Search NASA⌕ Search

SEARCH · Search NASA

Results for “Probability Distribution Function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 739 records · Page 41

A BBGKY framework for fluid turbulence

A framework is presented for a systematic kinetic theory of turbulence originating from the Liouville equation for the Fourier coefficients of fluid variables. The real and imaginary parts of these Fourier coefficients play the role that particle coordinates (positions and momenta) play in the BBGKY theory. The basic relations of the problem are the incompressible Navier-Stokes equations in two dimensions with zero viscosity, with the probability distributions of Fourier coefficients rather than moments being the basic variables of the theory. A kinetic equation is derived and shown to possess a number of requirements that any reasonable kinetic equation must have: conservation laws, positive-definite spectral densities, and an H-theorem. The major lack in the theory is any reliable information on the relaxation predicted by the complicated linear operator H. Closure of the hierarchy is achieved by the hypothesis that the five-coefficient correlation function is negligible. Problems associated with inclusion of viscosity and external driving forces are discussed.

Montgomery, D.↗

The statistics of peaks of Gaussian random fields

A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of 'upcrossing' points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima.

Bardeen, J. M.↗

Probabilistic Modeling of High-Temperature Material Properties of a 5-Harness 0/90 Sylramic Fiber/ CVI-SiC/ MI-SiC Woven Composite

An integrated probabilistic approach has been developed to assess composites for high temperature applications. This approach was used to determine thermal and mechanical properties and their probabilistic distributions of a 5-harness 0/90 Sylramic fiber/CVI-SiC/Mi-SiC woven Ceramic Matrix Composite (CMC) at high temperatures. The purpose of developing this approach was to generate quantitative probabilistic information on this CMC to help complete the evaluation for its potential application for HSCT combustor liner. This approach quantified the influences of uncertainties inherent in constituent properties called primitive variables on selected key response variables of the CMC at 2200 F. The quantitative information is presented in the form of Cumulative Density Functions (CDFs). Probability Density Functions (PDFS) and primitive variable sensitivities on response. Results indicate that the scatters in response variables were reduced by 30-50% when the uncertainties in the primitive variables, which showed the most influence, were reduced by 50%.

Nagpal, Vinod K.↗

Forest Disturbance Across the Conterminous United States from 1985-2012: The Emerging Dominance of Forest Decline

Evidence of shifting dominance among major forest disturbance agent classes regionally to globally has been emerging in the literature. For example, climate-related stress and secondary stressors on forests (e.g., insect and disease, fire) have dramatically increased since the turn of the century globally, while harvest rates in the western US and elsewhere have declined. For shifts to be quantified, accurate historical forest disturbance estimates are required as a baseline for examining current trends. We report annual disturbance rates (with uncertainties) in the aggregate and by major change causal agent class for the conterminous US and five geographic subregions between 1985 and 2012. Results are based on human interpretations of Landsat time series from a probability sample of 7200 plots (30 m) distributed throughout the study area. Forest disturbance information was recorded with a Landsat time series visualization and data collection tool that incorporates ancillary high-resolution data. National rates of disturbance varied between 1.5% and 4.5% of forest area per year, with trends being strongly affected by shifting dominance among specific disturbance agent influences at the regional scale. Throughout the time series, national harvest disturbance rates varied between one and two percent, and were largely a function of harvest in the more heavily forested regions of the US (Mountain West, Northeast, and Southeast). During the first part of the time series, national disturbance rates largely reflected trends in harvest disturbance. Beginning in the mid-90s, forest decline-related disturbances associated with diminishing forest health (e.g., physiological stress leading to tree canopy cover loss, increases in tree mortality above background levels), especially in the Mountain West and Lowland West regions of the US, increased dramatically. Consequently, national disturbance rates greatly increased by 2000, and remained high for much of the decade. Decline-related disturbance rates reached as high as 8% per year in the western regions during the early-2000s. Although low compared to harvest and decline, fire disturbance rates also increased in the early- to mid-2000s. We segmented annual decline-related disturbance rates to distinguish between newly impacted areas and areas undergoing gradual but consistent decline over multiple years. We also translated Landsat reflectance change into tree canopy cover change information for greater relevance to ecosystem modelers and forest managers, who can derive better understanding of forest-climate interactions and better adapt management strategies to changing climate regimes. Similar studies could be carried out for other countries where there are sufficient Landsat data and historic temporal snapshots of high-resolution imagery.

Cohen, Warren B.↗

Learning error distribution kernel‐enhanced neural network methodology for multi‐intersection signal control optimization

Traffic congestion has substantially induced significant mobility and energy inefficiency. Many research challenges are identified in traffic signal control and management associated with artificial intelligence (AI)-based models. For example, developing AI-driven dynamic traffic system models that accurately capture high-resolution traffic attributes and formulate robust control algorithms for traffic signal optimization is difficult. Additionally, uncertainties in traffic system modeling and control processes can further complicate traffic signal system controllability. To partially address these challenges, this study presents a novel, hybrid neural network model enhanced with a probability density function kernel shaping technique to formulate traffic system dynamics better and improve comprehensive traffic network modeling and control. The numerical experimental tests were conducted, and the results demonstrate that the proposed control approach outperforms the baseline control strategies and reduces overall average delays by 11.64% on average. By leveraging the capabilities of this innovative model, this study aims to address major challenges related to traffic congestion and energy inefficiency toward more effective and adaptable AI-based traffic control systems.

Wang, Hong [Oak Ridge National Laboratory (ORNL), ↗

Assessing the Sampleability of Bennu’s Surface for the OSIRIS-REx Asteroid Sample Return Mission

NASA’s first asteroid sample return mission, OSIRIS-REx, collected a sample from the surface of near-Earth asteroid Bennu in October 2020 and will deliver it to Earth in September 2023. Selecting a sample collection site on Bennu’s surface was challenging due to the surprising lack of large ponded deposits of regolith particles exclusively fine enough (≤ 2 cm diameter) to be ingested by the spacecraft’s Touch-and-Go Sample Acquisition Mechanism (TAGSAM). Here we describe the Sampleability Map of Bennu, which was constructed to aid in the selection of candidate sampling sites and to estimate the probability of collecting sufficient sample. “Sampleability” is a numeric score that expresses the compatibility of a given area’s surface properties with the sampling mechanism. The algorithm that determines sampleability is a best fit functional form to an extensive suite of laboratory testing outcomes tracking the TAGSAM performance as a function of four observable properties of the target asteroid. The algorithm and testing were designed to measure and subsequently predict TAGSAM collection amounts as a function of the minimum particle size, maximum particle size, particle size frequency distribution, and the tilt of the TAGSAM head off the surface. The sampleability algorithm operated at two general scales, consistent with the resolution and coverage of data collected during the mission. The first scale was global and evaluated nearly the full surface. Due to Bennu’s unexpected boulder coverage and lack of ponded regolith deposits, the global sampleability efforts relied heavily on additional strategies to find and characterize regions of interest based on quantifying and avoiding areas heavily covered by material too large to be collected. The second scale was site-specific and used higher-resolution data to predict collected mass at a given contact location. The rigorous sampleability assessments gave the mission confidence to select the best possible sample collection site and directly enabled successful collection of hundreds of grams of material.

Asteroid exploration↗

A Unifying View of Estimation and Control Using Belief Propagation With Application to Path Planning

The use of estimation techniques on stochastic models to solve control problems is an emerging paradigm that falls under the rubric of Active Inference (AI) and Control as Inference (CAI). In this work, we use probability propagation on factor graphs to show that various algorithms proposed in the literature can be seen as specific composition rules in a factor graph. We show how this unified approach, presented both in probability space and in log of the probability space, provides a very general framework that includes the Sum-product, the Max-product, Dynamic programming and mixed Reward/Entropy criteria-based algorithms. The framework also expands algorithmic design options that lead to new smoother or sharper policy distributions. We propose original recursions such as: a generalized Sum/Max-product algorithm, a Smooth Dynamic programming algorithm and a modified versions of the Reward/Entropy algorithm. The discussion is carried over with reference to a path planning problem where the recursions that arise from various cost functions, although they may appear similar in scope, bear noticeable differences. We provide a comprehensive table of composition rules and a comparison through simulations, first on a synthetic small grid with a single goal with obstacles, and then on a grid extrapolated from a real-world scene with multiple goals and a semantic map.

Francesco A. N. Palmieri↗

Directed Design of Experiments for Validating Probability of Detection Capability of NDE Systems (DOEPOD)

Directed Design of Experiments for Validating Probability of Detection Capability of NDE Systems (DOEPOD) Manual v.1.2 The capability of an inspection system is established by applications of various methodologies to determine the probability of detection (POD). One accepted metric of an adequate inspection system is that there is 95% confidence that the POD is greater than 90% (90/95 POD). Design of experiments for validating probability of detection capability of nondestructive evaluation (NDE) systems (DOEPOD) is a methodology that is implemented via software to serve as a diagnostic tool providing detailed analysis of POD test data, guidance on establishing data distribution requirements, and resolving test issues. DOEPOD demands utilization of observance of occurrences. The DOEPOD capability has been developed to provide an efficient and accurate methodology that yields observed POD and confidence bounds for both Hit-Miss or signal amplitude testing. DOEPOD does not assume prescribed POD logarithmic or similar functions with assumed adequacy over a wide range of flaw sizes and inspection system technologies, so that multi-parameter curve fitting or model optimization approaches to generate a POD curve are not required. DOEPOD applications for supporting inspector qualifications is included.

Generazio, Edward R.↗

Photoionization of the diffuse interstellar medium and galactic halo by OB associtations

Assuming smoothly varying H I distributions in te Galactic disk, we have calculated the geometry of diffuse II regions due to OB associations in the Galactic plane. Near the solar circle, OB associations with a Lyman continuum (Lyc) photon luminosity Psi(sub Lyc) = 3.3 x 10(exp 7) cm(exp -2) s(exp -1), produce H II regions that are density bounded in the vertical direction (H II chimneys) allowing Lyc to escape the gaseous disk and penetrate into the Galactic halo. We provide analytic formulae for the Lyc escape fraction as functions of S(sub 0) O-star catalog of Garmany and a new Lyc stellar stellar Lyc stellar flux calibration, we find a production rate of Lyc photons by OB associations within 2.5 kpc of Psi(sub Lyc) = 3.3 x 10(exp 7) cm(exp -2) s(exp -1). Integrating the fraction of Lyc photons that escape the disk over our adopted luminosity function of OB associations, we estimate that approximately 7% of the ionizing photons, or Phi(sub Lyc) = 2.3 x 10(exp 6) cm(exp -2) s(exp -1), escape each side of the H I disk layer and penetrate the diffuse ionized medium ('Reynolds layer'). This flux is sufficient to explain the potoionization of this, although we have not constructed a model for the observed H-alpha emission and pulsar dispersion measures that is fully consistent with the absorption rate of Lyc in the H II layer. Since our quiescent model does not account for the effects of dynamic chimneys and superbubbles, which should enhance Lyc escape, we conclude the O stars are the probable source of ionizing radiation for the Reynolds layer. For a random distribution of OB associations throughout the disk, the Lyc flux is nearly uniform for heights Z is greater than approximately 0.8 kpc above the midplane.

Dove, James B.↗

Gravity and count probabilities in an expanding universe

The time evolution of nonlinear clustering on large scales in cold dark matter, hot dark matter, and white noise models of the universe is investigated using N-body simulations performed with a tree code. Count probabilities in cubic cells are determined as functions of the cell size and the clustering state (redshift), and comparisons are made with various theoretical models. We isolate the features that appear to be the result of gravitational instability, those that depend on the initial conditions, and those that are likely a consequence of numerical limitations. More specifically, we study the development of skewness, kurtosis, and the fifth moment in relation to variance, the dependence of the void probability on time as well as on sparseness of sampling, and the overall shape of the count probability distribution. Implications of our results for theoretical and observational studies are discussed.

Bouchet, Francois R.↗

Lunar Outpost Life Support Architecture Study Based on a High-Mobility Exploration Scenario

This paper presents results of a life support architecture study based on a 2009 NASA lunar surface exploration scenario known as Scenario 12. The study focuses on the assembly complete outpost configuration and includes pressurized rovers as part of a distributed outpost architecture in both stand-alone and integrated configurations. A range of life support architectures are examined reflecting different levels of closure and distributed functionality. Monte Carlo simulations are used to assess the sensitivity of results to volatile high-impact mission variables, including the quantity of residual Lander oxygen and hydrogen propellants available for scavenging, the fraction of crew time away from the outpost on excursions, total extravehicular activity hours, and habitat leakage. Surpluses or deficits of water and oxygen are reported for each architecture, along with fixed and 10-year total equivalent system mass estimates relative to a reference case. System robustness is discussed in terms of the probability of no water or oxygen resupply as determined from the Monte Carlo simulations.

Lange, Kevin E.↗

Deep Learning-Based Weather-Related Power Outage Prediction with Socio-Economic and Power Infrastructure Data

This paper presents a deep learning-based approach for hourly power outage probability prediction within census tracts encompassing a utility company's service territory. Two distinct deep learning models, conditional Multi-Layer Perceptron (MLP) and unconditional MLP, were developed to forecast power outage probabilities, leveraging a rich array of input features gathered from publicly available sources including weather data, weather station locations, power infrastructure maps, socio-economic and demographic statistics, and power outage records. Given a one-hour-ahead weather forecast, the models predict the power outage probability for each census tract, taking into account both the weather prediction and the location's characteristics. The deep learning models employed different loss functions to optimize prediction performance. Our experimental results underscore the significance of socio-economic factors in enhancing the accuracy of power outage predictions at the census tract level.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A test of synthetic accretion disk spectra using ultraviolet flux distributions of novalike variables

Ultraviolet (UV) fluxes and other data for a sample of nine novalike cataclysmic variables are assembled from the literature. The UV fluxes and colors are compared to spectra of steady state model accretion disks, constructed using either Planck functions or model stellar atmosphere spectra as elementary radiators. Deficiencies are found with both sets of models. The restriction to steady state radial temperature profiles is relaxed for the 'stellar atmosphere' disks, but these generalized models still fail to account simultaneously for the absolute UV flux and the UV color of the observed spectra. The conclusion is that stellar atmosphere models do not reflect the physics of disks. More appropriate models probably can and definitely should be made.

Wade, Richard A.↗

Interval Predictor Models for Robust System Identification

This paper proposes a framework for the identification and uncertainty quantification of plant models according to multivariable data. The only restriction imposed upon such models is for their outputs to depend continuously on their parameters. An Interval Predictor Model (IPM) prescribes the parameters of a computational model as a path-connected set thereby making each predicted output an interval-valued function of its inputs. The formulation proposed seeks the parameter set for which the predicted outputs tightly enclose the data. This set, which is modeled as a semi-algebraic set of low-degree polynomials, enables the characterization of possibly strong parameter dependencies commonly found in practice. This uncertainty characterization makes the resulting plant model amenable to robust control approaches using polynomial optimization. Furthermore, we use non-convex scenario theory to assess the reliability of the resulting IPM. This assessment yields a distribution-free upper bound on the probability that future data will fall outside the predicted intervals.

interval↗

Closed-form solution of decomposable stochastic models

Markov and semi-Markov processes are increasingly being used in the modeling of complex reconfigurable systems (fault tolerant computers). The estimation of the reliability (or some measure of performance) of the system reduces to solving the process for its state probabilities. Such a model may exhibit numerous states and complicated transition distributions, contributing to an expensive and numerically delicate solution procedure. Thus, when a system exhibits a decomposition property, either structurally (autonomous subsystems), or behaviorally (component failure versus reconfiguration), it is desirable to exploit this decomposition in the reliability calculation. In interesting cases there can be failure states which arise from non-failure states of the subsystems. Equations are presented which allow the computation of failure probabilities of the total (combined) model without requiring a complete solution of the combined model. This material is presented within the context of closed-form functional representation of probabilities as utilized in the Symbolic Hierarchical Automated Reliability and Performance Evaluator (SHARPE) tool. The techniques adopted enable one to compute such probability functions for a much wider class of systems at a reduced computational cost. Several examples show how the method is used, especially in enhancing the versatility of the SHARPE tool.

Sjogren, Jon A.↗

Voltage Probability Density Function Shaping Control Strategy Considering Grid Operational Uncertainties

It is well-known that power systems operation always affected by various uncertainties which make the bus voltage a random process that can be characterized by its probability density function (PDF) at any time instant. In this context, this paper presents a novel PDF-based voltage control framework for power systems. By modeling voltage as a stochastic process, we formulate a stochastic differential equationthat captures grid uncertainties. The associated Fokker-Planck-Kolmogorov equation is derived to describe the evolution of the voltage PDF, which enables the formulation of a PDF-shaping control strategy. To simplify the PDF control formulation, a B-spline neural network is introduced for real-time estimation and regulation of the voltage distribution. The proposed PDF control law updates voltage references for energy storage systems and synchronous generators using real-time PDF measurements and feedback signals. The proposed method is validated on a modified Kundur’s two-area system. Simulation results demonstrate that the controller can significantly improve the voltage stability under stochastic conditions, highlighting its effectiveness in modern inverter-rich grids.

Gui, Yonghao [ORNL] (ORCID:0000000250435534)↗

Rayed craters on the moon and Mercury

Systems of bright rays are exhibited by many fresh craters on the moon and Mercury. Diameter/density distributions suggest that lunar-rayed craters represent the Class 1 craters, and that Mercurian rayed craters represent post-Caloris craters. Photogeological analyses of lunar imagery indicate that the ray systems are composed of finely divided material from the primary crater along with locally derived ejecta from secondary and tertiary craters. The primary ray material probably occurs in moderately thick (0.1-1 meter) deposits. The rate of darkening may depend more on the thickness of the ray material than on the rates of various darkening processes. Darkening rate may also be a function of crater size. It is observed that rays of craters more than 1 b.y. old remain bright, whereas those older than Class 1 generally fade to imperceptibility.

Allen, C. C.↗

Stochastic control system parameter identifiability

The parameter identification problem of general discrete time, nonlinear, multiple input/multiple output dynamic systems with Gaussian white distributed measurement errors is considered. The knowledge of the system parameterization was assumed to be known. Concepts of local parameter identifiability and local constrained maximum likelihood parameter identifiability were established. A set of sufficient conditions for the existence of a region of parameter identifiability was derived. A computation procedure employing interval arithmetic was provided for finding the regions of parameter identifiability. If the vector of the true parameters is locally constrained maximum likelihood (CML) identifiable, then with probability one, the vector of true parameters is a unique maximal point of the maximum likelihood function in the region of parameter identifiability and the constrained maximum likelihood estimation sequence will converge to the vector of true parameters.

Lee, C. H.↗