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A polynomial dimensional decomposition for stochastic computing
12 references·16 citing·29 second hop
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 1999General foundations of high‐dimensional model representations905 cited
  • 2004A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics568 cited
  • 2003Theorems and examples on high dimensional model representation450 cited
  • 2004A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics441 cited
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  • 1997An efficient method for parametric uncertainty analysis of numerical geophysical models334 cited
  • 2002Practical Approaches To Construct RS-HDMR Component Functions275 cited
  • 2004Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability218 cited
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Cited by

  • 2018A new reliability-based design optimization framework using isogeometric analysis93 cited
  • 2009Extended Polynomial Dimensional Decomposition for Arbitrary Probability Distributions

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72 cited
  • 2024Dimensional decomposition-aided metamodels for uncertainty quantification and optimization in engineering: A review70 cited
  • 2011Hybrid dimension reduction for mechanism reliability analysis with random joint clearances67 cited
  • 2015On the dual iterative stochastic perturbation-based finite element method in solid mechanics with Gaussian uncertainties56 cited
  • 2011Global sensitivity analysis by polynomial dimensional decomposition56 cited
  • 2010eXtended Stochastic Finite Element Method for the numerical simulation of heterogeneous materials with random material interfaces55 cited
  • 2017Dynamic response analysis of an overhung rotor with interval uncertainties50 cited
  • 2020A confidence-based reliability optimization with single loop strategy and second-order reliability method47 cited
  • 2011ORTHOGONAL POLYNOMIAL EXPANSIONS FOR SOLVING RANDOM EIGENVALUE PROBLEMS46 cited
  • 2014Adaptive-sparse polynomial dimensional decomposition methods for high-dimensional stochastic computing45 cited
  • 2016Adaptive surrogate modeling by ANOVA and sparse polynomial dimensional decomposition for global sensitivity analysis in fluid simulation44 cited
  • 2016A new hybrid uncertain analysis method for structural-acoustic systems with random and interval parameters42 cited
  • 2014A Generalized ANOVA Dimensional Decomposition for Dependent Probability Measures37 cited
  • 2015Reliability-based design optimization by adaptive-sparse polynomial dimensional decomposition33 cited
  • 2016The $f$-Sensitivity Index33 cited