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At least 1,063 records · Page 59

Performance Comparison of Circular and Spherical Error Probable Estimators

This report compares the performance of three Circular Error Probable (CEP) estimators: the Grubbs-Patnaik estimator, a new, non-iterative, radial-integration estimator, and a median estimator. It also compares the performance of two Spherical Error Probable (SEP) estimators. The performance of each estimator is assessed in terms of bias, uncertainty, robustness, and computational complexity. Robustness is evaluated with respect to outliers, variations in the underlying statistical distribution characterizing munition impact positions, and impact-position measurement errors. The performance assessments indicate the radial-integration and Grubbs-Patnaik estimators perform nearly identically providing the statistical distribution of impact-position coordinates is jointly normal with zero means. In that case, both estimators outperform the median estimator by about 2% relative to the true CEP in terms of estimator uncertainty. The bias performance of the radial-integration and median estimators is close to zero for jointly normal impacts, however, the Grubbs-Patnaik estimator can be significantly biased for jointly normal impacts with non-zero means. When the statistical distribution characterizing impact positions is known, but not jointly normal, the radial-integration estimator is superior. In this case, the median estimator also outperforms the Grubbs-Patnaik estimator but is not quite as good as the radial-integration estimator. If the statistical distribution characterizing impacts is unknown and not jointly normal, or if distribution parameters are difficult or impractical to estimate, or if test data is corrupted with outliers, then the median estimator dramatically outperforms the other estimators, especially in terms of estimation bias. Unexpectedly, measurement noise did not significantly degrade the performance of any of the estimators, except for cases with signal to noise ratios less than five. Although the Grubbs-Patnaik estimator has remained the gold standard for CEP estimation for over half a century, the performance assessments indicate the new, non-iterative, radial-integration estimator and the median estimator offer significant advantages and, in most practical real-world conditions, are superior estimators. These estimators are also useful for SEP estimation whereas the Grubbs-Patnaik estimator does not extend to three dimensions.

97 MATHEMATICS AND COMPUTING↗

Quantifying Graph Uncertainty from Communication Data

Graphs are a widely used abstraction for representing a variety of important real-world problems including emulating cyber networks for situational awareness, or studying social networks to understand human interactions or pandemic spread. Communication data is often converted into graphs to help understand social and technical patterns in the underlying communication data. However, prior to this project, little work had been performed analyzing how best to develop graphs from such data. Thus, many critical, national security problems were being performed against graph representations of questionable quality. Herein, we describe our analyses that were precursors to our final statistically grounded technique for creating static graph snapshots from a stream of communication events. The first analyzes the statistical distribution properties of a variety of real-world communication datasets generally fit best by Pareto, log normal, and extreme value distributions. The second derives graph properties that can be estimated given the expected statistical distribution for communication events and the communication interval to be viewed node observability, edge observability, and expected accuracy of node degree. Unfortunately, as that final process is under review for publication, we can't publish it here at this time.

97 MATHEMATICS AND COMPUTING↗

Equivalent Longitudinal Area Distributions of the B-58 and XB-70-1 Airplanes for Use in Wave Drag and Sonic Boom Calculations

A detailed geometric description, in wave drag format, has been developed for the Convair B-58 and North American XB-70-1 delta wing airplanes. These descriptions have been placed on electronic files, the contents of which are described in this paper They are intended for use in wave drag and sonic boom calculations. Included in the electronic file and in the present paper are photographs and 3-view drawings of the two airplanes, tabulated geometric descriptions of each vehicle and its components, and comparisons of the electronic file outputs with existing data. The comparisons include a pictorial of the two airplanes based on the present geometric descriptions, and cross-sectional area distributions for both the normal Mach cuts and oblique Mach cuts above and below the vehicles. Good correlation exists between the area distributions generated in the late 1950s and 1960s and the present files. The availability of these electronic files facilitates further validation of sonic boom prediction codes through the use of two existing data bases on these airplanes, which were acquired in the 1960s and have not been fully exploited.

Tinetti, Ana F.↗

Long–short-term memory encoder–decoder with regularized hidden dynamics for fault detection in industrial processes

The ability of recurrent neural networks (RNN) to model nonlinear dynamics of high dimensional process data has enabled data-driven RNN-based fault detection algorithms. Previous studies have focused on detecting faults by identifying the discrepancies in data distribution between the faulty and normal data, as reflected in prediction errors generated by RNN models. However, in industrial processes, variations in data distribution can also result from changes in normal control setpoints and compensatory control adjustments in response to disturbances, making it hard to differentiate between normal and faulty conditions. This paper proposes a fault detection method utilizing a long short-term memory (LSTM) encoder–decoder structure with regularized hidden dynamics and reversible instance normalization (RevIN) to compactly represent high-dimensional measurements for effective monitoring. During training, the hidden states of the model are regularized to form a low-dimensional latent space representation of the original multivariate time series data. As a result, the prediction errors of the latent states can be used to monitor the abnormal dynamic variations, while the reconstruction errors of the measured variables are used to monitor the abnormal static variations. Furthermore, the proposed indices can reflect operating conditions, even when the distribution of test data changes, which helps distinguish faults from normal adjustments and disturbances that controllers can settle. Here, data from numerical simulation and the Tennessee Eastman process are used to illustrate the effectiveness of the proposed fault detection method.

42 ENGINEERING↗

Salvaging Data Records with Missing Data: Data Imputation using the Multivariate t Distribution

When doing multivariate data analysis, one commonobstacle is the presence of incomplete observations, i.e., observationsfor which one or more key fields are blank. Missing datais often countered by deleting entire observations that containmissing data. The negative effects of deleting entire observationsare multiple: deleting observations reduces sample size andcan also result in biased inferences even if data is missing atrandom. In addition, knowledge contained within incompleteobservations is knowledge lost when they are deleted– and theeffort spent collecting that knowledge is effort wasted. Data imputationmethods, or methods of statistically “filling-in” missingdata, can help combat small sample sizes by using the existinginformation in partially complete observations with the end goalof producing less biased and higher confidence inferences. Whena sample from a multivariate normal population is only partiallycomplete, and the missing data meets appropriate assumptions(missing at random), robust data imputation of the missing datacan be implemented with monotone data augmentation (MDA)using the multivariate t distribution.Missing data imputation is applied to data from the NASA InstrumentCost Model (NICM) using the MDA algorithm underthe assumption of having a multivariate t distribution with fixeddegrees of freedom. A sensitivity analysis to the degrees offreedom parameter is presented to demonstrate robustness ofthe multivariate t distribution when dealing with small samplesas compared to the multivariate normal distribution.

DiNicola, Michael↗

Statistical Analysis of Hubble /WFC3 Transit Spectroscopy of Extrasolar Planets

Transmission spectroscopy provides a window to study exoplanetary atmospheres, but that window is fogged by clouds and hazes. Clouds and haze introduce a degeneracy between the strength of gaseous absorption features and planetary physical parameters such as abundances. One way to break that degeneracy is via statistical studies. We collect all published HST /WFC3 transit spectra for 1.1–1.65 μ m water vapor absorption and perform a statistical study on potential correlations between the water absorption feature and planetary parameters. We fit the observed spectra with a template calculated for each planet using the Exo-transmit code. We express the magnitude of the water absorption in scale heights, thereby removing the known dependence on temperature, surface gravity, and mean molecular weight. We find that the absorption in scale heights has a positive baseline correlation with planetary equilibrium temperature; our hypothesis is that decreasing cloud condensation with increasing temperature is responsible for this baseline slope. However, the observed sample is also intrinsically degenerate in the sense that equilibrium temperature correlates with planetary mass. We compile the distribution of absorption in scale heights, and we find that this distribution is closer to log-normal than Gaussian. However, we also find that the distribution of equilibrium temperatures for the observed planets is similarly log-normal. This indicates that the absorption values are affected by observational bias, whereby observers have not yet targeted a sufficient sample of the hottest planets.

79 ASTRONOMY AND ASTROPHYSICS↗

THE SIGNATURE OF THE WARM-HOT INTERGALACTIC MEDIUM IN WMAP AND THE FORTHCOMING PLANCK DATA

We compute the cross-correlation between the Warm-Hot Intergalactic Medium and maps of cosmic microwave background temperature anisotropies using a log-normal probability density function to describe the weakly nonlinear matter density field. We search for this contribution in the data measured by the Wilkinson Microwave Anisotropy Probe. We use a template of projected matter density reconstructed from the Two-Micron All-Sky Redshift Survey as a tracer of the electron distribution. The spatial distribution of filaments is modeled using the recently developed Augmented Lagrangian Perturbation Theory. On the scales considered here, the reconstructed density field is very well described by the assumed log-normal distribution function. We predict that the cross-correlation will have an amplitude of 0.03-0.3 {mu}K. The measured value is close to 1.5 {mu}K, compatible with random alignments between structure in the template and in the temperature anisotropy data. Using the W1 Differencing Assembly to remove this systematic gives a residual correlation dominated by Galactic foregrounds. Planck could detect the Warm-Hot Medium if it is well traced by the density field reconstructed from galaxy surveys. The 217 GHz channel will allow to eliminate spurious contributions and its large frequency coverage can show the sign change from the Rayleigh-Jeans to the Wien part of the spectrum, characteristic of the thermal Sunyaev-Zel'dovich effect.

79 ASTRONOMY AND ASTROPHYSICS↗

Far-infrared /FIR/ optical black bidirectional reflectance distribution function /BRDF/

A nonspecular reflectometer and its operation at far-infrared wavelengths are described. Large differences in nonspecular reflectance were found to exist between different optically black coatings. Normal incidence bidirectional reflectance distribution function /BRDF) measurements at wavelengths between 12 and 316 microns of three black coatings show that their mean BRDFs increase with wavelength. The specularity of two of these coatings also showed a strong wavelength dependence, while the specularity of one coating seemed independent of wavelength. The BRDF of one coating depended on the angle of incidence at 12 and 38 microns, but not at 316 microns. Beyond 200 microns, it was found necessary to correct the measurements for the beam spread of the instrument.

Smith, S. M.↗

Small-Sample Estimator Decisions – Certainly Uncertain in Human Spaceflight at NASA

Within statistics when estimating means, we rely heavily on the Central Limit Theorem (CLT) to aid in our inference, however in cases where the CLT does not apply we begin to be strongly limited in our choices. If a violation to the CLT comes in the form of small samples and unknown population variance, yet we maintain the assumption of normality, the use of t-distributions is perfectly valid. We explore cases where population normality is not assumed, where sample sizes are small, and where some actionable estimate of the central tendency of a distribution is needed such as for spaceflight operational decisions. Here we identify different scenarios based on measures taken from spaceflight, characterizing performance of estimators of central tendency within our set of simulations. We examine bias and variability of standard estimators of central tendency as they apply to varying small sample sizes and varying population distributions. Further work in this area is needed to develop a framework or set of guidelines for individuals set in these situations. Even with limited information, decisions need to be made.

Central Tendency↗

Normalization Method and Application for MODIS TEB Assessments using Earth Scene Measurements

Selected Earth targets are commonly used for satellite sensor calibration assessments (e.g. sensor stability and inter-comparisons). Moreover, typical scenes used for the calibration assessment of the thermal emissive bands (TEBs) includeDome Concordia (Dome-C), ocean, desert, and deep convective clouds (DCC). Reference data used for these calibration assessments can come from another band, another instrument, or ground measurements. The Dome-C site, covered with uniformly-distributed permanent snow, is normally used for the assessment of the TEBsat cold temperatures. Furthermore, ocean and desert measurements prove useful for scenes with higher temperatures. The DCC, one of the most consistent and coldest targets, can be used for the TEBs calibration and product stability assessments. MODIS band 31 (~ 11 m) can be used as a reference for these scenes. However, measurements over these scenes have seasonal variations, and the DCC brightness temperatures (BTs) have asymmetrical distributions. These features can introduce additional uncertainty to the stability assessments. A normalization method is applied by using an empirical model to derive reference-dependent BTs. Using the developed empirical model, measurements can be normalized to a reference BT in order to enhance the calibration assessment’s accuracy. This method is evaluated using all four scene types (i.e. ocean, desert, snow (Dome-C), and DCC) and applied to all the Terra and Aqua MODIS TEBs. Stability assessments over the instruments’ entire data records are presented and discussed. The technique can be applied in future efforts to support MODIS TEBs calibration assessments.

MODIS TEB↗

THE FERMI-GBM X-RAY BURST MONITOR: THERMONUCLEAR BURSTS FROM 4U 0614+09

Thermonuclear bursts from slowly accreting neutron stars (NSs) have proven difficult to detect, yet they are potential probes of the thermal properties of the NS interior. During the first year of a systematic all-sky search for X-ray bursts using the Gamma-ray Burst Monitor aboard the Fermi Gamma-ray Space Telescope we have detected 15 thermonuclear bursts from the NS low-mass X-ray binary 4U 0614+09 when it was accreting at nearly 1% of the Eddington limit. We measured an average burst recurrence time of 12 {+-} 3 days (68% confidence interval) between 2010 March and 2011 March, classified all bursts as normal duration bursts and placed a lower limit on the recurrence time of long/intermediate bursts of 62 days (95% confidence level). We discuss how observations of thermonuclear bursts in the hard X-ray band compare to pointed soft X-ray observations and quantify such bandpass effects on measurements of burst radiated energy and duration. We put our results for 4U 0614+09 in the context of other bursters and briefly discuss the constraints on ignition models. Interestingly, we find that the burst energies in 4U 0614+09 are on average between those of normal duration bursts and those measured in long/intermediate bursts. Such a continuous distribution in burst energy provides a new observational link between normal and long/intermediate bursts. We suggest that the apparent bimodal distribution that defined normal and long/intermediate duration bursts during the last decade could be due to an observational bias toward detecting only the longest and most energetic bursts from slowly accreting NSs.

79 ASTRONOMY AND ASTROPHYSICS↗

Characteristics of Multi-scale Current Sheets in the Solar Wind at 1 au Associated with Magnetic Reconnection and the Case for a Heliospheric Current Sheet Avalanche

Wind spacecraft measurements are analyzed to obtain a current sheet (CS) normal width dcs-distribution of 3374 confirmed magnetic reconnection exhausts in the ecliptic plane of the solar wind at 1 AU. The dcs-distribution displays a nearly exponential decay from a peak at dcs=25 di to a median at dcs=85 di and a 95th percentile at dcs=905 di with a maximum exhaust width at dcs=8077 di. A magnetic field ϴ-rotation angle distribution increases linearly from a relatively few high-shear events toward a broad peak at 35o<ϴ<65o. The azimuthal φ-angles of the CS normal directions of 430 thick dcs≥500 di exhausts are consistent with a dominant Parker-spiral magnetic field and a CS normal along the ortho-Parker direction. The CS normal orientations of 370 kinetic-scale dcs<25 di exhausts are isotropic in contrast, and likely associated with Alfvénic solar wind turbulence. We propose that the alignment of exhaust normal directions from narrow dcs~15-25 di widths to well beyond dcs~500 di with an ortho-Parker azimuthal direction of a large-scale HCS is a consequence of CS bifurcation and turbulence within the HCS exhaust that may trigger reconnection of the adjacent pair of bifurcated CSs. The proposed HCS-31 avalanche scenario suggests that the underlying large-scale parent HCS closer to the Sun evolves with heliocentric distance to fracture into many, more or less aligned, secondary current sheets due to reconnection. A few wide exhaust-associated HCS-like CSs could represent a population of HCSs that failed to reconnect as frequently between the Sun and 1 AU as other HCSs.

Stefan Eriksson↗

Ejected Particle Size Distributions from Shocked Metal Surfaces

Here, we present size distributions for particles ejected from features machined onto the surface of shocked Sn targets. The functional form of the size distributions is assumed to be log-normal, and the characteristic parameters of the distribution are extracted from the measured angular distribution of light scattered from a laser beam incident on the ejected particles. We also found strong evidence for a bimodal distribution of particle sizes with smaller particles evolved from features machined into the target surface and larger particles being produced at the edges of these features.

36 MATERIALS SCIENCE↗

Search for the Z_1(4050)^+ and Z_2(4250)^+ States in bar B^0 to chi_{c1} K^- pi^+ and B^+ to chi_{c1} K^0_S pi^+

We search for the Z{sub 1}(4050){sup +} and Z{sub 2}(4250){sup +} states, reported by the Belle Collaboration, decaying to {chi}{sub c1}{pi}{sup +} in the decays {bar B}{sup 0} {yields} {chi}{sub c1}K{sup -}{pi}{sup +} and B{sup +} {yields} {chi}{sub c1}K{sub S}{sup 0}{pi}{sup +} where {chi}{sub c1} {yields} J/{psi}{gamma}. The data were collected with the BABAR detector at the SLAC PEP-II asymmetric-energy e{sup +}e{sup -} collider operating at center-of-mass energy 10.58 GeV, and correspond to an integrated luminosity of 429 fb{sup -1}. In this analysis, we model the background-subtracted, efficiency-corrected {chi}{sub c1}{pi}{sup +} mass distribution using the K{pi} mass distribution and the corresponding normalized K{pi} Legendre polynomial moments, and then test the need for the inclusion of resonant structures in the description of the {chi}{sub c1}{pi}{sup +} mass distribution. No evidence is found for the Z{sub 1}(4050){sup +} and Z{sub 2}(4250){sup +} resonances, and 90% confidence level upper limits on the branching fractions are reported for the corresponding B-meson decay modes.

43 PARTICLE ACCELERATORS↗