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research-article

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

[+] Author and Article Information
Matthias Faes

KU Leuven, Department of Mechanical Engineering, Technology campus De Nayer, Jan De Nayerlaan 5, St.-Katelijne-Waver, Belgium
matthias.faes@kuleuven.be

Jonathan Sadeghi

University of Liverpool, Institute for Risk and Uncertainty, Peach Street, L69 7ZF Liverpool, United Kingdom
J.C.Sadeghi@liverpool.ac.uk

Matteo Broggi

Leibniz Universität Hannover, Institute for Risk and Reliability, Callinstrasse 34, Hannover, Germany
broggi@irz.uni-hannover.de

Marco De Angelis

University of Liverpool, Institute for Risk and Uncertainty, Peach Street, L69 7ZF Liverpool, United Kingdom
marco.de-Angelis@liverpool.ac.uk

Edoardo Patelli

University of Liverpool, Institute for Risk and Uncertainty, Peach Street, L69 7ZF Liverpool, United Kingdom
edoardo.patelli@liverpool.ac.uk

Michael Beer

Leibniz Universität Hannover, Institute for Risk and Reliability, Callinstrasse 34, Hannover, Germany; University of Liverpool, Institute for Risk and Uncertainty, Peach Street, L69 7ZF Liverpool, United Kingdom; Tongji University, International Joint Research Center for Engineering Reliability and Stochastic Mechanics, Shanghai 200092, China
beer@irz.uni-hannover.de

David Moens

KU Leuven, Department of Mechanical Engineering, Technology campus De Nayer, Jan De Nayerlaan 5, St.-Katelijne-Waver, Belgium
david.moens@kuleuven.be

1Corresponding author.

ASME doi:10.1115/1.4044044 History: Received September 12, 2018; Revised February 01, 2019

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 can provide accurate results for structural application. However, particular care should be taken into account when the reliability problems deal with high dimensional or strongly non-linear structural performances. 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 non-linear 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.

Copyright (c) 2019 by ASME
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