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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Use of the maximum entropy method to retrieve the vertical atmospheric ozone profile and predict atmospheric ozone content

A method is developed for prediction of ozone levels in planetary atmospheres. This method is formulated in terms of error covariance matrices, and is associated with both direct measurements, a priori first guess profiles, and a weighting function matrix. This is described by the following linearized equation: y = A(matrix) x X + eta, where A is the weighting matrix and eta is noise. The problems to this approach are: (1) the A matrix is near singularity; (2) the number of unknowns in the profile exceeds the number of data points, therefore, the solution may not be unique; and (3) even if a unique solution exists, eta may cause the solution to be ill conditioned.

Turner, B. Curtis↗
NASA NTRS1985

A high-precision finite element method for shock-tube calculations

A two-pass explicit scheme is developed in order to exploit some of the capabilities of finite difference modeling (FDM) for finite element modeling (FEM), which offers the opportunity to account for any type of geometry in fluid flow modeling. Features of the first-order upwind and the Lax-Wendroff high precision explicit finite difference algorithms are reviewed. A flux limiter is developed for FEM to serve as an analog for the single limiter function which has been defined for the various FDMs. It is shown that an antidiffusive limiter must be introduced into the weighting function which normally multiplies the time-derivative term in the variational equation. The two-pass scheme which results is demonstrated to be the equivalent of FDMs with five-point support. However, the present scheme is valid only for one-dimensional calculations and linear shape functions for shock tube flow phenomena. Further work is required for its use with nonlinear hyperbolic systems.

Hughes, T. J. R.↗
NASA NTRS1990

Galerkin finite difference Laplacian operators on isolated unstructured triangular meshes by linear combinations

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formulae in Cartesian coordinates for the Laplacian operator on isolated unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator along with linear combinations of the residual equations are used to develop the algorithm. The algorithm was tested for a wide variety of unstructured meshes and found to give satisfactory results.

Baumeister, Kenneth J.↗
NASA NTRS1992

A contribution toward understanding the biospherical significance of Antarctic ozone depletion

The paper presents and compares measurements of biologically active UV radiation made by the NSF scanning spectroradiometer (UV-monitor) at Palmer Station, Antarctica, during the Austral springs of 1988, 1989, and 1990. Column ozone abundance above Palmer Station is computed from these measurements using a multiple wavelength algorithm. Two contrasting action spectra are employed to estimate the biologically relevant dose from the spectral measurements: a standard weighting function for damage to DNA, and a new action spectrum representing the potential for photosynthesis inhibition in Antarctic phytoplankton. The former weights only UV-B wavelengths (280-320 nm) and gives the most weight to wavelengths shorter than 300 nm, while the latter includes large contributions out to 355 nm. Ozone abundances and dose-weighted irradiances provided by the NSF UV-monitor are used to derive the radiation amplification factors for both DNA- and phytoplankton-effective irradiance.

Lubin, Dan↗
NASA NTRS1999

The Effect of the Weight Scheme on DFT Vibrational Frequencies

All-electron B3LYP harmonic frequencies of Ge2H5 and Ge2H6 are computed for several choices of grid and using both the Becke and the Stratmann, Scuseria, and Frisch atomic partition functions (weight scheme). For large grids, the results are independent of the weighting scheme. The lowest frequency mode is much more stable with respect to the number of grid points when the Stratmann, Scuseria, and Frisch weights are used.

Bauschlicher, Charles↗
NASA NTRS1995

Statistically generated weighted curve fit of residual functions for modal analysis of structures

A statistically generated weighting function for a second-order polynomial curve fit of residual functions has been developed. The residual flexibility test method, from which a residual function is generated, is a procedure for modal testing large structures in an external constraint-free environment to measure the effects of higher order modes and interface stiffness. This test method is applicable to structures with distinct degree-of-freedom interfaces to other system components. A theoretical residual function in the displacement/force domain has the characteristics of a relatively flat line in the lower frequencies and a slight upward curvature in the higher frequency range. In the test residual function, the above-mentioned characteristics can be seen in the data, but due to the present limitations in the modal parameter evaluation (natural frequencies and mode shapes) of test data, the residual function has regions of ragged data. A second order polynomial curve fit is required to obtain the residual flexibility term. A weighting function of the data is generated by examining the variances between neighboring data points. From a weighted second-order polynomial curve fit, an accurate residual flexibility value can be obtained. The residual flexibility value and free-free modes from testing are used to improve a mathematical model of the structure. The residual flexibility modal test method is applied to a straight beam with a trunnion appendage and a space shuttle payload pallet simulator.

Bookout, P. S.↗
NASA NTRS1992

On adaptive weighted polynomial preconditioning for Hermitian positive definite matrices

The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modern architectures. Standard techniques for choosing the preconditioning polynomial are based only on bounds for the extreme eigenvalues. Here a different approach is proposed, which aims at adapting the preconditioner to the eigenvalue distribution of the coefficient matrix. The technique is based on the observation that good estimates for the eigenvalue distribution can be derived after only a few steps of the Lanczos process. This information is then used to construct a weight function for a suitable Chebyshev approximation problem. The solution of this problem yields the polynomial preconditioner. In particular, we investigate the use of Bernstein-Szego weights.

Fischer, Bernd↗
NASA NTRS1994

On the Gibbs phenomenon 4: Recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function

We continue our investigation of overcoming Gibbs phenomenon, i.e., to obtain exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. We show that if we are given the first N Gegenbauer expansion coefficients, based on the Gegenbauer polynomials C(sub k)(sup mu)(x) with the weight function (1 - x(exp 2))(exp mu - 1/2) for any constant mu is greater than or equal to 0, of an L(sub 1) function f(x), we can construct an exponentially convergent approximation to the point values of f(x) in any subinterval in which the function is analytic. The proof covers the cases of Chebyshev or Legendre partial sums, which are most common in applications.

Gottlieb, David↗
NASA NTRS1999

A Comparative Study of Interferometric Regridding Algorithms

THe paper discusses regridding options: (1) The problem of interpolating data that is not sampled on a uniform grid, that is noisy, and contains gaps is a difficult problem. (2) Several interpolation algorithms have been implemented: (a) Nearest neighbor - Fast and easy but shows some artifacts in shaded relief images. (b) Simplical interpolator - uses plane going through three points containing point where interpolation is required. Reasonably fast and accurate. (c) Convolutional - uses a windowed Gaussian approximating the optimal prolate spheroidal weighting function for a specified bandwidth. (d) First or second order surface fitting - Uses the height data centered in a box about a given point and does a weighted least squares surface fit.

Hensley, Scott↗
NASA NTRS2013

Visible Contrast Energy Metrics for Detection and Discrimination

Contrast energy was proposed by Watson, Robson, & Barlow as a useful metric for representing luminance contrast target stimuli because it represents the detectability of the stimulus in photon noise for an ideal observer. Like the eye, the ear is a complex transducer system, but relatively simple sound level meters are used to characterize sounds. These meters provide a range of frequency sensitivity functions and integration times depending on the intended use. We propose here the use of a range of contrast energy measures with different spatial frequency contrast sensitivity weightings, eccentricity sensitivity weightings, and temporal integration times. When detection threshold are plotting using such measures, the results show what the eye sees best when these variables are taken into account in a standard way. The suggested weighting functions revise the Standard Spatial Observer for luminance contrast detection and extend it into the near periphery. Under the assumption that the detection is limited only by internal noise, discrimination performance can be predicted by metrics based on the visible energy of the difference images

Ahumada, Albert↗
NASA NTRS1983

An improvement in SAR image interpretability provided by post-correlation signal processing

A presentation on the basis of subjective analysis of computer-generated SAR imagery depicts the improvement in interpretability obtained by post-correlation signal processing. A parametric study was conducted to determine the improvement in interpretability obtained by the application of signal weighting functions on the post-processed returns. The results suggest that a marked improvement in interpretability results from symmetrizing the exponential distribution of the fading signal. Preliminary analysis indicates that signal weighting improves the contrast ratio between the mean value of adjacent homogeneous regions in a SAR scene.

Matthews, N. D.↗
NASA NTRS1987

Some numerical calculations by using linear classical sonic theories approached from sub- or supersonic speeds

The unsteady aerodynamics of a two-dimensional wing at sonic speed are studied by using so-called classical sonic theories (linear), approached from supersonic flow (M=1+0) or subsonic flow (M=1-0). In the former approach, the exact expressions of lift and lift distribution are obtained in terms of Fresnel integrals, while in the latter approach an integral equation must be solved, the kernel function of which is obtained from the subsonic Possio's equation and has a root singularity. The discrete analysis is adopted on the basis of the semicircle method (SCM) and the weighting function for subsonic-flow-Gauss-quadrature, as well as modified characteristics obtained from both approaches agree quite well with each other. The results obtained by the present computations are compared with those of DLM-C (subsonic 2D code) developed by ANDO et al, and are found to give a reasonable outer boundary for subsonic unsteady aerodynamics.

Yamamoto, Y.↗
NASA NTRS1993

A numerical approach to controller design for the ACES facility

In recent years the employment of active control techniques for improving the performance of systems involving highly flexible structures has become a topic of considerable research interest. Most of these systems are quite complicated, using multiple actuators and sensors, and possessing high order models. The majority of analytical controller synthesis procedures capable of handling multivariable systems in a systematic way require considerable insight into the underlying mathematical theory to achieve a successful design. This insight is needed in selecting the proper weighting matrices or weighting functions to cast what is naturally a multiple constraint satisfaction problem into an unconstrained optimization problem. Although designers possessing considerable experience with these techniques have a feel for the proper choice of weights, others may spend a significant amount of time attempting to find an acceptable solution. Another disadvantage of such procedures is that the resulting controller has an order greater than or equal to that of the model used for the design. Of course, the order of these controllers can often be reduced, but again this requires a good understanding of the theory involved.

Frazier, W. Garth↗
NASA NTRS2010

TPSAS-NF1676L-10658-DND

The systematic methodology for constructing fourth-order finite domain Energy Stable WENO schemes is developed. We prove that for hyperbolic systems, the finite domain ESWENO scheme is stable in the energy norm for both continuous and discontinuous solutions. The eigenvalues of the finite domain ESWENO dissipation operator are located in the left-half plane. Based on the rigorous truncation error analysis, the new weight functions are developed, which drastically improve the accuracy of the ESWENO scheme and provide excellent shock-capturing capabilities. Numerical experiments show that the new finite domain ESWENO scheme with the new weights outperform the conventional WENO schemes in terms of accuracy.

Travis Fisher↗
NASA NTRS1994

Adjustable Fiber Optic Microwave Transversal Filters

Microwave transversal filters implemented as adjustable tapped fiber optic delay lines developed. Main advantages of these filters (in comparison with conventional microwave transversal filters) are small size, light weight, no need for matching of radio-frequency impedances, no need for shielding against electromagnetic radiation at suboptical frequencies, no need for mechanical tuning, high stability of amplitude and phase, and active control of transfer functions. Weights of taps in fiber optic delay lines adjusted.

Shadaram, Mehdi↗
NASA NTRS1979

Weighting in digital synthetic aperture radar processing

Weighting is employed in synthetic aperture radar (SAR) processing to reduce the sidelobe response at the expense of peak center response height and mainlobe resolution. The weighting effectiveness in digital processing depends not only on the choice of weighting function, but on the fineness of sampling and quantization, on the time bandwidth product, on the quadratic phase error, and on the azimuth antenna pattern. The results of simulations conducted to uncover the effect of these parameters on azimuth weighting effectiveness are presented. In particular, it is shown that multilook capabilities of future SAR systems may obviate the need for consideration of the antenna pattern, and that azimuth time-bandwidth products of over 200 are probably required before the digital results begin to approach the ideal results.

Dicenzo, A.↗
NASA NTRSDate not supplied

Higher-Order Approximations for Stabilizing Zero-Energy Modes in Peridynamics Crystal Plasticity Models with Large Horizon Interactions

The non-ordinary state-based peridynamics theory combines non-local dynamic techniques with a desirable correspondence material principle, allowing for the use of continuum mechanics constitutive models. Such an approach presents a unique capability for solving problems involving discontinuities (e.g., strain localization, fracture, and fragmentation). However, the correspondence-based peridynamics models often suffer from zero-energy mode instabilities in numerical implementation, primarily due to the approximations of the non-local deformation gradient tensor. This paper focuses on a computational scheme for eliminating the zero-energy mode oscillations using a choice of influence functions that improve the truncation error in a higher-order Taylor series expansion of the deformation gradient. The novelty here is a tensor-based derivation of the linear constraint equations, which can be used to systematically identify the particle interaction weight functions for various user-specified horizon radii. In this paper, the proposed higher-order stabilization scheme is demonstrated for multi-dimensional examples involving polycrystalline and composite microstructures, along with comparisons against conventional finite element methods. The proposed stabilization scheme is shown to be highly effective in suppressing the spurious zero-energy mode oscillations in all numerical examples while enabling efficient simulations of strain localizations across material interfaces.

Non-Ordinary State-Based Peridynamics↗
NASA NTRS1982

The inverse problem of constructing a gravimetric geoid

Computation of a single geoidal height from gravity acceleration data formally requires that the latter be known everywhere on the earth. A computational procedure based on linear inverse theory for estimating geoidal heights from incomplete sets of data is presented. The same scheme can be used to estimate gravity accelerations from altimetry-derived geoids. The systematic error owing to lack of data and the choice of a particular inverse operator is described by using resolution functions and their spherical harmonic expansions. An rms value of this error is also estimated by assuming a spectrum for the unknown geoid. The influence of the size of the data region, the spacing between data, the filtering applied to the data, and the model weighting function chosen are all quantified in a spherical geometry. The examples presented show that when low degree spherical harmonic coefficients are available - from satellite orbit analysis - a band-passed version of the geoid can be constructed from local gravity data, even with a relatively restricted data set.

Zlotnicki, V.↗