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A new method for stochastic analysis of structures under limited observations
16 references·7 citing·33 second hop
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polynomial ch…The principle of preservation of probability and the generalized density evolution equation (2006)The principle of preservation…Stochastic finite element: a non intrusive approach by regression (2006)Stochastic finite element: a …On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data (2006)On the construction and analy…Modeling Arbitrary Uncertainties Using Gram-Schmidt Polynomial Chaos (2006)Modeling Arbitrary Uncertaint…Simulation of strongly non-Gaussian processes using Karhunen–Loeve expansion (2005)Simulation of strongly non-Ga…Maximum likelihood estimation of stochastic chaos representations from experimental data (2005)Maximum likelihood estimation…Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure (2004)Physical Systems with Random …The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial 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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2010Adaptive sparse polynomial chaos expansion based on least angle regression1,507 cited
  • 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure609 cited
  • 2006The principle of preservation of probability and the generalized density evolution equation517 cited
  • 2006Stochastic finite element: a non intrusive approach by regression427 cited
  • 2021Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark275 cited
  • 2002Simulation of second-order processes using Karhunen–Loeve expansion269 cited
  • 2005Simulation of strongly non-Gaussian processes using Karhunen–Loeve expansion259 cited
  • 2019Direct probability integral method for stochastic response analysis of static and dynamic structural systems201 cited
  • 2006On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data191 cited
  • 2005Maximum likelihood estimation of stochastic chaos representations from experimental data146 cited
  • 2006Modeling Arbitrary Uncertainties Using Gram-Schmidt Polynomial Chaos146 cited
  • 2017A stochastic harmonic function representation for non-stationary stochastic processes

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121 cited
  • 2019Simulation of non-stationary non-Gaussian random fields from sparse measurements using Bayesian compressive sampling and Karhunen-Loève expansion120 cited
  • 2020Non-parametric simulation of non-stationary non-gaussian 3D random field samples directly from sparse measurements using signal decomposition and Markov Chain Monte Carlo (MCMC) simulation118 cited
  • Cited by

    • 2023Application of high-credible statistical results calculation scheme based on least squares Quasi-Monte Carlo method in multimodal stochastic problems27 cited
    • 2022A stochastic finite element scheme for solving partial differential equations defined on random domains26 cited
    • 2023An iterative multi-fidelity scheme for simulating multi-dimensional non-Gaussian random fields26 cited
    • 2025Adaptive Kriging-assisted multi-fidelity subset simulation for reliability analysis24 cited
    • 2022Stochastic analysis of structures under limited observations using kernel density estimation and arbitrary polynomial chaos expansion24 cited
    • 2025High-dimensional points selection strategy for PDEM-based stochastic dynamic analysis of structures22 cited
    • 2025Conditional uncertainty propagation of stochastic dynamical structures considering measurement conditions11 cited