AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation

By B. Echard, Nicolas Gayton, Maurice Lemaire. 2011

1,947 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b3610b7f2db09dd71708c799ff7cc9973b27cc80

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Citations in the corpus

Active learning for structural reliability: Survey, general framework and benchmark (2021, methodology): “In most of the literature (starting from the original AK-MCS algorithm (Echard et al., 2011) and in most subsequent variants), the candidate pool is defined prior to the analysis using Monte Carlo sampling.”
Estimation of the lower and upper bounds on the probability of failure using subset simulation and random set theory (2018, methodology): “Elishakoff (1999); Oberguggenberger and Fellin (2005)).”
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].”
A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models (2013, methodology): “sufficiently high probabilities of occurrence to have a significant impact on the failure probability (see [6] in Example 1).”
LIF: A new Kriging based learning function and its application to structural reliability analysis (2017, methodology): “AK-MCSþLIF means that the method raised by [34] is adopted but LIF is employed as the learning function.”
Metamodel-based importance sampling for structural reliability analysis (2011, methodology): “For instance, Echard et al. (2011) propose the so-called U -criterion which is defined as follows: U (x ) = 0−μ b G(x ) σ b G(x ) (35)”
The promise of implementing machine learning in earthquake engineering: A state-of-the-art review (2020, background): “…as active learning, reinforcement learning, and deep learning (Andriotis and Papakonstantinou, 2019; Blatman and Sudret, 2010; Cadini et al., 2014; Echard et al., 2011; Kong et al., 2020; Memarzadeh and Pozzi, 2019; Nguyen and Medjaher, 2019; Scho¨bi et al., 2017), are needed to (1) characterize…”
The future of risk assessment (2018, background): “The CRs may be identified corresponding to prior knowledge and expectation of the analysts or be “discovered”, i.e., the analysts are not a priori aware of such critical configurations and mining by simulation allows identifying them.”
An application of the Kriging method in global sensitivity analysis with parameter uncertainty (2013, background): “j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a p m [13] and reliability analysis [14].”
A sequential surrogate method for reliability analysis based on radial basis function (2017, methodology): “This type of iterative method is also called adaptive method or active learning [31-32, 45].”