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Evolution of probability densities in the phase space for reliability analysis of non-linear structures
16 references·0 citing·34 second hop
Evolution of probability densities in the phase space for reliability analysis of non-linear structures (2008)Evolution of probability densities in the…Application of line sampling simulation method to reliability benchmark problems (2006)Application of line sampling …Reliability of structures in high dimensions, part I: algorithms and applications (2004)Reliability of structures in …A critical appraisal of reliability estimation procedures for high dimensions (2004)A critical appraisal of relia…Equivalent linearization and Monte Carlo simulation in stochastic dynamics (2003)Equivalent linearization and …First excursion probabilities for linear systems by very efficient importance sampling (2001)First excursion probabilities…Estimation of small failure probabilities in high dimensions by subset simulation (2001)Estimation of small failure p…The geometry of random vibrations and solutions by FORM and SORM (2000)The geometry of random vibrat…Efficient path integration methods for nonlinear dynamic systems (2000)Efficient path integration me…On advanced Monte Carlo simulation procedures in stochastic structural dynamics (1997)On advanced Monte Carlo simul…A new path integration procedure based on Gauss-Legendre scheme (1997)A new path integration proced…Stochastic analysis of structural and mechanical vibrations (1996)Stochastic analysis of struct…On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems (1993)On the numerical solution of …The Generalized Cell Mapping Method in Nonlinear Random Vibration Based Upon Short-Time Gaussian Approximation (1990)The Generalized Cell Mapping …First-passage probabilities for randomly excited systems: Diffusion methods (1986)First-passage probabilities f…Probabilistic Theory of Structural Dynamics (1976)Probabilistic Theory of Struc…Probabilistic Structural Dynamics: Advanced Theory and Applications (1967)Probabilistic Structural Dyna…An analytical Wiener path integral technique for non-stationary response determination of nonlinear oscillators (2011)Probability density evolution method: Background, significance and recent developments (2015)Numerical solution of stochastic differential equations (2016)Direct probability integral method for stochastic response analysis of static and dynamic structural systems (2019)Reliability analysis—a review and some perspectives (2001)On Latin hypercube sampling for structural reliability analysis (2002)A survey on approaches for reliability-based optimization (2010)Assessing small failure probabilities by combined subset simulation and Support Vector Machines (2011)MCMC algorithms for Subset Simulation (2015)Simulation and the Monte Carlo Method (1981)The stochastic finite element method: Past, present and future (2008)A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models (2012)The generalization of Latin hypercube sampling (2015)Simulation and the Monte Carlo Method (2016)A new adaptive importance sampling scheme for reliability calculations (1999)Subset simulation for structural reliability sensitivity analysis (2008)Active learning for structural reliability: Survey, general framework and benchmark (2022)Method for Random Vibration of Hysteretic Systems (1976)Introduction to Random Vibrations (1983)Computational stochastic mechanics – recent advances (2001)Random field finite elements (1986)Nonlinear Vibration Models for Extremes and Fatigue (1988)A nonparametric model of random uncertainties for reduced matrix models in structural dynamics (2000)Benchmark study on reliability estimation in higher dimensions of structural systems – An overview (2006)Hybrid enhanced Monte Carlo simulation coupled with advanced machine learning approach for accurate and efficient structural reliability analysis (2021)Monte Carlo and variance reduction methods for structural reliability analysis: A comprehensive review (2023)Dynamic response and reliability analysis of non-linear stochastic structures (2004)Reliability engineering (2011)Generalized polynomial chaos and random oscillators (2004)Stochastic analysis of structures with uncertain-but-bounded parameters via improved interval analysis (2011)Reliability assessment in structural dynamics (2013)Applications of Hilbert–Huang transform to non‐stationary financial time series analysis (2003)The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters (2006)The principle of preservation of probability and the generalized density evolution equation (2006)
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References

  • 2001Estimation of small failure probabilities in high dimensions by subset simulation2,419 cited
  • 1976Probabilistic Theory of Structural Dynamics1,398 cited
  • 1967Probabilistic Structural Dynamics: Advanced Theory and Applications629 cited
  • 2004A critical appraisal of reliability estimation procedures for high dimensions476 cited
  • 2004Reliability of structures in high dimensions, part I: algorithms and applications370 cited
  • 2006Application of line sampling simulation method to reliability benchmark problems292 cited
  • 1993On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems289 cited
  • 2001First excursion probabilities for linear systems by very efficient importance sampling282 cited
  • 1996Stochastic analysis of structural and mechanical vibrations255 cited
  • 2000Efficient path integration methods for nonlinear dynamic systems250 cited
  • 2000The geometry of random vibrations and solutions by FORM and SORM238 cited
  • 1990The Generalized Cell Mapping Method in Nonlinear Random Vibration Based Upon Short-Time Gaussian Approximation199 cited
  • 2003Equivalent linearization and Monte Carlo simulation in stochastic dynamics152 cited
  • 1997A new path integration procedure based on Gauss-Legendre scheme137 cited

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  • 1997On advanced Monte Carlo simulation procedures in stochastic structural dynamics99 cited
  • 1986First-passage probabilities for randomly excited systems: Diffusion methods86 cited
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