A sequential simulation strategy for response bounds analysis of structures with interval uncertainties

Ni, Bingyu; Jiang, Chao; Wu, P.G.; Wang, Z.H.; Tian, Wenya

doi:10.1016/j.compstruc.2022.106785

Cited by 13 publications

(2 citation statements)

References 60 publications

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“…The marginal distributions can be fitted by GMM or kernel density estimation (KDE), the covariance between different marginal distributions can be computed and the covariance function can be further fitted with polynomial or exponential functions. Furthermore, the proposed TUP method is not suitable for problems with interval variables [50,51], evidence variables or fuzzy variables [52], and further investigations are needed for those cases [53,54].…”

Section: Discussionmentioning

confidence: 99%

A time variant uncertainty propagation method for high-dimensional dynamic structural system via K–L expansion and Bayesian deep neural network

Liu,

Jiang,

Liu

et al. 2023

Phil. Trans. R. Soc. A.

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In this paper, a time variant uncertainty propagation (TUP) method for dynamic structural system with high-dimensional input variables is proposed. Firstly, an arbitrary stochastic process simulation (ASPS) method based on Karhunen–Loève (K–L) expansion and numerical integration is developed, expressing the stochastic process as the combination of its marginal distributions and eigen functions at several discrete time points. Secondly, the iterative sorting method is implemented to the statistic samples of marginal distributions for matching the constraints of covariance function. Since marginal distributions are directly used to express the stochastic process, the proposed ASPS is suitable for stationary or non-stationary stochastic processes with arbitrary marginal distributions. Thirdly, the high-dimensional TUP problem is converted into several high-dimensional static uncertainty propagation (UP) problems after implementing ASPS. Then, the Bayesian deep neural network based UP method is used to compute the marginal distributions as well as the eigen functions of dynamic system response, the high-dimensional TUP problem can thus be solved. Finally, several numerical examples are used to validate the effectiveness of the proposed method. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

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Section: Discussionmentioning

confidence: 99%

A time variant uncertainty propagation method for high-dimensional dynamic structural system via K–L expansion and Bayesian deep neural network

Liu,

Jiang,

Liu

et al. 2023

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…Differently, the propagation of non-probabilistic uncertainty follows another district philosophy, more relaying on, e.g., interval arithmetic [26], optimization methods [27,28], perturbation methods [29,30] and etc. Also advanced sampling approaches for interval analysis have been introduced [31,32]. One can refer to [5] for a good review on recent trends in propagation of non-probabilistic uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Bayesian probabilistic propagation of hybrid uncertainties: Estimation of response expectation function, its variable importance and bounds

Dang¹,

Wei²,

Faes³

et al. 2022

Computers & Structures

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Correlation propagation for dynamic analysis of a multibody system with multiple interval parameters

Jiang,

Bai

2024

Multibody Syst Dyn

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A sequential simulation strategy for response bounds analysis of structures with interval uncertainties

Cited by 13 publications

References 60 publications

A time variant uncertainty propagation method for high-dimensional dynamic structural system via K–L expansion and Bayesian deep neural network

A time variant uncertainty propagation method for high-dimensional dynamic structural system via K–L expansion and Bayesian deep neural network

Bayesian probabilistic propagation of hybrid uncertainties: Estimation of response expectation function, its variable importance and bounds

Correlation propagation for dynamic analysis of a multibody system with multiple interval parameters

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