Efficient structural reliability analysis via a weak-intrusive stochastic finite element method

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  • Harbin Institute of Technology
  • University of Liverpool
  • Tongji University
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Original languageEnglish
Article number103414
JournalProbabilistic Engineering Mechanics
Volume71
Early online date13 Jan 2023
Publication statusPublished - Jan 2023

Abstract

This paper presents a novel methodology for structural reliability analysis by means of the stochastic finite element method (SFEM). The key issue of structural reliability analysis is to determine the limit state function and corresponding multidimensional integral that are usually related to the structural stochastic displacement and/or its derivative, e.g., the stress and strain. In this paper, a novel weak-intrusive SFEM is first used to calculate structural stochastic displacements of all spatial positions. In this method, the stochastic displacement is decoupled into a combination of a series of deterministic displacements with random variable coefficients. An iterative algorithm is then given to solve the deterministic displacements and the corresponding random variables. Based on the stochastic displacement obtained by the SFEM, the limit state function described by the stochastic displacement (and/or its derivative) and the corresponding multidimensional integral encountered in reliability analysis can be calculated in a straightforward way. Failure probabilities of all spatial positions can be obtained at once since the stochastic displacements of all spatial points have been known by using the proposed SFEM. Furthermore, the proposed method can be applied to high-dimensional stochastic problems without any modification. One of the most challenging problems encountered in high-dimensional reliability analysis, known as the curse of dimensionality, can be circumvented with great success. Three numerical examples, including low- and high-dimensional reliability analysis, are given to demonstrate the good accuracy and the high efficiency of the proposed method.

Keywords

    Curse of dimensionality, Reliability analysis, Stochastic displacements, Stochastic finite element method, Weakly intrusive approximation

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Cite this

Efficient structural reliability analysis via a weak-intrusive stochastic finite element method. / Zheng, Zhibao; Dai, Hongzhe; Beer, Michael.
In: Probabilistic Engineering Mechanics, Vol. 71, 103414, 01.2023.

Research output: Contribution to journalArticleResearchpeer review

Zheng Z, Dai H, Beer M. Efficient structural reliability analysis via a weak-intrusive stochastic finite element method. Probabilistic Engineering Mechanics. 2023 Jan;71:103414. Epub 2023 Jan 13. doi: 10.1016/j.probengmech.2023.103414
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abstract = "This paper presents a novel methodology for structural reliability analysis by means of the stochastic finite element method (SFEM). The key issue of structural reliability analysis is to determine the limit state function and corresponding multidimensional integral that are usually related to the structural stochastic displacement and/or its derivative, e.g., the stress and strain. In this paper, a novel weak-intrusive SFEM is first used to calculate structural stochastic displacements of all spatial positions. In this method, the stochastic displacement is decoupled into a combination of a series of deterministic displacements with random variable coefficients. An iterative algorithm is then given to solve the deterministic displacements and the corresponding random variables. Based on the stochastic displacement obtained by the SFEM, the limit state function described by the stochastic displacement (and/or its derivative) and the corresponding multidimensional integral encountered in reliability analysis can be calculated in a straightforward way. Failure probabilities of all spatial positions can be obtained at once since the stochastic displacements of all spatial points have been known by using the proposed SFEM. Furthermore, the proposed method can be applied to high-dimensional stochastic problems without any modification. One of the most challenging problems encountered in high-dimensional reliability analysis, known as the curse of dimensionality, can be circumvented with great success. Three numerical examples, including low- and high-dimensional reliability analysis, are given to demonstrate the good accuracy and the high efficiency of the proposed method.",
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author = "Zhibao Zheng and Hongzhe Dai and Michael Beer",
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AU - Beer, Michael

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