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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Color Histogram Diffusion for Image Enhancement

Various color histogram equalization (CHE) methods have been proposed to extend grayscale histogram equalization (GHE) for color images. In this paper a new method called histogram diffusion that extends the GHE method to arbitrary dimensions is proposed. Ranges in a histogram are specified as overlapping bars of uniform heights and variable widths which are proportional to their frequencies. This diagram is called the vistogram. As an alternative approach to GHE, the squared error of the vistogram from the uniform distribution is minimized. Each bar in the vistogram is approximated by a Gaussian function. Gaussian particles in the vistoram diffuse as a nonlinear autonomous system of ordinary differential equations. CHE results of color images showed that the approach is effective.

Kim, Taemin↗
NASA NTRS2013

Analytical Algorithms to Quantify the Uncertainty in Remaining Useful Life Prediction

This paper investigates the use of analytical algorithms to quantify the uncertainty in the remaining useful life (RUL) estimate of components used in aerospace applications. The prediction of RUL is affected by several sources of uncertainty and it is important to systematically quantify their combined effect by computing the uncertainty in the RUL prediction in order to aid risk assessment, risk mitigation, and decisionmaking. While sampling-based algorithms have been conventionally used for quantifying the uncertainty in RUL, analytical algorithms are computationally cheaper and sometimes, are better suited for online decision-making. While exact analytical algorithms are available only for certain special cases (for e.g., linear models with Gaussian variables), effective approximations can be made using the the first-order second moment method (FOSM), the first-order reliability method (FORM), and the inverse first-order reliability method (Inverse FORM). These methods can be used not only to calculate the entire probability distribution of RUL but also to obtain probability bounds on RUL. This paper explains these three methods in detail and illustrates them using the state-space model of a lithium-ion battery.

Sankararaman, Shankar↗
NASA NTRS2017

Chorus Whistler Wave Source Scales As Determined From Multipoint Van Allen Probe Measurements

Whistler mode chorus waves are particularly important in outer radiation belt dynamics due to their key role in controlling the acceleration and scattering of electrons over a very wide energy range. The key parameters for both nonlinear and quasi-linear treatment of wave-particle interactions are the temporal and spatial scales of the wave source region and coherence of the wave field perturbations. Neither the source scale nor the coherence scale is well established experimentally, mostly because of a lack of multipoint VLF waveform measurements. We present an unprecedentedly long interval of coordinated VLF waveform measurements (sampled at 16384 s(exp -1)) aboard the two Van Allen Probes spacecraft-9 h (0800-1200 UT and 1700-2200 UT) during two consecutive apogees on 15 July 2014. The spacecraft separations varied from about 100 to 5000 km (mostly radially); measurements covered an L shell range from 3 to 6; magnetic local time 0430-0900, and magnetic latitudes were approximately 15 and approximately 5 deg during the two orbits. Using time-domain correlation techniques, the single chorus source spatial extent transverse to the background magnetic field has been determined to be about 550-650 km for upper band chorus waves with amplitudes less than 100 pT and up to 800 km for larger amplitude, lower band chorus waves. The ratio between wave amplitudes measured on the two spacecraft is also examined to reveal that the wave amplitude distribution within a single chorus element generation area can be well approximated by a Gaussian exp(-0.5 x r (exp 2)/r(sub 0)(exp 2)), with the characteristic scale r(sub 0) around 300 km. Waves detected by the two spacecraft were found to be coherent in phase at distances up to 400 km.

Agapitov, O.↗
DOE OSTI2022

Bayesian Monte Carlo Evaluation Framework for Imperfect Data and Models [Abstract]

Nuclear data evaluation methods conventionally make the following assumptions: prior and posterior probability distribution functions (PDFs) of all model parameters and data are normal (Gaussian); the linear approximation is sufficiently accurate for minimization of a cost function (even for non-linear models); and that both the model (of, e.g., neutron cross section) and experimental data (including their covariance data) are perfect. These assumptions are inherent to the well-known generalized linear least squares (GLLS) minimization method commonly used for evaluations of resolved resonance region (RRR) neutron cross sections. However, these assumptions are often not justified due to the presence of non-normal PDFs, non-linear models (e.g. R -matrix formalism), and inherent imperfections in data and models (e.g. discrepant data sets, discrepancies between the previous evaluation and newly measured data, or imperfect covariance data). We remove the said assumptions in a mathematical framework of Bayes’ theorem, and implement it using the Metropolis-Hastings Monte Carlo method. Parameters of a new kind are introduced to parameterize inherent imperfections, e.g. , any discrepancies between the theoretical model and measured data. These new parameters enable evaluators to quantify their expert judgement about any discrepancies or imperfections in a reproducible manner. We demonstrate the framework with an ongoing evaluation of 233 U in the eV region using the ENDF-B/VIII library and transmission data measured by Guber, et al. , and compare the posterior parameters to those obtained by conventional evaluation methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1995

Interpretation of Extinction in Gaussian-Beam Scattering

The extinction efficiency for the interaction of a plane wave with a large nonabsorbing spherical particle is approximately 2.0. When a Gaussian beam of half-width w(sub 0) is incident upon a spherical particle of radius a with w(sub 0)/a less than 1, the extinction efficiency attains unexpectedly high or low values, contrary to intuitive expectations. The reason for this is associated with the so-called compensating term in the scattered field, which cancels the field of the Gaussian beam behind the particle, thereby producing the particle's shadow. I introduce a decomposition of the total exterior field into incoming and outgoing portions that are free of compensating terms. It is then shown that a suitably defined interaction efficiency has the intuitively expected asymptotic values of 2.0 for w(sub 0)/a much greater than 1 and 1.0 for w(sub 0)/a much less than 1.

Lock, James A.↗
NASA NTRS1980

Convolution of a Doppler line by a Gaussian instrument function

A simple and direct method is obtained for assessing the distortion of a Doppler line by a Gaussian instrument function. It is suggested that a close approximation to the width of a Gaussian instrument function, or an almost Gaussian function, may be obtained by measuring a line with a Doppler absorption coefficient. The method is applicable to diode laser measurements, and may be used whenever a Gaussian instrument function is a reasonable approximation to real conditions

Fridovich, B.↗
NASA NTRS2004

Bayesian Vision for Shape Recovery

We present a new Bayesian vision technique that aims at recovering a shape from two or more noisy observations taken under similar lighting conditions. The shape is parametrized by a piecewise linear height field, textured by a piecewise linear irradiance field, and we assume Gaussian Markovian priors for both shape vertices and irradiance variables. The observation process. also known as rendering, is modeled by a non-affine projection (e.g. perspective projection) followed by a convolution with a piecewise linear point spread function. and contamination by additive Gaussian noise. We assume that the observation parameters are calibrated beforehand. The major novelty of the proposed method consists of marginalizing out the irradiances considered as nuisance parameters, which is achieved by Laplace approximations. This reduces the inference to minimizing an energy that only depends on the shape vertices, and therefore allows an efficient Iterated Conditional Mode (ICM) optimization scheme to be implemented. A Gaussian approximation of the posterior shape density is computed, thus providing estimates both the geometry and its uncertainty. We illustrate the effectiveness of the new method by shape reconstruction results in a 2D case. A 3D version is currently under development and aims at recovering a surface from multiple images, reconstructing the topography by marginalizing out both albedo and shading.

Jalobeanu, Andre↗
NASA NTRS1982

Error probabilities in optical PPM receivers with Gaussian mixture densities

A Gaussian mixture density arises when a discrete variable (e.g., a photodetector count variable) is added to a continuous Gaussian variable (e.g., thermal noise). Making use of some properties of photomultiplier Gaussian mixture distributions, some approximate error probability formulas can be derived. These appear as averages of M-ary orthogonal Gaussian error probabilities. The use of a pure Gaussian assumption is considered, and when properly defined, appears as an accurate upper bound to performance.

Gagliardi, R. M.↗
NASA NTRS1987

Optical communication with semiconductor laser diodes

A 25 megabit/sec direct detection optical communication system that used Q=4 PPM signalling was constructed and its performance measured under laboratory conditions. The system used a single-mode AlGaAs laser diode transmitter and low noise silicon avalanche photodiode (APD) photodetector. Comparison of measured performance with the theoretical revealed that modeling the APD output as a Gaussian process under conditions of negligible background radiation and low (less than 10 to the -12 power A) APD bulk leakage currents leads to substantial underestimates of optimal APD gain to use and overestimates of system bit error probability. A procedure is given to numerically compute system performance which uses the more accurate Webb's Approximation of the exact Conradi distribution for the APD ouput signal that does not require excessive amounts of computer time (a few minutes of VAX 8600 CPU time per system operating point). Examples are given which illustrate the breakdown of the Gaussian approximation in assessing system performance. This system achieved a bit error probability of 10 to the -6 power at a received signal energy corresponding to an average of 60 absorbed photons/bit and optimal APD gain of 700.

Davidson, F.↗
NASA NTRS1985

The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.

Reimers, J. R.↗
DOE OSTI2026

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential applications in specialized areas such as segmented inverse beta decay neutrino detectors, astronomy, machine learning, and more. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Physics↗
DOE OSTI2025

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential for specialized applications in segmented inverse beta decay (IBD) neutrino detectors, astronomy, machine learning, and more. Although this method may easily extend to 3D scalar fields, our focus here is on 2D real-valued fields as it directly applies to directionality. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Data Analysis, Statistics and Probability (physics↗
DOE OSTI2022

Dark Energy Survey Year 3 results: Measurement of the baryon acoustic oscillations with three-dimensional clustering

The three-dimensional correlation function offers an effective way to summarize the correlation of the large-scale structure even for imaging galaxy surveys. We have applied the projected three-dimensional correlation function, ξ p to measure the baryonic acoustic oscillations (BAO) scale on the first-three years Dark Energy Survey data. The sample consists of about 7 million galaxies in the redshift range 0.6< z p < 1.1 over a footprint of 4108 deg 2 . Our theory modeling includes the impact of realistic true redshift distributions beyond Gaussian photo-z approximation. ξ p is obtained by projecting the three-dimensional correlation to the transverse direction. To increase the signal-to-noise of the measurements, we have considered a Gaussian stacking window function in place of the commonly used top-hat. ξ p is sensitive to D M (z eff )/r s , the ratio between the comoving angular diameter distance and the sound horizon. Using the full sample, D M (z eff )/r s is constrained to be19.00 ± 0.67 (top-hat) and 19.15 ± 0.58 (Gaussian) at z eff = 0.835. The constraint is weaker than the angular correlation w constraint 18.84 ± 0.50), and we trace this to the fact that the BAO signals are heterogeneous across redshift. While ξ p responds to the heterogeneous signals by enlarging the error bar, w can still give a tight bound on D M s in this case. When a homogeneous BAO-signal subsample in the range 0.7 < z p <1.0 (z eff = 0.845) is considered, ξp yields 19.80 ± 0.67 (top-hat) and 19.84 ± 0.53 (Gaussian). The latter is mildly stronger than the w constraint (19.86 ± 0.55). We find that the ξ p results are more sensitive to photo-z because ξ p keeps the three-dimensional clustering information causing it to be more prone to photo-z noise. The Gaussian window gives more robust results than the top-hat as the former is designed to suppress the low signal modes. ξ p and the angular statistics such as w have their own pros and cons, and they serve an important crosscheck with each other.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1993

Near grazing scattering from non-Gaussian ocean surfaces

We investigate the behavior of the scattered electromagnetic waves from non-Gaussian ocean surfaces at near grazing incidence. Even though the scattering mechanisms at moderate incidence angles are relatively well understood, the same is not true for near grazing rough surface scattering. However, from the experimental ocean scattering data, it has been observed that the backscattering cross section of a horizontally polarized wave can be as large as the vertical counterpart at near grazing incidence. In addition, these returns are highly intermittent in time. There have been some suggestions that these unexpected effects may come from shadowing or feature scattering. Using numerical scattering simulations, it can be shown that the horizontal backscattering cannot be larger than the vertical one for the Gaussian surfaces. Our main objective of this study is to gain a clear understanding of scattering mechanisms underlying the near grazing ocean scattering. In order to evaluate the backscattering cross section from ocean surfaces at near grazing incidence, both the hydrodynamic modeling of ocean surfaces and an accurate near grazing scattering theory are required. For the surface modeling, we generate Gaussian surfaces from the ocean surface power spectrum which is derived using several experimental data. Then, weakly nonlinear large scale ocean surfaces are generated following Longuet-Higgins. In addition, the modulation of small waves by large waves is included using the conservation of wave action. For surface scattering, we use MOM (Method of Moments) to calculate the backscattering from scattering patches with the two scale shadowing approximation. The differences between Gaussian and non-Gaussian surface scattering at near grazing incidence are presented.

Kim, Yunjin↗
DOE OSTI2022

Clustering with general photo- z uncertainties: application to Baryon Acoustic Oscillations

ABSTRACT Photometric data can be analysed using the 3D correlation function ξp to extract cosmological information via e.g. measurement of the Baryon Acoustic Oscillations (BAO). Previous studies modeled ξp assuming a Gaussian photo-z approximation. In this work we improve the modeling by incorporating realistic photo-z distribution. We show that the position of the BAO scale in ξp is determined by the photo-z distribution and the Jacobian of the transformation. The latter diverges at the transverse scale of the separation s⊥, and it explains why ξp traces the underlying correlation function at s⊥, rather than s, when the photo-z uncertainty σz/(1+ z) ≳ 0.02. We also obtain the Gaussian covariance for ξp. Due to photo-z mixing, the covariance of ξp shows strong off-diagonal elements. The high correlation of the data causes some issues to the data fitting. None the less, we find that either it can be solved by suppressing the largest eigenvalues of the covariance or it is not directly related to the BAO. We test our BAO fitting pipeline using a set of mock catalogs. The data set is dedicated for Dark Energy Survey Year 3 (DES Y3) BAO analyses and includes realistic photo-z distributions. The theory template is in good agreement with mock measurement. Based on the DES Y3 mocks, ξp statistic is forecast to constrain the BAO shift parameter α to be 1.001 ± 0.023, which is well consistent with the corresponding constraint derived from the angular correlation function measurements. Thus, ξp offers a competitive alternative for the photometric data analyses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Nonlinear sparse Bayesian learning for physics-based models

This paper addresses the issue of overfitting while calibrating unknown parameters of over-parameterized physics-based models with noisy and incomplete observations. Here, a semi-analytical Bayesian framework of nonlinear sparse Bayesian learning (NSBL) is proposed to identify sparsity among model parameters during Bayesian inversion. NSBL offers significant advantages over machine learning algorithm of sparse Bayesian learning (SBL) for physics-based models, such as 1) the likelihood function or the posterior parameter distribution is not required to be Gaussian, and 2) prior parameter knowledge is incorporated into sparse learning (i.e. not all parameters are treated as questionable). NSBL employs the concept of automatic relevance determination (ARD) to facilitate sparsity among questionable parameters through parameterized prior distributions. The analytical tractability of NSBL is enabled by employing Gaussian ARD priors and by building a Gaussian mixture-model approximation of the posterior parameter distribution that excludes the contribution of ARD priors. Subsequently, type-II maximum likelihood is executed using Newton's method whereby the evidence and its gradient and Hessian information are computed in a semi-analytical fashion. We show numerically and analytically that SBL is a special case of NSBL for linear regression models. Subsequently, a linear regression example involving multimodality in both parameter posterior pdf and model evidence is considered to demonstrate the performance of NSBL in cases where SBL is inapplicable. Next, NSBL is applied to identify sparsity among the damping coefficients of a mass-spring-damper model of a shear building frame. These numerical studies demonstrate the robustness and efficiency of NSBL in alleviating overfitting during Bayesian inversion of nonlinear physics-based models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

A test of the adhesion approximation for gravitational clustering

We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

Melott, Adrian L.↗