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Polynomial chaos expansion with random and fuzzy variables
14 references·16 citing·33 second hop
Polynomial chaos expansion with random and fuzzy variables (2015)Polynomial chaos expansion with random an…Polynomial Chaos Expansion and Steady-State Response of a Class of Random Dynamical Systems (2014)Polynomial Chaos Expansion an…Influence of Polynomial Chaos expansion order on an uncertain asymmetric rotor system response (2014)Influence of Polynomial Chaos…Imprecise probabilities in engineering analyses (2013)Imprecise probabilities in en…A spectral approach for fuzzy uncertainty propagation in finite element analysis (2013)A spectral approach for fuzzy…Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Adaptive sparse polynomial ch…An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis (2009)An adaptive algorithm to buil…The stochastic finite element method: Past, present and future (2008)The stochastic finite element…A fuzzy finite element procedure for the calculation of uncertain frequency-response functions of damped structures: Part 1—Procedure (2005)A fuzzy finite element proced…A survey of non-probabilistic uncertainty treatment in finite element analysis (2004)A survey of non-probabilistic…Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Modeling uncertainty in flow …The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…The stochastic finite-element method (1980)The stochastic finite-element…Fuzzy sets (1965)Fuzzy setsAn enhanced learning function for bootstrap polynomial chaos expansion-based enhanced active learning algorithm for reliability analysis of structure (2024)An enhanced learning function…Sparse polynomial chaos expansion based on Bregman-iterative greedy coordinate descent for global sensitivity analysis (2021)Sparse polynomial chaos expan…Polyphase uncertainty analysis through virtual modelling technique (2021)Polyphase uncertainty analysi…Advanced kriging-based surrogate modelling and sensitivity analysis for rotordynamics with uncertainties (2021)Advanced kriging-based surrog…A hybrid method for analysing stationary random vibration of structures with uncertain parameters (2021)A hybrid method for analysing…Uncertain Frequency Responses of Clamp-Pipeline Systems Using an Interval-Based Method (2020)Uncertain Frequency Responses…Multi-scale uncertainty quantification of composite laminated plate considering random and interval variables with data driven PCE method (2020)Multi-scale uncertainty quant…An expanded sparse Bayesian learning method for polynomial chaos expansion (2019)An expanded sparse Bayesian l…Uncertainty analysis of composite laminated plate with data-driven polynomial chaos expansion method under insufficient input data of uncertain parameters (2018)Uncertainty analysis of compo…Steady-state response analysis of cracked rotors with uncertain‑but‑bounded parameters using a polynomial surrogate method (2018)Steady-state response analysi…Statistical moment analysis of multi-degree of freedom dynamic system based on polynomial dimensional decomposition method (2018)Statistical moment analysis o…Safety life analysis under the required failure possibility constraint for structure involving fuzzy uncertainty (2018)Safety life analysis under th…Dual interval-and-fuzzy analysis method for temperature prediction with hybrid epistemic uncertainties via polynomial chaos expansion (2018)Dual interval-and-fuzzy analy…Polynomial Chaos Expansion for Probabilistic Uncertainty Propagation (2017)Polynomial Chaos Expansion fo…A novel uncertainty analysis method for composite structures with mixed uncertainties including random and interval variables (2017)A novel uncertainty analysis …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…A mathematical theory of evidence (1977)Fuzzy sets (1996)Engineering computation under uncertainty – Capabilities of non-traditional models (2007)Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics: Recent advances (2010)A Chebyshev interval method for nonlinear dynamic systems under uncertainty (2012)Exact and Invariant Second-Moment Code Format (1974)Random field finite elements (1986)A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics (2004)Fast Numerical Methods for Stochastic Computations: A Review (2009)Fuzzy Sets and Systems - Theory and Applications (1980)Fuzzy Set Theory and Its Applications (1993)Advanced Line Sampling for efficient robust reliability analysis (2014)Recent Trends in the Modeling and Quantification of Non-probabilistic Uncertainty (2019)Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey (2020)A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (2000)Efficient computation of global sensitivity indices using sparse polynomial chaos expansions (2010)UQLab: A Framework for Uncertainty Quantification in Matlab (2014)POLYNOMIAL-CHAOS-BASED KRIGING (2015)Structural Reliability Methods (1996)Global sensitivity analysis using polynomial chaos expansions (2007)Reliability-based design optimization using kriging surrogates and subset simulation (2011)A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models (2012)LIF: A new Kriging based learning function and its application to structural reliability analysis (2016)Estimation of small failure probabilities in high dimensions by subset simulation (2001)Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion (2014)Direct probability integral method for stochastic response analysis of static and dynamic structural systems (2019)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)An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)Family resemblances: Studies in the internal structure of categories (1975)Basic objects in natural categories (1976)Soft set theory—First results (1999)
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  • 2010Adaptive sparse polynomial chaos expansion based on least angle regression1,507 cited
  • 2003Modeling uncertainty in flow simulations via generalized polynomial chaos1,428 cited
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  • 2014Influence of Polynomial Chaos expansion order on an uncertain asymmetric rotor system response68 cited
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  • 2013A spectral approach for fuzzy uncertainty propagation in finite element analysis57 cited

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Cited by

  • 2018Steady-state response analysis of cracked rotors with uncertain‑but‑bounded parameters using a polynomial surrogate method49 cited
  • 2017A novel uncertainty analysis method for composite structures with mixed uncertainties including random and interval variables47 cited
  • 2017A new evidence-theory-based method for response analysis of acoustic system with epistemic uncertainty by using Jacobi expansion44 cited
  • 2018Uncertainty analysis of composite laminated plate with data-driven polynomial chaos expansion method under insufficient input data of uncertain parameters38 cited
  • 2020Uncertain Frequency Responses of Clamp-Pipeline Systems Using an Interval-Based Method38 cited
  • 2021Sparse polynomial chaos expansion based on Bregman-iterative greedy coordinate descent for global sensitivity analysis35 cited
  • 2020Multi-scale uncertainty quantification of composite laminated plate considering random and interval variables with data driven PCE method34 cited
  • 2021Polyphase uncertainty analysis through virtual modelling technique27 cited
  • 2018Safety life analysis under the required failure possibility constraint for structure involving fuzzy uncertainty26 cited
  • 2021Advanced kriging-based surrogate modelling and sensitivity analysis for rotordynamics with uncertainties26 cited
  • 2018Dual interval-and-fuzzy analysis method for temperature prediction with hybrid epistemic uncertainties via polynomial chaos expansion25 cited
  • 2021A hybrid method for analysing stationary random vibration of structures with uncertain parameters24 cited
  • 2019An expanded sparse Bayesian learning method for polynomial chaos expansion23 cited
  • 2017Polynomial Chaos Expansion for Probabilistic Uncertainty Propagation22 cited
  • 2024An enhanced learning function for bootstrap polynomial chaos expansion-based enhanced active learning algorithm for reliability analysis of structure19 cited
  • 2018Statistical moment analysis of multi-degree of freedom dynamic system based on polynomial dimensional decomposition method19 cited