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At least 145 records · Page 8

Self-Supervised Anomaly Detection via Neural Autoregressive Flows with Active Learning

Many self-supervised methods have been proposed with the target of image anomaly detection. These methods often rely on the paradigm of data augmentation with predefined transformations such as flipping, cropping, and rotations. However, it is not straightforward to apply these techniques for non-image data, such as time series or tabular data, while the performance of the existing deep approaches has been under our expectation on tasks beyond images. In this work, we propose a novel active learning (AL) scheme that relied on neural autoregressive flows (NAF) for self-supervised anomaly detection, specifically on small-scale data. Unlike other generative models such as GANs or VAEs, flow-based models allow to explicitly learn the probability density and thus can assign accurate likelihoods to normal data which makes it usable to detect anomalies. The proposed NAF-AL method is achieved by efficiently generating random samples from latent space and transforming them into feature space along with likelihoods via invertible mapping. The samples with lower likelihoods are selected and further checked by outlier detection using Mahalanobis distance. The augmented samples incorporating with normal samples are used for training a better detector so as to approach decision boundaries. Compared with random transformations, NAF-AL can be interpreted as a likelihood-oriented data augmentation that is more efficient and robust. Extensive experiments show that our approach outperforms existing baselines on multiple time series and tabular datasets, and a real-world application in advanced manufacturing, with significant improvement on anomaly detection accuracy and robustness over the state-of-the-art.

Zhang, Jiaxin↗

Neutron and Gamma Correlations using CGM in MCNP 6.2.0

The general-purpose Monte Carlo radiation-transport code MCNP6{sup TM} came from the integration of MCNP5{sup TM} and MCNPX{sup TM}. The most recent release of MCNP, version 6.2.0, is scheduled for release in early 2017, which includes a variety of bug fixes and new features to the code. MCNP traditionally models nuclear reactions using Monte Carlo sampling techniques on measured and modeled cross-sectional data contained within ACE (A Compact Evaluated Nuclear Data File) libraries. In addition to reaction cross-sections, ACE libraries contain information relating to the production of secondary particles, such as secondary neutrons and photons. For example, an incident neutron on a nucleus can produce a nuclear reaction in the form (n, M{sub n}n'), where n is the incident neutron and M{sub n} is the number of secondary neutrons n' produced. Using this notation, different reactions can be described based on their neutron multiplicity, such as neutron capture (M{sub n} = 0), elastic and inelastic scattering (M{sub n} = 1), and reactions with multiple secondary neutrons (M{sub n} > 1). Accounting for secondary γ-rays emitted from the residual nuclei, this reaction can further be generalized as n, Mnn'M to describe a reaction producing M{sub n} neutrons and M -rays. These values M{sub n} and M are referred to as the neutron and multiplicities, respectively. ACE libraries contain the cross-sectional data for each reaction, and their corresponding statistically averaged multiplicities for neutrons and photons, M-bar{sub n} and M-bar{sub γ}. However, there are several limitations to reaction sampling using ACE libraries. First, the data contained within ACE libraries is limited by the accuracy of the model and/or experiment, which out of necessity can greatly simplify the true physics behind a reaction. For example, the value M{sub γ} in a (n, M{sub n}n'M{sub γ}γ) reaction is determined by the statistically averaged multiplicity M-bar{sub γ} instead of a distribution. Consequently, MCNP, unable to produce a continuous distribution, will utilizes a binary sampling around M-bar{sub γ}. While this sampling method provides a statistically average M{sub γ} over a large simulation, it is an inaccurate representation of an individual reaction and its corresponding secondary particles. Secondary neutrons are affected in a similar manner, such that different kinds of secondary neutrons can be sampled from the same interaction (eg., an inelastic neutron with an [n, 2n] neutron). Lastly, the random sampling technique for secondary particles remains completely independent of the sampled reaction, eliminating the ability to correlate secondary particles for a given reaction. To supplement these data libraries, additional codes and models describing certain nuclear reactions are employed. These codes can fill in the information missing from ACE, provide a better model to the true physics distribution, and can provide true correlated secondary particles, which has many useful applications in research and industry.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Rapid estimation of photosynthetic leaf traits of tropical plants in diverse environmental conditions using reflectance spectroscopy

Tropical forests are one of the main carbon sinks on Earth, but the magnitude of CO 2 absorbed by tropical vegetation remains uncertain. Terrestrial biosphere models (TBMs) are commonly used to estimate the CO 2 absorbed by forests, but their performance is highly sensitive to the parameterization of processes that control leaf-level CO 2 exchange. Direct measurements of leaf respiratory and photosynthetic traits that determine vegetation CO 2 fluxes are critical, but traditional approaches are time-consuming. Reflectance spectroscopy can be a viable alternative for the estimation of these traits and, because data collection is markedly quicker than traditional gas exchange, the approach can enable the rapid assembly of large datasets. However, the application of spectroscopy to estimate photosynthetic traits across a wide range of tropical species, leaf ages and light environments has not been extensively studied. Here, we used leaf reflectance spectroscopy together with partial least-squares regression (PLSR) modeling to estimate leaf respiration ( R dark25 ), the maximum rate of carboxylation by the enzyme Rubisco ( V cmax25 ), the maximum rate of electron transport ( J max25 ), and the triose phosphate utilization rate ( T p25 ), all normalized to 25°C. We collected data from three tropical forest sites and included leaves from fifty-three species sampled at different leaf phenological stages and different leaf light environments. Our resulting spectra-trait models validated on randomly sampled data showed good predictive performance for V cmax25 , J max25 , T p25 and R dark25 (RMSE of 13, 20, 1.5 and 0.3 μmol m -2 s -1 , and R 2 of 0.74, 0.73, 0.64 and 0.58, respectively). The models showed similar performance when applied to leaves of species not included in the training dataset, illustrating that the approach is robust for capturing the main axes of trait variation in tropical species. We discuss the utility of the spectra-trait and traditional gas exchange approaches for enhancing tropical plant trait studies and improving the parameterization of TBMs.

54 ENVIRONMENTAL SCIENCES↗

Analysis and Monte Carlo simulation of near-terminal aircraft flight paths

The flight paths of arriving and departing aircraft at an airport are stochastically represented. Radar data of the aircraft movements are used to decompose the flight paths into linear and curvilinear segments. Variables which describe the segments are derived, and the best fitting probability distributions of the variables, based on a sample of flight paths, are found. Conversely, given information on the probability distribution of the variables, generation of a random sample of flight paths in a Monte Carlo simulation is discussed. Actual flight paths at Dulles International Airport are analyzed and simulated.

Schiess, J. R.↗

Absolute proper motions to B approximately 22.5: Evidence for kimematical substructure in halo field stars

Radial velocities have been obtained for six of nine stars identified on the basis of similar distances and common, extreme transverse velocities in the proper motion survey of Majewski (1992) as a candidate halo moving group at the north Galactic pole. These radial velocities correspond to velocities perpendicular to the Galactic plane which span the range -48 +/- 21 to -128 +/- 9 km/sec (but a smaller range, -48 +/- 21 to -86 +/- 19 km/sec, when only our own measurements are considered), significantly different than the expected distribution, with mean 0 km/sec, for a random sample of either halo or thick disk stars. The probability of picking such a set of radial velocities at random is less than 1%. Thus the radial velocity data support the hypothesis that these stars constitute part of a halo moving group or star stream at a distance of approximately 4-5 kpc above the Galactic plane. If real, this moving group is evidence for halo phase space substructure which may be the fossil remains of a destroyed globular cluster, Galactic satellite, or Searle & Zinn (1978) 'fragment.'

Majewski, Steven R.↗

i- flow: High-dimensional integration and sampling with normalizing flows

In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows. Normalizing flows are machine-learned, bijective mappings between two distributions. i-flow can also be used to sample random points according to complicated distributions in high dimensions. We compare i-flow to other algorithms for high-dimensional numerical integration and show that i-flow outperforms them for high dimensional correlated integrals. The i-flow code is publicly available on gitlab at https://gitlab.com/i-flow/i-flow.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

(U) A General-Purpose Code for Correlated Sampling Using Batch Statistics with MCNP6 for Fixed-Source Problems

Correlated sampling can be used to reduce the uncertainty of a difference of tallies by taking advantage of the negative covariance term in the sandwich formula. Booth first showed how correlated sampling can be applied with batch statistics using MCNP’s tally fluctuation chart (TFC) to reduce the uncertainty of a difference of tallies in fixed-source problems. Booth presented a problem in which a 1273% uncertainty in a difference was reduced to 8% by accounting for correlations. Researchers He and Su recently studied correlated sampling using the TFC in MCNP version 5. They determined that the code did not print enough digits in the TFC tally means for accurate batch statistics in some cases. After modifying the source code, they concluded that “correlated sampling can yield a standard deviation of about one magnitude smaller than that predicted by the direct, un-correlated simulation when the changes in system response are small (say about 1%), which is equivalent to saving in CPU time by a factor of 100. Such saving [sic] becomes less significant as the change in system response becomes larger.” He and Su provided the formulas needed to apply batch statistics to compute the correlated uncertainty of a difference of tallies. In this report, we follow up on their work by providing the formulas needed to apply batch statistics to compute the correlated uncertainty of a ratio of tallies and of a difference of two tallies divided by a third tally. We extend these formulas to differences and ratios of ratios. These formulas are applied to reduce the uncertainty associated with calculating a relative sensitivity. He and Su did not investigate the accuracy of their correlated sampling uncertainty estimates. We use their test problems and evaluate the accuracy of the uncertainty estimates by comparing with results obtained from random sampling, and, in simple cases, with theoretical values of the “exact” uncertainties. We find that the uncertainties obtained from batch statistics are accurate as long as at least 100 batches are used. We present a new computer code, COSUBS (COrrelated Sampling Using Batch Statistics), that reads MCNP6 TFCs and applies correlated sampling using batch statistics for the tally combinations that the user specifies. COSUBS is a very general tool that compares all TFCs for a base case and one or two perturbed cases. It computes uncertainties for ratios if given only a base case. This report is organized as follows. The equations to apply batch statistics to the difference of random tallies are reviewed in Sec. II. Section III presents the equations for applying batch statistics to a ratio of random tallies; this is useful for computing relative sensitivities using a one-sided finite difference and the relative sensitivity using the differential operator method. Section IV presents the equations for applying batch statistics to a difference of two random tallies divided by a third; this is useful for computing a relative sensitivities using a central difference. Section V presents the equations for applying batch statistics to a difference of two ratios with four random tallies. Section VI presents the equations for applying batch statistics to a one-sided finite difference estimate of the relative sensitivity of a ratio (this uses four random tallies). Section VII presents the equations for applying batch statistics to a central difference estimate of the relative sensitivity of a ratio (this uses six random tallies). Section VIII presents the equations for applying batch statistics to a sum of random tallies. Section IX discusses how to apply batch statistics using MCNP6. Section X presents COSUBS, describing its command-line options and logic. Sections XI through XVI present numerical results for various test problems. Section XVII is a summary and conclusions. Appendix A derives the theoretical Monte Carlo tally variance given certain assumptions; these variances are used to verify the batch statistics for some of the problems. Appendix B lists the MCNP6 input for the unperturbed example problem. Appendix C presents modifications made to MCNP6.3 to support this work.

97 MATHEMATICS AND COMPUTING↗

Compositional and Geochronological Constraints on the Lunar Cataclysm from Planetary Samples

Radiometric dating and compositional clustering of lunar impact-melt rocks form the backbone of the lunar cataclysm hypothesis. Precise age determinations of Apollo and Luna impact-melt rocks define the classic formulation of the cataclysm: a large number of samples 3.9 Ga old, a steep decline after 3.9 Ga, and few impact rocks older than ~4.0 Ga. Lunar meteorites more randomly sample the lunar surface, but impact-melt clasts in these rocks show the same apparent age cutoff at 4.0 Ga (though their ages extend approx.500 Myr later). Neither do impact-formed glass spherules and fragments, formed by impacts of all sizes throughout lunar history, predate 4.0 Ga. Geological associations between compositional groups of impact-melt rocks and specific impact basins imply that five large basins formed on the Moon within 200 Myr but a counter-argument postulates they are all products of the Imbrium basin-forming impact; it is not yet proven whether groups of impact melt that are resolvable from each other in age and in trace-element composition represent multiple impacts. The 3.9 Ga age peak and subsequent steep decline are not well mirrored in meteorite data. Radiometric ages in ordinary chondrites and HED meteorites peak around 3.9 Ga but ages older and younger than 3.9 Ga are common. Among Martian meteorites, there is a single impact-related age: ALH 84001 was shocked at 3.92 Ga. Differences in relative impact velocity, impact-melt production, and sampling rate could explain differences between the meteorite and lunar records. One way to anchor the early end of the lunar flux is to directly sample the impact-melt sheet of a large lunar basin distant from Imbrium, such as the South Pole-Aitken basin, where melt rocks probably still resides on the basin floor and could be directly sampled by a human or robotic mission.

Cohen, Barbara A.↗

Adaptive Data-Driven Deep-Learning Surrogate Model for Frontal Polymerization in Dicyclopentadiene

Frontal polymerization (FP) is a self-sustaining curing process that enables rapid and energy-efficient manufacturing of thermoset polymers and composites. Computational methods conventionally used to simulate the FP process are time-consuming, and repeating simulations are required for sensitivity analysis, uncertainty quantification, or optimization of the manufacturing process. Here, in this work, we develop an adaptive surrogate deep-learning model for FP of dicyclopentadiene (DCPD), which predicts the evolution of temperature and degree of cure orders of magnitude faster than the finite-element method (FEM). The adaptive algorithm provides a strategy to select training samples efficiently and save computational costs by reducing the redundancy of FEM-based training samples. The adaptive algorithm calculates the residual error of the FP governing equations using automatic differentiation of the deep neural network. A probability density function expressed in terms of the residual error is used to select training samples from the Sobol sequence space. The temperature and degree of cure evolution of each training sample are obtained by a 2D FEM simulation. The adaptive method is more efficient and has a better prediction accuracy than the random sampling method. With the well-trained surrogate neural network, the FP characteristics (front speed, shape, and temperature) can be extracted quickly from the predicted temperature and degree-of-cure fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Milky Way mass with K giants and BHB stars using LAMOST, SDSS/SEGUE, and Gaia : 3D spherical Jeans equation and tracer mass estimator

ABSTRACT We measure the enclosed Milky Way mass profile to Galactocentric distances of ∼70 and ∼50 kpc using the smooth, diffuse stellar halo samples of Bird et al. The samples are Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) and Sloan Digital Sky Survey/Sloan Extension for Galactic Understanding and Exploration (SDSS/SEGUE) K giants (KG) and SDSS/SEGUE blue horizontal branch (BHB) stars with accurate metallicities. The 3D kinematics are available through LAMOST and SDSS/SEGUE distances and radial velocities and Gaia DR2 proper motions. Two methods are used to estimate the enclosed mass: 3D spherical Jeans equation and Evans et al. tracer mass estimator (TME). We remove substructure via the Xue et al. method based on integrals of motion. We evaluate the uncertainties on our estimates due to random sampling noise, systematic distance errors, the adopted density profile, and non-virialization and non-spherical effects of the halo. The tracer density profile remains a limiting systematic in our mass estimates, although within these limits we find reasonable agreement across the different samples and the methods applied. Out to ∼70 and ∼50 kpc, the Jeans method yields total enclosed masses of 4.3 ± 0.95 (random) ±0.6 (systematic) × 1011 M⊙ and 4.1 ± 1.2 (random) ±0.6 (systematic) × 1011 M⊙ for the KG and BHB stars, respectively. For the KG and BHB samples, we find a dark matter virial mass of $M_{200}=0.55^{+0.15}_{-0.11}$ (random) ±0.083 (systematic) × 1012 M⊙ and $M_{200}=1.00^{+0.67}_{-0.33}$ (random) ±0.15 (systematic) × 1012 M⊙, respectively.

79 ASTRONOMY AND ASTROPHYSICS↗

Grover-QAOA for 3-SAT: quadratic speedup, fair-sampling, and parameter clustering

Abstract The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and quantum algorithms. This study shows numerical evidence for a quadratic speedup of the Grover Quantum Approximate Optimization Algorithm (G-QAOA) over random sampling for finding all solutions to 3-SAT (All-SAT) and Max-SAT problems. G-QAOA is less resource-intensive and more adaptable for these problems than Grover’s algorithm, and it surpasses conventional QAOA in its ability to sample all solutions. We show these benefits by classical simulations of many-round G-QAOA on thousands of random 3-SAT instances. We also observe G-QAOA advantages on the IonQ Aria quantum computer for small instances, finding that current hardware suffices to determine and sample all solutions. Interestingly, a single-angle-pair constraint that uses the same pair of angles at each G-QAOA round greatly reduces the classical computational overhead of optimizing the G-QAOA angles while preserving its quadratic speedup. We also find parameter clustering of the angles. The single-angle-pair protocol and parameter clustering significantly reduce obstacles to classical optimization of the G-QAOA angles.

Zhang, Zewen (ORCID:000000032258613X)↗

Structure of nonevaporating sprays - Measurements and predictions

Structure measurements were completed within the dilute portion of axisymmetric nonevaporating sprays (SMD of 30 and 87 microns) injected into a still air environment, including: mean and fluctuating gas velocities and Reynolds stress using laser-Doppler anemometry; mean liquid fluxes using isokinetic sampling; drop sizes using slide impaction; and drop sizes and velocities using multiflash photography. The new measurements were used to evaluate three representative models of sprays: (1) a locally homogeneous flow (LHF) model, where slip between the phases was neglected; (2) a deterministic separated flow (DSF) model, where slip was considered but effects of drop interaction with turbulent fluctuations were ignored; and (3) a stochastic separated flow (SSF) model, where effects of both interphase slip and turbulent fluctuations were considered using random sampling for turbulence properties in conjunction with random-walk computations for drop motion. The LHF and DSF models were unsatisfactory for present test conditions-both underestimating flow widths and the rate of spread of drops. In contrast, the SSF model provided reasonably accurate predictions, including effects of enhanced spreading rates of sprays due to drop dispersion by turbulence, with all empirical parameters fixed from earlier work.

Solomon, A. S. P.↗

Power Grid Reliability Estimation via Adaptive Importance Sampling

Electricity production currently generates approximately 25% of greenhouse gas emissions in the USA. Thus, increasing the amount of renewable energy is a key step to carbon neutrality. However, integrating a large amount of fluctuating renewable generation is a significant challenge for power grid operating and planning. Grid reliability, i.e., an ability to meet operational constraints under power fluctuations, is probably the most important of them. In this letter, we propose computationally efficient and accurate methods to estimate the probability of line overflow, i.e., reliability constraints violation, under a known distribution of renewable energy generation. To this end, we investigate an importance sampling approach, a flexible extension of Monte-Carlo methods, which adaptively changes the sampling distribution to generate more samples near the reliability boundary. The approach allows to estimate overload probability in real-time based only on a few dozens of random samples, compared to thousands required by the plain Monte-Carlo. Our study focuses on high voltage direct current power transmission grids with linear reliability constraints on power injections and line currents. Herein, we propose a novel theoretically justified physics-informed adaptive importance sampling algorithm and compare its performance to state-of-the-art methods on multiple IEEE power grid test cases.

power system faults↗

Hashed Binary Search Sampling for Convolutional Network Training with Large Overhead Image Patches

Very large overhead imagery associated with ground truth maps has the potential to generate billions of training image patches for machine learning algorithms. However, random sampling selection criteria often leads to redundant and noisy-image patches for model training. With minimal research efforts behind this challenge, the current status spells missed opportunities to develop supervised learning algorithms that generalize over wide geographical scenes. In addition, much of the computational cycles for large scale machine learning are poorly spent crunching through noisy and redundant image patches. We demonstrate a potential framework to address these challenges specifically, while evaluating a human settlement detection task. A novel binary search tree sampling scheme is fused with a kernel based hashing procedure that maps image patches into hash-buckets using binary codes generated from image content. The framework exploits inherent redundancy within billions of image patches to promote mostly high variance preserving samples for accelerating algorithmic training and increasing model generalization.

Lunga, Dalton↗

Curiosity driven exploration to optimize structure–property learning in microscopy

Rapidly determining structure–property correlations in materials is an important challenge in better understanding fundamental mechanisms and greatly assists in materials design. In microscopy, imaging data provides a direct measurement of the local structure, while spectroscopic measurements provide relevant functional property information. Deep kernel active learning approaches have been utilized to rapidly map local structure to functional properties in microscopy experiments, but are computationally expensive for multi-dimensional and correlated output spaces. Here, we present an alternative lightweight curiosity algorithm which actively samples regions with unexplored structure–property relations, utilizing a deep-learning based surrogate model for error prediction. We show that the algorithm outperforms random sampling for predicting properties from structures, and provides a convenient tool for efficient mapping of structure–property relationships in materials science.

36 MATERIALS SCIENCE↗

FORTÉ Machine Learning

Of the non-corrupted data collected by the Orbiting Experiment (forté) satellite’s Photo-Diode Detector during the year 2001, I estimate that 7.9% of 914 894 signals are noise. My result differs dramatically from Guillen’s estimate of 96%. To arrive at this estimate, I used Gaussian mixture model (GMM) clustering–unsupervised machine learning–to aggregate the wave forms into groups based on the absolute value of the lowest 25 positive frequency discrete Fourier transform coefficients. Then, I marked several of the groups as noise by inspecting a random sampling of wave forms from each group. Marking groups as either noise or non-noise is a supervised binary classification operation. After removing the signals in noise groups from further consideration, I clustered the remaining signals into families. Again, I used a GMM, but for the familial clustering I used a Non-Negative Matrix Factorization feature vector transform. The result was 9 distinct families of lightning signals, as well as a second stage of noise filtering. To efficiently represent the entirety of the signal space, I broke each family into deciles based on their distance from the family mean. In this case, distance means the log-likelihood based on the GMM. Signals in lower deciles are more similar in shape and amplitude to their family average. I took the top 200 samples from each decile of each group, resulting in 18 000 signals. These signal approximately represent the entirety of the forté observations. To represent outliers, I also kept a zoo of the 1000 signals furthest from any family’s average. All told, the resulting data set represents the forté data with a reduction of about 51:1. To allow synthesis of an arbitrarily large number of test signals, I also captured each family’s average signal and the time-sample covariance matrix over the signals in each family. Using these two pieces of information, I can synthesize new waveforms by using a Gaussian random realization from the family average and covariance matrix. I wrote a program to test the synthesis quality. The program shows me two signals on the screen, one synthesized and one randomly drawn from the data. I attempted to identify the synthesized signal. Although the synthesis is imperfect, in an A/B comparison I only correctly chose the synthesized signal 36% of the time.

97 MATHEMATICS AND COMPUTING↗

Total Lightning Observations of Extreme Weather Events over the Contiguous United States

The overall objective is to investigate total lightning characteristics of extreme weather events over the contiguous United States (CONUS) using TRMM (Tropical Rainfall Measuring Mission) LIS (Lightning Image Sensor) and OTD (Optical Transient Detector) satellite observations. A large LIS (10+ years) and OTD (5 years) data base is available to study the instantaneous total or cloud-to-ground (CG) plus intracloud (IC) lightning characteristics of extreme weather events. More specifically, the LIS and OTD data are combined with National Lightning Detection Network (NLDN) observations to examine the total and CG lightning flash rate and density, the IC:CG ratio, and positive CG percentage. These instantaneous lightning characteristics can be used for basic science studies to better understand the physical and dynamical linkages between lightning and precipitation and their environmental controls. They can also provide a first-look of extreme weather events leading up to future satellite observations (e.g., NOAA GOES-R Geostationary Lightning Mapper [GLM]) for use in climate studies and the short-term prediction and warning process. Extreme weather events are defined by the NOAA Storm Data reports of tornadoes, large hail (at least 0.75 inch) and strong straight-line winds (at least 50 kts). Over CONUS, there are over 70,000 severe storm reports in the TRMM spatial domain (< 35 N) from 1998-2007 and over 100,000 storm reports in the OTD spatial domain (5/1995-4/2000). Temporal co-location is on the order of 1% (i.e., 1000 s of coincident overpasses), providing a statistically significant sample of instantaneous total lightning properties. This instantaneous behavior of lightning in extreme weather is then compared to that of typical thunderstorm events, or randomly sampled LIS/OTD events in which the extreme events have been eliminated from the population. Results describing the instantaneous behavior of total lightning within a large sample of extreme and typical thunderstorms over CONUS will be presented. When possible, coincident VHF lightning observations from the ground-based Northern Alabama Lightning Mapping Array (LMA) are compared to the LIS/OTD optical lightning signatures, providing a validation source for instantaneous space-based optical lightning properties and a means to extend lightning inferences over the life-cycle of extreme weather.

Carey, Lawrence D.↗

Graphite Characterization: Baseline Variability Analysis Report

The Idaho National INL’s Baseline Material Property program provides many measurements of different material properties on a variety of nuclear graphite grades being investigated for irradiation-induced changes in material properties. The baseline material properties provide an unirradiated reference for comparison with measurements of those properties after irradiation. This study describes how uncertainty, or variance, in estimates of important material properties, like compressive strength, may depend on sample size, sample distribution and parameter estimation methods. Compressive strength data from two large collections of specimens from a billet of PCEA graphite (sample size = 230) and a billet of IG-110 graphite (sample size = 48) are used to illustrate these dependencies. The grades of graphite used represent approximate end members in terms of relative variability in strength measurements. Monte Carlo simulation and bootstrapping methods were used to examine variance in Weibull-parameter estimates as a function of sample size. Results were consistent with what previous statistical analyses have shown about the relationship between sample size and width of the confidence interval for maximum likelihood (ML) estimated parameters when samples are repeatedly drawn from a Weibull distribution. As a function of sample size, the precision of the modulus estimate increases faster than that of the characteristic strength. The modulus maximum likelihood estimates (MLEs) are biased for low sample sizes. The American Society for Testing and Materials document ASTM D7846-16 provides equations that describe the dependence of the variance of parameter MLEs on sample size. Using the same methodology, we show that the polynomials provided for variance dependence on sample size are inaccurate for sample sizes greater than ~120. We provide approximations to that relationship that illustrate relative constancy for sample size > ~10, in the logspace relationship of the modulus variance and the log transformed characteristic strength variance. Bootstrapping provided a means of comparing Weibull parameters obtained using ASME’s guidance for specimen collection to those obtained using different weighting in a case where strength is related to position in a billet and to grain orientation and a single distribution is used to characterize the billet. ASME specifies that samples be collected with equal representation in all locations and grain orientations. Parameter values obtained using ASME’s method were different from those obtained using random sampling of the complete data sets, and this was particularly true for the PCEA data. In addition, while the ASME approach yielded more conservative parameters for the PCEA data, the opposite was true for the IG-110 data. The difference observed for the PCEA data set likely reflects the larger number of against-grain specimens collected, which had generally higher strength than the with-grain specimens. This emphasizes the importance of the dependence of strength on location or grain orientation and suggests that it may be prudent to weight specimen collection toward the weaker subgroups if a conservative estimate as desired, as the equal weighting method recommended by ASME would will not always provide the most conservative Weibull parameters. Because spatial correlations commonly exist in certain grades of graphite, future work may involve developing a methodology for parameter inference that relaxes the assumption of independent specimens. ASTM and ASME codes recommend different parameter estimation methods and models of the Weibull distribution in different situations. Descriptions of the effects on parameter estimates for the example billets used in this study provide an example of how the method may affect the parameter estimate, and how—in this case—that compares to differences due to other factors, such as sample size and dependence on grain orientation or sample location.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗