Uncertainty analysis of discharge coefficient of circular crested weirs

AbstractThe circular crested weir (CCW) has been introduced as weirs having a high discharge coefficient (Cd). The ratio of flow head to the radius of the crest (H/R) is the most important parameter affecting the Cd, that the $${\text{Cd}} \approx a\left( {H/R} \right)^{b}$$ Cd ≈ a H / R b can mathematical model their relation. In this study, the parameters of the Cd formula (i.e., a and b) were uncertainty analyzed using Monte Carlo (MC) and Bootstrap methods (BM). To perform these methods, some of the built-in functions of Excel software were utilized. The results declared that the average values of a and b were 1.187 and 0.140. The outcome of the MC method showed that the range of a and b at 95% confidence interval changed between 1.179 to 1.194 and 0.134 to 0.146, respectively, while at the same confidence interval the BM ranged from 1.187 to 1.200 and 0.133 to 0.147.

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The Establishment of Mathematical Model of LED Based on Monte Carlo Method

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.480-481.1571 ◽

2011 ◽

Vol 480-481 ◽

pp. 1571-1576

Author(s):

Zhi Qin Huang ◽

Xiao Hui Fan ◽

Gai Ling Zheng

Keyword(s):

Mathematical Model ◽

Computer Simulation ◽

Monte Carlo ◽

Monte Carlo Method ◽

Numerical Solutions ◽

Light Emitting Diode ◽

Effective Means ◽

Light Emitting ◽

Optical Structure ◽

Mc Method

Monte Carlo (MC method) of the computer simulation of the traditional forms of light-emitting diode (LED) is used for modeling and simulation. MC method than the method of geometrical optics of the LED is more suitable for complex optical structure on a Computer. MC method, the more accurate numerical solutions can improve the efficiency of LED design that is an effective means of LED design. MC method is with a very clear and unique advantage in the establishment of LED structure model.This paper first introduces the research background and purpose of the LED, then Monte Carlo methods Are outlined, and finally, some mathematical models of LED are given based on Monte Carlo method

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QMC integration errors and quasi-asymptotics

Monte Carlo Methods and Applications ◽

10.1515/mcma-2020-2067 ◽

2020 ◽

Vol 26 (3) ◽

pp. 171-176

Author(s):

Ilya M. Sobol ◽

Boris V. Shukhman

Keyword(s):

Monte Carlo ◽

Error Estimate ◽

Numerical Experiments ◽

Probable Error ◽

Quasi Monte Carlo ◽

Integration Error ◽

Asymptotic Error ◽

Dimensional Cube ◽

Integration Errors ◽

Mc Method

AbstractA crude Monte Carlo (MC) method allows to calculate integrals over a d-dimensional cube. As the number N of integration nodes becomes large, the rate of probable error of the MC method decreases as {O(1/\sqrt{N})}. The use of quasi-random points instead of random points in the MC algorithm converts it to the quasi-Monte Carlo (QMC) method. The asymptotic error estimate of QMC integration of d-dimensional functions contains a multiplier {1/N}. However, the multiplier {(\ln N)^{d}} is also a part of the error estimate, which makes it virtually useless. We have proved that, in the general case, the QMC error estimate is not limited to the factor {1/N}. However, our numerical experiments show that using quasi-random points of Sobol sequences with {N=2^{m}} with natural m makes the integration error approximately proportional to {1/N}. In our numerical experiments, {d\leq 15}, and we used {N\leq 2^{40}} points generated by the SOBOLSEQ16384 code published in 2011. In this code, {d\leq 2^{14}} and {N\leq 2^{63}}.

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Improvement of sensitivity and uncertainty analysis capabilities of generalized response in Monte Carlo code RMC

Annals of Nuclear Energy ◽

10.1016/j.anucene.2020.108099 ◽

2021 ◽

Vol 154 ◽

pp. 108099

Author(s):

Guanlin Shi ◽

Yuchuan Guo ◽

Conglong Jia ◽

Zhiyuan Feng ◽

Kan Wang ◽

...

Keyword(s):

Monte Carlo ◽

Uncertainty Analysis ◽

Monte Carlo Code ◽

Sensitivity And Uncertainty Analysis

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Estimation and uncertainty analysis of the CO2 storage volume in the Sleipner field via 4D reversible-jump Markov-chain Monte Carlo

Journal of Petroleum Science and Engineering ◽

10.1016/j.petrol.2020.108333 ◽

2021 ◽

pp. 108333

Author(s):

Yongchae Cho ◽

Hyunggu Jun

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Uncertainty Analysis ◽

Co2 Storage ◽

Reversible Jump ◽

Storage Volume

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Mathematical Formulation and Analytic Solutions for Uncertainty Analysis in Probabilistic Safety Assessment of Nuclear Power Plants

Energies ◽

10.3390/en14040929 ◽

2021 ◽

Vol 14 (4) ◽

pp. 929

Author(s):

Gyun Seob Song ◽

Man Cheol Kim

Keyword(s):

Monte Carlo ◽

Uncertainty Analysis ◽

Probability Density ◽

Nuclear Power ◽

Safety Assessment ◽

Power Plants ◽

Mathematical Formulation ◽

Analytic Solutions ◽

Probabilistic Safety Assessment ◽

Probabilistic Safety

Monte Carlo simulations are widely used for uncertainty analysis in the probabilistic safety assessment of nuclear power plants. Despite many advantages, such as its general applicability, a Monte Carlo simulation has inherent limitations as a simulation-based approach. This study provides a mathematical formulation and analytic solutions for the uncertainty analysis in a probabilistic safety assessment (PSA). Starting from the definitions of variables, mathematical equations are derived for synthesizing probability density functions for logical AND, logical OR, and logical OR with rare event approximation of two independent events. The equations can be applied consecutively when there exist more than two events. For fail-to-run failures, the probability density function for the unavailability has the same probability distribution as the probability density function (PDF) for the failure rate under specified conditions. The effectiveness of the analytic solutions is demonstrated by applying them to an example system. The resultant probability density functions are in good agreement with the Monte Carlo simulation results, which are in fact approximations for those from the analytic solutions, with errors less than 12.6%. Important theoretical aspects are examined with the analytic solutions such as the validity of the use of a right-unbounded distribution to describe the uncertainty in the unavailability/probability. The analytic solutions for uncertainty analysis can serve as a basis for all other methods, providing deeper insights into uncertainty analyses in probabilistic safety assessment.

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