Multilevel Monte Carlo for Reliability Theory

Aslett, Louis J. M.; Nagapetyan, Tigran; Vollmer, Sebastian J.

doi:10.1016/j.ress.2017.03.003

Cited by 46 publications

(36 citation statements)

References 25 publications

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“…All results were averaged over ten independent runs. We also give an approximate coefficient of variation, although we caution that this is not the same coefficient of variation defined in (2), since at the intermediate levels, subset simulation produces correlated samples. Thus, we used an approximated coefficient of variation as suggested in [45,Eq.…”

Section: Comparison To Subset Simulation Methodsmentioning

confidence: 99%

“…Nevertheless, this framework requires all knowledge about the small probability event to be available in the form of biasing densities, and is therefore only applicable to importance sampling estimators. Multilevel Monte Carlo [15,2] methods use a hierarchy of approximations to the high-fidelity model in the sampling scheme. However, those model hierarchies have to satisfy certain error decay criteria, an assumption we do not make here.…”

Section: Introductionmentioning

confidence: 99%

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Multifidelity probability estimation via fusion of estimators

Krämer

Marques

Peherstorfer

et al. 2019

Journal of Computational Physics

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This paper develops a multifidelity method that enables estimation of failure probabilities for expensive-to-evaluate models via information fusion and importance sampling. The presented general fusion method combines multiple probability estimators with the goal of variance reduction. We use low-fidelity models to derive biasing densities for importance sampling and then fuse the importance sampling estimators such that the fused multifidelity estimator is unbiased and has mean-squared error lower than or equal to that of any of the importance sampling estimators alone. By fusing all available estimators, the method circumvents the challenging problem of selecting the best biasing density and using only that density for sampling. A rigorous analysis shows that the fused estimator is optimal in the sense that it has minimal variance amongst all possible combinations of the estimators. The asymptotic behavior of the proposed method is demonstrated on a convection-diffusion-reaction partial differential equation model for which 10 5 samples can be afforded. To illustrate the proposed method at scale, we consider a model of a free plane jet and quantify how uncertainties at the flow inlet propagate to a quantity of interest related to turbulent mixing. Compared to an importance sampling estimator that uses the high-fidelity model alone, our multifidelity estimator reduces the required CPU time by 65% while achieving a similar coefficient of variation.

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Section: Comparison To Subset Simulation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multifidelity probability estimation via fusion of estimators

Krämer

Marques

Peherstorfer

et al. 2019

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…Subsequently, [20,21,22] presented the use of the survival signature in an inferential setting, with nonparametric predictive inference and Bayesian posterior predictive inference respectively, and [23] presented methods for analyzing imprecise system reliability using the survival signature. Patelli et al [24] developed a survival signature-based simulation method to calculate the reliability of large and complex systems and [25] presents a simulation method which can be used if the dependency structure is too complex for a survival signature approach. Walter et al [26] proposed a new conditionbased maintenance policy for complex systems using the survival signature.…”

Section: Phased Mission Systemsmentioning

confidence: 99%

Reliability analysis of general phased mission systems with a new survival signature

Huang

Aslett

Coolen

2019

Reliability Engineering & System Safety

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It is often difficult for a phased mission system (PMS) to be highly reliable, because this entails achieving high reliability in every phase of operation. Consequently, reliability analysis of such systems is of critical importance. However, efficient and interpretable analysis of PMSs enabling general component lifetime distributions, arbitrary structures, and the possibility that components skip phases has been an open problem.In this paper, we show that the survival signature can be used for reliability analysis of PMSs with similar types of component in each phase, providing an alternative to the existing limited approaches in the literature. We then develop new methodology addressing the full range of challenges above. The new method retains the attractive survival signature property of separating the system structure from the component lifetime distributions, simplifying computation, insight into, and inference for system reliability.

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“…To avoid the existing shortcoming, MC method is applied to perform the dynamic probabilistic analysis of multicomponent structure, resulting from high efficiency and accuracy in determining limit state function of complex structure. Besides, the convergence of this method dependents on the number of simulations, and is not affected by the dimension of parameters [25], [41].…”

Section: E Transient Probabilistic Approachmentioning

confidence: 99%

Decomposed-Coordinated Framework With Enhanced Extremum Kriging for Multicomponent Dynamic Probabilistic Failure Analyses

Feng

Fei

et al. 2019

IEEE Access

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For multicomponent structures enduring dynamic workloads coming from multi-physical fields, safety assessment is significant to guarantee the normal operation of entire structure system. In this paper, an enhanced extremum Kriging-based decomposed coordinated framework (E2K-DCF) is proposed to improve the dynamic probabilistic failure analyses of multicomponent structures. In this method, extremum Kriging model (EKM) is developed by introducing Kriging model into extremum response surface method (ERSM) to process the transient response problem and shorten computational burden in dynamic probabilistic failure analyses. Multiple population genetic algorithm (MPGA) is employed to solve maximum likelihood equation (MLE) and find the optimal hyperparameter θ in the EKM, which is promising to enhance approximate accuracy; decomposed-coordinated (DC) strategy is used to handle the coordinated relationship of multiple analytical objectives. To validate the proposed E2K-DCF, the probabilistic failure analysis of turbine blisk radial deformation is conducted by comparing with different methods within time domain [0 s, 215 s], considering fluid-thermal-structural interaction. It is revealed that the failure probability of blisk radial deformation is only 0.0022 when the allowable value is 2.5702 × 10 −3 m acquired from real world practice. Compared to the other approaches, this E2K-DCF has obvious advantages in fitting time and accuracy as well as simulation efficiency and accuracy. The results illustrate that the E2K-DCF is effective and applicable in dynamic probabilistic failure analysis. The efforts of this paper provide a novel viewpoint for the transient reliability evaluation of multicomponent structures, which is likely to enrich mechanical reliability theory. INDEX TERMS E2K-DCF, multicomponent structure, multiple population genetic algorithm, probabilistic failure, turbine blisk.

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Multilevel Monte Carlo for Reliability Theory

Cited by 46 publications

References 25 publications

Multifidelity probability estimation via fusion of estimators

Multifidelity probability estimation via fusion of estimators

Reliability analysis of general phased mission systems with a new survival signature

Decomposed-Coordinated Framework With Enhanced Extremum Kriging for Multicomponent Dynamic Probabilistic Failure Analyses

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