Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Gaussian distribution”

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 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Scattering of 42-MeV alpha particles from Cu-65

The extended particle-core coupling model was used to predict the properties of low-lying levels of Cu-65. A 42-MeV alpha particle cyclotron beam was used for the experiment. The experiment included magnetic analysis of the incident beam and particle detection by lithium-drifted silicon semiconductors. Angular distributions were measured for 10 to 50 degrees in the center of mass system. Data was reduced by fitting the peaks with a skewed Gaussian function using a least squares computer program with a linear background search. The energy calibration of each system was done by pulsar, and the excitation energies are accurate to + or - 25 keV. The simple weak coupling model cannot account for the experimentally observed quantities of the low-lying levels of Cu-65. The extended particle-core calculation showed that the coupling is not weak and that considerable configuration mixing of the low-lying states results.

Stewart, W. M.↗
NASA NTRS1994

Modes in light wave propagating in semiconductor laser

The study of semiconductor laser based on an analogy of the Schrodinger equation and an equation describing light wave propagation in nonhomogeneous medium is developed. The active region of semiconductor laser is considered as optical waveguide confining the electromagnetic field in the cross-section (x,y) and allowing waveguide propagation along the laser resonator (z). The mode structure is investigated taking into account the transversal and what is the important part of the suggested consideration longitudinal nonhomogeneity of the optical waveguide. It is shown that the Gaussian modes in the case correspond to spatial squeezing and correlation. Spatially squeezed two-mode structure of nonhomogeneous optical waveguide is given explicitly. Distribution of light among the laser discrete modes is presented. Properties of the spatially squeezed two-mode field are described. The analog of Franck-Condon principle for finding the maxima of the distribution function and the analog of Ramsauer effect for control of spatial distribution of laser emission are discussed.

Manko, Margarita A.↗
DOE OSTI2025

A Scalable Gaussian Process Approach to Shear Mapping with MuyGPs

Analysis of cosmic shear is an integral part of understanding structure growth across cosmic time, which in turn provides us with information about the nature of dark energy. Conventional methods generate shear maps from which we can infer the matter distribution in the universe. Current methods (e.g., Kaiser–Squires inversion) for generating these maps, however, are tricky to implement and can introduce bias. Recent alternatives construct a spatial process prior for the lensing potential, which allows for inference of the convergence and shear parameters given lensing shear measurements. Realizing these spatial processes, however, scales cubically in the number of observations—an unacceptable expense as near-term surveys expect billions of correlated measurements. Therefore, we present a linearly scaling shear map construction alternative using a scalable Gaussian process prior called MuyGPs. MuyGPs avoids cubic scaling by conditioning interpolation on only nearest neighbors and fits hyperparameters using batched leave-one-out cross-validation. This work is the first step toward a full, scalable mass mapping method. We work in a simplified regime where we validate our method by interpolating and analyzing maps given noisy point-estimate data from all three shear fields, taken from a suite of N -body ray-tracing simulations. We also show that we can perform these operations at the scale of billions of galaxies on high-performance computing platforms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Probability Density Function Control for Stochastic Nonlinear Systems using Monte Carlo Simulation

This paper presents a fast implementation framework of output probability density function (PDF) control for a class of stochastic nonlinear systems which are subjected to non-Gaussian noises. The statistical properties of the system outputs can be adjusted by shaping the dynamic output probability density function to track the reference stochastic distribution. However, the dynamic probability density function evolution is very difficult to obtain analytically even if the system model and the stochastic distributions of the noises are known. Motivated by Monte Carlo simulation, the dynamic probability density function can be estimated by sampling data which forms the contribution of this paper. In particular, the sampling points are generated following the stochastic distribution of the noise for each instant. These points go through the system would generate the histogram for system outputs, then the dynamic model can be established based on the dynamic histogram which reflects the randomness and the nonlinear dynamics of the investigated system. Based on the established model, the output probability density function tracking can be achieved and the simulation results and discussions show the effectiveness and benefits of the presented framework.

Zhang, Qichun↗
DOE OSTI2025

Effect of likelihood misspecification in Gaussian process-driven autonomous experimentation

In recent years, several groups have designed Autonomous Experiment (AE) models with the aim of using them as an alternative method for neutron scattering scanning. In an AE, Gaussian processes (GPs) are most frequently used due to their interpretability, their non-parametric nature, their universal approximation, and their closed-form predictive distribution. GPs have two key components, namely, the model for the likelihood of a neutron count knowing the underlying dynamic structure factor and the acquisition function. In this paper, we investigate the impact, on the quality of an AE, of the likelihood and acquisition function choices, in energy scans and (Q, ω) ones, with respect to the signal-over-noise ratio. While we hypothesized that the quality of GP predictions would decrease when the normal to Poisson likelihood approximation breaks down at low count rates, we found that the use of the correct Poisson likelihood does not improve the quality of the data collected, as well as yields very poor results in (Q, ω) scans at low count rates. In fact, the best results are obtained with a combination of normal likelihood, including the observation noise, and the change in variance acquisition function. In addition, we find that the performance, or quality of the predictive distribution, is a misleading measure of efficiency, that is, of the quality of the data collected.

Perryman, David Elliott [Inst. Laue-Langevin (ILL)↗
DOE OSTI2024

Parasitic Modulation of Microwave Signals by a Hypersonic Plasma Layer

During hypersonic flight, compressional and viscous heating of the air can form a plasma layer which encases the aircraft. If the boundary layer becomes turbulent, then the electron density fluctuations can effect a parasitic modulation in microwave signals transmitted through the plasma. We developed an approach for studying the interaction of microwave signals with a turbulent, hypersonic plasma layer. The approach affords a great deal of flexibility in both the plasma layer model and the antenna configuration. We then analyzed a situation in which microwaves, transmitted from a rectangular aperture antenna, propagate through a turbulent plasma layer to a distant receiver. We characterized the first-and second-order statistics of the computed parasitic modulation and quantified the depolarization of the signal. The amplitude fluctuations are lognormally distributed at low frequencies and Rice-distributed at high frequencies. Fluctuations in the copolarized phase and amplitude of the far-field signal are strongly anticorrelated. Here, we used a multioutput Gaussian process (MOGP) to model these quantities. The efficacy of the MOGP model is demonstrated by recovering the time evolution of the copolarized phase given the copolarized amplitude and occasional measurements of the phase.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

Efficient numerical method for computation of the thermohydrodynamics of laminar lubricating films

The purpose of this paper is to describe an accurate, yet economical, method for computing temperature effects in laminar lubricating films in two dimensions. Because of the marked dependence of lubricant viscosity on temperature, the effect of viscosity variation both across and along a lubricating film can dwarf other deviations from ideal constant-property lubrication. In practice, a thermohydrodynamics program will involve simultaneous solution of the film lubrication problem, together with heat conduction in a solid, complex structure. In pursuit of computational economy, techniques similar to those for Gaussian quadrature are used; it is shown that, for many purposes, the use of just two properly positioned temperatures (Lobatto points) characterizes the transverse temperature distribution.

Elrod, H. G.↗
DOE OSTI2021

A method for predicting failure statistics for steady state elevated temperature structural components

This paper presents the initial development of a high temperature life prediction method that accounts for the variability in the material properties of Grade 91 steel. The method accounts for material variability by fitting a variable 3-parameter Weibull distribution to experimental rupture data and accounts for the variability of creep deformation on the steady-state stresses via a Monte Carlo approach. To ensure reasonable computational times, the model represents the material as an extremely viscous Stokes fluid with a non-Newtonian viscosity, therefore solving the stress relaxation problem with a steady, static, instead of transient, analysis. Furthermore, the complete statistical analysis combines this model for creep deformation with a probabilistic model for creep rupture to evaluate the probability of premature failure for a set of sample problems, comparing the predicted failure statistics to the design life predicted by the ASME Boiler and Pressure Vessel Code rules.

42 ENGINEERING↗
DOE OSTI2023

A Multi-Fidelity Gaussian Process Regression Method for Probabilistic Wind Farm Power Curve Estimation

Accurate estimation of the power curve for wind turbines or wind farms is crucial to ensure their efficient operation and management. However, conventional methods for power curve estimation rely either on expensive and infrequent measurements or on low-quality numerical simulations. Moreover, the majority of previous studies on power curve estimation for wind turbines or wind farms focused on deterministic estimation, which provides a point estimate of the relationship between wind speed and power generation. Nevertheless, the deterministic approach fails to consider the inherent uncertainty associated with wind energy production resulting from varying turbine characteristics. This can lead to inaccurate power generation estimation and suboptimal decisions regarding energy management. In this paper, a kernel density estimation (KDE) based Multi-Fidelity Gaussian Process Regression (MFGPR) model is proposed to fuse theoretical power curve data and the ground true measurements to create a mapping of wind speed and wind power. By conducting a case study on an actual wind farm in China, the efficacy of the proposed MFGPR model was demonstrated in characterizing the variability of wind power. The probabilistic MFGPR model was also able to generate confidence intervals that encompassed the measured power, thereby improving the accuracy and confidence in wind power estimation or wind resource assessment. Overall, the proposed MFGPR model offers a reliable approach to integrate high-fidelity ground measurements and theoretical power curve data, resulting in precise wind resource assessment and power estimation.

Gaussian process regression↗
DOE OSTI2020

Surface Cloud Grid Version 2 (SFCCLDGRID2) Value-Added Product: Description of Update"

This document describes the algorithm used for the Surface Cloud Grid Value-Added Product (VAP). This VAP uses as input the 15-min. output from the Shortwave (SW) Flux Analysis VAP (see Long 2001; Long and Ackerman 2000; Long et al. 1999) from the Atmospheric Radiation Measurement (ARM) Climate Reseach Facility (ACRF) Southern Great Plains (SGP) Central Facility and extended facilities. This network of 21 sites is unevenly spaced over northern Oklahoma into southern Kansas, covering an area from 95.5° to 99.5° west longitude and 34.5° to 38.5° north latitude. For research applications such as single-column modeling, an estimate of the cloud and cloud effects distribution over this entire domain is desirable. The Surface Cloud Grid VAP applies a multi-pass weighted sum analytic approximation technique (Caracena 1987), which uses Gaussian weighting and an imposed scale length, to interpolate to a 0.25° by 0.25° lat/long grid over the SGP domain. The output, like the input, includes solar elevation angles of 10° or greater.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Power Density Distributions in Electron Beams

Measuring and controlling the power density distribution of electron beams used for welding is critical for producing repeatable welds and for transferring welding parameters between different machines. On any given machine, the power density distribution is controlled by defocusing the beam relative to its sharpest focused condition. However, measuring the power density distribution can be difficult due to the intense nature of welding beams and is further complicated by imperfect electron optics that can distort the beam, making it difficult to quantify. The enhanced modified Faraday cup (EMFC) diagnostic method was used here for beam analysis that utilizes computed tomography to reconstruct the beam’s power density distribution. These results were compared to the International Standards Organization (ISO) method for characterizing laser beams using a second-moment D4σ calculation. For ideal Gaussian-shaped beams, both methods would give the same result. However, for imperfect beams, the calculated D4σ diameter was shown to be about 25% larger relative to the FWe2 diameter measured by the EMFC due to the heavier weighting of data in the tails of the beam by D4σ. Finally, although both methods produce repeatable welds, it is important to understand the differences in the reported beam diameters, divergence angles, and beam parameter products when transferring parameters between machines.

36 MATERIALS SCIENCE↗
NASA NTRS1978

Molecular collisions in a laser field - Effect of the laser linewidth

The effect of the laser linewidth on molecular collision processes taking place in a laser field is studied, using an approximation scheme that replaces the actual frequency distribution of the field by a finite number of frequencies and weights. The choice of the frequencies and weights is conveniently accomplished by the method of Gaussian quadrature. Close-coupling calculations are performed on model systems, and the results indicate that the neglect of the laser linewidth may be justified in most collision processes in a laser field.

Lee, H. W.↗
NASA NTRS1990

An analytical approach to gravitational lensing by an ensemble of axisymmetric lenses

The problem of gravitational lensing by an ensemble of identical axisymmetric lenses randomly distributed on a single lens plane is considered and a formal expression is derived for the joint probability density of finding shear and convergence at a random point on the plane. The amplification probability for a source can be accurately estimated from the distribution in shear and convergence. This method is applied to two cases: lensing by an ensemble of point masses and by an ensemble of objects with Gaussian surface mass density. There is no convergence for point masses whereas shear is negligible for wide Gaussian lenses.

Lee, Man Hoi↗
NASA NTRS1994

Comparison of dynamical approximation schemes for nonlinear gravitaional clustering

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.

Melott, Adrian L.↗
DOE OSTI2023

An Analysis of the Johnson-Lindenstrauss Lemma with the Bivariate Gamma Distribution

Probabilistic proofs of the Johnson-Lindenstrauss lemma imply that random projection can reduce the dimension of a data set and approximately preserve pairwise distances. If a distance being approximately preserved is called a success, and the complement of this event is called a failure, then such a random projection likely results in no failures. Assuming a Gaussian random projection, the lemma is proved by showing that the no-failure probability is positive using a combination of Bonferroni's inequality and Markov's inequality. This paper modifies this proof in two ways to obtain a greater lower bound on the no-failure probability. First, Bonferroni's inequality is applied to pairs of failures instead of individual failures. Second, since a pair of projection errors has a bivariate gamma distribution, this probability of a pair of successes is bounded using an inequality from [Jensen, 1969]. If n is the number of points to be embedded and μ is the probability of success, then this leads to an increase in the lower bound on the no-failure probability of $\frac{1}{2}$ ($\genfrac{}{}{0pt}{}{n}{2}$) (1- μ ) 2 is ($\genfrac{}{}{0pt}{}{n}{2}$) is even and $\frac{1}{2}$ (($\genfrac{}{}{0pt}{}{n}{2}$)-1) (1- μ ) 2 if ($\genfrac{}{}{0pt}{}{n}{2}$) is odd. For example, if n =10 5 points are to be embedded in k =10 4 dimensions with a tolerance of ϵ=0.1, then the improvement in the lower bound is on the order of 10 -14 . We also show that further improvement is possible if the inequality in [Jensen, 1969] extends to three successes, though we do not have a proof of this result.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
NASA NTRS2004

Gamma-Ray Burst Intensity Distributions

We use the lag-luminosity relation to calculate self-consistently the redshifts, apparent peak bolometric luminosities L(sub B1), and isotropic energies E(sub iso) for a large sample of BATSE bursts. We consider two different forms of the lag-luminosity relation; for both forms the median redshift, for our burst database is 1.6. We model the resulting sample of burst energies with power law and Gaussian dis- tributions, both of which are reasonable models. The power law model has an index of a = 1.76 plus or minus 0.05 (95% confidence) as opposed to the index of a = 2 predicted by the simple universal jet profile model; however, reasonable refinements to this model permit much greater flexibility in reconciling predicted and observed energy distributions.

Band, David L.↗
DOE OSTI2023

A Stochastic Approach to Reconstruct Gamma-Ray-burst Light Curves

Gamma-ray bursts (GRBs), as they are observed at high redshift ( z = 9.4), are vital to cosmological studies and investigating Population III stars. To tackle these studies, we need correlations among relevant GRB variables with the requirement of small uncertainties on their variables. Thus, we must have good coverage of GRB light curves (LCs). However, gaps in the LC hinder the precise determination of GRB properties and are often unavoidable. Therefore, extensive categorization of GRB LCs remains a hurdle. We address LC gaps using a stochastic reconstruction, wherein we fit two preexisting models (the Willingale model; W07; and a broken power law; BPL) to the observed LC, then use the distribution of flux residuals from the original data to generate data to fill in the temporal gaps. We also demonstrate a model-independent LC reconstruction via Gaussian processes. At 10% noise, the uncertainty of the end time of the plateau, its correspondent flux, and the temporal decay index after the plateau decreases by 33.3%, 35.03%, and 43.32% on average for the W07, and by 33.3%, 30.78%, 43.9% for the BPL, respectively. The uncertainty of the slope of the plateau decreases by 14.76% in the BPL. After using the Gaussian process technique, we see similar trends of a decrease in uncertainty for all model parameters for both the W07 and BPL models. These improvements are essential for the application of GRBs as standard candles in cosmology, for the investigation of theoretical models, and for inferring the redshift of GRBs with future machine-learning analyses.

79 ASTRONOMY AND ASTROPHYSICS↗