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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.

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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Statistical Characterization of 18650-Format Lithium-Ion Cell Thermal Runaway Energy Distributions

Effective thermal management systems, designed to handle the impacts of thermal runaway (TR) and to prevent cell-to-cell propagation, are key to safe operation of lithium-ion (Li-ion) battery assemblies. Critical factors for optimizing these systems include the total energy released during a single cell TR event and the fraction of the total energy that is released through the cell casing vs. through the ejecta material. A unique calorimeter was utilized to examine the TR behavior of a statistically significant number of 18650-format Li-ion cells with varying manufacturers, chemistries, and capacities. The calorimeter was designed to contain the TR energy in a format conducive to discerning the fractions of energy released through the cell casing vs. through the ejecta material. Other benefits of this calorimeter included the ability to rapidly test of large quantities of cells and the intentional minimization of secondary combustion effects. High energy (270 Wh/kg) and moderate energy (200 Wh/kg) 18650 cells were tested. Some of the cells had an imbedded short circuit (ISC) device installed to aid in the examination of TR mechanisms under more realistic conditions. Other variations included cells with bottom vent (BV) features and cells with thin casings (0.22 1/4m). After combining the data gathered with the calorimeter, a statistical approach was used to examine the probability of certain TR behavior, and the associated energy distributions, as a function of capacity, venting features, cell casing thickness and temperature.

Thermal Runaway Energy Distribution↗
NASA NTRS1972

Distribution of error in least-squares solution of an overdetermined system of linear simultaneous equations

Probability density functions were derived for errors in the evaluation of unknowns by the least squares method in system of nonhomogeneous linear equations. Coefficients of the unknowns were assumed correct and computational precision were also assumed. A vector space was used, with number of dimensions equal to the number of equations. An error vector was defined and assumed to have uniform distribution of orientation throughout the vector space. The density functions are shown to be insensitive to the biasing effects of the source of the system of equations.

Miller, C. D.↗
DOE OSTI2024

Computing the Instantaneous Collision Probability between Satellites using Characteristic Function Inversion

The probability that two satellites overlap in space at a specified instant of time is called their instantaneous collision probability. Assuming Gaussian uncertainties and spherical satellites, this probability is the integral of a Gaussian distribution over a sphere. This paper shows how to compute the probability using an established numerical procedure called characteristic function inversion. The collision probability in the short-term encounter scenario is also evaluated with this approach, where the instant at which the probability is computed is the time of closest approach between the objects. Python and R code is provided to evaluate the probability in practice. Overall, the approach has been established for over fifty years, is implemented in existing software, does not rely on analytical approximations, and can be used to evaluate two and three dimensional collision probabilities.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2010

Probabilistic Design Analysis (PDA) Approach to Determine the Probability of Cross-System Failures for a Space Launch Vehicle

Quantifying the probability of significant launch vehicle failure scenarios for a given design, while still in the design process, is critical to mission success and to the safety of the astronauts. Probabilistic risk assessment (PRA) is chosen from many system safety and reliability tools to verify the loss of mission (LOM) and loss of crew (LOC) requirements set by the NASA Program Office. To support the integrated vehicle PRA, probabilistic design analysis (PDA) models are developed by using vehicle design and operation data to better quantify failure probabilities and to better understand the characteristics of a failure and its outcome. This PDA approach uses a physics-based model to describe the system behavior and response for a given failure scenario. Each driving parameter in the model is treated as a random variable with a distribution function. Monte Carlo simulation is used to perform probabilistic calculations to statistically obtain the failure probability. Sensitivity analyses are performed to show how input parameters affect the predicted failure probability, providing insight for potential design improvements to mitigate the risk. The paper discusses the application of the PDA approach in determining the probability of failure for two scenarios from the NASA Ares I project

Shih, Ann T.↗
DOE OSTI2025

Bayesian reconstruction of anisotropic flow fluctuations at fixed impact parameter

The cumulants of the distribution of anisotropic flow are measured accurately in Pb+Pb collisions at the LHC as a function of centrality classifiers (charged multiplicity and/or transverse energy). Using Bayesian inference, we reconstruct from these measurements the probability distribution of anisotropic flow in the ``theorists' frame'' where the impact parameter has a fixed magnitude and orientation, up to ∼70% centrality. The variation of flow fluctuations with impact parameter displays direct evidence of viscous damping, which is larger for higher Fourier harmonics, in line with expectations from hydrodynamics. We use intensive measures of non-Gaussian flow fluctuations, which have reduced dependence on centrality. Here, we infer from ATLAS data the magnitude of these intensive non-Gaussianities in each Fourier harmonic. They provide data-driven estimates of response coefficients to initial anisotropies, without resorting to any specific microscopic model of initial conditions. These estimates agree with viscous hydrodynamic calculations.

Bayesian methods↗
NASA NTRS2015

A Metric to Quantify Shared Visual Attention in Two-Person Teams

Introduction: Critical tasks in high-risk environments are often performed by teams, the members of which must work together efficiently. In some situations, the team members may have to work together to solve a particular problem, while in others it may be better for them to divide the work into separate tasks that can be completed in parallel. We hypothesize that these two team strategies can be differentiated on the basis of shared visual attention, measured by gaze tracking. 2) Methods: Gaze recordings were obtained for two-person flight crews flying a high-fidelity simulator (Gontar, Hoermann, 2014). Gaze was categorized with respect to 12 areas of interest (AOIs). We used these data to construct time series of 12 dimensional vectors, with each vector component representing one of the AOIs. At each time step, each vector component was set to 0, except for the one corresponding to the currently fixated AOI, which was set to 1. This time series could then be averaged in time, with the averaging window time (t) as a variable parameter. For example, when we average with a t of one minute, each vector component represents the proportion of time that the corresponding AOI was fixated within the corresponding one minute interval. We then computed the Pearson product-moment correlation coefficient between the gaze proportion vectors for each of the two crew members, at each point in time, resulting in a signal representing the time-varying correlation between gaze behaviors. We determined criteria for concluding correlated gaze behavior using two methods: first, a permutation test was applied to the subjects' data. When one crew member's gaze proportion vector is correlated with a random time sample from the other crewmember's data, a distribution of correlation values is obtained that differs markedly from the distribution obtained from temporally aligned samples. In addition to validating that the gaze tracker was functioning reasonably well, this also allows us to compute probabilities of coordinated behavior for each value of the correlation. As an alternative, we also tabulated distributions of correlation coefficients for synthetic data sets, in which the behavior was modeled as a first-order Markov process, and compared correlation distributions for identical processes with those for disparate processes, allowing us to choose criteria and estimate error rates. 3) Discussion: Our method of gaze correlation is able to measure shared visual attention, and can distinguish between activities involving different instruments. We plan to analyze whether pilots strategies of sharing visual attention can predict performance. Possible measurements of performance include expert ratings from instructors, fuel consumption, total task time, and failure rate. While developed for two-person crews, our approach can be applied to larger groups, using intra-class correlation coefficients instead of the Pearson product-moment correlation.

Gontar, Patrick↗
NASA NTRS1974

Long-duration life tests of slip ring capsule assemblies for inertial guidance platforms

Eight slip ring capsules, each having 80 or 100 circuits, were operated for time periods ranging from 14,300 hours to 24,700 hours. The test mode simulated the motion of gimbal axes of the Saturn inertial guidance the platform in an organic free nitrogen environment. Computer-compiled noise data (approximately 45,000 recordings) were graphed as a function of test time and position within the capsules and as extreme probability distributions. Greater than ninety-nine percent of the noise measurements for the capsules with sufficient lubrication were less than 10 milliohms. Capsules with glass dielectrics did not perform significantly differently than those with filled epoxy dielectrics. The initial wear mode of prow formation was followed by rider wear. After 10 to the 8th power wipes, ring wear depth did not exceed the surface finish and the radial rider wear depth was less than 13 microns.

Cole, S. R.↗
NASA NTRS1980

Bivariate normal, conditional and rectangular probabilities: A computer program with applications

Some results for the bivariate normal distribution analysis are presented. Computer programs for conditional normal probabilities, marginal probabilities, as well as joint probabilities for rectangular regions are given: routines for computing fractile points and distribution functions are also presented. Some examples from a closed circuit television experiment are included.

Swaroop, R.↗
NASA NTRS1991

Gamma ray pulsar analysis from photon pobability maps

We present a new method of analyzing skymap-type gamma ray data. Each photon event is replaced by a probability distribution on the sky corresponding to the observing instrument's point spread function. The skymap produced by this process may be used for source detection or identification. Most important, the use of these photon weights for pulsar analysis promises significant improvement over traditional techniques.

Brown, Lawrence E.↗
NASA NTRS1992

Gamma ray pulsar analysis from photon probability maps

A new method is presented of analyzing skymap-type gamma ray data. Each photon event is replaced by a probability distribution on the sky corresponding to the observing instrument's point spread function. The skymap produced by this process may be used for source detection or identification. Most important, the use of these photon weights for pulsar analysis promises significant improvement over traditional techniques.

Brown, Lawrence E.↗
NASA NTRS2006

Distributed Constrained Optimization with Semicoordinate Transformations

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by translating the problem into an iterated game, where each agent controls a different variable of the problem, so that the joint probability distribution across the agents moves gives an expected value of the objective function. The dynamics of the agents is designed to minimize a Lagrangian function of that joint distribution. Here we illustrate how the updating of the Lagrange parameters in the Lagrangian is a form of automated annealing, which focuses the joint distribution more and more tightly about the joint moves that optimize the objective function. We then investigate the use of "semicoordinate" variable transformations. These separate the joint state of the agents from the variables of the optimization problem, with the two connected by an onto mapping. We present experiments illustrating the ability of such transformations to facilitate optimization. We focus on the special kind of transformation in which the statistically independent states of the agents induces a mixture distribution over the optimization variables. Computer experiment illustrate this for &sat constraint satisfaction problems and for unconstrained minimization of NK functions.

Macready, William↗
NASA NTRS1972

Kullback-Leibler information function and the sequential selection of experiments to discriminate among several linear models

The error variance of the process prior multivariate normal distributions of the parameters of the models are assumed to be specified, prior probabilities of the models being correct. A rule for termination of sampling is proposed. Upon termination, the model with the largest posterior probability is chosen as correct. If sampling is not terminated, posterior probabilities of the models and posterior distributions of the parameters are computed. An experiment was chosen to maximize the expected Kullback-Leibler information function. Monte Carlo simulation experiments were performed to investigate large and small sample behavior of the sequential adaptive procedure.

Sidik, S. M.↗
NASA NTRS1997

Internal Luminosity Distribution of Bright Gamma-Ray Bursts and its Relation to Duration and Spectral Hardness

We present first results from a comprehensive investigation into the distribution of luminosity within the 50 brightest cosmic gamma-ray bursts detected by the Burst and Transient Source Experiment (BATSE). The internal luminosity function psi(L) is defined such that the quantity psi(L)dL represents the fraction of total emission time during which the burst possesses a luminosity between L and L + dL. For these brightest bursts, the psi(L) functions are quasi-power-law-like and decrease in amplitude with increasing luminosity. Through investigation of both individual psi(L) distributions and data from the ensemble of bursts, we demonstrate a high probability for correlation between the shape of the internal luminosity function as measured by the average logarithmic slope and the burst duration as measured by the T(sub 90) parameter and, with lower significance, between the shape of psi(L) and the burst photon-fluence spectral index. We furthermore demonstrate a correlation between burst hardness ratio and duration in these brightest bursts which is opposite to that of the entire gamma-ray burst ensemble.

Horack, John M.↗
NASA NTRS1971

Comments on the continuity of distribution functions obtained by superposition.

Assuming that Y is a nonnegative random variable independent of the differential process X(t), attention is given to the question of whether or not the superposition X(Y) can have a continuous probability distribution. If the process has continuous distributions, then the superposition is continuous if and only if P/Y = 0/ = 0. If the process has discontinuous distributions and no trend, then no superposition can have continuous distribution. If the process has discontinuous distributions and nonzero trend, then the superposition onto a random epoch has continuous distribution if and only if Y has continuous distribution.

Huff, B. W.↗
NASA NTRS1993

Presenting the Rain-Sea Interaction Facility

The new Rain-Sea Interaction Facility (RSIF) was established at GSFC/WFF and the first finds are presented. The unique feature of this laboratory is the ability to systematically study microwave scattering from a water surface roughened by artificial rain, for which the droplets are at terminal velocity. The fundamental instruments and systems (e.g., the rain simulator, scatterometers, and surface elevation probes) were installed and evaluated during these first experiments - so the majority of the data were obtained with the rain simulator at 1 m above the water tank. From these initial experiments, three new models were proposed: the square-root function for NCS vs. R, the log Gaussian model for ring-wave elevation frequency spectrum, and the Erland probability density distribution for back scattered power. Rain rate is the main input for these models, although the coefficients may be dependent upon other factors (drop-size distribution, fall velocity, radar configuration, etc.). The facility is functional and we foresee collaborative studies with investigators who are engaged in measuring and modeling rain-sea interaction processes.

Bliven, Larry F.↗
DOE OSTI2024

A Corrected Score Function Framework for Modelling Circadian Gene Expression

Many biological processes display oscillatory behaviour based on an approximately 24 h internal timing system specific to each individual. One process of particular interest is gene expression, for which several circadian transcriptomic studies have identified associations between gene expression during a 24 h period and an individual's health. A challenge with analysing data from these studies is that each individual's internal timing system is offset relative to the 24 h day-night cycle, where day–night cycle time is recorded for each collected sample. Laboratory procedures can accurately determine each individual's offset and determine the internal time of sample collection. However, these laboratory procedures are labour-intensive and expensive. Here, in this paper, we propose a corrected score function framework to obtain a regression model of gene expression given internal time when the offset of each individual is too burdensome to determine. A feature of this framework is that it does not require the probability distribution generating offsets to be symmetric with a mean of zero. Simulation studies validate the use of this corrected score function framework for cosinor regression, which is prevalent in circadian transcriptomic studies. Illustrations with data from three circadian transcriptomic studies further demonstrate that the proposed framework consistently mitigates bias relative to using a score function that does not account for this offset.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1984

A model function for ocean radar cross sections at 14.6 GHz

The relationship between the ocean's normalized radar cross section (NRCS) at 14.6 GHz and the surface wind vector is derived using the 3 months of Seasat microwave scatterometer (SASS) measurements. The derivation is based on the statistics of the SASS observations, and no in situ measurements are required, other than a mean global wind speed, which comes from climatology. The frequency distribution of the global wind vectors observed by SASS is assumed to be a bivariate normal probability function. A NRCS model function is found that maps the assumed wind vector statistics into the observed SASS NRCS statistics. This function is compared with a NRCS model coming from the Joint Air Sea Interaction Experiment (JASIN) and with aircraft scatterometer measurements. The results indicate that the statistically derived NRCS model is an improvement over the JASIN model, which was based on a limited number of in situ anemometer measurements.

Wentz, F. J.↗
NASA NTRS1973

Path-length distributions of photons diffusely reflected from a semi-infinite atmosphere.

Knowledge of the probability distribution of photon path lengths for diffuse reflection in the continuum from a planetary atmosphere greatly simplifies computation of the shape and strength of absorption lines formed under conditions of multiple scattering. Graphs of this probability distribution are presented for diffuse reflection from a semiinfinite conservative atmosphere for both isotropic and forward-directed scattering, and for several angles of incidence and reflection. Graphs showing distributions for the case of absorption in the continuum are also discussed. The distributions are obtained from an analytic expression for the path-length distribution for nth-order scattering and a tabulation of nth-order intensities. It is found that te shape of the probability distribution depends markedly on the degree of forward scattering due to the phase function. The results are compared with those obtained by a Monte Carlo computation of the sort which might be used if tabulated nth-order intensities were not available.

Appleby, J. F.↗