Download or read book MONTE CARLO BURNUP CALCULATION UNCERTAINTY QUANTIFICATION AND PROPAGATION DETERMINATION written by and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: MONTEBURNS is a Monte-Carlo depletion routine utilizing MCNP and ORIGEN 2.2. Uncertainties exist in the MCNP transport calculation, but this information is not passed to the depletion calculation in ORIGEN or saved. To quantify this transport uncertainty and determine how it propagates between burnup steps, a statistical analysis of a multiple repeated depletion runs is performed. The reactor model chosen is the Oak Ridge Research Reactor (ORR) in a single assembly, infinite lattice configuration. This model was burned for a 25.5 day cycle broken down into three steps. The output isotopics as well as effective multiplication factor (k-effective) were tabulated and histograms were created at each burnup step using the Scott Method to determine the bin width. It was expected that the gram quantities and k-effective histograms would produce normally distributed results since they were produced from a Monte-Carlo routine, but some of results do not. The standard deviation at each burnup step was consistent between fission product isotopes as expected, while the uranium isotopes created some unique results. The variation in the quantity of uranium was small enough that, from the reaction rate MCNP tally, round off error occurred producing a set of repeated results with slight variation. Statistical analyses were performed using the?2 test against a normal distribution for several isotopes and the k-effective results. While the isotopes failed to reject the null hypothesis of being normally distributed, the?2 statistic grew through the steps in the k-effective test. The null hypothesis was rejected in the later steps. These results suggest, for a high accuracy solution, MCNP cell material quantities less than 100 grams and greater kcode parameters are needed to minimize uncertainty propagation and minimize round off effects.
Download or read book Correlations in Monte Carlo Eigenvalue Simulations written by Jilang Miao and published by . This book was released on 2018 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods have mostly been used as a benchmark tool for other transport and diffusion methods in nuclear reactor analysis. One important feature of Monte Carlo calculations is the report of the variance of the estimators as a measure of uncertainty. In the current production codes, the assumption of independence of neutron generations in Monte Carlo eigenvalue simulations leads to the oversimplified estimate of the uncertainty of tallies. The correlation of tallies between neutron generations can make reported uncertainty underestimated by a factor of 8 in assembly size tallies in a typical LWR. This work analyzes the variance/uncertainty convergence rate in Monte Carlo eigenvalue simulations and develops different methods to properly report the variance. To correct the underestimated variance as a post-processing step, a simple correction factor can be calculated from the correlation coefficients estimated from a sufficient number of active generations and fitted to decreasing exponentials. If the variance convergence rate is needed before or during the simulation to optimize the run strategy (number of generations and neutrons per generation), a discrete model can be constructed from the inactive generations that can predict the correlation behavior of the original problem. Since it is not efficient to perform variance correction to all tallies on all problems, a simple correlation indicator is also developed to quickly determine the potential impact of correlations on a given tally in a given problem. This can help decide if more complicated correction analysis or the use of independent simulations should be used to calculate the true variance. Run strategy to reduce correlations is also investigated by introducing the notion of delayed neutrons. A predictive model for the new source update scheme was developed to help identify optimal delayed neutron parameters before implementing in OpenMC. Optimal run strategies in terms of delayed bank size, frequency of delayed bank sampling and true simulation costs are proposed.
Download or read book Monte Carlo Approaches for Uncertainty Quantification of Criticality for System Dimensions written by and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods of Steady state Reactor Physics in Nuclear Design written by Rudi J. J. Stamm'ler and published by . This book was released on 1983-01-01 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo Uncertainty Quantification of the Effective Delayed Neutron Fraction written by and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multilevel Monte Carlo Methods and Uncertainty Quantification written by Aretha Leonore Teckentrup and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such equations arise, for example, in stochastic groundwater ow modelling. Models for random coefficients frequently used in these applications, such as log-normal random fields with exponential covariance, lack uniform coercivity and boundedness with respect to the random parameter and have only limited spatial regularity. To give a rigorous bound on the cost of the multilevel Monte Carlo estimator to reach a desired accuracy, one needs to quantify the bias of the estimator. The bias, in this case, is the spatial discretisation error in the numerical solution of the partial differential equation. This thesis is concerned with establishing bounds on this discretisation error in the practically relevant and technically demanding case of coefficients which are not uniformly coercive or bounded with respect to the random parameter. Under mild assumptions on the regularity of the coefficient, we establish new results on the regularity of the solution for a variety of model problems. The most general case is that of a coefficient which is piecewise Hölder continuous with respect to a random partitioning of the domain. The established regularity of the solution is then combined with tools from classical discretisation error analysis to provide a full convergence analysis of the bias of the multilevel estimator for finite element and finite volume spatial discretisations. Our analysis covers as quantities of interest several spatial norms of the solution, as well as point evaluations of the solution and its gradient and any continuously Fréchet differentiable functional. Lastly, we extend the idea of multilevel Monte Carlo estimators to the framework of Markov chain Monte Carlo simulations. We develop a new multilevel version of a Metropolis Hastings algorithm, and provide a full convergence analysis.
Download or read book A Monte Carlo Framework for Nuclear Data Uncertainty Propagation Via the Windowed Multipole Formalism written by Abdulla Abdulaziz Alhajri and published by . This book was released on 2020 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new framework has been developed that calculates the uncertainty in calculated quantities, such as K[subscript eff], reactivity coefficients, multigroup cross sections, and reaction rate ratios, that arise due to uncertainties in the underlying nuclear data. This framework relies on first order uncertainty analysis using sensitivity methods. The major innovation in the proposed framework is the use of the windowed multipole formalism for calculating the sensitivities. The use of the windowed multipole formalism provides a natural, physics-inspired binning strategy for the sensitivity coefficients, while also aiding in the statistical convergence of the calculated sensitivity tallies. Additionally, our framework improves on existing methods by fully accounting for temperature effects. The proposed method allows for identifying exactly the resonances and parameters that are driving the uncertainty, and thus provides guidance to nuclear data evaluators and experimenters on how to reduce the uncertainty in the most efficient manner. Calculating the uncertainty requires two key pieces of information; the windowed multipole sensitivity coefficients, and the windowed multipole covariance matrix. A sensitivity coefficient calculation algorithm based on the CLUTCH-FM methodology was implemented in OpenMC. Several methods for obtaining the windowed multipole covariance matrix from the resonance parameter covariance matrix were explored, and ultimately an approach based on random-sampling was selected. Along the way, an analytical benchmark was developed for the purposes of validating the framework, as well as the implementation. This analytical benchmark consists of a solution to the forward and adjoint neutron transport equations. The windowed multipole covariance matrix was calculated for three isotopes; 238U , 157Gd , and 23Na . The uncertainty in K[subscript eff] due to the uncertainty in the 238U and 157Gd cross sections was calculated for two criticality safety benchmarks, and a beginning-of-life PWR model. The uncertainty of several reaction rate ratios due to the uncertainty in the 157Gd cross section was also calculated for the PWR model. The resonances of 238U and 157Gd that have the largest contribution to the uncertainty were identified for the criticality safety benchmarks.
Download or read book Monte Carlo Based Technique for Uncertainty Calculations written by Raul R. Cordero and published by Sudwestdeutscher Verlag Fur Hochschulschriften AG. This book was released on 2012-08 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo-based techniques allow comprehensively describing the uncertainty propagation through any measuring process or any retrieving scheme. In this work, they have been used to evaluate the uncertainty of both modeled and measured UV spectra. These applications have shown that Monte Carlo-based techniques have the potential to become useful tools for exploiting spectral UV measurements and for ensuring their quality. In a context of climate change, quality-ensured UV series are required for an improved understanding of the global UV climate.
Download or read book Propagation of Uncertainty from a Source Computed with Monte Carlo written by and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Uncertainty of Measurement written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multi Level Monte Carlo Finite Volume Methods for Uncertainty Quantification of Acoustic Wave Propagation in Random Heterogeneous Layered Medium written by Siddharta Sankar Mishra and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Uncertainty Quantification of Engineering Systems Using the Multilevel Monte Carlo Method written by Helena Juliette Thomasin Unwin and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multilevel Monte Carlo Methods for Uncertainty Quantification in Brain Simulations written by Matteo Croci and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Forecast Uncertainty Quantification Using Monte Carlo Polynomial Chaos Expansion and Unscented Transformation Methods written by Junjun Hu and published by . This book was released on 2015 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Neutron Physics written by Karl-Heinrich Beckurts and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based upon a series of lectures I have occasionally given at the University of Gottingen since 1951. They were meant to introduce the students of experimental physics to the work in a neutron physics laboratory dealing with the problem of measuring neutron flux, diffusion length, Fermi age, effective neutron temperature, absorption cross sections and similar problems. Moreover, these lectures were intended to prepare the students for a subsequent lecture covering the physics of nuclear reactors. The original character of this series of lectures has been retained in the book. It is intended for use by students as well as anyone desiring to work on neutron physics measurements. The first half mainly covers the theory of neutron fields, i. e. essentially diffusion and slowing down theory. The second half is largely concerned with measurements in neutron fields. The appendix contains information and data which, in our experience, are frequently required in a neutron laboratory. The field of nuclear physics proper is briefly touched upon in the first two chapters, but only to the extent necessary for the understanding of the following chapters. The multitude of applications of neutron radiation has not been covered. The conclusion of this manuscript coincided with the end of my long period of activity with the Max-Planck-Institut fur Physik at Gottingen. To Professor HEISENBERG lowe thanks for his advice and suggestions for many of the subjects treated here.
Download or read book Numerical Study of Error Propagation in Monte Carlo Depletion Simulations written by Timothy Joseph Wyant and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Improving computer technology and the desire to more accurately model the heterogeneity of the nuclear reactor environment have made the use of Monte Carlo depletion codes more attractive in recent years, and feasible (if not practical) even for 3-D depletion simulation. However, in this case statistical uncertainty is combined with error propagating through the calculation from previous steps. In an effort to understand this error propagation, four test problems were developed to test error propagation in the fuel assembly and core domains. Three test cases modeled and tracked individual fuel pins in four 17x17 PWR fuel assemblies. A fourth problem modeled a well-characterized 330MWe nuclear reactor core. By changing the code's initial random number seed, the data produced by a series of 19 replica runs of each test case was used to investigate the true and apparent variance in k-eff, pin powers, and number densities of several isotopes. While this study does not intend to develop a predictive model for error propagation, it is hoped that its results can help to identify some common regularities in the behavior of uncertainty in several key parameters.
Download or read book Monte Carlo Solution for Uncertainty Propagation in Particle Transport with a Stochastic Galerkin Method written by and published by . This book was released on 2013 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
