Assessing small failure probabilities by combined subset simulation and Support Vector Machines

By Jean-Marc Bourinet, François Deheeger, Maurice Lemaire. 2011

425 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1b8a6fb6fe7f55fb08c4aaabb578ed71518afd89

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Statistics and Probability

Citations in the corpus

A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models (2013, methodology): “If such a hypothesis cannot be formulated, the (2)SMART method [15], which combines subset simulation with Support Vector Machine (SVM) metamodel can be adapted in an approach denoted as AK-SS that associates Kriging with subset simulation.”
Reliability-based design optimization using kriging surrogates and subset simulation (2011, background): “Note that the idea is inspired from Hurtado (2004); Deheeger and Lemaire (2007); Deheeger (2008); Bourinet et al. (2010) where the authors use the same idea applied to support vector classiﬁers .”
Rare event estimation with sequential directional importance sampling (2022, methodology): “Existing methods in the literature can be categorized into four types: approximate analytical methods [2, 3], moment-based methods [4-8], surrogate-assisted methods [9-13] and numerical simulation methods [14-16].”
Estimation of the lower and upper bounds on the probability of failure using subset simulation and random set theory (2018, methodology): “, 2012), combination of subset simulation with machine learning-based surrogate models (Bourinet et al., 2013; Papadopoulos et al., 2013), and the subset simulation enhancements proposed by Papaioannou et al. (2015) and Au and Patelli (2016). Perhaps one of the most significant developments was prop”
A sequential surrogate method for reliability analysis based on radial basis function (2017, background): “This example consists of a nonlinear undamped single degree of freedom system with six random variables [20, 34, 53].”
Metamodel-based importance sampling for structural reliability analysis (2011, methodology): “FORM results were obtained by Der Kiureghian and de Stefano (1991) and confirmed by Bourinet et al. (2011) using the iHLRF algorithm (Zhang and Der Kiureghian, 1995).”
A new adaptive response surface method for reliability analysis (2013, background): “Suppose that one studies a mechanical system, described by a performance function, say GðXÞ, defined such as, for a realization x of vector X, GðxÞo0 is called the domain of failure, GðxÞ ¼ 0 is the limit state and GðxÞ40 is the domain of success.”
Support vector machine in structural reliability analysis: A review (2023, positive): “Bourinet et al. [22] developed a new approach based on SVM classification for estimating small failure probability by employing the subset simulation procedure proposed by Au and Beck [57].”
Active learning for structural reliability: Survey, general framework and benchmark (2021, background): “Similarly, other contributions have targeted the surrogate model type, introducing for instance support vector machines (Hurtado, 2004; Deheeger and Lemaire, 2007; Bourinet et al., 2011; Bourinet, 2018) or polynomial chaos expansions (Marelli and Sudret, 2018).”