Journal ArticleDOI
An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis
Géraud Blatman,Bruno Sudret +1 more
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TLDR
A non-intrusive method that builds a sparse PC expansion and an adaptive regression-based algorithm is proposed for automatically detecting the significant coefficients of the PC expansion in a suitable polynomial chaos basis.About:
This article is published in Probabilistic Engineering Mechanics.The article was published on 2010-04-01. It has received 710 citations till now. The article focuses on the topics: Polynomial chaos & Multivariate random variable.read more
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AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation
TL;DR: An iterative approach based on Monte Carlo Simulation and Kriging metamodel to assess the reliability of structures in a more efficient way and is shown to be very efficient as the probability of failure obtained with AK-MCS is very accurate and this, for only a small number of calls to the performance function.
Journal ArticleDOI
Adaptive sparse polynomial chaos expansion based on least angle regression
Géraud Blatman,Bruno Sudret +1 more
TL;DR: A non intrusive method that builds a sparse PC expansion, which may be obtained at a reduced computational cost compared to the classical ''full'' PC approximation.
Journal ArticleDOI
A non-adapted sparse approximation of PDEs with stochastic inputs
Alireza Doostan,Houman Owhadi +1 more
TL;DR: The method converges in probability as a consequence of sparsity and a concentration of measure phenomenon on the empirical correlation between samples, and it is shown that the method is well suited for truly high-dimensional problems.
Journal ArticleDOI
A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models
TL;DR: An original and easily implementable method called AK-IS for active learning and Kriging-based Importance Sampling, based on the AK-MCS algorithm, that enables the correction or validation of the FORM approximation with only a very few mechanical model computations.
Journal ArticleDOI
Reliability-based design optimization using kriging surrogates and subset simulation
TL;DR: The aim of the present paper is to develop a strategy for solving reliability-based design optimization (RBDO) problems that remains applicable when the performance models are expensive to evaluate.
References
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Book
The Nature of Statistical Learning Theory
TL;DR: Setting of the learning problem consistency of learning processes bounds on the rate of convergence ofLearning processes controlling the generalization ability of learning process constructing learning algorithms what is important in learning theory?
Book
An Introduction to Copulas
TL;DR: This book discusses the fundamental properties of copulas and some of their primary applications, which include the study of dependence and measures of association, and the construction of families of bivariate distributions.
Journal ArticleDOI
Cross-Validatory Choice and Assessment of Statistical Predictions
TL;DR: In this article, a generalized form of the cross-validation criterion is applied to the choice and assessment of prediction using the data-analytic concept of a prescription, and examples used to illustrate the application are drawn from the problem areas of univariate estimation, linear regression and analysis of variance.
Journal ArticleDOI
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
TL;DR: This work represents the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error.
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