Exploring A Two-Level, Control-Variate Monte Carlo Method for Uncertainty Quantification in Criticality Safety
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Elzohery, Rabab [ORNL] (ORCID:0000000160043633)↗
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Methods for Monte Carlo simulation of the exospheres of the moon and Mercury
A general form of the integral equation of exospheric transport on moon-like bodies is derived in a form that permits arbitrary specification of time varying physical processes affecting atom creation and annihilation, atom-regolith collisions, adsorption and desorption, and nonplanetocentric acceleration. Because these processes usually defy analytic representation, the Monte Carlo method of solution of the transport equation, the only viable alternative, is described in detail, with separate discussions of the methods of specification of physical processes as probabalistic functions. Proof of the validity of the Monte Carlo exosphere simulation method is provided in the form of a comparison of analytic and Monte Carlo solutions to three classical, and analytically tractable, exosphere problems. One of the key phenomena in moonlike exosphere simulations, the distribution of velocities of the atoms leaving a regolith, depends mainly on the nature of collisions of free atoms with rocks. It is shown that on the moon and Mercury, elastic collisions of helium atoms with a Maxwellian distribution of vibrating, bound atoms produce a nearly Maxwellian distribution of helium velocities, despite the absence of speeds in excess of escape in the impinging helium velocity distribution.
Hodges, R. R., Jr.↗
Fission Matrix Convergence Diagnostic of the Iterated Fission Probability Method
Monte Carlo methods have been applied to reactor problems in order to solve for adjoint-weighted quantities. The Iterated Fission Probability (IFP) method allows adjoint-weighted tallies to be recorded during a forward Monte-Carlo simulation. A key parameter in the IFP method is the number of generations that must pass before the progeny neutrons of a progenitor neutron are tallied. A convergence diagnostic for the IFP is developed using a deterministic code. In particular, a discrete ordinates code is used as a surrogate to demonstrate the theoretical properties of the proposed Monte Carlo convergence diagnostic. The diagnostic is applied to 1-D slab problems and quantifies the error associated with tallying the neutron progeny before an asymptotic distribution is achieved. The results show that the default value of 10 for the number of generations used in MCNP is acceptable for most classes of problems. (authors)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Advanced Computational Methods for Monte Carlo Calculations
This course is intended for graduate students who already have a basic understanding of Monte Carlo methods. It focuses on advanced topics that may be needed for thesis research, for developing new state-of-the-art methods, or for working with modern production Monte Carlo codes.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
SU-E-T-635: Quantitative Study On Beam Flatness Variation with Beam Energy Change
Purpose: Beam flatness check has been proposed for beam energy check for photon beams with flattering filters. In this work, beam flatness change with beam energy was investigated quantitatively using the Monte Carlo method and its significance was compared with depth dose curve change. Methods: Monte Carlo simulations for a linear accelerator with flattering filter were performed with different initial electron energies for photon beams of 6MV and 10MV. Dose calculations in a water phantom were then perform with the phase space files obtained from the simulations. The beam flatness was calculated based on the dose profile at 10 cm depth for all the beams with different initial electron energies. The percentage depth dose (PDD) curves were also analyzed. The dose at 10cm depth (D10) and the ratio of the dose at 10cm and 20cm depth (D10/D20) and their change with the beam energy were calculated and compared with the beam flatness variation. Results: It was found that the beam flatness variation with beam energy change was more significant than the change of D10 and the ratio between D10 and D20 for both 6MV and 10MV beams. Half MeV difference on the initial electron beam energy brought in at least 20% variation on the beam flatness but only half percent change on the ratio of D10 and D20. The change of D10 or D20 alone is even less significant. Conclusion: The beam energy impact on PDD is less significant than that on the beam flatness. If the PDD is used for checking the beam energy, uncertainties of the measurement could possibly disguise its change. Beam flatness changes more significantly with beam energy and therefore it can be used for monitoring the energy change for photon beams with flattering filters. However, other factors which may affect the beam flatness should be watched as well.
07 ISOTOPE AND RADIATION SOURCES↗
The Random Ray Method Versus Multigroup Monte Carlo: The Method of Characteristics in OpenMC and SCONE
The Random Ray Method (TRRM) is a recently developed approach to solving neutral particle transport problems based on the Method of Characteristics. While the method previously has been implemented only in closed-source or limited-functionality codes, this work describes its implementation in two open-source Monte Carlo codes: OpenMC and SCONE. The random ray implementations required small modifications to the existing Multigroup Monte Carlo (MGMC) solvers, offering a rare venue for redundant, fine-grained, "apples-to-apples" speed and accuracy comparisons between transport methods. To this end, TRRM and MGMC solvers are evaluated against each other using each code's native capabilities on reactor eigenvalue problems with different degrees of energy discretization. On the C5G7 benchmark (featuring only seven energy groups), TRRM achieves a maximum pin power error comparable to or lower than that of MGMC for a given run time. On a problem with 69 energy groups, MGMC is found to scale more efficiently, obtaining a lower pin power error for a given run time. However, the defining difference between the two transport methods is found to be their vastly different uncertainty distributions. Specifically, TRRM is found to maintain similar levels of accuracy and uncertainty throughout the simulation domain whereas MGMC can exhibit orders-of-magnitude greater errors in areas of the problem that feature low neutron flux. For instance, TRRM provided an up to 373 times speed advantage compared with MGMC for computing the flux in low-flux regions in the moderator surrounding the C5G7 core.
42 ENGINEERING↗
Generalized Sensitivity Calculation in the Monte Carlo Wielandt Method
Recently the Monte Carlo (MC) adjoint-weighted perturbation (AWP) methods with k-adjoint have been developed for the k sensitivity calculations. In order to extend the MC AWP methods to estimate sensitivities of a ratio of two reaction rates, Perfetti and Rearden devised a MC sensitivity calculation method with the generalized adjoint expressed by the intra-generational and intergenerational effects. Aufiero et al. suggested the collision history-based approach to calculate sensitivities of responses in the form of ratios of linear or bilinear functions by applying the correlated sampling for multi-generational collisions. However these methods may require a huge size of computer memory to save inter-generational contributions proportional to the number of the sensitivity tallies. In order to reduce memories required for the k-adjoint estimation, the present authors proposed the AWP algorithm in the MC Wielandt method where multiple generations from a fission source neutron are simulated in single history calculations. In this paper, we present perturbation formulations to estimate sensitivities for general tallies such as volume flux, reaction rates, etc. in the MC Wielandt calculations. The proposed method has been implemented into the Seoul National University MC code, McCARD and tested in two-group infinite homogeneous problems. (authors)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
SU-E-T-285: Dose Variation at Bone in Small-Animal Irradiation: A Monte Carlo Study Using Monoenergetic Photon Beams
Purpose: The aim of this study is to investigate the variation of bone dose on photon beam energy (keV – MeV) in small-animal irradiation. Dosimetry of homogeneous and inhomogeneous phantoms as per the same mouse computed tomography image set were calculated using the DOSCTP and DOSXYZnrc based on the EGSnrc Monte Carlo code. Methods: Monte Carlo simulations for the homogeneous and inhomogeneous mouse phantom irradiated by a 360 degree photon arc were carried out. Mean doses of the bone tissue in the irradiated volumes were calculated at various photon beam energies, ranging from 50 keV to 1.25 MeV. The effect of bone inhomogeneity was examined through the Inhomogeneous Correction Factor (ICF), a dose ratio of the inhomogeneous to the homogeneous medium. Results: From our Monte Carlo results, higher mean bone dose and ICF were found when using kilovoltage photon beams compared to megavoltage. In beam energies ranging from 50 keV to 200 keV, the bone dose was found maximum at 50 keV, and decreased significantly from 2.6 Gy to 0.55 Gy, when 2 Gy was delivered at the center of the phantom (isocenter). Similarly, the ICF were found decreasing from 4.5 to 1 when the photon beam energy was increased from 50 keV to 200 keV. Both mean bone dose and ICF remained at about 0.5 Gy and 1 from 200 keV to 1.25 MeV with insignificant variation, respectively. Conclusion: It is concluded that to avoid high bone dose in the small-animal irradiation, photon beam energy higher than 200 keV should be used with the ICF close to one, and bone dose comparable to the megavoltage beam where photoelectric effect is not dominant.
60 APPLIED LIFE SCIENCES↗
Modeling of the SPERT Transients Using SERPENT2 with Time Dependent Capabilities
Over the last decade, multiphysics coupled calculations have become one of the most important research topics in the area of development and enhancement of reactor analysis and simulation tools. One of the main applications of these coupled simulations is transient analysis, which may involve modeling of experiments, normal plant operation or accident scenarios. Traditionally, the reactor physics side of coupled simulations has been represented by deterministic or hybrid Monte Carlo - deterministic methods. Monte Carlo techniques are limited by their high computational cost. However increased computing power makes their application to multiphysics modeling of transients feasible. Active research is underway to develop algorithms for time dependent calculations, implement them in Monte Carlo codes, and evaluate their performance. In this paper time dependent simulations of the SPERT experiments using the Serpent2 code are presented.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
A compact neutron spectrometer system
A portable neutron spectrometer, nSpec, has been developed for passive interrogation of fast neutrons ( 1 MeV) from neutron sources. The design of the system includes four EJ-301 liquid scintillation cells, a custom stand, and tungsten caps for gamma-ray shielding. Data acquisition settings were optimized to provide a dynamic range of up to > 15 MeV neutron energy. Additionally, the detector response matrix was characterized using a time-of-flight method based on gamma-ray tagged neutron emission from 252 Cf. The spectrum unfolding was characterized using measured and simulated spectra of AmBe and 252 Cf with the GRAVEL and MLEM methods. Monte Carlo methods were used to examine the uncertainty propagation and determine sufficient counts for a measurement.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Monte Carlo Calculations of Polarized Microwave Radiation Emerging from Cloud Structures
The last decade has seen tremendous growth in cloud dynamical and microphysical models that are able to simulate storms and storm systems with very high spatial resolution, typically of the order of a few kilometers. The fairly realistic distributions of cloud and hydrometeor properties that these models generate has in turn led to a renewed interest in the three-dimensional microwave radiative transfer modeling needed to understand the effect of cloud and rainfall inhomogeneities upon microwave observations. Monte Carlo methods, and particularly backwards Monte Carlo methods have shown themselves to be very desirable due to the quick convergence of the solutions. Unfortunately, backwards Monte Carlo methods are not well suited to treat polarized radiation. This study reviews the existing Monte Carlo methods and presents a new polarized Monte Carlo radiative transfer code. The code is based on a forward scheme but uses aliasing techniques to keep the computational requirements equivalent to the backwards solution. Radiative transfer computations have been performed using a microphysical-dynamical cloud model and the results are presented together with the algorithm description.
Kummerow, Christian↗
Variance Estimation in Monte Carlo Eigenvalue Simulations Using Spectral Analysis Method
Monte Carlo (MC) simulation is widely used to solve the eigenvalue form of the Boltzmann transport equation that mathematically represents the neutron transport process through complex multiplying (fissionable) systems. Monte Carlo eigenvalue simulation starts with an assumed fission source distribution and uses the fission sites from the previous iteration (cycle) as the starting source in the current iteration. Important system parameters (MC tallies) such as fuel pin-power distribution are estimated over several cycles after the convergence of the fission source distribution to a stationary distribution. However, the MC fission source iteration algorithm that uses fission source sites from the previous cycle introduces a cycle-to-cycle correlation. Monte Carlo simulations that do not account for the cycle-to-cycle correlation systematically underestimate the variance of the estimated system parameters (sample mean). This paper presents the relationship between the spectral density in the frequency domain at frequency zero and the variance of the sample mean. This paper introduces a novel method in the frequency domain for the MC variance estimation. For the three test problems used in this paper, researchers have observed that the new method results in an improvement of more than one order of magnitude to the standard deviation of the sample mean. The new method also compares favorably with the previously introduced batch, bootstrap, and covariance-adjusted methods when applied to the three test problems investigated in this paper. This new method does not require modification of the MC eigenvalue algorithm (power iteration), is code agnostic, and is therefore easy to use when implementing in any existing MC code. In conclusion, the new estimate can be calculated without saving tally results of all active/stationary cycles.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Monte Carlo simulation methods in moment-based scale-bridging algorithms for thermal radiative-transfer problems
We present a moment-based acceleration algorithm applied to Monte Carlo simulation of thermal radiative-transfer problems. Our acceleration algorithm employs a continuum system of moments to accelerate convergence of stiff absorption–emission physics. The combination of energy-conserving tallies and the use of an asymptotic approximation in optically thick regions remedy the difficulties of local energy conservation and mitigation of statistical noise in such regions. We demonstrate the efficiency and accuracy of the developed method. We also compare directly to the standard linearization-based method of Fleck and Cummings [1]. A factor of 40 reduction in total computational time is achieved with the new algorithm for an equivalent (or more accurate) solution as compared with the Fleck–Cummings algorithm.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On-the-fly nuclear data processing methods for Monte Carlo simulations of fast spectrum systems
The presentation summarizes work performed over summer 2015 related to Monte Carlo simulations. A flexible probability table interpolation scheme has been implemented and tested with results comparing favorably to the continuous phase-space on-the-fly approach.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Analysis of Monte Carlo accelerated iterative methods for sparse linear systems: Analysis of Monte Carlo accelerated iterative methods for sparse linear systems
Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.
97 MATHEMATICS AND COMPUTING↗
Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals
Not provided.
Mathematics↗
Multi-Model and Multi-Scale Global Sensitivity Analysis for Identifying Controlling Processes of Complex Systems
An environmental model consists of multiple process level sub-models, and each sub-model represents a process that is key to the operation of the simulated system. Global sensitivity analysis methods have been widely used to identify important processes for system model development and improvement. The existing methods of global sensitivity analysis only consider parametric uncertainty, and are not capable of handling model uncertainty caused by multiple process models that arise from competing hypotheses about one or more processes. To address this problem, this project develops a new method to probe model output sensitivity to competing process models by integrating model averaging methods with variance-based global sensitivity analysis to address uncertainty in process models and parameters. The new method yields three process sensitivity indices. The first one is called first-order process sensitivity index, and it is derived as a single summary measure of relative process importance. Evaluating the index is computationally expensive, because it relies in a Monte Carlo scheme that requires thousands and even millions of model executions. To reduce computational cost, this project develops a computationally efficient, quasi Monte Carlo method, and this method is presented in Chapter 2 of this report with and a numerical example for demonstration. The numerical example shows that the results of the quasi Monte Carlo method are substantially close to those of the full Monte Carlo method, but the computational cost of the quasi Monte Carlo method is only 0.7% of that of the full Monte Carlo method. The second index is called total-effect process sensitivity index, and it measures interactions between different processes. Therefore, this sensitivity index includes the first-order process sensitivity index, and can be used to identify influential processes. On the other hand, the total-effect process sensitivity index can also be used to screen non-influential processes. This is demonstrated by two numerical examples using the Sobol-G* functions and groundwater flow models that consider recharge process, geological process, and snowmelt process. The numerical examples shows that the total-effect process sensitivity index is more informative than the first-order process sensitivity. The derivation of the process sensitivity index and the numerical examples are discussed in Chapter 3. Chapter 4 presents two computationally efficient methods for screening non-influential processes to exclude them from further investigation. The two methods are the multi-model difference-based sensitivity (MMDS) analysis method, which can be implemented using the Latin Hypercube Sampling. The second one is the implementation of MMDS method using a binning method. The numerical example for the Sobol-G* function indicates the two methods are capable of identifying non-influential models, and the numerical examples for the groundwater flow and reactive transport show that the two methods are effective for groundwater problems. However, it should be noted that the two methods are numerical approximations, and they can only be used for screening non-influential processes, not for ranking importance of system processes. All the sensitivity analysis methods are implemented by developing python codes, and the codes are in a software called SAMMPY: a python package for process sensitivity analysis under multiple models. The SAMMPY design and structure are discussed in Chapter 5, and the package is released to the public for free download.
54 ENVIRONMENTAL SCIENCES↗
Monte Carlo Estimates of Eigenvalue Sensitivity to System Dimensions using Kernel Density Estimators
In the last decade there has been an increasing interest in calculating sensitivity coefficients in order to quantify the impact of uncertainty in material properties and system parameters on quantities of interest. Extensive work has been done developing Monte Carlo methods to estimate eigenvalue sensitivity to material properties. While deterministic methods exist for determining the eigenvalue sensitivity to system dimensions, the use of Monte Carlo methods to efficiently calculate eigenvalue sensitivity coefficients to system dimensions is still an open topic. Current Monte Carlo methods for calculating eigenvalue sensitivity coefficients to system dimensions are inefficient. Direct Monte Carlo perturbations require two additional simulations of high statistical precision in order to determine the eigenvalue sensitivity to the location of a single boundary. If the sensitivity to the location of multiple surfaces are desired, two additional simulations must be run for each surface. Kiedrowski and Favorite extended continuous energy Monte Carlo methods for sensitivities of nuclear cross sections to calculate sensitivities to interface boundaries or system dimensions to create the only current alternative to direct Monte Carlo calculations. However this method relies on the simulation of additional random walks launched at each surface crossing event. The present method extends upon Kiedrowski's work and eliminates the inefficient portions of the calculation through the use of Kernel Density Estimators (KDEs). The new method efficiently estimates eigenvalue sensitivities to the uniform expansion or contraction of material interface boundaries or system dimensions, negligibly impacting the runtime performance of the Monte Carlo code. The new estimator is tested on bare and reflected critical configurations in spherical geometry and is compared to estimates obtained from direct Monte Carlo perturbations.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗