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DOE OSTI2013

Summary Statistics for TA_MH02_130827: Micro-CT Data Acquired at LLNL, Specimen 2 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, tartaric acid (TA). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, TA_MH03_130827, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images. The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗
DOE OSTI2013

Summary Statistics for TA_MC03_130806: Micro-CT Data Acquired at LLNL, Specimen 3 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, tartaric acid (TA). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, TA_MC03_130806, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images. The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗
DOE OSTI2013

Summary Statistics for TA_MC02_130701: Micro-CT Data Acquired at LLNL, Specimen 2 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, tartaric acid (TA). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, TA_MC02_130701, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images. The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗
DOE OSTI2013

Summary Statistics for TA_ST01_130731: Micro-CT Data Acquired at LLNL, Specimen 1 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, tartaric acid (TA). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, TA_ST01_130731, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images. The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗
DOE OSTI2013

Summary Statistics for TA_SH02_130820: Micro-CT Data Acquired at LLNL, Specimen 2 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, tartaric acid (TA). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, TA_SH02_130820, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images. The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗
DOE OSTI2013

Summary Statistics for TA_MT03_130730: Micro-CT Data Acquired at LLNL, Specimen 3 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, tartaric acid (TA). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, TA_MT03_130730, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images. The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗
DOE OSTI2013

Summary Statistics for TA_SH01_130819: Micro-CT Data Acquired at LLNL, Specimen 1 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, tartaric acid (TA). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, TA_SH01_130819, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images. The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗
DOE OSTI2013

Summary Statistics for TA_MT01_130725: Micro-CT Data Acquired at LLNL, Specimen 1 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, tartaric acid (TA). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, TA_MT01_130725, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images. The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗
DOE OSTI2013

Summary Statistics for TA_MT02_130729: Micro-CT Data Acquired at LLNL, Specimen 2 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, tartaric acid (TA). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, TA_MT02_130729, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images. The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗
DOE OSTI2013

Summary Statistics for LC_HT02_130812: Micro-CT Data Acquired at LLNL, Specimen 2 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, lithium carbonate (LC). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, LC_HT02_130812, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images. The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗
DOE OSTI2013

Summary Statistics for LC_HT01_130808: Micro-CT Data Acquired at LLNL, Specimen 1 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, lithium carbonate (LC). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, LC_HT01_130808, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images. The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗
DOE OSTI2015

A Divergence Statistics Extension to VTK for Performance Analysis

This report follows the series of previous documents ([PT08, BPRT09b, PT09, BPT09, PT10, PB13], where we presented the parallel descriptive, correlative, multi-correlative, principal component analysis, contingency, k -means, order and auto-correlative statistics engines which we developed within the Visualization Tool Kit ( VTK ) as a scalable, parallel and versatile statistics package. We now report on a new engine which we developed for the calculation of divergence statistics, a concept which we hereafter explain and whose main goal is to quantify the discrepancy, in a stasticial manner akin to measuring a distance, between an observed empirical distribution and a theoretical, "ideal" one. The ease of use of the new diverence statistics engine is illustrated by the means of C++ code snippets. Although this new engine does not yet have a parallel implementation, it has already been applied to HPC performance analysis, of which we provide an example.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Metrology in Introductory Statistics Courses

The idea for this course in metrology (the science of measurement) grew out of a statistics course offered to engineering students at the junior level (Statistical Quality Assurance). The intention for teaching this course is to increase students' understanding of variability and their perception of the usefulness of statistics through immediate applicability of statistical concepts to everyday life and relevancy to coursework in introductory lab science courses such as biology, chemistry and physics. Slides from this webinar provide course material for two lectures with accompanying small group activities which require about 3 to 4-1/2 hours to teach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Statistical Approach to Safety Margin Evaluation of Irradiation Experiments in the ATR

The current safety basis of the INL Advanced Test Reactor requires that irradiation experiments meet minimum safety margins to critical heat flux and flow instability during anticipated reactor fault conditions. Compliance to these requirements may be demonstrated by calculating safety margins using safety factors that account for uncertainties, or using a statistical approach to quantify the uncertainty in the safety margins. Safety margins obtained from the first approach are conservative since the individual events leading to the cumulative safety factor are assumed to occur simultaneously at their maximum uncertainty. The statistical approach is less conservative in the case where the uncertainties are not too large, and may reduce the conservatism resulting from an overabundance of safety factors. This report describes the procedure for safety margin evaluation using a statistical approach and identifies the important thermal-hydraulic variables to consider in an uncertainty analysis. In particular, safety margins to critical heat flux and flow instability are evaluated for three recent high power fueled experiments (MP-1, FSP-1 and AFIP-6) using RELAP5 coupled to RAVEN to perform statistical analysis and uncertainty quantification. The results demonstrate adequate safety margins to critical heat flux and flow instability during an anticipated loss of commercial power to the reactor.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Essential Statistical Concepts

Statistical methods are an essential element to making quality measurements, allowing the organization and interrogation of data in a structured way. This introductory chapter describes key concepts of measurement statistics that are used in many nondestructive assay (NDA) methods and is intended as a primer to the reading list provided in the reference section. (Croft and Burr 2016; Smith 1991; Smith 2013; Taylor 1997; Triola 2017). The textbooks by Triola on elementary statistics (Figure 1), Taylor, and Smith (2013) introduce uncertainty analysis in the physical sciences. Smith (1991) provides a rigorous introduction with examples to correlated variables. These texts collectively offer an excellent foundation for understanding essential statistical concepts.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Validation of LOCA2 and STAR-ESDM Statistically Downscaled Products

The National Climate Assessment (NCA) is the preeminent national report examining current and future risks posed by climate change. Countless agencies, policymakers, stakeholders and other end-users rely upon guidance from the NCA to plan for an uncertain future. These groups all depend on modern curated data, provided alongside the NCA, to quantify the impact of climate change on metrics of relevance for their decision processes. In its fifth iteration (NCA5), two statistically downscaled ensemble products, each providing data at grid spacing of approximately 5km over the contiguous United States, were selected to accompany the report. These include LOCalized Analogs version 2 (LOCA2) and Seasonal Trends and Analysis of Residuals Empirical-Statistical Downscaling Model (STAR-ESDM). Both data products are produced through a process known as statistical downscaling, where relatively coarse Global Climate Model (GCM) data is refined to locally relevant scales through the application of scientifically-supported empirical and algorithmic relationships. In support of the NCA effort, this report provides an independent validation of these two products against historical observations, with a focus on precipitation and near-surface temperature variables. Based on the results of this validation, several recommendations are provided related to the use of these data products. The structure of this report is as follows: In section 2, we review three gridded observational products that are used as part of our intercomparison. In section 3, we describe the two statistical downscaling techniques and their corresponding datasets that are the focus of this study. In section 4, the methodology we employ for validation is described. Section 5 provides results of the validation, which in turn motivate our recommendations on the use of these data products. A brief summary is provided in section 6.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

(U) Correlated Sampling Using Batch Statistics to Reduce the Uncertainty of Combinations of KSEN Outputs with MCNP6

The relative sensitivity of k eff to the densities of nuclides in a material are combined to compute relative sensitivities to other inputs. When computed in a single Monte Carlo run, the nuclide density sensitivities are correlated, and the statistical uncertainties propagated to other inputs will be incorrect unless those correlations are accounted for. Equations are presented to apply correlated sampling using batch statistics for the sum of an arbitrary number of random tallies and the difference of two random tallies when each is multiplied by a different constant. When correlated sampling is used on a recent benchmark evaluation, the correct statistical uncertainties for certain combinations of sensitivities are dramatically smaller than the incorrect uncertainties. A user-controlled, regular output of MCNP6’s KSEN sensitivities that allows batch statistics to be applied to combinations would be extremely valuable.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

The Spiral Arm Segments of the Galaxy within 3 kpc from the Sun: A Statistical Approach

As can be reasonably expected, upcoming large-scale APOGEE, GAIA, GALAH, LAMOST, and WEAVE stellar spectroscopic surveys will yield rather noisy Galactic distributions of stars. In view of the possibility of employing these surveys, our aim is to present a statistical method to extract information about the spiral structure of the Galaxy from currently available data, and to demonstrate the effectiveness of this method. The model differs from previous works studying how objects are distributed in space in its calculation of the statistical significance of the hypothesis that some of the objects are actually concentrated in a spiral. A statistical analysis of the distribution of cold dust clumps within molecular clouds, H ii regions, Cepheid stars, and open clusters in the nearby Galactic disk within 3 kpc from the Sun is carried out. As an application of the method, we obtain distances between the Sun and the centers of the neighboring Sagittarius arm segment, the Orion arm segment in which the Sun is located, and the Perseus arm segment. Pitch angles of the logarithmic spiral segments and their widths are also estimated. The hypothesis that the collected objects accidentally form spirals is refuted with almost 100% statistical confidence. We show that these four independent distributions of young objects lead to essentially the same results. We also demonstrate that our newly deduced values of the mean distances and pitch angles for the segments are not too far from those found recently by Reid et al. using VLBI-based trigonometric parallaxes of massive star-forming regions.

79 ASTRONOMY AND ASTROPHYSICS↗