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Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions
16 references·15 citing·28 second hop
Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions (2015)Quantification of margins and mixed uncer…Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)Uncertainty Quantification an…Efficient Sampling for Non-Intrusive Polynomial Chaos Applications with Multiple Uncertain Input Variables (2007)Efficient Sampling for Non-In…Uncertainty quantification using evidence theory in multidisciplinary design optimization (2004)Uncertainty quantification us…Engineering Design Reliability Handbook (2004)Engineering Design Reliabilit…An exploration of alternative approaches to the representation of uncertainty in model predictions (2004)An exploration of alternative…Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Modeling uncertainty in flow …Constructing Probability Boxes and Dempster-Shafer Structures (2003)Constructing Probability Boxe…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Error and uncertainty in modeling and simulation (2002)Error and uncertainty in mode…Combination of Evidence in Dempster-Shafer Theory (2002)Combination of Evidence in De…Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty (1997)Uncertainty and sensitivity a…Uncertainties in risk analysis: Six levels of treatment (1996)Uncertainties in risk analysi…Propagation of Uncertainty in Risk Assessments: The Need to Distinguish Between Uncertainty Due to Lack of Knowledge and Uncertainty Due to Variability (1994)Propagation of Uncertainty in…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination (1986)A simple view of the Dempster…A mathematical theory of evidence (1977)A mathematical theory of evid…High-cycle fatigue life prediction for fan blades considering aleatory and epistemic uncertainty with random damage (2025)High-cycle fatigue life predi…A new probabilistic transformation technique for evidence-theory-based structural reliability analysis (2025)A new probabilistic transform…A novel multiple linearization method for reliability analysis based on evidence theory (2024)A novel multiple linearizatio…An interval uncertainty analysis method for structural response bounds using feedforward neural network differentiation (2020)An interval uncertainty analy…Interval uncertainty analysis for static response of structures using radial basis functions (2019)Interval uncertainty analysis…The Hurwicz Decision Rule’s Relationship to Decision Making with the Triangle and Beta Distributions and Exponential Utility (2018)The Hurwicz Decision Rule’s R…Review of Robust Aerodynamic Design Optimization for Air Vehicles (2018)Review of Robust Aerodynamic …An arbitrary polynomial chaos expansion approach for response analysis of acoustic systems with epistemic uncertainty (2018)An arbitrary polynomial chaos…A unified model approach for probability response analysis of structure-acoustic system with random and epistemic uncertainties (2018)A unified model approach for …A polynomial expansion approach for response analysis of periodical composite structural–acoustic problems with multi-scale mixed aleatory and epistemic uncertainties (2018)A polynomial expansion approa…A Bayesian collocation method for static analysis of structures with unknown-but-bounded uncertainties (2018)A Bayesian collocation method…Kernel density estimation with bounded data (2017)Kernel density estimation wit…An integrated QMU approach to structural reliability assessment based on evidence theory and kriging model with adaptive sampling (2017)An integrated QMU approach to…A novel evidence theory model dealing with correlated variables and the corresponding structural reliability analysis method (2017)A novel evidence theory model…A new evidence-theory-based method for response analysis of acoustic system with epistemic uncertainty by using Jacobi expansion (2017)A new evidence-theory-based m…On the dempster-shafer framework and new combination rules (1987)Risks and decisions for conservation and environmental management (2005)Robust optimization – A comprehensive survey (2007)Judgment Under Uncertainty: Heuristics and Biases. (1984)On ordered weighted averaging aggregation operators in multicriteria decisionmaking (1988)Fuzzy sets (1996)Proceedings of the 2002 Winter Simulation Conference (2002)Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation (2004)Theory of Games and Economic Behavior (1945)Risk, Ambiguity, and the Savage Axioms (1961)Challenge problems: uncertainty in system response given uncertain parameters (2004)Verification, validation, and predictive capability in computational engineering and physics (2004)On The Quantitative Definition of Risk (1981)Different methods are needed to propagate ignorance and variability (1996)Decision Making in Health and Medicine: Integrating Evidence and Values (2001)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)Point-Collocation Nonintrusive Polynomial Chaos Method for Stochastic Computational Fluid Dynamics (2010)A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing (2011)Simulation-based optimal Bayesian experimental design for nonlinear systems (2012)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Evidential reasoning rule for evidence combination (2013)Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy (2018)An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)Fast Numerical Methods for Stochastic Computations: A Review (2009)k-order additive discrete fuzzy measures and their representation (1997)A new distance between two bodies of evidence (2001)
this work references cited by second hop

References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 1977A mathematical theory of evidence1,783 cited
  • 2003Modeling uncertainty in flow simulations via generalized polynomial chaos1,428 cited
  • 2002Combination of Evidence in Dempster-Shafer Theory1,096 cited
  • 1996Uncertainties in risk analysis: Six levels of treatment811 cited
  • 1986A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination800 cited
  • 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics769 cited
  • 2003Constructing Probability Boxes and Dempster-Shafer Structures745 cited
  • 1994Propagation of Uncertainty in Risk Assessments: The Need to Distinguish Between Uncertainty Due to Lack of Knowledge and Uncertainty Due to Variability701 cited
  • 2002Error and uncertainty in modeling and simulation629 cited
  • 2004Engineering Design Reliability Handbook468 cited
  • 1997Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty369 cited
  • 2004An exploration of alternative approaches to the representation of uncertainty in model predictions362 cited

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2007
Efficient Sampling for Non-Intrusive Polynomial Chaos Applications with Multiple Uncertain Input Variables
347 cited
  • 2004Uncertainty quantification using evidence theory in multidisciplinary design optimization324 cited
  • Cited by

    • 2019Interval uncertainty analysis for static response of structures using radial basis functions54 cited
    • 2018Review of Robust Aerodynamic Design Optimization for Air Vehicles51 cited
    • 2017A new evidence-theory-based method for response analysis of acoustic system with epistemic uncertainty by using Jacobi expansion44 cited
    • 2018An arbitrary polynomial chaos expansion approach for response analysis of acoustic systems with epistemic uncertainty40 cited
    • 2020An interval uncertainty analysis method for structural response bounds using feedforward neural network differentiation38 cited
    • 2017Kernel density estimation with bounded data35 cited
    • 2018A Bayesian collocation method for static analysis of structures with unknown-but-bounded uncertainties34 cited
    • 2025A new probabilistic transformation technique for evidence-theory-based structural reliability analysis28 cited
    • 2017An integrated QMU approach to structural reliability assessment based on evidence theory and kriging model with adaptive sampling21 cited
    • 2017A novel evidence theory model dealing with correlated variables and the corresponding structural reliability analysis method20 cited
    • 2025High-cycle fatigue life prediction for fan blades considering aleatory and epistemic uncertainty with random damage18 cited
    • 2018A unified model approach for probability response analysis of structure-acoustic system with random and epistemic uncertainties17 cited
    • 2018A polynomial expansion approach for response analysis of periodical composite structural–acoustic problems with multi-scale mixed aleatory and epistemic uncertainties17 cited
    • 2024A novel multiple linearization method for reliability analysis based on evidence theory16 cited
    • 2018The Hurwicz Decision Rule’s Relationship to Decision Making with the Triangle and Beta Distributions and Exponential Utility5 cited