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First excursion probability of dynamical systems: A review on computational methods
16 references·0 citing·39 second hop
First excursion probability of dynamical systems: A review on computational methods (2025)First excursion probability of dynamical …Active learning for structural reliability: Survey, general framework and benchmark (2022)Active learning for structura…A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters (2015)A GF-discrepancy for point se…Bayesian Updating with Structural Reliability Methods (2014)Bayesian Updating with Struct…AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)AK-MCS: An active learning re…High-order limit state functions in the response surface method for structural reliability analysis (2007)High-order limit state functi…The principle of preservation of probability and the generalized density evolution equation (2006)The principle of preservation…The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters (2006)The extreme value distributio…The equivalent extreme-value event and evaluation of the structural system reliability (2006)The equivalent extreme-value …Application of line sampling simulation method to reliability benchmark problems (2006)Application of line sampling …Probability density evolution method for dynamic response analysis of structures with uncertain parameters (2004)Probability density evolution…The PHI2 method: a way to compute time-variant reliability (2003)The PHI2 method: a way to com…Important sampling in high dimensions (2002)Important sampling in high di…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…Directional methods for structural reliability analysis (2000)Directional methods for struc…Probability Integration by Directional Simulation (1988)Probability Integration by Di…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)The stochastic finite-element method (1980)Neumann Expansion for Stochastic Finite Element Analysis (1988)A state-of-the-art report on computational stochastic mechanics (1997)The Number Theoretical Method in Response Analysis of Nonlinear Stochastic Structures (2006)Advances of the probability density evolution method for nonlinear stochastic systems (2011)Monte Carlo techniques in computational stochastic mechanics (1998)A response surface method based on weighted regression for structural reliability analysis (2004)Methods of structural safety (2006)Monte Carlo and variance reduction methods for structural reliability analysis: A comprehensive review (2023)Stochastic Finite Elements: A Spectral Approach (1991)Structural Reliability Methods (1996)Kriging metamodeling in simulation: A review (2007)Metamodel-based importance sampling for structural reliability analysis (2013)LIF: A new Kriging based learning function and its application to structural reliability analysis (2016)Probability Concepts in Engineering Planning and Design (1975)Method for Random Vibration of Hysteretic Systems (1976)A Nested Extreme Response Surface Approach for Time-Dependent Reliability-Based Design Optimization (2012)Random function based spectral representation of stationary and non-stationary stochastic processes (2016)Time-Dependent Reliability Analysis Through Response Surface Method (2017)Exact and Invariant Second-Moment Code Format (1974)Probabilistic Structural Dynamics: Advanced Theory and Applications (1967)Probability density evolution method: Background, significance and recent developments (2015)Direct probability integral method for stochastic response analysis of static and dynamic structural systems (2019)Optimization algorithms for structural reliability (1991)Reliability-based design sensitivity by efficient simulation (2005)Sequential importance sampling for structural reliability analysis (2016)A review and assessment of importance sampling methods for reliability analysis (2022)Optimal Discretization of Random Fields (1993)Analytical derivation of the outcrossing rate in time-variant reliability problems (2008)A Single-Loop Kriging Surrogate Modeling for Time-Dependent Reliability Analysis (2016)Monte Carlo solution of structural dynamics (1972)Stochastic Dynamics of Structures (2009)A unified analysis framework of static and dynamic structural reliabilities based on direct probability integral method (2021)System reliability analyses of static and dynamic structures via direct probability integral method (2021)
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References

  • 2001Estimation of small failure probabilities in high dimensions by subset simulation2,419 cited
  • 2011AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation2,048 cited
  • 2006The principle of preservation of probability and the generalized density evolution equation517 cited
  • 2003The PHI2 method: a way to compute time-variant reliability460 cited
  • 2006The equivalent extreme-value event and evaluation of the structural system reliability447 cited
  • 2015A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters410 cited
  • 2002Important sampling in high dimensions375 cited
  • 2004Probability density evolution method for dynamic response analysis of structures with uncertain parameters368 cited
  • 2006The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters352 cited
  • 1988Probability Integration by Directional Simulation339 cited
  • 2014Bayesian Updating with Structural Reliability Methods339 cited
  • 2006Application of line sampling simulation method to reliability benchmark problems292 cited
  • 2001First excursion probabilities for linear systems by very efficient importance sampling282 cited
  • 2022Active learning for structural reliability: Survey, general framework and benchmark

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282 cited
  • 2000Directional methods for structural reliability analysis278 cited
  • 2007High-order limit state functions in the response surface method for structural reliability analysis273 cited
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