A single-loop Kriging surrogate model method by considering the first failure instant for time-dependent reliability analysis and safety lifetime analysis

Hu, Yingshi; Lü, Zhenzhou; Wei, Ning; Zhou, Changcong

doi:10.1016/j.ymssp.2020.106963

Cited by 33 publications

(14 citation statements)

References 38 publications

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“…Then, BDNN is employed to construct a high-dimensional surrogate model. As shown in figure 1, the parameters of BDNN are usually estimated by the Bayesian treatment [4,43], e.g. Markov chain Monte Carlo [44] or variational inference [45].…”

Section: High-dimensional Time Variant Uncertainty Propagation Methodsmentioning

confidence: 99%

“…Time variant uncertainties exist extensively in practical engineering [1,2], due to the existence of time variant uncertain factors such as material degeneration, random dynamic loads, etc. [3][4][5][6]. It is crucial to quantify the effects of these time variant uncertainties on system response for improving a system's life-cycle safety [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

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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: High-dimensional Time Variant Uncertainty Propagation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

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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“…Many TRA methods have been developed in recent years, including composite limit state methods, 7,8 Gamma process methods, 9 extremum-based methods, [10][11][12][13][14][15] and outcrossing rate methods. [16][17][18] In these methods, outcrossing rate methods [19][20][21][22] have been widely applied, where failure probability is estimated with the integral of outcrossing rates over time domain.…”

Section: Introductionmentioning

confidence: 99%

Moment‐based outcrossing rate method for time‐dependent reliability assessment including finite element analysis

Li,

Zhang,

Zhao

2023

Quality & Reliability Eng

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In practice, structural limit state function (LSF) is often combined with finite element (FE) models, and the corresponding time‐dependent reliability assessment (TRA) inevitably involves dealing with computational inefficiency. In this paper, a general moment‐based outcrossing rate (GMO) method is proposed to conduct TRA efficiently, with no limitation in the form of LSF. There are two innovations of GMO method: firstly, an explicit moment‐based outcrossing rate is developed; secondly, a separate algorithm is proposed that facilitates the separation of FE analysis from TRA cycle. The proposed method minimizes the computational cost associated with FE analysis and enables TRA cycle to be conducted more efficiently with the assistance of an explicit moment‐based outcrossing rate and explicit moment‐based outcrossing rate. Three numerical examples are investigated to examine the accuracy and efficiency of GMO method for TRA cycle. GMO method is found from the results that it can efficient and accurate to conduct TRA. Such improvements in computational efficiency are particularly valuable for complex structures where FE analysis is computationally expensive and time‐consuming.

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“…A common way to proceed is to consider the random variable G min = min [0,T ] g (X d , X p , X r , Y(t), t) and the probability (2) can then be obtained with a RA method (Hawchar (2017); Hu and Du (2015)). Others methods based on adaptive kriging have been proposed and rely on different metamodel strategies (Hu et al (2020a); Wang and Chen (2016); Jiang et al (2019); Hu et al (2020b)). For all of these methods, a sequential enrichment strategy is usually performed to improve the accuracy of the metamodel.…”

Section: Introductionmentioning

confidence: 99%

A two-step procedure for time-dependent reliability-based design optimization involving piece-wise stationary Gaussian processes

Cousin

Garnier

Guiton

et al. 2022

Struct Multidisc Optim

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We consider in this paper a time-dependent reliability-based design optimization (RBDO) problem with constraints involving the maximum and/or the integral of a random process over a time interval. We focus especially on problems where the process is a stationary or a piece-wise stationary Gaussian process. A two-step procedure is proposed to solve the problem. First, we use ergodic theory and extreme value theory to reformulate the original constraints into timeindependent ones. We obtain an equivalent RBDO problem for which classical algorithms perform poorly. The second step of the procedure is to solve the reformulated problem with a new method introduced in this paper and based on an adaptive kriging strategy well suited to the reformulated constraints called AK-ECO for Adaptive Kriging for Expectation Constraints Optimization. The procedure is applied to two toy examples involving a harmonic oscillator subjected to random forces. It is then applied to an optimal design problem for a floating offshore wind turbine.

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A single-loop Kriging surrogate model method by considering the first failure instant for time-dependent reliability analysis and safety lifetime analysis

Cited by 33 publications

References 38 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

Moment‐based outcrossing rate method for time‐dependent reliability assessment including finite element analysis

A two-step procedure for time-dependent reliability-based design optimization involving piece-wise stationary Gaussian processes

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