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Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability
9 references·16 citing·31 second hop
Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability (2004)Polynomial Chaos Expansion with Latin Hyp…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos (2002)Modeling uncertainty in stead…A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (2000)A Comparison of Three Methods…Uncertainty Analysis of Transport-Transformation Models (1999)Uncertainty Analysis of Trans…A user`s guide to LHS: Sandia`s Latin Hypercube Sampling Software (1998)A user`s guide to LHS: Sandia…Optimal Latin-hypercube designs for computer experiments (1994)Optimal Latin-hypercube desig…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Designs for Computer Experiments (1989)Designs for Computer Experime…A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (1979)A Comparison of Three Methods…Reliability based design optimization of bridges considering bridge-vehicle interaction by Kriging surrogate model (2021)Reliability based design opti…Using polynomial chaos expansion for uncertainty and sensitivity analysis of bridge structures (2018)Using polynomial chaos expans…A cubature collocation based sparse polynomial chaos expansion for efficient structural reliability analysis (2018)A cubature collocation based …Sequential Design of Experiment for Sparse Polynomial Chaos Expansions (2017)Sequential Design of Experime…Least squares polynomial chaos expansion: A review of sampling strategies (2017)Least squares polynomial chao…Global sensitivity analysis via multi-fidelity polynomial chaos expansion (2017)Global sensitivity analysis v…Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions (2016)Polynomial meta-models with c…A robust and efficient stepwise regression method for building sparse polynomial chaos expansions (2016)A robust and efficient stepwi…Surrogate Modeling for Uncertainty Assessment with Application to Aviation Environmental System Models (2010)Surrogate Modeling for Uncert…Computational uncertainty analysis in multiresolution materials via stochastic constitutive theory (2010)Computational uncertainty ana…Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineering systems (2010)Adaptive-sparse polynomial ch…Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009)Recent Developments in Spectr…Design of Composite Wings Including Uncertainties: A Probabilistic Approach (2009)Design of Composite Wings Inc…A polynomial dimensional decomposition for stochastic computing (2008)A polynomial dimensional deco…Quantifying uncertainty in chemical systems modeling (2005)Quantifying uncertainty in ch…Structural reliability under non-Gaussian stochastic behavior (2004)Structural reliability under …A distribution-free approach to inducing rank correlation among input variables (1982)Fortran 77 program and user's guide for the generation of Latin hypercube and random samples for use with computer models (1984)DAKOTA, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis Version 3.0 Reference Manual (2001)DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. (2011)Diesel engine optimization with multi-objective performance characteristics by non-evolutionary Nelder-Mead algorithm: Sobol sequence and Latin hypercube sampling methods comparison in DoE process (2018)Design and Analysis of Computer Experiments (1989)Orthogonal Column Latin Hypercubes and Their Application in Computer Experiments (1998)Algorithmic construction of optimal symmetric Latin hypercube designs (2000)An efficient algorithm for constructing optimal design of computer experiments (2004)Simulation Modeling and Analysis. (1983)Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions (2008)An Introduction to Copulas (1999)Time-variant reliability assessment through equivalent stochastic process transformation (2016)Bayesian sparse polynomial chaos expansion for global sensitivity analysis (2017)Modeling, analysis, and optimization under uncertainties: a review (2021)Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2004)Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)Empirical Model Building and Response Surfaces (1988)Fuzzy sets (1996)Distributional uncertainty analysis using power series and polynomial chaos expansions (2007)Point-Collocation Nonintrusive Polynomial Chaos Method for Stochastic Computational Fluid Dynamics (2010)A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry (2015)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)A review of techniques for parameter sensitivity analysis of environmental models (1994)Importance measures in global sensitivity analysis of nonlinear models (1996)Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems (2003)
this work references cited by second hop

References

  • 2000A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code8,233 cited
  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 1979A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code3,766 cited
  • 1989Designs for Computer Experiments970 cited
  • 1994Optimal Latin-hypercube designs for computer experiments634 cited
  • 2002Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos552 cited
  • 1999Uncertainty Analysis of Transport-Transformation Models329 cited
  • 1998A user`s guide to LHS: Sandia`s Latin Hypercube Sampling Software218 cited

Cited by

  • 2010Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineering systems183 cited
  • 2009Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations181 cited
  • 2017Least squares polynomial chaos expansion: A review of sampling strategies157 cited
  • 2008A polynomial dimensional decomposition for stochastic computing140 cited
  • 2016Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions

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120 cited
  • 2016A robust and efficient stepwise regression method for building sparse polynomial chaos expansions114 cited
  • 2005Quantifying uncertainty in chemical systems modeling104 cited
  • 2018Using polynomial chaos expansion for uncertainty and sensitivity analysis of bridge structures92 cited
  • 2010Surrogate Modeling for Uncertainty Assessment with Application to Aviation Environmental System Models92 cited
  • 2017Sequential Design of Experiment for Sparse Polynomial Chaos Expansions83 cited
  • 2017Global sensitivity analysis via multi-fidelity polynomial chaos expansion80 cited
  • 2004Structural reliability under non-Gaussian stochastic behavior73 cited
  • 2010Computational uncertainty analysis in multiresolution materials via stochastic constitutive theory68 cited
  • 2018A cubature collocation based sparse polynomial chaos expansion for efficient structural reliability analysis68 cited
  • 2009Design of Composite Wings Including Uncertainties: A Probabilistic Approach62 cited
  • 2021Reliability based design optimization of bridges considering bridge-vehicle interaction by Kriging surrogate model53 cited