Applications of asymptotic sampling on high dimensional structural dynamic problems

Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian

doi:10.1016/j.strusafe.2011.05.002

Cited by 25 publications

(10 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Asymptotic Sampling technique (Bucher, 2009;Sichani et al, 2011a;Sichani et al, 2011b;Sichani et al, 2014) was developed based on the asymptotic behavior of failure probabilities as the standard deviation of the random variables tends to zero. One advantage over Importance Sampling is that it does not require previous knowledge of the design point.…”

Section: Asymptotic Samplingmentioning

confidence: 99%

“…Several intelligent sampling techniques for Monte Carlo simulation have been proposed in recent years (Au and Beck, 2001;Au, 2005;Au et al, 2007;Bucher, 2009;Sichani et al, 2011a;Sichani et al, 2011b;Sichani et al, 2014;Naess et al, 2009;Naess et al, 2012). However, when such techniques are introduced, they are generally compared with one or two existing techniques, and their performance is evaluated over two or three problems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A benchmark study on intelligent sampling techniques in Monte Carlo simulation

Santos

Beck

2015

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

In recent years, new, intelligent and efficient sampling techniques for Monte Carlo simulation have been developed. However, when such new techniques are introduced, they are compared to one or two existing techniques, and their performance is evaluated over two or three problems. A literature survey shows that benchmark studies, comparing the performance of several techniques over several problems, are rarely found. This article presents a benchmark study, comparing Simple or Crude Monte Carlo with four modern sampling techniques: Importance Sampling Monte Carlo, Asymptotic Sampling, Enhanced Sampling and Subset Simulation; which are studied over six problems. Moreover, these techniques are combined with three schemes for generating the underlying samples: Simple Sampling, Latin Hypercube Sampling and Antithetic Variates Sampling. Hence, a total of fifteen sampling strategy combinations are explored herein. Due to space constrains, results are presented for only three of the six problems studied; conclusions, however, cover all problems studied. Results show that Importance Sampling using design points is extremely efficient for evaluating small failure probabilities; however, finding the design point can be an issue for some problems. Subset Simulation presented very good performance for all problems studied herein. Although similar, Enhanced Sampling performed better than Asymptotic Sampling for the problems considered: this is explained by the fact that in Enhanced Sampling the same set of samples is used for all support points; hence a larger number of support points can be employed without increasing the computational cost. Finally, the performance of all the above techniques was improved when combined with Latin Hypercube Sampling, in comparison to Simple or Antithetic Variates sampling.

show abstract

Section: Asymptotic Samplingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A benchmark study on intelligent sampling techniques in Monte Carlo simulation

Santos

Beck

2015

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

show abstract

“…Asymptotic sampling (AS) is a type of advanced Monte Carlo method which has been proposed for high-dimensional reliability analysis (Bucher 2009). Sichani et al (2011a) applied this method for high-dimensional dynamics problem such as wind turbines. In a similar study, asymptotic sampling has been proposed as an efficient method for estimating low, first passage probabilities of high-dimensional nonlinear systems (Sichani et al 2011b).…”

Section: Materials Properties and Geometrymentioning

confidence: 99%

“…Applying the AS method, several values of f ∈]0;1] are chosen as f i , i{1, ..., w}, where w is the number of f factors, cf. (Sichani et al 2011a). The estimation process is performed for each selected threshold level , where l{1, ..., w} and k is the number of considered threshold levels to estimate the cumulative distribution function (CDF) of samples (here the stiffness of the monopile).…”

Section: Concept Of Asymptotic Samplingmentioning

confidence: 99%

Probabilistic Finite Element Stiffness of a Laterally Loaded Monopile Based on an Improved Asymptotic Sampling Method

Vahdatirad

Bayat

Andersen

et al. 2015

Journal of Civil Engineering and Management

View full text Add to dashboard Cite

The mechanical responses of an offshore monopile foundation mounted in over-consolidated clay are calculated by employing a stochastic approach where a nonlinear p-y curve is incorporated with a finite element scheme. The random field theory is applied to represent a spatial variation for undrained shear strength of clay. Normal and Sobol sampling are employed to provide the asymptotic sampling method to generate the probability distribution of the foundation stiffnesses. Monte Carlo simulation is used as a benchmark. Asymptotic sampling accompanied with Sobol quasi random sampling demonstrates an efficient method for estimating the probability distribution of stiffnesses for the offshore monopile foundation. tcem interests include reliability analysis in geotechnical engineering, design of offshore foundations, computational methods, soil liquefaction, mechanized tunnelling, soil improvement.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Applications of asymptotic sampling on high dimensional structural dynamic problems

Cited by 25 publications

References 21 publications

A benchmark study on intelligent sampling techniques in Monte Carlo simulation

A benchmark study on intelligent sampling techniques in Monte Carlo simulation

Probabilistic Finite Element Stiffness of a Laterally Loaded Monopile Based on an Improved Asymptotic Sampling Method

Application of Asymptotic Sampling to Structural Reliability Problems

Contact Info

Product

Resources

About