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Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion
13 references·16 citing·29 second hop
Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012)Data-driven uncertainty quantification us…Polynomial chaos expansion for sensitivity analysis (2008)Polynomial chaos expansion fo…Global sensitivity analysis using polynomial chaos expansions (2007)Global sensitivity analysis u…Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)Multi-Element Generalized Pol…Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure (2004)Physical Systems with Random …Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2004)Galerkin methods for linear a…Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Modeling uncertainty in flow …Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems (2003)Latin hypercube sampling and …The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates (2001)Global sensitivity indices fo…Structural Reliability Methods (1996)Structural Reliability MethodsStochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Nonlinear Vibration Models for Extremes and Fatigue (1988)Nonlinear Vibration Models fo…Structural Reliability under Incomplete Probability Information (1986)Structural Reliability under …Dimensional decomposition-aided metamodels for uncertainty quantification and optimization in engineering: A review (2024)Dimensional decomposition-aid…Uncertainty quantification and global sensitivity analysis of composite wind turbine blades (2022)Uncertainty quantification an…An efficient multi-fidelity Kriging surrogate model-based method for global sensitivity analysis (2022)An efficient multi-fidelity K…Surrogate modeling of high-dimensional problems via data-driven polynomial chaos expansions and sparse partial least square (2020)Surrogate modeling of high-di…Reliability analysis with stratified importance sampling based on adaptive Kriging (2020)Reliability analysis with str…Arbitrary polynomial chaos expansion method for uncertainty quantification and global sensitivity analysis in structural dynamics (2020)Arbitrary polynomial chaos ex…Review of statistical model calibration and validation—from the perspective of uncertainty structures (2019)Review of statistical model c…Polynomial chaos expansions for dependent random variables (2019)Polynomial chaos expansions f…Certain trends in uncertainty and sensitivity analysis: An overview of software tools and techniques (2019)Certain trends in uncertainty…Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits (2018)Review of Polynomial Chaos-Ba…Arbitrary Polynomial Chaos for Uncertainty Propagation of Correlated Random Variables in Dynamic Systems (2017)Arbitrary Polynomial Chaos fo…Spacecraft Uncertainty Propagation Using Gaussian Mixture Models and Polynomial Chaos Expansions (2016)Spacecraft Uncertainty Propag…SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos (2016)SAMBA: Sparse Approximation o…An introduction to sensitivity assessment of simulation models (2015)An introduction to sensitivit…Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations (2014)Polynomial chaos expansions f…Efficiency enhancement of optimized Latin hypercube sampling strategies: Application to Monte Carlo uncertainty analysis and meta-modeling (2014)Efficiency enhancement of opt…Exact and Invariant Second-Moment Code Format (1974)Structural reliability under combined random load sequences (1978)Narrow Reliability Bounds for Structural Systems (1979)Second‐Order Reliability Approximations (1987)Optimal Discretization of Random Fields (1993)Reliability analysis—a review and some perspectives (2001)A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output (1999)UQLab: A Framework for Uncertainty Quantification in Matlab (2014)Sensitivity analysis of environmental models: A systematic review with practical workflow (2016)Probability Concepts in Engineering Planning and Design (1975)Aleatory or epistemic? 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this work references cited by second hop

References

  • 2001Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates6,377 cited
  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2003Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems2,707 cited
  • 2007Global sensitivity analysis using polynomial chaos expansions2,547 cited
  • 1996Structural Reliability Methods2,192 cited
  • 2003Modeling uncertainty in flow simulations via generalized polynomial chaos1,428 cited
  • 1986Structural Reliability under Incomplete Probability Information853 cited
  • 2008Polynomial chaos expansion for sensitivity analysis747 cited
  • 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure609 cited
  • 2004Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations556 cited
  • 1988Nonlinear Vibration Models for Extremes and Fatigue535 cited
  • 2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures498 cited

Cited by

  • 2015An introduction to sensitivity assessment of simulation models186 cited

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  • 2020Reliability analysis with stratified importance sampling based on adaptive Kriging127 cited
  • 2018Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits121 cited
  • 2014Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations115 cited
  • 2019Certain trends in uncertainty and sensitivity analysis: An overview of software tools and techniques114 cited
  • 2016SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos100 cited
  • 2019Review of statistical model calibration and validation—from the perspective of uncertainty structures99 cited
  • 2014Efficiency enhancement of optimized Latin hypercube sampling strategies: Application to Monte Carlo uncertainty analysis and meta-modeling93 cited
  • 2016Spacecraft Uncertainty Propagation Using Gaussian Mixture Models and Polynomial Chaos Expansions89 cited
  • 2020Arbitrary polynomial chaos expansion method for uncertainty quantification and global sensitivity analysis in structural dynamics81 cited
  • 2019Polynomial chaos expansions for dependent random variables80 cited
  • 2022An efficient multi-fidelity Kriging surrogate model-based method for global sensitivity analysis79 cited
  • 2024Dimensional decomposition-aided metamodels for uncertainty quantification and optimization in engineering: A review70 cited
  • 2022Uncertainty quantification and global sensitivity analysis of composite wind turbine blades61 cited
  • 2020Surrogate modeling of high-dimensional problems via data-driven polynomial chaos expansions and sparse partial least square55 cited
  • 2017Arbitrary Polynomial Chaos for Uncertainty Propagation of Correlated Random Variables in Dynamic Systems54 cited