Solutions of the First-Passage Problem by Importance Sampling

Bucher, Christian; Macke, Michael

doi:10.1007/978-94-010-0179-3_35

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…Other methods based on MCS which require a low number of samples, could be addressed to the asymptotic sampling method (Bucher, 2013) and sampling strategy by Podrouzek and Bucher (2013).…”

Section: Introductionmentioning

confidence: 99%

A fast and robust method for estimating the failure probability of structures

Arab¹,

Ghasemi²

2015

Proceedings of the Institution of Civil Engineers - Structures

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A new approach is presented to estimate quickly and accurately the probability of failure of structures. The approach works by employing first-order reliability methods to determine the closest point to the mean of random variables in a failure region. Then, by presenting sub-intervals in various layers and by grouping the generated samples in a Monte Carlo simulation (MCS), it was possible to reduce the number of structural calculations with controllable error where acceptable accuracy was introduced. Various numerical and engineering examples with complex limit state functions were solved by the proposed approach and the results were compared with those of common reliability methods. The outcome shows the high accuracy of the proposed approach. Furthermore, the number of required structural calculations was significantly reduced compared to normal MCS.

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“…Other methods based on MCS which require a low number of samples, could be addressed to the asymptotic sampling method (Bucher, 2013) and sampling strategy by Podrouzek and Bucher (2013).…”

Section: Introductionmentioning

confidence: 99%

A fast and robust method for estimating the failure probability of structures

Arab¹,

Ghasemi²

2015

Proceedings of the Institution of Civil Engineers - Structures

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“…A fairly recent overview of currently available Monte Carlo simulation methods for structural reliability assessment with an attempt to evaluate their suitability for high-dimensional problems involving several thousands of random variables has been presented in the Benchmark study [7]. Specifically, in the present paper the relatively recent Asymptotic Sampling Method [2,3,8] is discussed in detail. This method and other recent developments in structural reliability are focussing on Monte Carlo simulation methods designed to explore the geometric properties of the safe (or failure) domain by scaling the spatial coordinates [5,6].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic sampling – a tool for efficient reliability computation in high dimensions

Bucher

2015

Proc Appl Math and Mech

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Monte Carlo methods are most versatile regarding applications to the reliability analysis of high-dimensional nonlinear structural systems. In addition to its versatility, the computational efficacy of Monte Carlo method is not adversely affected by the dimensionality of the problem. Crude Monte Carlo techniques, however, are very inefficient for extremely small failure probabilities such as typically required for sensitive structural systems. Therefore methods to increase the efficacy for small failure probability while keeping the adverse influence of dimensionality small are desirable.On such method is the asymptotic sampling method. Within the framework of this method, well-known asymptotic properties of the reliability index regarding the scaling of the basic variables are exploited to construct a regression model which allows to determine the reliability index for extremely small failure probabilities with high precision using a moderate number of Monte Carlo samples.

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“…Specifically, in the present paper the relatively recent Asymptotic Sampling Method [2,11,4] is discussed in detail. This method and other recent developments in structural reliability are focussing on Monte Carlo simulation methods designed to explore the geometric properties of the safe (or failure) domain by scaling the spatial coordinates [7,8].…”

Section: Introductionmentioning

confidence: 99%

Application of Asymptotic Sampling to Structural Reliability Problems

Bucher¹

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. Monte Carlo methods are most versatile regarding applications to the reliability analysis of high-dimensional nonlinear structural systems. In addition to its versatility, the computational efficacy of Monte Carlo method is not adversely affected by the dimensionality of the problem. Crude Monte Carlo techniques, however, are very inefficient for extremely small failure probabilities such as typically required for sensitive structural systems. Therefore methods to increase the efficacy for small failure probability while keeping the adverse influence of dimensionality small are desirable.On such method is the asymptotic sampling method. Within the framework of this method, well-known asymptotic properties of the reliability index regarding the scaling of the basic variables are exploited to construct a regression model which allows to determine the reliability index for extremely small failure probabilities with high precision using a moderate number of Monte Carlo samples.The basic concepts underlying this method are explained in detail. Its applicability is demonstrated by solving the first passage problem involving several thousands of random variables. All results are cross-checked agains crude Monte Carlo results with an extremely large sample size. It is shown that the necessary number of samples can be reduced by several orders of magnitude as compared to crude Monte Carlo.

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Solutions of the First-Passage Problem by Importance Sampling

Cited by 3 publications

References 14 publications

A fast and robust method for estimating the failure probability of structures

A fast and robust method for estimating the failure probability of structures

Asymptotic sampling – a tool for efficient reliability computation in high dimensions

Application of Asymptotic Sampling to Structural Reliability Problems

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