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An efficient method for solving high-dimension stationary FPK equation of strongly nonlinear systems under additive and/or multiplicative white noise
16 references·2 citing·37 second hop
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References

  • 1967Probabilistic Structural Dynamics: Advanced Theory and Applications629 cited
  • 2011An analytical Wiener path integral technique for non-stationary response determination of nonlinear oscillators181 cited
  • 2006Solution of Fokker-Planck equation by finite element and finite difference methods for nonlinear systems157 cited
  • 2006Stochastic Dynamics and Control149 cited
  • 1997A new path integration procedure based on Gauss-Legendre scheme137 cited
  • 2015An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems86 cited
  • 2012Nonlinear MDOF system stochastic response determination via a dimension reduction approach62 cited
  • 2021First-passage reliability of high-dimensional nonlinear systems under additive excitation by the ensemble-evolving-based generalized density evolution equation57 cited
  • 2018Dimension-reduced FPK equation for additive white-noise excited nonlinear structures56 cited
  • 2014Dimension Reduction of the FPK Equation via an Equivalence of Probability Flux for Additively Excited Systems47 cited
  • 2019Non-stationary response of MDOF dynamical systems under combined Gaussian and Poisson white noises by the generalized cell mapping method38 cited
  • 2005A finite element analysis on random vibration of nonlinear shell structures35 cited
  • 2017Stationary Response Probability Distribution of SDOF Nonlinear Stochastic Systems29 cited

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  • 2020An exact closed-form solution for linear multi-degree-of-freedom systems under Gaussian white noise via the Wiener path integral technique27 cited
  • 2024An extrapolation approach within the Wiener path integral technique for efficient stochastic response determination of nonlinear systems24 cited
  • 2022Transient response of Bouc–Wen hysteretic system under random excitation via RBFNN method22 cited
  • Cited by

    • 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
    • 2025Non-markovian dynamics: the memory-dependent probability density evolution equations8 cited