Global sensitivity analysis using polynomial chaos expansions

By Bruno Sudret. Reliability Engineering & System Safety, 2008

2,456 citations recorded by the source corpus.

Subfields: Building and Construction, Civil and Structural Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c341f470f2c3d66669090a37c11732f722810769

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Citations in the corpus

Efficient posterior exploration of a high‐dimensional groundwater model from two‐stage Markov chain Monte Carlo simulation and polynomial chaos expansion (2013, methodology): “[69] The gPC technique is well suited for global sensitivity analysis (GSA) [e.g., Saltelli et al., 2006] because the associated computational cost becomes practically equivalent to the time it takes to estimate the expansion coefficients [e.g., Sudret, 2008].”
Asymptotic normality and efficiency of two Sobol index estimators (2013, neutral): “Well-known metamodels include Kriging [24], polynomial chaos expansion [30] and reduced bases [12, 19], to name a few.”
UQLab: a framework for uncertainty quantification in MATLAB (2014, methodology): “Because the current MODEL is the newly created PCE metamodel, the global Sobol’ indices are automatically calculated from its coefﬁcients (Sudret 2008”
Weighted stochastic response surface method considering sample weights (2011, methodology): “For this reason, Sudret has suggested that the probabilistic weights of sample points should be taken into account in SRSM ( Sudret 2008 ).”
Calculations of Sobol indices for the Gaussian process metamodel (2008, methodology): “ible (Jacques [11]). The metamodel’s predictor have to be evaluated a large number of times to compute Sobol indices via Monte Carlo methods. Recent works based on polynomial chaos expansions (Sudret [27]) have used the special form of this orthogonal functions expansion to derive analytical estimat”
Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: methodology and application to history matching for carbon dioxide storage in geological formations (2013, background): “Because the reduced model is merely a polynomial and has exploitable properties due to the orthogonal basis, it is vastly faster than the original one and offers a large playground for stochastic analysis [24, 57, 85], risk assessment [58, 84], and global sensitivity analysis [10, 57, 79].”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, methodology): “⋄ Regression Regression methods [29,28,15,124] rely on the same principles as classical response surface methods [64].”
An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis (2010, methodology): “Two approaches based on a PC representation of the response are usually distinguished: – the projection approach: each PC coefficient is recast as a multidimensional integral [6, 7] which can be computed either by simulation or quadrature; – the regression approach [8, 9, 10, 11]: the PC coefficient”
Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion (2011, methodology): “This allows one to calculate the system response using an approximate simple analytical equation [9-13, 17-18, 22-26].”