Efficient estimation of first passage probability of high-dimensional nonlinear systems

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

doi:10.1016/j.probengmech.2011.05.013

Cited by 20 publications

(11 citation statements)

References 25 publications

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“…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%

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A benchmark study on intelligent sampling techniques in Monte Carlo simulation

Santos

Beck

2015

Lat. Am. j. solids struct.

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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.

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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.

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“…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). Several researches have been conducted on stochastic analysis of laterally loaded piles.…”

Section: Materials Properties and Geometrymentioning

confidence: 99%

“…This curve can satisfy asymptotically linear behaviour as mentioned before. In a general case, Eqn (11) can be rewritten as (Sichani et al 2011b):…”

Section: Curve Fittingmentioning

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

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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.

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“…Under such background, more and more researchers and engineers are concerned with the reliability of wind turbines for both serviceability and safety (Duenas-Osorio & Basu, 2008;Sichani et al, 2011), including not only theoretical studies but also experimental investigations Chen & Georgakis, 2013). For instance, considering the flapwise bending failure on the blade roof, Ronold and Larsen (2000) investigate the reliability under operating conditions according to field measurement data by involving FORM.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Reliability of Offshore Wind Turbine Tower Systems

Chen¹,

Liu²,

Li³

2014

Vulnerability, Uncertainty, and Risk

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Due to the aerodynamic effects on rotating blades and wave action on the tower, the offshore wind turbine tower system is actually a high-dimensional time-variant nonlinear system. With the increase of their size, the safety and serviceability of offshore wind turbines becomes increasingly important. Generally, to evaluate the global reliability of such systems involves high-dimensional nonlinear stochastic dynamics which is still a great challenge. In the present paper, a simplified integrated multi-degree-of-freedom model which characterizes the rotation of blades and the aerodynamics of blades is adopted. The probability density evolution method (PDEM) is then employed to evaluate the global reliability when the randomness of wind is involved. The example shows that it is feasible to design a complex structure exhibiting nonlinearity subjected to concurrent external dynamic excitations based on the global reliability.

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Efficient estimation of first passage probability of high-dimensional nonlinear systems

Cited by 20 publications

References 25 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

Dynamic Reliability of Offshore Wind Turbine Tower Systems

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