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First order reliability method for time-variant problems using series expansions
13 references·16 citing·31 second hop
First order reliability method for time-variant problems using series expansions (2014)First order reliability method for time-v…International Encyclopedia of Statistical Science (2025)International Encyclopedia of…Time-dependent reliability analysis with joint upcrossing rates (2013)Time-dependent reliability an…Recent Advances in Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design (2009)Recent Advances in Non-Intrus…Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification (2009)Comparison of Non-Intrusive P…Global sensitivity analysis using polynomial chaos expansions (2007)Global sensitivity analysis u…The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters (2006)The extreme value distributio…Reliability-based Structural Design (2006)Reliability-based Structural …The PHI2 method: a way to compute time-variant reliability (2003)The PHI2 method: a way to com…Comparison of finite element reliability methods (2002)Comparison of finite element …A state-of-the-art report on computational stochastic mechanics (1997)A state-of-the-art report on …Orthogonal Series Expansions of Random Fields in Reliability Analysis (1994)Orthogonal Series Expansions …Vector Process Out‐Crossing as Parallel System Sensitivity Measure (1991)Vector Process Out‐Crossing a…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Modeling, analysis, and optimization under uncertainties: a review (2021)Modeling, analysis, and optim…Surrogate-assisted global sensitivity analysis: an overview (2020)Surrogate-assisted global sen…On reliability analysis method through rotational sparse grid nodes (2020)On reliability analysis metho…Efficient adaptive Kriging-based reliability analysis combining new learning function and error-based stopping criterion (2020)Efficient adaptive Kriging-ba…An active-learning method based on multi-fidelity Kriging model for structural reliability analysis (2020)An active-learning method bas…Adaptive Bayesian support vector regression model for structural reliability analysis (2020)Adaptive Bayesian support vec…A computational framework of kinematic accuracy reliability analysis for industrial robots (2020)A computational framework of …An adaptive multiple-Kriging-surrogate method for time-dependent reliability analysis (2019)An adaptive multiple-Kriging-…An active learning method combining Kriging and accelerated chaotic single loop approach (AK-ACSLA) for reliability-based design optimization (2019)An active learning method com…A novel single-loop procedure for time-variant reliability analysis based on Kriging model (2019)A novel single-loop procedure…An improved TRPD method for time-variant reliability analysis (2018)An improved TRPD method for t…An importance learning method for non-probabilistic reliability analysis and optimization (2018)An importance learning method…Principal component analysis and polynomial chaos expansion for time-variant reliability problems (2017)Principal component analysis …A hybrid self-adaptive conjugate first order reliability method for robust structural reliability analysis (2017)A hybrid self-adaptive conjug…Time-variant reliability assessment through equivalent stochastic process transformation (2016)Time-variant reliability asse…A new directional stability transformation method of chaos control for first order reliability analysis (2016)A new directional stability t…Structural reliability under combined random load sequences (1978)The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation (2011)Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis version 6.0 theory manual (2014)Global Sensitivity Analysis for multivariate output using Polynomial Chaos Expansion (2014)A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output (1999)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)UQLab: A Framework for Uncertainty Quantification in Matlab (2014)Sensitivity analysis of environmental models: A systematic review with practical workflow (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)Simulation of Stochastic Processes by Spectral Representation 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this work references cited by second hop

References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2007Global sensitivity analysis using polynomial chaos expansions2,547 cited
  • 2006Reliability-based Structural Design588 cited
  • 2003The PHI2 method: a way to compute time-variant reliability460 cited
  • 1997A state-of-the-art report on computational stochastic mechanics424 cited
  • 2009Recent Advances in Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design371 cited
  • 2006The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters352 cited
  • 2009Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification348 cited
  • 2025International Encyclopedia of Statistical Science296 cited
  • 1994Orthogonal Series Expansions of Random Fields in Reliability Analysis265 cited
  • 2002Comparison of finite element reliability methods258 cited
  • 2013Time-dependent reliability analysis with joint upcrossing rates234 cited
  • 1991Vector Process Out‐Crossing as Parallel System Sensitivity Measure201 cited

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  • 2021Modeling, analysis, and optimization under uncertainties: a review166 cited

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2020
Surrogate-assisted global sensitivity analysis: an overview
165 cited
  • 2016A new directional stability transformation method of chaos control for first order reliability analysis162 cited
  • 2016Time-variant reliability assessment through equivalent stochastic process transformation140 cited
  • 2019An active learning method combining Kriging and accelerated chaotic single loop approach (AK-ACSLA) for reliability-based design optimization130 cited
  • 2017Principal component analysis and polynomial chaos expansion for time-variant reliability problems125 cited
  • 2020Adaptive Bayesian support vector regression model for structural reliability analysis121 cited
  • 2017A hybrid self-adaptive conjugate first order reliability method for robust structural reliability analysis116 cited
  • 2018An importance learning method for non-probabilistic reliability analysis and optimization115 cited
  • 2020Efficient adaptive Kriging-based reliability analysis combining new learning function and error-based stopping criterion90 cited
  • 2020An active-learning method based on multi-fidelity Kriging model for structural reliability analysis88 cited
  • 2020A computational framework of kinematic accuracy reliability analysis for industrial robots80 cited
  • 2019An adaptive multiple-Kriging-surrogate method for time-dependent reliability analysis76 cited
  • 2018An improved TRPD method for time-variant reliability analysis76 cited
  • 2020On reliability analysis method through rotational sparse grid nodes75 cited
  • 2019A novel single-loop procedure for time-variant reliability analysis based on Kriging model74 cited