The role of the design point for calculating failure probabilities in view of dimensionality and structural nonlinearities

Valdebenito, Marcos A.; Pradlwarter, H. J.; Schuëller, Gerhart I.

doi:10.1016/j.strusafe.2009.08.004

Cited by 104 publications

(40 citation statements)

References 40 publications

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“…[25]; top, right: direction of the design point of the problem in the standard normal space [27], [36] …”

Section: Discussionmentioning

confidence: 99%

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An optimized Line Sampling method for the estimation of the failure probability of nuclear passive systems

Zio

Pedroni

2010

Reliability Engineering & System Safety

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“…[25]; top, right: direction of the design point of the problem in the standard normal space [27], [36] …”

Section: Discussionmentioning

confidence: 99%

“…A plausible selection of α could be the direction of the "design point" in the standard normal space [27], [36]. According to a geometrical interpretation, the "design point" is defined as the point * θ on the limit state surface…”

Section: Direction Of the Design Point In The Standard Normal Spacementioning

confidence: 99%

An optimized Line Sampling method for the estimation of the failure probability of nuclear passive systems

Zio

Pedroni

2010

Reliability Engineering & System Safety

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“…In addition we use the modified ML-var estimator introduced in §5.2. The sequence of KL modes per level is (4,8,16,64,256, 512, 1024, 1024, . .…”

Section: Exceedence Of Outflow Through Boundarymentioning

confidence: 99%

“…In high dimensions this approach can be expensive since it requires the solution of an optimisation problem. Moreover, the approximation error can be considerably large [55,64].…”

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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“…However, results presented by Valdebenito et al (2010) indicate that approximation methods may be inappropriate for treating high-dimensional, non-linear problems.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Analysis of a Rock Salt Cavern with Application to Energy Storage Systems

et al. 2016

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The role of the design point for calculating failure probabilities in view of dimensionality and structural nonlinearities

Cited by 104 publications

References 40 publications

An optimized Line Sampling method for the estimation of the failure probability of nuclear passive systems

An optimized Line Sampling method for the estimation of the failure probability of nuclear passive systems

Multilevel Estimation of Rare Events

Probabilistic Analysis of a Rock Salt Cavern with Application to Energy Storage Systems

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