Metamodel-based importance sampling for structural reliability analysis
By V. Dubourg, François Deheeger, Bruno Sudret. 2011
530 citations recorded by the source corpus.
Structural reliability methods aim at computing the probability of failure of systems with respect to some prescribed performance functions. In modern engineering such functions usually resort to running an expensive-to-evaluate computational model (e.g. a finite element model). In this respect simulation methods, which may require $10^{3-6}$ runs cannot be used directly. Surrogate models such as quadratic response surfaces, polynomial chaos expansions or kriging (which are built from a limited number of runs of the original model) are then introduced as a substitute of the original model to cope with the computational cost. In practice it is almost impossible to quantify the error made by this substitution though. In this paper we propose to use a kriging surrogate of the performance function as a means to build a quasi-optimal importance sampling density. The probability of failure is eventually obtained as the product of an augmented probability computed by substituting the meta-model for the original performance function and a correction term which ensures that there is no bias in the estimation even if the meta-model is not fully accurate. The approach is applied to analytical and finite element reliability problems and proves efficient up to 100 random variables.
Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/2d64ffd3fe288e54ec0901e00d4258b03899d188
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In Computational Theory and Mathematics
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Citations in the corpus
- Polynomial-Chaos-based Kriging (2015, unknown): “…applications can be found in many fields, such as structural reliability analysis Kaymaz (2005); Bect et al. (2012); Echard et al. (2011); Bichon et al. (2008); Dubourg et al. (2013); Dubourg and Sudret (2014) and design optimization Jones et al. (1998); Dubourg et al. (2011); Dubourg (2011).”
- A new adaptive response surface method for reliability analysis (2013, background): “Recent contributions have been made on kriging [37,14,4] and support vector machine”