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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Filter Tuning Using the Chi-Squared Statistic

This paper examines the use of the Chi-square statistic as a means of evaluating filter performance. The goal of the process is to characterize the filter performance in the metric of covariance realism. The Chi-squared statistic is the value calculated to determine the realism of a covariance based on the prediction accuracy and the covariance values at a given point in time. Once calculated, it is the distribution of this statistic that provides insight on the accuracy of the covariance. The process of tuning an Extended Kalman Filter (EKF) for Aqua and Aura support is described, including examination of the measurement errors of available observation types, and methods of dealing with potentially volatile atmospheric drag modeling. Predictive accuracy and the distribution of the Chi-squared statistic, calculated from EKF solutions, are assessed.

Filter Tuning↗
NASA NTRS2015

North American Extreme Temperature Events and Related Large Scale Meteorological Patterns: A Review of Statistical Methods, Dynamics, Modeling, and Trends

The objective of this paper is to review statistical methods, dynamics, modeling efforts, and trends related to temperature extremes, with a focus upon extreme events of short duration that affect parts of North America. These events are associated with large scale meteorological patterns (LSMPs). The statistics, dynamics, and modeling sections of this paper are written to be autonomous and so can be read separately. Methods to define extreme events statistics and to identify and connect LSMPs to extreme temperature events are presented. Recent advances in statistical techniques connect LSMPs to extreme temperatures through appropriately defined covariates that supplement more straightforward analyses. Various LSMPs, ranging from synoptic to planetary scale structures, are associated with extreme temperature events. Current knowledge about the synoptics and the dynamical mechanisms leading to the associated LSMPs is incomplete. Systematic studies of: the physics of LSMP life cycles, comprehensive model assessment of LSMP-extreme temperature event linkages, and LSMP properties are needed. Generally, climate models capture observed properties of heat waves and cold air outbreaks with some fidelity. However they overestimate warm wave frequency and underestimate cold air outbreak frequency, and underestimate the collective influence of low-frequency modes on temperature extremes. Modeling studies have identified the impact of large-scale circulation anomalies and landatmosphere interactions on changes in extreme temperatures. However, few studies have examined changes in LSMPs to more specifically understand the role of LSMPs on past and future extreme temperature changes. Even though LSMPs are resolvable by global and regional climate models, they are not necessarily well simulated. The paper concludes with unresolved issues and research questions.

Cold Spells↗
NASA NTRS2017

Filter Tuning Using the Chi-Squared Statistic

The Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF) performs orbit determination (OD) for the Aqua and Aura satellites. Both satellites are located in low Earth orbit (LEO), and are part of what is considered the A-Train satellite constellation. Both spacecraft are currently in the science phase of their respective missions. The FDF has recently been tasked with delivering definitive covariance for each satellite.The main source of orbit determination used for these missions is the Orbit Determination Toolkit developed by Analytical Graphics Inc. (AGI). This software uses an Extended Kalman Filter (EKF) to estimate the states of both spacecraft. The filter incorporates force modelling, ground station and space network measurements to determine spacecraft states. It also generates a covariance at each measurement. This covariance can be useful for evaluating the overall performance of the tracking data measurements and the filter itself. An accurate covariance is also useful for covariance propagation which is utilized in collision avoidance operations. It is also valuable when attempting to determine if the current orbital solution will meet mission requirements in the future.This paper examines the use of the Chi-square statistic as a means of evaluating filter performance. The Chi-square statistic is calculated to determine the realism of a covariance based on the prediction accuracy and the covariance values at a given point in time. Once calculated, it is the distribution of this statistic that provides insight on the accuracy of the covariance.For the EKF to correctly calculate the covariance, error models associated with tracking data measurements must be accurately tuned. Over estimating or under estimating these error values can have detrimental effects on the overall filter performance. The filter incorporates ground station measurements, which can be tuned based on the accuracy of the individual ground stations. It also includes measurements from the NASA space network (SN), which can be affected by the assumed accuracy of the TDRS satellite state at the time of the measurement.The force modelling in the EKF is also an important factor that affects the propagation accuracy and covariance sizing. The dominant force in the LEO orbit regime is the drag force caused by atmospheric drag. Accurate accounting of the drag force is especially important for the accuracy of the propagated state. The implementation of a box and wing model to improve drag estimation accuracy, and its overall effect on the covariance state is explored.The process of tuning the EKF for Aqua and Aura support is described, including examination of the measurement errors of available observation types (Doppler and range), and methods of dealing with potentially volatile atmospheric drag modeling. Predictive accuracy and the distribution of the Chi-square statistic, calculated based of the ODTK EKF solutions, are assessed versus accepted norms for the orbit regime.

Covariance Analysis↗
NASA NTRS2020

Statistical Analysis of Factors Riving Surface Ozone Variability over Continental South Africa

Statistical relationships between surface ozone (O3) concentration, precursor species and meteorological conditions in continental South Africa were examined from data obtained from measurement stations in north-eastern South Africa. Three multivariate statistical methods were applied in the investigation, i.e. multiple linear regression (MLR), principal component analysis (PCA) and –regression (PCR), and generalised additive model (GAM) analysis. The daily maximum 8-h moving average O3 concentrations were considered in these statistical models (dependent variable). MLR models indicated that meteorology and precursor species concentrations are able to explain ~50% of the variability in daily maximum O3 levels. MLR analysis revealed that atmospheric carbon monoxide (CO), temperature and relative humidity were the strongest factors affecting the daily O3 variability. In summer, daily O3 variances were mostly associated with relative humidity, while winter O3 levels were mostly linked to temperature and CO. PCA indicated that CO, temperature and relative humidity were not strongly collinear. GAM also identified CO, temperature and relative humidity as the strongest factors affecting the daily variation of O3. Partial residual plots found that temperature, radiation and nitrogen oxides most likely have a non-linear relationship with O3,while the relationship with relative humidity and CO is probably linear. An inter-comparison between O3 levels modelled with the three statistical models compared to measured O3 concentrations showed that the GAM model offered a slight improvement over the MLR model. These findings emphasise the critical role of regional-scale O3 precursors coupled with meteorological conditions in daily variances of O3 levels in continental South Africa.

multiple linear regression (MLR)↗
NASA NTRSDate not supplied

A New Statistical Estimate of the Radar Coverage of the Low Earth Orbit Debris Environment

For over three decades, the NASA Orbital Debris Program Office (ODPO) has used the Goldstone Orbital Debris Radar, Haystack Ultrawideband Satellite Imaging Radar (HUSIR), and Haystack Auxiliary (HAX) radar assets to collect data on the low Earth orbit (LEO) debris environment. Each radar, with its unique beamwidth, altitude and inclination coverage, and limiting size threshold, operates in a beam park mode to statistically sample the orbital debris population in LEO. Provided that these assets are shared with other users, the orbital debris data collection is not continuous; rather, intermittent data collects are acquired and sent to the NASA ODPO. To understand the sampling process conducted by each radar over time and any related observational biases, a Statistical Confirmation of Radar Uniformity or Bias (SCRUB) code has been implemented to model the coverage of these assets for informing future operations, as well as usage of the data collected from these ground-based sensors. For this analysis, Right Ascension of the Ascending Node (RAAN) is used as a metric to measure statistical coverage. A complete survey of the LEO environment is understood to be measurements that sufficiently sample all values of RAAN for each altitude-inclination pair visible from the radar asset. Regions of incompleteness or statistical bias can help inform future observation campaigns. The SCRUB tool evaluates the coverage of the LEO environment, not by examining individual objects that may pass through a sensor’s field of view (FOV), but by determining which orbit planes pass through the FOV. Once a pointing geometry for a radar site, observation time, and range extent are configured by the user, SCRUB computes the inclinations and altitudes that are visible by the sensor. For each inclination-altitude pair, there is a distinct pair of possible RAAN values, corresponding to the ascending and descending orbit passing through that point in the sensor cone. Repeating this process for all points in the beam, and for multiple time periods during an observation window, creates a matrix of all inclination-altitude-RAAN combinations that are visible during a sensor run. This process can then be repeated for all observations within a year (for an annual survey), propagating all the RAAN values to a common epoch, typically the start of a calendar year, and combining the observations to assemble a full estimate of the RAAN coverage of the LEO environment. This RAAN coverage can then be analyzed for uniformity of sampling, within a certain inclination-altitude pair, or between larger regions of the space environment. This paper provides a general overview of the radar assets utilized by ODPO, typical analysis data products assuming circular orbits, and a discussion of the algorithms that feed between modeling and measurement operations. Following the description of the algorithm, estimates of coverage using HUSIR radar data collected from multiple years are developed and compared.

Chris L Ostrom↗
NASA NTRSDate not supplied

Infusing Statistical Thinking into the NASA Quesst Community Test Campaign

Statistical thinking permeates many important decisions as NASA plans its Quesst mission, which will culminate in a series of community overflights using the X-59 aircraft to demonstrate low-noise supersonic flight. Month-long longitudinal surveys will be deployed to assess human perception and annoyance to this new acoustic phenomenon. NASA works with a large contractor team to develop systems and methodologies to estimate noise doses, to test and field socio-acoustic surveys, and to study the relationship between the two quantities, dose and response, through appropriate choices of statistical models. This latter dose-response relationship will serve as an important tool as national and international noise regulators debate whether overland supersonic flights could be permitted once again within permissible noise limits. In this presentation we highlight several areas where statistical thinking has come into play, including issues of sampling, classification and data fusion, and analysis of longitudinal survey data that are subject to rare events and the consequences of measurement error. We note several operational constraints that shape the appeal or feasibility of some decisions on statistical approaches, and we identify several important remaining questions to be addressed.

Bayesian model↗
NASA NTRSDate not supplied

Statistical Practice and Research at NASA

The discipline of statistics has gained recognition within NASA by spurring innovation and efficiency, and it has demonstrated significant impact and value. In aerospace research and development, it accelerates learning, maximizes knowledge, ensures strategic resource investment, and informs rigorous data-driven decisions. In practice, it requires immersive multidisciplinary collaboration to develop solution strategies that integrate statistical methods with subject-matter expertise to address challenging research objectives. This presentation provides an overview of statistical case studies in aeronautics, space exploration, and atmospheric science, and it highlights statistical research motivated by NASA’s challenging applications.

Peter A. Parker↗
DOE OSTI2018

Statistics of Peaks in Chi-Squared Fields

Chi-squared random fields arise naturally from the study of fluctuations in field theories with SO(n) symmetry. The extrema of chi-squared fields are of particular physical interest. In this paper, we undertake a statistical analysis of the stationary points of chi-squared fields, with particular emphasis on extrema. We begin by describing the neighborhood of a stationary point in terms of a biased chi-squared random field, and then compute the expected profile of this field, as well as a variety of associated statistics. We are interested in understanding how spherically symmetric the neighborhood of a stationary point is, on average. To this end, we decompose the biased field into its spherical harmonic modes about this point, and explore their statistics. Using these mode statistics, we construct a metric to gauge the degree of spherical symmetry of the field in this neighborhood. Finally, we show how to leverage the harmonic decomposition to efficiently sample both Gaussian and chi-squared fields about a stationary point.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Statistical Methods for Effective Spatial and Temporal Scaling in Support of Probabilistic Performance Assessments - 17340

Performance assessments (PAs) for the disposal of low-level radioactive waste have traditionally been performed in a deterministic manner, with inputs specified as single values as if they carry no uncertainty. Modern PAs, however, explicitly incorporate uncertainty through use of probability distributions for inputs instead of single values. While this is clearly an improvement, challenges remain in specifying appropriate distributions, many of which relate to capturing the appropriate spatial and/or temporal scale given the PA model, and matching the scale(s) of data and information to that specified by the model. More careful attention to scaling will lead to more defensible characterizations of physical variability and uncertainty in model inputs, thus leading to more defensible information regarding outcomes of interest to be used in decision making, and hence more defensible decisions. This work introduces general strategies and considerations for explicitly incorporating considerations of scale into distribution development. The strategies are explained as a series of steps and then presented with an example that starts to illustrate the new statistical concepts. This work frames the problem in terms of hierarchical statistical modeling, providing important connections to current statistical approaches to formally and rigorously account for temporal and spatial scaling. The larger goal is to build a more formal and unified approach to distribution development to help teams of modelers, subject matter experts, and statisticians work together to develop distributions and justify the choices made in the process, ultimately leading to more informed decision-making. Without this rigor, statistical distributions are not specified correctly and can have unexpected consequences for modeling and sensitivity analysis. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Utilizing Advanced Statistics to Determine Anomalistic Conditions in Pebble-Bed Reactors

Pebble-bed reactors (PBRs) utilize hundreds of thousands of fuel pebbles, which continuously circulate through the core, in lieu of traditional fuel assemblies to generate fissions and produce power. The use of unmarked fuel pebbles presents a challenge for international safeguards verification that nuclear material is not being diverted. To ensure pebble diversion is not taking place, new methods for accounting for and monitoring the pebbles should be examined to determine an appropriate methodology for performing bulk accountancy with pebbles. Here, this work examines the use of statistical methods for determining if the reactor is within a declared range of operation by examining the statistical distribution of pebble burnup as they are discharged from the core. Using this methodology, we created a model that detects diversion over 95% of the time, over multiple diversion pathways, if the reactor core maintains a constant power density during the diversion process and only falsely labels a diversion case nominal 2% of the time. For a diversion scenario where the reactor is maintained at a constant power, the statistical analysis can correctly identify if diversion is occurring over 80% of the time; however, nearly 20% of specific diversion pathways are mislabeled nominal. These results provide a basis and framework for exploring the further use of statistical methods to determine where these methods could be most useful and where additional methods, such as machine learning, could be used to capture if diversion is occurring in pebble-bed reactors.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2017

Modeling Soot Oxidation and Gasification with Bayesian Statistics

This paper presents a statistical method for model calibration using data collected from literature. The method is used to calibrate parameters for global models of soot consumption in combustion systems. This consumption is broken into two different submodels: first for oxidation where soot particles are attacked by certain oxidizing agents; second for gasification where soot particles are attacked by H 2 O or CO 2 molecules. Rate data were collected from 19 studies in the literature and evaluated using Bayesian statistics to calibrate the model parameters. Bayesian statistics are valued in their ability to quantify uncertainty in modeling. The calibrated consumption model with quantified uncertainty is presented here along with a discussion of associated implications. The oxidation results are found to be consistent with previous studies. Significant variation is found in the CO 2 gasification rates.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2022

Persona of Transition Metal Ions in Solids: A Statistical Learning on Local Structures of Transition Metal Oxides

Abstract The local structure of a transition metal (TM) ion is a function of cation elements and valence states. More than that, in this work, by employing a trove of first‐principles data of TM oxides, the local structures of TM cations are statistically analyzed to extract detailed information about cation site preference, bond length, site structural distortion, and cation magnetization. It is found that cation radius alone poorly describes the local structure of a transition metal oxide, while the statistics of coordination number as well as the TMO bond length distribution, especially that of the 3d TMs, can provide comprehensive knowledge for understanding the behavior of TM elements. Based on these statistics, the interplay of site distortion due to the Jahn–Teller effect, cation site similarity, and a new set of ionic radii are all obtained to chart the “persona” of transition metal ions in solids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Statistical analysis of the performance and long-term stability of unquenched LSC standards ( 3 H, 14 C) used for radiochemical measurements

Multiple sets of toluene-based unquenched standards, procured over the last 3 decades, were analyzed to determine their stability over time. A statistical analysis was performed to provide insight into the variability for tSIE and counting efficiency measurements of 3 H and 14 C isotopes. Our data suggests that standards remain viable even 30 years after the manufacturer’s recommended expiration date. Overall, these standards have shown no statistically significant sign of performance degradation. We have proven through statistical analysis that these standards can provide comparable performance over time well past their manufactured expiration date.

LSC standards↗
DOE OSTI2019

Quantum statistics and spacetime topology: Quantum surgery formulas

To formulate the universal constraints of quantum statistics data of generic long-range entangled quantum systems, we introduce the geometric-topology surgery theory on spacetime manifolds where quantum systems reside, cutting and gluing the associated quantum amplitudes, specifically in 2+1 and 3+1 spacetime dimensions. First, we introduce the fusion data for worldline and worldsheet operators capable of creating anyonic excitations of particles and strings, well-defined in gapped states of matter with intrinsic topological orders. Second, we introduce the braiding statistics data of particles and strings, such as the geometric Berry matrices for particle–string Aharonov–Bohm, 3-string, 4-string, or multi-string adiabatic loop braiding process, encoded by submanifold links, in the closed spacetime 3-manifolds and 4-manifolds. Third, we derive new “quantum surgery” formulas and constraints, analogous to Verlinde formula associating fusion and braiding statistics data via spacetime surgery, essential for defining the theory of topological orders, 3d and 4d TQFTs and potentially correlated to bootstrap boundary physics such as gapless modes, extended defects, 2d and 3d conformal field theories or quantum anomalies. This article is meant to be an extended and further detailed elaboration of our previous work Wang, Wen and Yau (2016) [1] and Chapter 6 of Wang (2015) [2]. Our theory applies to general quantum theories and quantum mechanical systems, also applicable to, but not necessarily requiring the quantum field theory description.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Statistical analysis of historic hydrocarbon production data from Gulf of Mexico oil and gas fields and application to dynamic capacity assessment in CO 2 storage

Numerical modeling of CO 2 injection and reservoir flow is typically performed to forecast the number of wells, sustainable injection rates, and total storage volume (or mass). A critical determination for CO 2 storage in depleted oil and gas reservoirs is characterization of reservoir compartmentalization which informs boundary conditions in simulating injection scenarios. Constraining boundary conditions during CO 2 injection into geological formations is a key factor for feasible deployment project. Production history data from 616 wells in 100 oil and gas fields from Gulf of Mexico (GOM) offshore basin can be used to evaluate boundary conditions and total production (oil and gas) and therefor constrain the capacity for potential carbon storage. In general, the combination of decline curve analysis and statistical analysis (to specify constraining boundary conditions) allows the determination of the range of reservoir performance if existing inactive production wells in GOM area of study are used reversibly for CO 2 injection. To constrain the mass of CO 2 which can be injected, it is useful to consider estimates of cumulative bulk (hydrocarbon + brine) production (CBP), which can be converted to equivalent CO 2 mass considering reservoir conditions. Summary CBP statistics are presented as a probability of non-exceedance (PNE), providing a forecast of likely injection rates and masses for other located CO 2 storage projects with similar geology and boundary conditions in the future. The 50% PNE for Equivalent CO 2 is a novel quantitative approach to investigate the possible injection capacity in CO 2 storage projects. The PNE sensitivity analysis shows that reservoir age, drive mechanism, reservoir trap, and reservoir porosity are the key controlling parameters for productivity and consequently optimum CO 2 storage capacity. Furthermore another key finding is the negligible correlation between CBP with reservoir transmissivity and porosity, which implies that other factors than just petrophysical parameters should be studied as constraining factors for CO 2 storage statistical analysis.

42 ENGINEERING↗
DOE OSTI2021

Turbulence theories and statistical closure approaches

When discussing research in physics and in science more generally, it is common to ascribe equal importance to the three components of the scientific trinity: theoretical, experimental, and computational studies. This review will explore the future of modern turbulence theory by tracing its history, which began in earnest with Kolmogorov’s 1941 analysis of turbulence cascade and inertial range [A.N. Kolmogorov, Dokl. Akad. Nauk SSSR, 30, 299, (1941); 32, 19, (1941)]. The 80th Anniversary of Kolmogorov’s landmark study is a welcome opportunity to survey the achievements and evaluate the future of the theoretical approach of turbulence research. Over the years, turbulence theories have been critically important in laying the foundation of our understanding of the nature of turbulent flows. In particular, the Direct Interaction Approximation (DIA) [R.H. Kraichnan, J. Fluid Mech., 5, 497 (1959)] and its subsequent development, known as the statistical closure approach, can be identified as perhaps the most profound single advancement. The remarkable success of the statistical closure has furnished a platform to study such essential concepts as the energy transfer process and interacting scales, and the roles of the straining and sweeping motions. More recently, the quasi-Lagrangian formulation of V. L’vov & I. Procaccia and Kraichnan’s solvable passive scalar model provided powerful ways to explore another fundamental aspect of turbulent flows, the phenomena of intermittency, and the associated anomalous scaling exponents. In the meantime, the theory of fluid equilibria has been developed to describe the large-scale structures that can emerge from turbulent cascades of two-dimensional and geophysical flows at a later time. And yet, despite all these successes, analytical treatments suffer from mathematical complexities. As a result, the utility of theoretical approaches has been limited to relatively idealized flows. On the other hand, in recent decades, computational abilities and experimental facilities have reached an unprecedented scale. Looking beyond the horizon, the imminent deployment of exascale supercomputers will generate complete datasets of the entire flow field of key benchmark flows, allowing researchers to extract additional measurements concerning fully developed, complex turbulent flow fields far beyond those available from the statistical closure theories. Some other developments that could potentially influence the future course of turbulence theories include the advancement of machine learning, artificial intelligence, and data science; likely disruptions arising from the advent of quantum computation; and the increasingly prominent role of turbulence research in providing more accurate climate scientific data. Finally, turbulence theorists can leverage these developments by asking the right questions and developing advanced, sophisticated frameworks that will be able to predict and correlate vast amounts of data from the other two components of the trinity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Municipal solid waste composition: Sampling methodology, statistical analyses, and case study evaluation

Highlights: • Tiered approach to waste sorting ensures flexibility and facilitates comparison of solid waste composition data. • Food and miscellaneous wastes are the main fractions contributing to the residual household waste. • Separation of food packaging from food leftovers during sorting is not critical for determination of the solid waste composition. - Abstract: Sound waste management and optimisation of resource recovery require reliable data on solid waste generation and composition. In the absence of standardised and commonly accepted waste characterisation methodologies, various approaches have been reported in literature. This limits both comparability and applicability of the results. In this study, a waste sampling and sorting methodology for efficient and statistically robust characterisation of solid waste was introduced. The methodology was applied to residual waste collected from 1442 households distributed among 10 individual sub-areas in three Danish municipalities (both single and multi-family house areas). In total 17 tonnes of waste were sorted into 10–50 waste fractions, organised according to a three-level (tiered approach) facilitating comparison of the waste data between individual sub-areas with different fractionation (waste from one municipality was sorted at “Level III”, e.g. detailed, while the two others were sorted only at “Level I”). The results showed that residual household waste mainly contained food waste (42 ± 5%, mass per wet basis) and miscellaneous combustibles (18 ± 3%, mass per wet basis). The residual household waste generation rate in the study areas was 3–4 kg per person per week. Statistical analyses revealed that the waste composition was independent of variations in the waste generation rate. Both, waste composition and waste generation rates were statistically similar for each of the three municipalities. While the waste generation rates were similar for each of the two housing types (single-family and multi-family house areas), the individual percentage composition of food waste, paper, and glass was significantly different between the housing types. This indicates that housing type is a critical stratification parameter. Separating food leftovers from food packaging during manual sorting of the sampled waste did not have significant influence on the proportions of food waste and packaging materials, indicating that this step may not be required.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2014

Photon-number statistics of twin beams: Self-consistent measurement, reconstruction, and properties

A method for the determination of photon-number statistics of twin beams using the joint signal-idler photocount statistics obtained by an iCCD camera is described. It also provides absolute quantum detection efficiency of the camera. Using the measured photocount statistics, quasi-distributions of integrated intensities are obtained. They attain negative values occurring in characteristic strips an a consequence of pairing of photons in twin beams.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗