Accelerated subset simulation with neural networks for reliability analysis

Papadopoulos, Vissarion; Giovanis, Dimitris G.; Lagaros, Nikos D.; Papadrakakis, Manolis

doi:10.1016/j.cma.2012.02.013

Cited by 170 publications

(61 citation statements)

References 16 publications

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“…Nie and Ellingwood [40] used Fekete deterministic point set for the direction identification, while Papadopoulos et al [14] implemented ANN into subset simulation method for reliability estimations.…”

Section: Ann-based Methods Of Failure Probability Computationmentioning

confidence: 99%

“…The simulation techniques have their origin in Monte Carlo simulation (MCS) method, which generates a large sample set of limit state evaluations and approximates the true value of the probability of failure by = , where is the number of samples lying in the failure region and S the total number of samples. In order to further improve the computational efficiency of MCS, many variance reduction techniques have been proposed [9], including importance sampling ( [10], [11]), directional simulation [12] or subset simulation ( [13], [14]). Despite these improvements, the MCS method is still timeconsuming and further development is crucial.…”

Section: Introductionmentioning

confidence: 99%

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Review and application of Artificial Neural Networks models in reliability analysis of steel structures

et al. 2015

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Section: Ann-based Methods Of Failure Probability Computationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Review and application of Artificial Neural Networks models in reliability analysis of steel structures

et al. 2015

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“…The first method solves the structural response or the probability feature quantity of performance function [29][30][31]; however, the computational accuracy in this method is heavily dependent on the form of performance functions. The second method was the Monte Carlo method, which directly applies sampling statistics [32][33][34]. The disadvantage of this method is the large computational complexity.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

The Method of Solving Structural Reliability with Multiparameter Correlation Problem

2017

Mathematical Problems in Engineering

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Correlation among variables must be considered to accurately reflect the level of structure reliability. This problem has referential value to engineering practice and has attracted attention from relevant scholars and industries. In this paper, Copula function was used to build the joint probability density function among all variables. The key is to describe the correlation among variables, solve the correlation parameter of Copula function, and select the type of correlation structure among variables. The correlation parameter of Copula function was solved using Pearson linear correlation coefficient and maximum likelihood estimation. Based on the Akaike information criteria (AIC) and Bayesian information criteria (BIC), the optimal Copula function was selected, and the correlation structure among variables was determined. Monte Carlo method, which is based on Nataf inverse transformation, was introduced and used to evaluate the reliability of the correlated variable. Finally, this paper proposed the reliability calculation method based on dual neural network and direct integration by establishing the dual neural network of original and integrand functions. Compared with the Monte Carlo method, the proposed method can be utilized to efficiently and precisely calculate the structure reliability of multiple correlated random variables.

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“…An enhanced version of the method was proposed in [67]. Moreover, subset simulation has been combined with surrogates based on machine learning theory in [11,50]. In the statistics and probability theory literature the idea of subset simulation is known under the names splitting and sequential Monte Carlo.…”

Section: Introductionmentioning

confidence: 99%

Multilevel Estimation of Rare Events

Ullmann¹,

Papaioannou²

2015

SIAM/ASA J. Uncertainty Quantification

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This work is motivated by the need to estimate the probability of rare events in engineering systems with random inputs. We introduce a multilevel estimator which is based on and generalises the idea of subset simulation. The novel estimator employs a hierarchy of approximations to the system response computed with different resolutions. This leads to reduced computational costs compared to subset simulation. We study the statistical properties and implementation details of the proposed estimator. Markov chain Monte Carlo runs are required within the estimator and we demonstrate that the nestedness of the associated multilevel failure domains enables a perfect MCMC simulation without burn-in. We show that nestedness follows from certain simple one-dimensional failure domains. In high dimensions we propose a modification of the multilevel estimator which uses level-dependent stochastic input dimensions. We report on numerical experiments in 1D and 2D physical space; in particular, we estimate rare events arising from a Darcy flow problem with random permeability.

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Accelerated subset simulation with neural networks for reliability analysis

Cited by 170 publications

References 16 publications

Review and application of Artificial Neural Networks models in reliability analysis of steel structures

Review and application of Artificial Neural Networks models in reliability analysis of steel structures

The Method of Solving Structural Reliability with Multiparameter Correlation Problem

Multilevel Estimation of Rare Events

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