On the robust estimation of small failure probabilities for strong non-linear models

Matthias Faes, Jonathan Sadeghi, Matteo Broggi, Marco de Angelis, Edoardo Patelli, Michael Beer, David Moens

Research output: Contribution to journalArticle

Abstract

Structural reliability methods are nowadays a cornerstone for the design of robustly performing structures, thanks to advancements in modeling and simulation tools. Monte Carlo-based simulation tools have been shown to provide the necessary accuracy and flexibility. While standard Monte Carlo estimation of the probability of failure is not hindered in its applicability by approximations or limiting assumptions, it becomes computationally unfeasible when small failure probability needs to be estimated, especially when the underlying numerical model evaluation is time consuming. In this case, variance reduction techniques are commonly employed, allowing for the estimation of small failure probabilities with a reduced number of samples and model calls. As a competing approach to variance reduction techniques, surrogate models can be used to substitute the computationally expensive model and performance function with an easy to evaluate numerical function calibrated through a supervised learning procedure. Both these tools provide accurate results for structural application. However, particular care should be taken into account when the reliability problems deal with high-dimensional or strongly nonlinear structural performances since the accuracy of the estimate is largely dependent on choices made during the surrogate modeling process. In this work, we compare the performance of the most recent state-of-the-art advance Monte Carlo techniques and surrogate models when applied to strongly nonlinear performance functions. This will provide the analysts with an insight to the issues that could arise in these challenging problems and help to decide with confidence on which tool to select in order to achieve accurate estimation of the failure probabilities within feasible times with their available computational capabilities.
LanguageEnglish
Article number041007
Number of pages8
JournalASCE-ASME Journal of Risk and Uncertainty in Engineering Systems Part B - Mechanical Engineering
Volume5
Issue number4
Early online date25 Sep 2019
DOIs
Publication statusE-pub ahead of print - 25 Sep 2019

Fingerprint

Supervised learning
Numerical models

Keywords

  • credal networks
  • kriging
  • interval predictor
  • failure probability
  • surrogate modeling
  • model emulation

Cite this

Faes, M., Sadeghi, J., Broggi, M., Angelis, M. D., Patelli, E., Beer, M., & Moens, D. (2019). On the robust estimation of small failure probabilities for strong non-linear models. 5(4), [041007]. https://doi.org/10.1115/1.4044044
Faes, Matthias ; Sadeghi, Jonathan ; Broggi, Matteo ; Angelis, Marco de ; Patelli, Edoardo ; Beer, Michael ; Moens, David. / On the robust estimation of small failure probabilities for strong non-linear models. 2019 ; Vol. 5, No. 4.
@article{6f9ed02c40d4435d96e04ae1f6db9ccf,
title = "On the robust estimation of small failure probabilities for strong non-linear models",
abstract = "Structural reliability methods are nowadays a cornerstone for the design of robustly performing structures, thanks to advancements in modeling and simulation tools. Monte Carlo-based simulation tools have been shown to provide the necessary accuracy and flexibility. While standard Monte Carlo estimation of the probability of failure is not hindered in its applicability by approximations or limiting assumptions, it becomes computationally unfeasible when small failure probability needs to be estimated, especially when the underlying numerical model evaluation is time consuming. In this case, variance reduction techniques are commonly employed, allowing for the estimation of small failure probabilities with a reduced number of samples and model calls. As a competing approach to variance reduction techniques, surrogate models can be used to substitute the computationally expensive model and performance function with an easy to evaluate numerical function calibrated through a supervised learning procedure. Both these tools provide accurate results for structural application. However, particular care should be taken into account when the reliability problems deal with high-dimensional or strongly nonlinear structural performances since the accuracy of the estimate is largely dependent on choices made during the surrogate modeling process. In this work, we compare the performance of the most recent state-of-the-art advance Monte Carlo techniques and surrogate models when applied to strongly nonlinear performance functions. This will provide the analysts with an insight to the issues that could arise in these challenging problems and help to decide with confidence on which tool to select in order to achieve accurate estimation of the failure probabilities within feasible times with their available computational capabilities.",
keywords = "credal networks, kriging, interval predictor, failure probability, surrogate modeling, model emulation",
author = "Matthias Faes and Jonathan Sadeghi and Matteo Broggi and Angelis, {Marco de} and Edoardo Patelli and Michael Beer and David Moens",
year = "2019",
month = "9",
day = "25",
doi = "10.1115/1.4044044",
language = "English",
volume = "5",
number = "4",

}

Faes, M, Sadeghi, J, Broggi, M, Angelis, MD, Patelli, E, Beer, M & Moens, D 2019, 'On the robust estimation of small failure probabilities for strong non-linear models' vol. 5, no. 4, 041007. https://doi.org/10.1115/1.4044044

On the robust estimation of small failure probabilities for strong non-linear models. / Faes, Matthias; Sadeghi, Jonathan; Broggi, Matteo; Angelis, Marco de; Patelli, Edoardo; Beer, Michael; Moens, David.

Vol. 5, No. 4, 041007, 31.12.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On the robust estimation of small failure probabilities for strong non-linear models

AU - Faes, Matthias

AU - Sadeghi, Jonathan

AU - Broggi, Matteo

AU - Angelis, Marco de

AU - Patelli, Edoardo

AU - Beer, Michael

AU - Moens, David

PY - 2019/9/25

Y1 - 2019/9/25

N2 - Structural reliability methods are nowadays a cornerstone for the design of robustly performing structures, thanks to advancements in modeling and simulation tools. Monte Carlo-based simulation tools have been shown to provide the necessary accuracy and flexibility. While standard Monte Carlo estimation of the probability of failure is not hindered in its applicability by approximations or limiting assumptions, it becomes computationally unfeasible when small failure probability needs to be estimated, especially when the underlying numerical model evaluation is time consuming. In this case, variance reduction techniques are commonly employed, allowing for the estimation of small failure probabilities with a reduced number of samples and model calls. As a competing approach to variance reduction techniques, surrogate models can be used to substitute the computationally expensive model and performance function with an easy to evaluate numerical function calibrated through a supervised learning procedure. Both these tools provide accurate results for structural application. However, particular care should be taken into account when the reliability problems deal with high-dimensional or strongly nonlinear structural performances since the accuracy of the estimate is largely dependent on choices made during the surrogate modeling process. In this work, we compare the performance of the most recent state-of-the-art advance Monte Carlo techniques and surrogate models when applied to strongly nonlinear performance functions. This will provide the analysts with an insight to the issues that could arise in these challenging problems and help to decide with confidence on which tool to select in order to achieve accurate estimation of the failure probabilities within feasible times with their available computational capabilities.

AB - Structural reliability methods are nowadays a cornerstone for the design of robustly performing structures, thanks to advancements in modeling and simulation tools. Monte Carlo-based simulation tools have been shown to provide the necessary accuracy and flexibility. While standard Monte Carlo estimation of the probability of failure is not hindered in its applicability by approximations or limiting assumptions, it becomes computationally unfeasible when small failure probability needs to be estimated, especially when the underlying numerical model evaluation is time consuming. In this case, variance reduction techniques are commonly employed, allowing for the estimation of small failure probabilities with a reduced number of samples and model calls. As a competing approach to variance reduction techniques, surrogate models can be used to substitute the computationally expensive model and performance function with an easy to evaluate numerical function calibrated through a supervised learning procedure. Both these tools provide accurate results for structural application. However, particular care should be taken into account when the reliability problems deal with high-dimensional or strongly nonlinear structural performances since the accuracy of the estimate is largely dependent on choices made during the surrogate modeling process. In this work, we compare the performance of the most recent state-of-the-art advance Monte Carlo techniques and surrogate models when applied to strongly nonlinear performance functions. This will provide the analysts with an insight to the issues that could arise in these challenging problems and help to decide with confidence on which tool to select in order to achieve accurate estimation of the failure probabilities within feasible times with their available computational capabilities.

KW - credal networks

KW - kriging

KW - interval predictor

KW - failure probability

KW - surrogate modeling

KW - model emulation

U2 - 10.1115/1.4044044

DO - 10.1115/1.4044044

M3 - Article

VL - 5

IS - 4

M1 - 041007

ER -