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At least 109 records · Page 6
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NASA NTRS1986

Scattering from mirrors contaminated by particulates - A model

A model has been used to fit the bidirectional reflectance distribution function for a variety of samples with different angles of incidence and degrees of contamination and roughness by the proper adjustment of six parameters. Exponential and Gaussian composite surface height autocorrelation functions are used to simulate the data at the small and medium angles, and a perturbation of these functions with two additional parameters allows the fit of the upward and downward curve portions of the data at the large angles. Good agreement is found with previous results. The present approach is the same as the classical dispersion equation in treating the index of refraction of optical materials.

Wang, Yaujen↗
NASA NTRS2002

Eulerian Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows

The Eulerian mapping closure approach is developed for uncertainty propagation in computational fluid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear flow. An analytical argument shows that fluctuation of the concentration field at one point in space is non-Gaussian and exhibits stretched exponential form. An Eulerian mapping approach provides an appropriate approximation to both convection and diffusion terms and leads to a closed mapping equation. The results obtained describe the evolution of the initial Gaussian field, which is in agreement with direct numerical simulations.

He, Guowei↗
NASA NTRS1999

Tilt Modulation Distortions in Wave Topography Measured by a Scanning Radar Altimeter

Work continues on estimating tilt modulation distortions in the wave topography measured by a scanning radar altimeter. To quantify this effect, a two-dimensional simulation has been performed in the cross-track plane only which assumed that sinusoidal waves of constant wavelength propagate in the cross-track direction (and are infinitely long-crested in the along-track direction). The initial results reported earlier for a Gaussian surface scattering model indicated that when the highest reasonable value of mss is used in the simulation (the Plant limit of 0.08), the nadir values of the ratio of the apparent to actual wave height are the same as for the omnidirectional scattering case. But as the off-nadir angle increased, the apparent wave height increased and became larger than the actual wave height by about 10 degrees off-nadir. And the shorter the wavelength, the larger the apparent wave height increase. This represented a systematic over-estimate of the wave amplitude for waves propagating in the cross-track direction. For lower values of mss the situation worsened. The simulation has been improved by incorporating actual variations of backscattered power with incidence angle measured by the SRA instead of the Gaussian model. The resulting distortion was about half that originally reported. The 3-dimensional simulation to model waves propagating at various azimuthal angles relative to the cross-track plane is still in progress. The results of this model will be verified by comparing them with Scanning Radar Altimeter (SRA) data and optimum correction procedures will be developed. An assessment of the improved 2-dimensional model indicates that the distortion will generally be small in the data taken during the Southern Ocean Waves Experiment (SOWEX) presently be analyzed. But tilt modulation effects are of great concern for SRA data collected during the 1998 hurricane season since the minimum aircraft altitude was 1.5 km and it frequently flew higher. For a given wave length and steepness, the effect increases with increasing aircraft altitude, and is larger for waves propagating in the cross-track direction, which was generally the situation during the hurricane flights.

Walsh, Edward J.↗
NASA NTRS1994

Voids and constraints on nonlinear clustering of galaxies

Void statistics of the galaxy distribution in the Center for Astrophysics Redshift Survey provide strong constraints on galaxy clustering in the nonlinear regime, i.e., on scales R equal to or less than 10/h Mpc. Computation of high-order moments of the galaxy distribution requires a sample that (1) densely traces the large-scale structure and (2) covers sufficient volume to obtain good statistics. The CfA redshift survey densely samples structure on scales equal to or less than 10/h Mpc and has sufficient depth and angular coverage to approach a fair sample on these scales. In the nonlinear regime, the void probability function (VPF) for CfA samples exhibits apparent agreement with hierarchical scaling (such scaling implies that the N-point correlation functions for N greater than 2 depend only on pairwise products of the two-point function xi(r)) However, simulations of cosmological models show that this scaling in redshift space does not necessarily imply such scaling in real space, even in the nonlinear regime; peculiar velocities cause distortions which can yield erroneous agreement with hierarchical scaling. The underdensity probability measures the frequency of 'voids' with density rho less than 0.2 -/rho. This statistic reveals a paucity of very bright galaxies (L greater than L asterisk) in the 'voids.' Underdensities are equal to or greater than 2 sigma more frequent in bright galaxy samples than in samples that include fainter galaxies. Comparison of void statistics of CfA samples with simulations of a range of cosmological models favors models with Gaussian primordial fluctuations and Cold Dark Matter (CDM)-like initial power spectra. Biased models tend to produce voids that are too empty. We also compare these data with three specific models of the Cold Dark Matter cosmogony: an unbiased, open universe CDM model (omega = 0.4, h = 0.5) provides a good match to the VPF of the CfA samples. Biasing of the galaxy distribution in the 'standard' CDM model (omega = 1, b = 1.5; see below for definitions) and nonzero cosmological constant CDM model (omega = 0.4, h = 0.6 lambda(sub 0) = 0.6, b = 1.3) produce voids that are too empty. All three simulations match the observed VPF and underdensity probability for samples of very bright (M less than M asterisk = -19.2) galaxies, but produce voids that are too empty when compared with samples that include fainter galaxies.

Vogeley, Michael S.↗
NASA NTRS1976

Development and application of an atmospheric turbulence model for use in flight simulators in flight simulators

The influence of simulated turbulence on aircraft handling qualities was investigated. Pilot opinion of the handling qualities of a light general aviation aircraft were evaluated in a motion-base simulator using a simulated turbulence environment. A realistic representation of turbulence disturbances is described in terms of rms intensity and scale length and their random variations with time. The time histories generated by the proposed turbulence models showed characteristics which appear to be more similar to real turbulence than the frequently-used Gaussian turbulence model. In addition, the proposed turbulence models can flexibly accommodate changes in atmospheric conditions and be easily implemented in flight simulator studies. Six turbulence time histories, including the conventional Gaussian model, were used in an IFR-tracking task. The realism of each of the turbulence models and the handling qualities of the simulated airplane were evaluated. Analysis of pilot opinions shows that at approximately the same rms intensities of turbulence, the handling quality ratings transit from the satisfactory level, for the simple Gaussian model, to an unacceptable level for more realistic and compositely structured turbulence models.

Jacobson, I. D.↗
NASA NTRS1994

Mean sea surface height of the Antarctic Circumpolar Current from Geosat data: Method and application

The mean sea surface height across the Antarctic Circumpolar Current (ACC) has been reconstructed from height variability measured by the Geosat altimeter without assuming prior knowledge of the geoid. For this study, an automated technique has been developed to estimate mean sea surface height for each satellite ground track using a meandering Gaussian jet model, and errors have been estimated using Monte Carlo simulation. The results are objectively mapped to produce a picture of the mean Subantarctic and Polar Fronts, which together comprise the major components of the Antarctic Circumpolar Current. The meandering jet model explains between 40% and 70% of the height variance along the jet axes. The results show that the fronts are substantially steered by topography and that the jets have an average Gaussian width of about 44 km in the meridional direction and meander about 75 km to either side of their mean locations. The average height difference across the Subantarctic Front (SAF) is 0.7 m and across the Polar Front (PF) 0.6 m. The mean widths of the fronts are correlated with the size of the baroclinic Rossby radius.

Gille, Sarah T.↗
NASA NTRSDate not supplied

Sampling Functions from Gaussian Processes and Structured Covariance Gaussian Networks

When learning aerodynamic models from data, it is critical to incorporate estimates of model uncertainty. This motivates the design of probabilistic aerodynamic databases which can be sampled to generate physically and statistically plausible aerodynamic models. In this talk we discuss how to sample deterministic functions from two different kinds of probabilistic models and demonstrate their use. First, Gaussian Process Regressors (GPRs) are a widely used probabilistic kernel-based model which can be thought of as Gaussian distributions over functions. GPRs are generally trained by maximizing the marginal likelihood of seeing the training data over the kernel parameter space. Sample functions are easily generated by drawing points from the Gaussian distribution at desired input points. However, when the points are not known ahead of time, the classical sampling approach is not possible since successive function samples will generate different function realizations. We present an approach for sampling consistent function evaluations from a GPR over multiple samples. Second, we describe a neural network architecture which learns a conditional Gaussian distribution by maximizing the marginal likelihood at each point in the input space. We then discuss and compare several options for generating sample functions which match this distribution. Finally, we demonstrate the use of these probabilistic aerodynamic models in an atmospheric reentry simulation.

Gaussian process regression↗
NASA NTRS1976

Use of thin ionization calorimeters for measurements of cosmic ray energy spectra

The reliability of performing measurements of cosmic ray energy spectra with a thin ionization calorimeter was investigated. Monte Carlo simulations were used to determine whether energy response fluctuations would cause measured spectra to be different from the primary spectra. First, Gaussian distributions were assumed for the calorimeter energy resolutions. The second method employed a detailed Monte Carlo simulation of cascades from an isotropic flux of protons. The results show that as long as the energy resolution does not change significantly with energy, the spectral indices can be reliably determined even for sigma sub e/e = 50%. However, if the energy resolution is strongly energy dependent, the measured spectra do not reproduce the true spectra. Energy resolutions greatly improving with energy result in measured spectra that are too steep, while resolutions getting much worse with energy cause the measured spectra to be too flat.

Jones, W. V.↗
NASA NTRS1996

An Overdetermined System for Improved Autocorrelation Based Spectral Moment Estimator Performance

Autocorrelation based spectral moment estimators are typically derived using the Fourier transform relationship between the power spectrum and the autocorrelation function along with using either an assumed form of the autocorrelation function, e.g., Gaussian, or a generic complex form and applying properties of the characteristic function. Passarelli has used a series expansion of the general complex autocorrelation function and has expressed the coefficients in terms of central moments of the power spectrum. A truncation of this series will produce a closed system of equations which can be solved for the central moments of interest. The autocorrelation function at various lags is estimated from samples of the random process under observation. These estimates themselves are random variables and exhibit a bias and variance that is a function of the number of samples used in the estimates and the operational signal-to-noise ratio. This contributes to a degradation in performance of the moment estimators. This dissertation investigates the use autocorrelation function estimates at higher order lags to reduce the bias and standard deviation in spectral moment estimates. In particular, Passarelli's series expansion is cast in terms of an overdetermined system to form a framework under which the application of additional autocorrelation function estimates at higher order lags can be defined and assessed. The solution of the overdetermined system is the least squares solution. Furthermore, an overdetermined system can be solved for any moment or moments of interest and is not tied to a particular form of the power spectrum or corresponding autocorrelation function. As an application of this approach, autocorrelation based variance estimators are defined by a truncation of Passarelli's series expansion and applied to simulated Doppler weather radar returns which are characterized by a Gaussian shaped power spectrum. The performance of the variance estimators determined from a closed system is shown to improve through the application of additional autocorrelation lags in an overdetermined system. This improvement is greater in the narrowband spectrum region where the information is spread over more lags of the autocorrelation function. The number of lags needed in the overdetermined system is a function of the spectral width, the number of terms in the series expansion, the number of samples used in estimating the autocorrelation function, and the signal-to-noise ratio. The overdetermined system provides a robustness to the chosen variance estimator by expanding the region of spectral widths and signal-to-noise ratios over which the estimator can perform as compared to the closed system.

Keel, Byron M.↗
NASA NTRS1990

High accuracy optical rate sensor

Optical rate sensors, in particular CCD arrays, will be used on Space Station Freedom to track stars in order to provide inertial attitude reference. An algorithm to provide attitude rate information by directly manipulating the sensor pixel intensity output is presented. The star image produced by a sensor in the laboratory is modeled. Simulated, moving star images are generated, and the algorithm is applied to this data for a star moving at a constant rate. The algorithm produces accurate derived rate of the above data. A step rate change requires two frames for the output of the algorithm to accurately reflect the new rate. When zero mean Gaussian noise with a standard deviation of 5 is added to the simulated data of a star image moving at a constant rate, the algorithm derives the rate with an error of 1.9 percent at a rate of 1.28 pixels per frame.

Uhde-Lacovara, J.↗
NASA NTRS1990

A line-of-sight performance criterion for controller design of a proposed laboratory model

A line-of-sight performance criterion is derived for a proposed Controls Structures Interaction model, and its many uses in the control design process for fine pointing control are illustrated. A linearized line-of-sight (LOS) criterion is used for direct controller design and as a performance measure to judge different control methodologies. Numerical simulation results are shown where the three approaches: linear quadratic Gaussian theory, robust eigensystem assignment, and local velocity feedback are used for vibration control. Results indicate that the linear quadratic Gaussian controller, which incorporates a linearized LOS weighting matrix directly, yields good performance without wasting energy to control motions that have no influence on the LOS.

Lim, Kyong B.↗
NASA NTRS1989

Equivalent linearization for fatigue life estimates of a nonlinear structure

An analysis is presented of the suitability of the method of equivalent linearization for estimating the fatigue life of a nonlinear structure. Comparisons are made of the fatigue life of a nonlinear plate as predicted using conventional equivalent linearization and three other more accurate methods. The excitation of the plate is assumed to be Gaussian white noise and the plate response is modeled using a single resonant mode. The methods used for comparison consist of numerical simulation, a probabalistic formulation, and a modification of equivalent linearization which avoids the usual assumption that the response process is Gaussian. Remarkably close agreement is obtained between all four methods, even for cases where the response is significantly linear.

Miles, R. N.↗
NASA NTRS1989

Equivalent linearization for fatigue life estimates of a nonlinear structure

An analysis is presented of the suitability of the method of equivalent linearization for estimating the fatigue life of a nonlinear structure. Comparisons are made of the fatigue life of a nonlinear plate as predicted using conventional equivalent linearization and three other more accurate methods. The excitation of the plate is assumed to be Gaussian white noise and the plate response is modeled using a single resonant mode. The methods used for comparison consist of numerical simulation, a probabilistic formulation, and a modification of equivalent linearization which avoids the usual assumption that the response process is Gaussian. Remarkably close agreement is obtained between all four methods, even for cases where the response is significantly linear.

Miles, R. N.↗
NASA NTRS1972

Digital simulation of hybrid loop operation in RFI backgrounds.

A digital computer model for Monte-Carlo simulation of an imperfect second-order hybrid phase-locked loop (PLL) operating in radio-frequency interference (RFI) and Gaussian noise backgrounds has been developed. Characterization of hybrid loop performance in terms of cycle slipping statistics and phase error variance, through computer simulation, indicates that the hybrid loop has desirable performance characteristics in RFI backgrounds over the conventional PLL or the costas loop.

Ziemer, R. E.↗
NASA NTRS1976

MHD solution of interplanetary disturbances generated by simulated velocity perturbations

An MHD time-dependent numerical simulation, restricted to the solar equatorial plane, is used to demonstrate the interplanetary disturbances caused by several simplified coronal holes. Each 'hole' is assumed to have a configuration such that the higher solar wind velocity produced within their longitudinal extent is Gaussian over a 7-day period at the inner boundary (0.3 AU) of the numerical simulation. A second, twin coronal hole is assumed to rotate on the solar disk behind its predecessor. It is shown that the first coronal hole-produced interplanetary shock ensemble is overtaken by the second ensemble because of the higher velocity, lower density environment into which the latter propagates. A number of features predicted by MHD similarity theory are confirmed by the numerical simulation. These features include (1) strong azimuthal magnetic and plasma density compression, accompanied with average temperature depression, at the contact surface between forward and reverse shock ensembles, and (2) increasing spatial separation distance between forward and reverse shocks.

Dryer, M.↗
NASA NTRS1973

On Digital Simulation of Multicorrelated Random Processes and Its Applications

Two methods are described to simulate, on a digital computer, a set of correlated, stationary, and Gaussian time series with zero mean from the given matrix of power spectral densities and cross spectral densities. The first method is based upon trigonometric series with random amplitudes and deterministic phase angles. The random amplitudes are generated by using a standard random number generator subroutine. An example is given which corresponds to three components of wind velocities at two different spatial locations for a total of six correlated time series. In the second method, the whole process is carried out using the Fast Fourier Transform approach. This method gives more accurate results and works about twenty times faster for a set of six correlated time series.

Sinha, A. K.↗