Uncertainty Quantification of NEPTUN Analysis Using Wilks’ Formula With an Extended Number of Calculations

2006 ◽  
Author(s):  
Moonkyu Hwang ◽  
Young-Jin Lee ◽  
Bub-Dong Chung
Keyword(s):  
Monte Carlo ◽  
Uncertainty Quantification ◽  
System Analysis ◽  
Sensitivity Study ◽  
Mean Value ◽  
Model Parameters ◽  
Phase System ◽  
Two Phase ◽  
Mars Model ◽  
Calculation Results

The two-phase system analysis code MARS [1] has been used for the uncertainty quantification of NEPTUN reflood test [2] analysis. By performing 10,000 calculations based on a random variation of the MARS model parameters and measured data, a mean value, and the 95% upper bounds are traced along the number of calculations. The CPU-intensive calculations were performed using the 11 node PC-cluster under Linux platform. The Monte-Carlo calculation results suggest a total number of 2,000 calculations would be sufficient to determine the stable mean and 95% upper bound values. The peak temperatures predictions are also used to find the 95% bounding values by using the Wilks’ method. For the 1st order one-sided formula, every 59 peak temperatures are examined to locate the bounding temperature, with a 95% confidence. The 2nd and 3rd order values were found in a similar way. The uncertainty band by the Wilks’ formula, when compared with the true 95% bounding value, is observed to be quite broad, especially in the case of the 1st order. The 2nd or 3rd orders or a full Monte-Carlo method would be necessary to demonstrate that the safety of the plant is ensured with a sufficient margin. A supplementary sensitivity study, for the nine uncertain parameters selected for the NEPTUN analysis, is also performed to find the degree of influence of each parameter on the peak rod temperature.

scholarly journals Methods for the Calculation of Thermoacoustic Stability Margins and Monte Carlo-Free Uncertainty Quantification

2017 ◽  
Author(s):  
Georg A. Mensah ◽  
Luca Magri ◽  
Jonas P. Moeck
Keyword(s):  
Monte Carlo ◽  
Factor Analysis ◽  
Risk Factor ◽  
Uncertainty Quantification ◽  
Frequency Domain ◽  
Gas Turbines ◽  
Network Models ◽  
System Stability ◽  
Risk Factor Analysis ◽  
Model Parameters

Thermoacoustic instabilities are a major threat for modern gas turbines. Frequency-domain based stability methods, such as network models and Helmholtz solvers, are common design tools because they are fast compared to compressible CFD computations. Frequency-domain approaches result in an eigenvalue problem, which is nonlinear with respect to the eigenvalue. Nonlinear functions of the frequency are, for example, the n–τ model, impedance boundary conditions, etc. Thus, the influence of the relevant parameters on mode stability is only given implicitly. Small changes in some model parameters, which are obtained by experiments with some uncertainty, may have a great impact on stability. The assessment of how parameter uncertainties propagate to system stability is therefore crucial for safe gas turbine operation. This question is addressed by uncertainty quantification. A common strategy for uncertainty quantification in thermoacoustics is risk factor analysis. It quantifies the uncertainty of a set of parameters in terms of the probability of a mode to become unstable. One general challenge regarding uncertainty quantification is the sheer number of uncertain parameter combinations to be quantified. For instance, uncertain parameters in an annular combustor might be the equivalence ratio, convection times, geometrical parameters, boundary impedances, flame response model parameters etc. Assessing also the influence of all possible combinations of these parameters on the risk factor is a numerically very costly task. A new and fast way to obtain algebraic parameter models in order to tackle the implicit nature of the eigenfrequency problem is using adjoint perturbation theory. Though adjoint perturbation methods were recently applied to accelerate the risk factor analysis, its potential to improve the theory has not yet been fully exploited. This paper aims to further utilize adjoint methods for the quantification of uncertainties. This analytical method avoids the usual random Monte Carlo simulations, making it particularly attractive for industrial purposes. Using network models and the open-source Helmholtz solver PyHoltz it is also discussed how to apply the method with standard modeling techniques. The theory is exemplified based on a simple ducted flame and a combustor of EM2C laboratory for which experimental validation is available.

Parametric uncertainty quantification in the Rothermel model with randomised quasi-Monte Carlo methods

2015 ◽  
Vol 24 (3) ◽  
pp. 307 ◽  
Author(s):  
Yaning Liu ◽  
Edwin Jimenez ◽  
M. Yousuff Hussaini ◽  
Giray Ökten ◽  
Scott Goodrick
Keyword(s):  
Monte Carlo ◽  
Uncertainty Quantification ◽  
Monte Carlo Methods ◽  
Wildland Fire ◽  
Parametric Uncertainty ◽  
Monte Carlo Sampling ◽  
Model Parameters ◽  
Quasi Monte Carlo ◽  
Control Variate ◽  
Fuel Model

Rothermel's wildland surface fire model is a popular model used in wildland fire management. The original model has a large number of parameters, making uncertainty quantification challenging. In this paper, we use variance-based global sensitivity analysis to reduce the number of model parameters, and apply randomised quasi-Monte Carlo methods to quantify parametric uncertainties for the reduced model. The Monte Carlo estimator used in these calculations is based on a control variate approach applied to the sensitivity derivative enhanced sampling. The chaparral fuel model, selected from Rothermel's 11 original fuel models, is studied as an example. We obtain numerical results that improve the crude Monte Carlo sampling by factors as high as three orders of magnitude.

scholarly journals Methods for the Calculation of Thermoacoustic Stability Boundaries and Monte Carlo-Free Uncertainty Quantification

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Georg A. Mensah ◽  
Luca Magri ◽  
Jonas P. Moeck
Keyword(s):  
Monte Carlo ◽  
Uncertainty Quantification ◽  
Gas Turbines ◽  
Network Models ◽  
System Stability ◽  
Model Parameters ◽  
Geometrical Parameters ◽  
Parameter Uncertainties ◽  
Flame Response ◽  
Mode Stability

Thermoacoustic instabilities are a major threat for modern gas turbines. Frequency-domain-based stability methods, such as network models and Helmholtz solvers, are common design tools because they are fast compared to compressible flow computations. They result in an eigenvalue problem, which is nonlinear with respect to the eigenvalue. Thus, the influence of the relevant parameters on mode stability is only given implicitly. Small changes in some model parameters, may have a great impact on stability. The assessment of how parameter uncertainties propagate to system stability is therefore crucial for safe gas turbine operation. This question is addressed by uncertainty quantification. A common strategy for uncertainty quantification in thermoacoustics is risk factor analysis. One general challenge regarding uncertainty quantification is the sheer number of uncertain parameter combinations to be quantified. For instance, uncertain parameters in an annular combustor might be the equivalence ratio, convection times, geometrical parameters, boundary impedances, flame response model parameters, etc. A new and fast way to obtain algebraic parameter models in order to tackle the implicit nature of the problem is using adjoint perturbation theory. This paper aims to further utilize adjoint methods for the quantification of uncertainties. This analytical method avoids the usual random Monte Carlo (MC) simulations, making it particularly attractive for industrial purposes. Using network models and the open-source Helmholtz solver PyHoltz, it is also discussed how to apply the method with standard modeling techniques. The theory is exemplified based on a simple ducted flame and a combustor of EM2C laboratory for which experimental data are available.

scholarly journals Monte Carlo Algorithms for the Extracting of Electrical Capacitance

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2922
Author(s):  
Andrei Kuznetsov ◽  
Alexander Sipin
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Harmonic Functions ◽  
Statistical Error ◽  
Mean Value ◽  
Difference Problem ◽  
Monte Carlo Algorithms ◽  
Calculation Results ◽  
Biased Estimators ◽  
New Algorithms

We present new Monte Carlo algorithms for extracting mutual capacitances for a system of conductors embedded in inhomogeneous isotropic dielectrics. We represent capacitances as functionals of the solution of the external Dirichlet problem for the Laplace equation. Unbiased and low-biased estimators for the capacitances are constructed on the trajectories of the Random Walk on Spheres or the Random Walk on Hemispheres. The calculation results show that the accuracy of these new algorithms does not exceed the statistical error of estimators, which is easily determined in the course of calculations. The algorithms are based on mean value formulas for harmonic functions in different domains and do not involve a transition to a difference problem. Hence, they do not need a lot of storage space.

Using Monte Carlo Method and Adaptive Sampling to Estimate the Limit Surface

2021 ◽  
Author(s):  
Lixuan Zhang ◽  
Zhijian Zhang ◽  
He Wang ◽  
Yuhang Zhang ◽  
Dabin Sun
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Adaptive Sampling ◽  
Nuclear Power ◽  
Power Plants ◽  
Safety Margin ◽  
Model Parameters ◽  
Limit Surface ◽  
Calculation Results ◽  
Low Efficiency

Abstract In the research on the risk-informed safety margin characterization (RISMC) methodology, how to estimate the limit surface is important. Using the reduced Order Models (ROMs) to simulate calculations can obtain results more quickly and estimate the limit surface. For example, we use ROMs instead of Complex simulation model, Parameters that are critical to the safety of nuclear power plants, such as the peak temperature of the fuel cladding, can be calculated relatively quickly. Using Monte Carlo method to analyze nuclear accident is low efficiency and poor accuracy. To get relatively accurate results, a large amount of simulation experiments is needed. Based on adaptive sampling, the samples which will cause failure will be acquired more easily. Adaptive sampling uses the calculation results of the previous step to guide the next step of sampling, which can quickly obtain the samples points near the failure edge. This article will introduce the definition of the limit surface and use the Monte Carlo method and the adaptive sampling to estimate the limit surface through ROMs. And compare the calculation results of the two methods and the number of samples required. The two methods are verified by a case.

Impact of sewer condition on urban flooding: an uncertainty analysis based on field observations and Monte Carlo simulations on full hydrodynamic models

2012 ◽  
Vol 65 (12) ◽  
pp. 2219-2227 ◽  
Author(s):  
M. van Bijnen ◽  
H. Korving ◽  
F. Clemens
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Surface Damage ◽  
Model Parameters ◽  
Field Observations ◽  
Sewer System ◽  
Sewer Systems ◽  
Calculation Results ◽  
Urban Pluvial Flooding ◽  
The Impact

In-sewer defects are directly responsible for affecting the performance of sewer systems. Notwithstanding the impact of the condition of the assets on serviceability, sewer performance is usually assessed assuming the absence of in-sewer defects. This leads to an overestimation of serviceability. This paper presents the results of a study in two research catchments on the impact of in-sewer defects on urban pluvial flooding at network level. Impacts are assessed using Monte Carlo simulations with a full hydrodynamic model of the sewer system. The studied defects include root intrusion, surface damage, attached and settled deposits, and sedimentation. These defects are based on field observations and translated to two model parameters (roughness and sedimentation). The calculation results demonstrate that the return period of flooding, number of flooded locations and flooded volumes are substantially affected by in-sewer defects. Irrespective of the type of sewer system, the impact of sedimentation is much larger than the impact of roughness. Further research will focus on comparing calculated and measured behaviour in one of the research catchments.

Modeling biodegradation of toluene in rotating drum biofilter

2006 ◽  
Vol 54 (9) ◽  
pp. 137-144 ◽  
Author(s):  
C.P. Yang ◽  
H. Chen ◽  
G.M. Zeng ◽  
W. Qu ◽  
Y.Y. Zhong ◽  
...  
Keyword(s):  
Film Theory ◽  
Cost Effective ◽  
Phase System ◽  
Rotating Drum ◽  
Orthogonal Collocation ◽  
Two Phase ◽  
Biofilm Growth ◽  
Calculation Results ◽  
Model Equations ◽  
Fifth Order

Rotating drum biofilters (RDBs) are cost-effective for control of emissions of volatile organic compounds (VOCs) from waste gas streams. In this paper, a dynamic mathematical model is presented which simulates and predicts the variation in performance of a multi-layer RDB with time on the basis of the two-film theory. The model takes into account factors including biofilm growth and biomass loss, and a changing biofilm surface area and thickness assuming quasi-steady-state conditions in the two-phase system and uniform bacterial population. Toluene was assumed to be the only rate-limiting substrate. The model equations for the gas-phase mass balance and biofilm growth were solved using MATLAB based on the fourth-fifth-order Runge–Kutta technique, and the concentration profiles in the biofilms were obtained using the method of orthogonal collocation. Simulation results showed that the toluene removal efficiency decreased with increased toluene loading or increased duration of operation of the biofilter. Calculation results were compared to the experimental results, which demonstrated that the dynamic model provided a good simulation of the performance of the biofilter.

An Ultrathin Liquid Film Lubrication Theory—Calculation Method of Solvation Pressure and Its Application to the EHL Problem

1997 ◽  
Vol 119 (1) ◽  
pp. 217-226 ◽  
Author(s):  
Hiroshige Matsuoka ◽  
Takahisa Kato
Keyword(s):  
Film Thickness ◽  
Hard Spheres ◽  
Experimental Parameter ◽  
Elastohydrodynamic Lubrication ◽  
Solid Surfaces ◽  
New Method ◽  
Phase System ◽  
Two Phase ◽  
Calculation Results ◽  
Theory Calculation

This paper describes a new method for calculating the solvation pressure that acts between solid surfaces when the surfaces approach each other to within a very small distance in a liquid medium. Solvation pressure is calculated by solving the transformed Ornstein-Zernike equation for hard-spheres in a two-phase system with Perram’s method and using the Derjaguin approximation. Furthermore, the authors apply the new method to the elastohydrodynamic lubrication problem in which the film thickness is very small and solvation force and van der Waals force cannot be neglected. It will be shown that the calculation results agree well with experimental data. The results are then compared with two conventional solvation pressure models proposed so far, namely, Chan and Horn’s model, and, Jang and Tichy’s model. It is found that these two models neglect the elastic deformation of solid surface when obtaining the experimental parameter used in their models; thus they overestimate the solvation pressure resulting in the prediction of larger film thickness than the experiments.

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