An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis

By Géraud Blatman, Bruno Sudret. 2010

861 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dd6a19af45cb436b0e3c6cf1953bf0b1babe1d72

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

1. Bruno Sudret
2. V. Dubourg
3. Stefano Marelli
4. T. Al‐Bittar
5. A. Soubra
6. Sondipon Adhikari
7. Roland Schöbi
8. J. Wiart

In Statistics and Probability

1. Bruno Sudret
2. Stefano Marelli
3. V. Dubourg
4. Rui Li
5. Jian Wang
6. Zhili Sun
7. Cao Tong
8. T. Al‐Bittar

Citations in the corpus

• Reliability-based design optimization using kriging surrogates and subset simulation (2011, background): “…and Bourgund, 1990; Kim and Na, 1997; Das and Zheng, 2000), polynomial chaos expansions (Sudret and Der Kiureghian, 2002; Berveiller et al., 2006; Blatman and Sudret, 2008, 2010), support vector machines (Hurtado, 2004; Deheeger, 2008; Bourinet et al., 2010), neural networks (Papadrakakis and…”
• A new adaptive response surface method for reliability analysis (2013, methodology): “As in previous example, reference value of the generalized reliability index has been estimated by Blatman and Sudret [7] with FORM followed by Importance Sampling with 500,000 simulations, and is b 1⁄4 3:51.”
• A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equations (2018, methodology): “The gPC solution is generally obtained according to two different approaches of stochastic Galerkin [6] and stochastic collocation [9–11].”
• LIF: A new Kriging based learning function and its application to structural reliability analysis (2017, methodology): “14 38 According to [18], the referential failure probability ( Pf ) is 3.”
• Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion (2011, methodology): “To address such problem, the sparse polynomial chaos expansion developed by Blatman and Sudret [18] in the framework of the non-intrusive approaches is used herein.”
• A sequential sparse polynomial chaos expansion using Bayesian regression for geotechnical reliability estimations (2020, methodology): “0 × 10 , See details in.(17) 886 PAN ET AL.”
• A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models (2013, background): “and of the polynomial degrees are tricky [13].”