Improving accuracy of failure probability estimates with separable Monte Carlo

Smarslok, Benjamin P.; Haftka, Raphael T.; Carraro, Laurent; Ginsbourger, David

doi:10.1504/ijrs.2010.035577

Cited by 24 publications

(18 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Separable Monte Carlo (SMC) method [5] is a variation of the Monte Carlo method, which was designed specifically to take advantage of a common situation where the response, R, and capacity, C, are stochastically independent random variables. Given this independence the limit state function can be sampled separately for response and capacity, which has the potential of requiring fewer expensive samples for estimating a probability of failure.…”

Section: Monte Carlo and Separable Monte Carlomentioning

confidence: 99%

See 1 more Smart Citation

How Adaptively Constructed Reduced Order Models Can Benefit Sampling-Based Methodsfor Reliability Analyses

Gogu

Chaudhuri

Bès

2016

Int. J. Rel. Qual. Saf. Eng.

View full text Add to dashboard Cite

Many sampling-based approaches are currently available for calculating the reliability of a design. The most efficient methods can achieve reductions in the computational cost by one to several orders of magnitude compared to the basic Monte Carlo method. This paper is specifically targeted at sampling-based approaches for reliability analysis, in which the samples represent calls to expensive finite element models. The aim of this paper is to illustrate how these methods can further benefit from reduced order modeling to achieve drastic additional computational cost reductions, in cases where the reliability analysis is carried out on finite element models. Standard Monte Carlo, importance sampling, separable Monte Carlo and a combined importance separable Monte Carlo approach are presented and coupled with reduced order modeling. An adaptive construction of the reduced basis models is proposed. The various approaches are compared on a thermal reliability design problem, where the coupling with the adaptively constructed reduced order models is shown to further increase the computational efficiency by up to a factor of six.

show abstract

Section: Monte Carlo and Separable Monte Carlomentioning

confidence: 99%

“…Several methods have been developed in the past allowing to decrease the number of samples required for a given accuracy on the probability of failure estimate. Such methods, that we refer to as advanced Monte Carlo approaches, include importance sampling [3] [4], separable Monte Carlo [5] [6], Markov chain Monte Carlo [7] [8].…”

Section: Introductionmentioning

confidence: 99%

How Adaptively Constructed Reduced Order Models Can Benefit Sampling-Based Methodsfor Reliability Analyses

Gogu

Chaudhuri

Bès

2016

Int. J. Rel. Qual. Saf. Eng.

View full text Add to dashboard Cite

show abstract

“…The standard error of the correlation coefficient assuming a large sample is Freund and Williams, [1996]: (1) In the above equation ρ is the correlation coefficient, n is the sample size and σ ρ the standard deviation of the correlation coefficient. A sample size of 10 8 is needed to estimate the correlation coefficient with a prescribed coefficient of variation of 0.1.…”

Section: Problem Formulationmentioning

confidence: 99%

“…MCS may not be capable of providing the desired accuracy when sampling is limited due to expensive structural analysis especially when the calculation of the limit state function involves Finite Element Analysis (FEA) of large-scale models. Smarslok et al [2006Smarslok et al [ , 2008Smarslok et al [ , 2010 and Ravishankar [2010] developed a sampling method named Separable Monte Carlo (SMC) simulation. When the performance function of the system can be written in terms of functions with no common variables, SMC can take advantage of this property to increase the sampling domain.…”

Section: Introductionmentioning

confidence: 99%

Bootstrapping and Separable Monte Carlo Simulation Methods Tailored for Efficient Assessment of Probability of Failure of Structural Systems

Jehan

2015

SAE Int. J. Mater. Manf.

View full text Add to dashboard Cite

There is randomness in both the applied loads and the strength of systems. Therefore, to account for the uncertainty, the safety of the system must be quantified using its reliability. Monte Carlo Simulation (MCS) is widely used for probabilistic analysis because of its robustness. However, the high computational cost limits the accuracy of MCS. Smarslok et al. [2010] developed an improved sampling technique for reliability assessment called Separable Monte Carlo (SMC) that can significantly increase the accuracy of estimation without increasing the cost of sampling. However, this method was applied to time-invariant problems involving two random variables. This paper extends SMC to problems with multiple random variables and develops a novel method for estimation of the standard deviation of the probability of failure of a structure. The method is demonstrated and validated on reliability assessment of an offshore wind turbine under turbulent wind loads. The results show the method can reduce the computational cost by two orders of magnitude compared to standard MCS for failure probabilities as low as 10 −4 .

show abstract

“…Since the two types of uncertainty (computational errors and variability in material properties and geometry) in the response are independent, separable Monte Carlo sampling [12] can be used when evaluating the probability of failure. The limit state equation can be reformulated so that the computational error is on the capacity side, and all random variables associated with material properties and geometry lie on the response side: Fig.…”

Section: Analyst-estimated Probability Of Failure Calculationmentioning

confidence: 99%

Including the Effect of a Future Test and Redesign in Reliability Calculations

2011

Self Cite

View full text Add to dashboard Cite

It is common to test components after they are designed and redesign if necessary. The reduction of the uncertainty in the probability of failure that can occur after a test is usually not incorporated in reliability calculations at the design stage. This reduction in uncertainty is accomplished by additional knowledge provided by the test and by redesign when the test reveals that the component is unsafe or overly conservative. In this paper, a methodology is developed to estimate the effect of a single future thermal test followed by redesign and to model the effect of the resulting reduction of the uncertainty in the probability of failure. Using assumed distributions of computation and experimental errors and given redesign rules, possible outcomes of the future test and redesign through Monte Carlo sampling are obtained to determine what changes in probability of failure, design, and weight will occur. In addition, Bayesian updating is used to gain accurate estimates of the probability of failure after a test. These methods are demonstrated through a future thermal test on an integrated thermal protection system. Performing redesign following a single future test can reduce the probability of failure by orders of magnitude, on average, when the objective of the redesign is to restore original safety margins. Redesign for a given reduced probability of failure allows additional weight reduction. = lower bound for probabilistic redesign criterion P U = upper bound for probabilistic redesign criterion p f;analyst = analyst-estimated probability of failure, % p f;target = probabilistic redesign probability of failure target, % p f;true = true probability of failure, % R = response r = random variable

show abstract

Improving accuracy of failure probability estimates with separable Monte Carlo

Cited by 24 publications

References 12 publications

How Adaptively Constructed Reduced Order Models Can Benefit Sampling-Based Methodsfor Reliability Analyses

How Adaptively Constructed Reduced Order Models Can Benefit Sampling-Based Methodsfor Reliability Analyses

Bootstrapping and Separable Monte Carlo Simulation Methods Tailored for Efficient Assessment of Probability of Failure of Structural Systems

Including the Effect of a Future Test and Redesign in Reliability Calculations

Contact Info

Product

Resources

About