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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Accuracy of least-squares methods for the Navier-Stokes equations

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

Bochev, Pavel B.↗
NASA NTRS1993

Accuracy of least-squares methods for the Navier-Stokes equations

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

Bochev, Pavel B.↗
NASA NTRS1989

Methods for local gravity field approximation

The most widely known modern method for estimating gravity field values from observed data is least-squares collocation. Its advantages are that it can make estimates at arbitrary locations based on irregularly spaced observations, and that it makes use of statistical information about errors in the input data while providing corresponding information about the quality of the output estimates. Disadvantages of collocation include the necessity of inverting square matrices of dimension equal to the number of data values and the need to assume covariance models for the gravity field and the data errors. Fourier methods are an important alternative to collocation; having the advantage of greater computational efficiency, but requiring data estimates to be on a regular grid and not using or providing statistical accuracy information. The GEOFAST algorithm is an implementation of collocation that achieves high computational efficiency by transforming the estimation equations into the frequency domain where an accurate approximation may be made to reduce the workload. The forward and inverse Fast Fourier Transforms (FFTs) are utilized. The accuracy and computational efficiency of the GEOFAST algorithm is demonstrated using two sets of synthetic gravity data: marine gravity for an ocean trench region including wavelengths longer than 200 km; and local land gravity containing wavelengths as short as 5 km. These results are discussed along with issues such as the advantages of first removing reference field models before carrying out the estimation algorithm.

Sailor, R. V.↗
DOE OSTI2020

A Method for Dimensionally Adaptive Sparse Trigonometric Interpolation of Periodic Functions

We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved and the precise anisotropy is not known a priori. To the authors' knowledge, this is the first instance of a dimensionally adaptive sparse interpolation algorithm that uses a trigonometric interpolation basis. The motivating application behind this work is the adaptive approximation of a multi-input model for a molecular potential energy surface (PES) where each input represents an angle of rotation. Our method is based on an anisotropic quasi-optimal estimate for the decay rate of the Fourier coefficients of the model; a least-squares fit to the coefficients of the interpolant is used to estimate the anisotropy. Thus, our adaptive approximation strategy begins with a coarse isotropic interpolant, which is gradually refined using the estimated anisotropic rates. The procedure takes several iterations where ever-more accurate interpolants are used to generate ever-improving anisotropy rates. We present several numerical examples of our algorithm where the adaptive procedure successfully recovers the theoretical “best” convergence rate, including an application to a periodic PES approximation. An open-source implementation of our algorithm resides in the Tasmanian UQ library developed at Oak Ridge National Laboratory.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1982

Reconstruction of the 1st Space Shuttle (STS-1) entry trajectory

A discussion of the generation of the best estimate trajectory (BET) of the first Space Shuttle Orbiter entry flight is presented. The BET defines a time history of the state, attitude, and atmospheric relative parameters throughout the Shuttle entry from an altitude of approximately 183 km to rollout. The inertial parameters were estimated utilizing a weighted least squares batch filter algorithm. Spacecraft angular rate and acceleration data derived from the Inertial Measurement Unit were utilized to predict the state and attitude which was constrained in a weighted least squares process to fit external tracking data consisting of ground based S-band and C-band data. Refined spacecraft altitude and velocity during and post rollout were obtained by processing artificial altimeter and Doppler data. The BET generation process is discussed. Software and data interface discussions are included. The variables and coordinate systems utilized are defined. STS-1 mission peculiar inputs are summarized. A listing of the contents of the actual BET is provided.

Findlay, J. T.↗
NASA NTRS1982

Modeling the thermal structure and magnetic properties of the crust of active regions with application to the Rio Grande rift

Experiments in Curie depth estimation from long wavelength magnetic anomalies are summarized. The heart of the work is equivalent-layer-type magnetization models derived by inversion of high-elevation, long wavelength magnetic anomaly data. The methodology is described in detail in the above references. A magnetization distribution in a thin equivalent layer at the Earth's surface having maximum detail while retaining physical significance, and giving rise to a synthetic anomaly field which makes a best fit to the observed field in a least squares sense is discussed. The apparent magnetization contrast in the equivalent layer is approximated using an array of dipoles distributed in equal area at the Earth's surface. The dipoles are pointed in the direction of the main magnetic field, which carries the implicit assumption that crustal magnetization is dominantly induced or viscous. The determination of the closest possible dipole spacing giving a stable inversion to a solution having physical significance is accomplished by plotting the standard deviation of the solution parameters against their spatial separation for a series of solutions.

Source record↗
NASA NTRS1992

Sea surface mean square slope from Ku-band backscatter data

A surface mean-square-slope parameter analysis is conducted for 14-GHz airborne radar altimeter near-nadir, quasi-specular backscatter data, which in raw form obtained by least-squares fitting of an optical scattering model to the return waveform show an approximately linear dependence over the 7-15 m/sec wind speed range. Slope data are used to draw inferences on the structure of the high-wavenumber portion of the spectrum. A directionally-integrated model height spectrum that encompasses wind speed-dependent k exp -5/2 and classical Phillips k exp -3 power laws subranges in the range of gravity waves is supported by the data.

Jackson, F. C.↗
NASA NTRS1984

Approximation methods for inverse problems involving the vibration of beams with tip bodies

Two cubic spline based approximation schemes for the estimation of structural parameters associated with the transverse vibration of flexible beams with tip appendages are outlined. The identification problem is formulated as a least squares fit to data subject to the system dynamics which are given by a hybrid system of coupled ordinary and partial differential equations. The first approximation scheme is based upon an abstract semigroup formulation of the state equation while a weak/variational form is the basis for the second. Cubic spline based subspaces together with a Rayleigh-Ritz-Galerkin approach were used to construct sequences of easily solved finite dimensional approximating identification problems. Convergence results are briefly discussed and a numerical example demonstrating the feasibility of the schemes and exhibiting their relative performance for purposes of comparison is provided.

Rosen, I. G.↗
DOE OSTI2024

Gradient Coding With Iterative Block Leverage Score Sampling

Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this study, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ℓ 2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ℓ 2 -subspace embedding, and that our resulting approximation converges to the optimal solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Learning Distribution Grid Topologies: A Tutorial

Unveiling feeder topologies from data is of paramount importance to advance situational awareness and proper utilization of smart resources in power distribution grids. This tutorial summarizes, contrasts, and establishes useful links between recent works on topology identification and detection schemes that have been proposed for power distribution grids. The primary focus is to highlight methods that overcome the limited availability of measurement devices in distribution grids, while enhancing topology estimates using conservation laws of power-flow physics and structural properties of feeders. Grid data from phasor measurement units or smart meters can be collected either passively in the traditional way, or actively, upon actuating grid resources and measuring the feeder's voltage response. Analytical claims on feeder identifiability and detectability are reviewed under disparate meter placement scenarios. Such topology learning claims can be attained exactly or approximately so via algorithmic solutions with various levels of computational complexity, ranging from least-squares fits to convex optimization problems, and from polynomial-time searches over graphs to mixed-integer programs. Although the emphasis is on radial single-phase feeders, extensions to meshed and/or multiphase circuits are sometimes possible and discussed. Here this tutorial aspires to provide researchers and engineers with knowledge of the current state-of-the-art in tractable distribution grid learning and insights into future directions of work.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1972

Adjoint variational methods in nonconservative stability problems.

A general nonself-adjoint eigenvalue problem is examined and it is shown that the commonly employed approximate methods, such as the Galerkin procedure, the method of weighted residuals and the least square technique lack variational descriptions. When used in their previously known forms they do not yield stationary eigenvalues and eigenfunctions. With the help of an adjoint system, however, several analogous variational descriptions may be developed and it is shown in the present study that by properly restating the method of least squares, stationary eigenvalues may be obtained. Several properties of the adjoint eigenvalue problem, known only for a restricted group, are shown to exist for the more general class selected for study.

Prasad, S. N.↗
NASA NTRS1988

Boundary identification for 2-D parabolic problems arising in thermal testing of materials

Problems on the identification of two-dimensional spatial domains arising in the detection and characterization of structural flaws in materials are considered. For a thermal diffusion system with external boundary input, observations of the temperature on the surface are used in an output least square approach. Parameter estimation techniques based on the method of mappings are discussed, and approximation schemes are developed based on a finite-element Galerkin approach. Theoretical convergence results for computational techniques are given, and the results are applied to the identification of two kinds of boundary shapes.

Banks, H. T.↗
NASA NTRS1989

Boundary estimation problems arising in thermal tomography

Problems on the identification of two-dimensional spatial domains arising in the detection and characterization of structural flaws in materials are considered. For a thermal diffusion system with external boundary input, observations of the temperature on the surface are used in a output least squares approach. Parameter estimation techniques based on the method of mappings are discussed and approximation schemes are developed based on a finite element Galerkin approach. Theoretical convergence results for computational techniques are given and the results are applied to experimental data for the identification of flaws in the thermal testing of materials.

Banks, H. T.↗
NASA NTRS1990

Analysis of pressure-broadened ozone spectra in the 3 micron region

The Molecular Spectroscopy Lab at NASA-Langley has been involved in a long term effort to carefully characterize the infrared spectra of small molecules of atmospheric interest, including methane, water vapor, ozone, and their isotopic counterparts. High resolution gas phase infrared spectra are obtained using both a tunable diode laser system, and the McMath Fourier transform spectrometer at the Kitt Peak Solar Observatory. Spectra are obtained at various pressures and temperatures for pure gas samples, and for samples containing mixtures of the species of interest in nitrogen, oxygen, or air. From these spectra, using a nonlinear least squares fitting technique, spectral parameters of position, intensity, and half-width were determined for varying laboratory conditions that approximate atmospheric conditions experienced in remote sensing situations. These parameters are of interest in theoretical studies of these species, as well as in allowing more accurate interpretation of remote sensing data. The current work involves the analysis of a series of McMath FTIR spectra of ozone broadened by mixing with air, nitrogen, or oxygen. Each spectrum covers the region from 2396 to 4057/cm. Each vibrational band is analyzed by first diving its region into small intervals containing a few well isolated absorption lines of reasonable intensity. Each of these small intervals is fit by multiple iterations of the nonlinear least square program until residuals are minimized to a reasonable value which corresponds to the noise level of the measured spectrum. Intervals for the 3 nu(sub 3) ozone band in the region from 3000 to 3060 wavenumbers are being examined.

Prochaska, Eleanor S.↗
NASA NTRS1995

OSSE observations of GX 339-4

The Oriented Scintillation Spectrometer Experiment (OSSE) on the Compton Gamma Ray Observatory (CGRO) observed the Galactic black hole candidate GX 339-4 as a target of oppurtunity in 1991 September, in response to the outburst reported by Burst and Transient Source Experiment (BATSE). We report here on energy spectra in the 50 keV-10 MeV range obtained by OSSE. The source was detected from 50 to 400 keV at a level relative to the Crab Nebula of approximately 30%. The observed spectrum was prescribed reasonably well by a power law with an exponential cutoff; a least-squares fit yielded a photon index of 0.88 +/- 0.05 and a cutoff energy of 68 +/- 2 keV. The addition of a Compton reflection component did not significantly improve the overall fit. An optically thin thermal bremsstrahlung spectrum also provides a good fit, and the thermal Comptonization model of Sunyaev & Titarchuk, while deficient in describing the data above approximately 200 keV, cannot formally be ruled out. A pure power law with reflection does not fit the observed spectrum. During a follow-up observation made in 1991 November the intensity of the source below 100 keV had dropped by more than a factor of 40, and it was no longer detected above approximately 100 keV. The energy spectrum during the November observation could be characterized by a power law with a photon index of 2.3 +/- 0.3; the spectrum was fitted equally well with the same exponentially cutoff power-law model applied to the September observation, reduced in intensity by a factor of approximately 40. During the 1991 September observation, the luminosity in the 50-400 keV band was approximately 2 x 10(exp 37) ergs/s (assuming a distance of 4 kpc), no more than a factor of 5 below the soft X-ray luminosity of GX 339-4 observed in its X-ray high state. The luminosity during the 1991 November observation was approximately 5 x 10(exp 35) ergs/s. Extrapolations of both the exponentially cutoff power-law and Sunyaev-Titarchuk models to the approximately 5-20 keV X-ray band yield flux levels very close to that observed by Ginga during an overlapping interval in 1991 September, when GX 339-4 was reported to be in its low state. This may be one of the strongest indications to date of a direct correspondence between the low X-ray state and gamma-ray outbursts of GX 339-4.

Grabelsky, D. A.↗
DOE OSTI2025

A New Hybrid Quantum-Classical Algorithm for Solving the Unit Commitment Problem

Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach these problems. We develop a hybrid quantum-classical algorithm for the Unit Commitment (UC) problem in power systems which aims at minimizing the total cost while optimally allocating generating units to meet the hourly demand of the power loads. The hybrid algorithm combines a variational quantum algorithm (VQA) with a classical Benders-type heuristic. The resulting algorithm computes approximate solutions to UC in three stages: i) a collection of UC vectors capable meeting the power demand with lowest possible operating costs is generated based on VQA; ii) a classical sequential least squares programming (SLSQP) routine is leveraged to find the optimal power level corresponding to a predetermined number of candidate vectors; iii) in the last stage, the approximate solution of UC along with generating units power level combination is given. To demonstrate the effectiveness of the presented method, three different systems with 3 generating units, 10 generating units, and 26 generating units were tested for different time periods. In addition, convergence of the hybrid quantum-classical algorithm for select time periods is proven out on IonQ's Forte system.

Aboumrad, Willie [IonQ, Inc]↗
NASA NTRS1961

A Method of Estimating Residuals in Orbital Theory

The degree of approximation used in determining the orbits of earth satellites is reflected in the residuals (differences between calculated and observed positions). The least-squares procedure generally used to fit theory to observation tends to obscure the significance of theoretical parameters, so that the physical sources of residuals cease to be apparent. A method is outlined herein for estimating the magnitude of the residuals to be expected from an approximate theory presumed to have one missing or incorrect term.

Lecar, Myron↗