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Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations
16 references·9 citing·36 second hop
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References

  • 1976Method for Random Vibration of Hysteretic Systems2,686 cited
  • 2001Estimation of small failure probabilities in high dimensions by subset simulation2,419 cited
  • 2014Dependence Modeling with Copulas1,564 cited
  • 1991Simulation of Stochastic Processes by Spectral Representation1,379 cited
  • 2007Goodness-of-fit tests for copulas: A review and a power study1,321 cited
  • 2008The stochastic finite element method: Past, present and future999 cited
  • 2009Stochastic Dynamics of Structures923 cited
  • 1990Polynomial Chaos in Stochastic Finite Elements416 cited
  • 2004Reliability of structures in high dimensions, part I: algorithms and applications370 cited
  • 2011Advances of the probability density evolution method for nonlinear stochastic systems247 cited
  • 2019Direct probability integral method for stochastic response analysis of static and dynamic structural systems201 cited
  • 2011An analytical Wiener path integral technique for non-stationary response determination of nonlinear oscillators181 cited
  • 1983Random Vibration: A Survey of Recent Developments122 cited
  • 2019A novel fractional moments-based maximum entropy method for high-dimensional reliability analysis115 cited
  • 1976

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A probabilistic model for spatial distribution of material properties
74 cited
  • 2017Uncertainty propagation of p-boxes using sparse polynomial chaos expansions72 cited
  • Cited by

    • 2024Simulation-free reliability analysis with importance sampling-based adaptive training physics-informed neural networks: Method and application to chloride penetration37 cited
    • 2022Stochastic response determination of multi-dimensional nonlinear systems endowed with fractional derivative elements by the GE-GDEE36 cited
    • 2025First excursion probability of dynamical systems: A review on computational methods32 cited
    • 2025Efficient stochastic response analysis of high-dimensional nonlinear systems subject to multiplicative noise via the DR-PDEE20 cited
    • 2025Structural design optimization under stochastic excitations considering first-passage probability constraint based on dimension-reduced probability density evolution equation20 cited
    • 2024Stochastic Response Analysis of a Spar-Type FOWT Subjected to Extreme Waves by a Novel Filter Wave Model and the DR-PDEE18 cited
    • 2025DR-PDEE-based probabilistic response analysis for high-dimensional nonlinear dynamical systems under general non-white and non-stationary random excitations via constructing the auxiliary diffusion process15 cited
    • 2025Stochastic dynamic response analysis via dimension-reduced probability density evolution equation (DR-PDEE) with enhanced tail-accuracy14 cited
    • 2023Property of intrinsic drift coefficients in globally-evolving-based generalized density evolution equation for the first-passage reliability assessment13 cited