A Monte Carlo method for uncertainty evaluation implemented on a distributed computing system

Esward, T J; Ginestous, A de; Harris, P M; Hill, I. D.; Salim, S. G. R.; Smith, I. M.; Wichmann, Brian; Winkler, R.; Woolliams, Emma

doi:10.1088/0026-1394/44/5/008

Cited by 22 publications

(25 citation statements)

References 14 publications

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“…Among all the $\left( {\matrix{ {I} \cr {n} \cr } } \right)$ possible combinations of standards sharing q replicates, the identity of the standards $i \in \left\{ {1,...,I} \right\}$ was chosen so as to minimize $E\left[ {Var\left( {\hat {y}|\{ n,i,q\} } \right)} \right]$ . As $E\left[ {Var\left( {\hat {y}|\{ n,i,q\} } \right)} \right]$ may be estimated for each $\left\{ {n,i,q} \right\}$ tuple separately, the Monte Carlo simulations may be implemented using a distributed computing system 15. The simulations were implemented in the R software (R Development Core Team 200816), and uses R's native pseudo random number generator (the ‘Mersenne‐Twister’ with period $2^{19937} - 1$ reported at double precision).…”

Section: Methodsmentioning

confidence: 99%

Error propagation in normalization of stable isotope data: a Monte Carlo analysis

Skrzypek

Sadler

Paul

2010

Rapid Comm Mass Spectrometry

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A higher analytical precision of a stable isotope ratio mass spectrometer does not automatically guarantee accurate determination of the true isotope composition (delta-value) of samples, since estimates of true delta-values are obtained from the normalization of raw isotope data. We performed both Monte Carlo simulations and laboratory experiments to investigate aspects of error propagation during the normalization of carbon stable isotope data. We found that increasing both the number of different reference standards and the number of repetitions of each of these standards reduces the normalization error. A 50% reduction in the normalization error can be achieved over the two-point normalization by either analyzing two standards four times each, or four standards two times each. If the true delta-value of a sample is approximately known a priori, the normalization error may then be reduced through a targeted choice of locally optimal standards. However, the difference in improvement is minimal and, therefore, a more practical strategy is to use two or more standards covering the whole stable isotope scale. The selection of different sets of standards by different laboratories or for different batches of samples in the same laboratory may lead to significant differences in the normalized delta-values of the same samples, leading to inconsistent results. Hence, the same set of standards should always be used for a particular element and a particular stable isotope analytical technique.

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Section: Methodsmentioning

confidence: 99%

Error propagation in normalization of stable isotope data: a Monte Carlo analysis

Skrzypek

Sadler

Paul

2010

Rapid Comm Mass Spectrometry

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“…To get around this, software was written to use the power of the NPLgrid-allowing calculations to be performed simultaneously on some 100 computers. A paper [7] and dissertation [8] describe the mathematics and software developments required to ensure that this approach is valid, for example, that the different computers did not generate the same random numbers.…”

Section: Monte Carlo Calculationmentioning

confidence: 99%

The Double-Wavelength Technique—An Alternative Technique to Determine Thermodynamic Temperature

et al. 2008

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Filter radiometry provides thermodynamic temperatures traceable to a cryogenic radiometer. An alternative technique is possible which provides absolute thermodynamic temperature through a different traceability chain, with the radiometric measurements purely relative. If this technique could be experimentally realized with similar uncertainties to those associated with filter radiometry, then this would provide a metrologically valuable 'second opinion' that would test for systematic effects common to all filter radiometry measurements. This paper describes the theoretical analysis prior to an experimental investigation of this technique. This theoretical analysis implies that with Re-C and Cu as the two blackbodies, the Re-C temperature can be determined with an uncertainty of approximately twice that expected with filter radiometry. For higher-temperature metal-carbide/carbon eutectics, the uncertainty difference would be smaller.

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“…In this paper, the reliability analysis is based on Monte Carlo simulation, which has long been considered to be the most accurate method to evaluate the probability of the characteristics, and does not need to know the distribution characteristics [31][32][33]. The reliability expression of the approximate model can be described as follows.…”

Section: Multi-objective Robust Optimization Based On Approximate Modelmentioning

confidence: 99%

Multi-objective robust optimization method for the modified epoxy resin sheet molding compounds of the impeller

Liu

Duan

et al. 2016

Journal of Computational Design and Engineering

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Multi-objective robust optimization method for the modified epoxy resin sheet molding compounds of the impeller Abstract A kind of modified epoxy resin sheet molding compounds of the impeller has been designed. Through the test, the non-metal impeller has a better environmental aging performance, but must do the waterproof processing design. In order to improve the stability of the impeller vibration design, the influence of uncertainty factors is considered, and a multi-objective robust optimization method is proposed to reduce the weight of the impeller. Firstly, based on the fluid-structure interaction，the analysis model of the impeller vibration is constructed. Secondly, the optimal approximate model of the impeller is constructed by using the Latin hypercube and radial basis function, and the fitting and optimization accuracy of the approximate model is improved by increasing the sample points. Finally, the micro multi-objective genetic algorithm is applied to the robust optimization of approximate model, and the Monte Carlo simulation and Sobol sampling techniques are used for reliability analysis. By comparing the results of the deterministic, different sigma levels and different materials, the multi-objective optimization of the SMC molding impeller can meet the requirements of engineering stability and lightweight. And the effectiveness of the proposed multi-objective robust optimization method is verified by the error analysis. After the SMC molding and the robust optimization of the impeller, the optimized rate reached 42.5%, which greatly improved the economic benefit, and greatly reduce the vibration of the ventilation system.

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A Monte Carlo method for uncertainty evaluation implemented on a distributed computing system

Cited by 22 publications

References 14 publications

Error propagation in normalization of stable isotope data: a Monte Carlo analysis

Error propagation in normalization of stable isotope data: a Monte Carlo analysis

The Double-Wavelength Technique—An Alternative Technique to Determine Thermodynamic Temperature

Multi-objective robust optimization method for the modified epoxy resin sheet molding compounds of the impeller

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