods based on first/second-order reliability methods (FORM/SORM) improved by suitable importance sampling methods are introduced. This approach combines the simplicity of the analytic concept with the flexibility of additional MC estimates. So the structuralist view based on design points, which was given up in favor of pure probability estimates by MC, is reintroduced.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The author would like to thank Z. Botev (UNSW), M. Faes (KU Leuven), M. Gasser (TU Vienna), I. Papaiaonnou (TU Munich), and F. Uribe (TU Denmark) for various discussions and help. Further, he would like to thank M. Broccardo (University of Trento) and M. Maes (University of Calgary) for confirming that there is an error in the study by Katafygiotis and Zuev (2008). Special thanks to S. Scheffler (UniBW Munich) for explaining some important concepts of the optimization theory to the author.
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Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7 • Issue 4 • December 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Aug 22, 2020
Accepted: Apr 28, 2021
Published online: Aug 4, 2021
Published in print: Dec 1, 2021
Discussion open until: Jan 4, 2022
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