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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

An improved calibration technique for wind tunnel model attitude sensors

Aerodynamic wind tunnel tests at NASA Langley Research Center (LaRC) require accurate measurement of model attitude. Inertial accelerometer packages have been the primary sensor used to measure model attitude to an accuracy of +/- 0.01 deg as required for aerodynamic research. The calibration parameters of the accelerometer package are currently obtained from a seven-point tumble test using a simplified empirical approximation. The inaccuracy due to the approximation exceeds the accuracy requirement as the misalignment angle between the package axis and the model body axis increases beyond 1.4 deg. This paper presents the exact solution derived from the coordinate transformation to eliminate inaccuracy caused by the approximation. In addition, a new calibration procedure is developed in which the data taken from the seven-point tumble test is fit to the exact solution by means of a least-squares estimation procedure. Validation tests indicate that the new calibration procedure provides +/- 0.005-deg accuracy over large package misalignments, which is not possible with the current procedure.

Tripp, John S.↗
NASA NTRS1980

A feasibility study of a 3-D finite element solution scheme for aeroengine duct acoustics

The advantage from development of a 3-D model of aeroengine duct acoustics is the ability to analyze axial and circumferential liner segmentation simultaneously. The feasibility of a 3-D duct acoustics model was investigated using Galerkin or least squares element formulations combined with Gaussian elimination, successive over-relaxation, or conjugate gradient solution algorithms on conventional scalar computers and on a vector machine. A least squares element formulation combined with a conjugate gradient solver on a CDC Star vector computer initially appeared to have great promise, but severe difficulties were encountered with matrix ill-conditioning. These difficulties in conditioning rendered this technique impractical for realistic problems.

Abrahamson, A. L.↗
NASA NTRS1973

An application of a linear programing technique to nonlinear minimax problems

A differential correction technique for solving nonlinear minimax problems is presented. The basis of the technique is a linear programing algorithm which solves the linear minimax problem. By linearizing the original nonlinear equations about a nominal solution, both nonlinear approximation and estimation problems using the minimax norm may be solved iteratively. Some consideration is also given to improving convergence and to the treatment of problems with more than one measured quantity. A sample problem is treated with this technique and with the least-squares differential correction method to illustrate the properties of the minimax solution. The results indicate that for the sample approximation problem, the minimax technique provides better estimates than the least-squares method if a sufficient amount of data is used. For the sample estimation problem, the minimax estimates are better if the mathematical model is incomplete.

Schiess, J. R.↗
NASA NTRS1978

Estimate of procession and polar motion errors from planetary encounter station location solutions

Jet Propulsion Laboratory Deep Space Station (DSS) location solutions based on two JPL planetary ephemerides, DE 84 and DE 96, at eight planetary encounters were used to obtain weighted least squares estimates of precession and polar motion errors. The solution for precession error in right ascension yields a value of 0.3 X 10 to the minus 5 power plus or minus 0.8 X 10 to the minus 6 power deg/year. This maps to a right ascension error of 1.3 X 10 to the minus 5 power plus or minus 0.4 X 10 to the minus 5 power deg at the first Voyager 1979 Jupiter encounter if the current JPL DSS location set is used. Solutions for precession and polar motion using station locations based on DE 84 agree well with the solution using station locations referenced to DE 96. The precession solution removes the apparent drift in station longitude and spin axis distance estimates, while the encounter polar motion solutions consistently decrease the scatter in station spin axis distance estimates.

Pease, G. E.↗
NASA NTRS1995

The origin of spurious solutions in computational electromagnetics

The origin of spurious solutions in computational electromagnetics, which violate the divergence equations, is deeply rooted in a misconception about the first-order Maxwell's equations and in an incorrect derivation and use of the curl-curl equations. The divergence equations must be always included in the first-order Maxwell's equations to maintain the ellipticity of the system in the space domain and to guarantee the uniqueness of the solution and/or the accuracy of the numerical solutions. The div-curl method and the least-squares method provide rigorous derivation of the equivalent second-order Maxwell's equations and their boundary conditions. The node-based least-squares finite element method (LSFEM) is recommended for solving the first-order full Maxwell equations directly. Examples of the numerical solutions by LSFEM for time-harmonic problems are given to demonstrate that the LSFEM is free of spurious solutions.

Jiang, Bo-Nan↗
NASA NTRS1978

On least squares approximations to indefinite problems of the mixed type

A least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The method retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency, i.e., the resulting matrix system is always symmetric and positive definite. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.

Fix, G. J.↗
NASA NTRS1988

Accuracy study of the Upper Atmosphere Research Satellite (UARS) definitive attitude determination

The Upper Atmosphere Research Satellite (UARS) has two definitive attitude determination requirements: the definitive attitude of the Modular Attitude Control Subsystem (MACS) and the definitive attitude of the gimbaled Solar-Stellar Pointing Platform (SSPP). The onboard computer (OBC) will compute the MACS attitude using a Kalman filter and will transform this attitude solution through the SSPP gimbals to calculate the SSPP attitude. The attitude ground support system (AGSS) will compute the MACS attitude using a batch least-squares differential corrector algorithm and will also transform this solution through the gimbals to obtain the SSPP attitude. This paper reports the results of a prelaunch study to predict the accuracy of the OBC attitude solutions and the accuracy of the AGSS attitude solutions. The OBC and AGSS solution accuracies are then compared to establish the relative quality. The effects of star observability, sensor noise, and sensor misalignment uncertainties on attitude determination accuracy are analyzed for each case.

Snow, Frank↗
NASA NTRS1993

Analyzing Martian winds and tracer concentrations using Mars Observer data

During the courses of a day, the Mars Observer spacecraft will acquire globally distributed profiles of the martian atmosphere. It is highly desirable that this data be assembled into synoptic weather maps (complete specifications of the atmospheric pressure, temperature, and winds at a given time), which can in turn be used as starting points in the study of many meteorological phenomena. Unfortunately, the special nature of the Mars Observer data presents several challenges above and beyond the usual difficult problem of data initialization. Mars Observer atmospheric data will consist almost exclusively of asynoptic vertical profiles of temperatures (or radiances) and pressures, whereas winds are generally in balance with horizontal gradients of these quantities (which will not be observed). It will therefore be necessary to resort to dynamical models to analyze the wind fields. As a rule, data assimilation into atmospheric models can result in the generation of spurious gravity waves, so special steps must be taken to suppress these. In addition, the asynoptic nature of the data will require a four-dimensional (space and time) data assimilation scheme. The problem is to find a full set of meteorological fields (winds and temperatures) such that, when marched forward in time in the model, they achieve a best fit (in the weighted least-squares sense) to the data. The proposed solution is to develop a model especially for the Mars Observer data assimilation problem. Gravity waves are filtered from the model by eliminating all divergence terms from the prognostic divergence equation. This leaves a diagnostic gradient wind relation between the rotational wind and the temperature field. The divergent wind is diagnosed as the wind required to maintain the gradient wind balance in the presence of the diabatic heating. The primitive equations of atmospheric dynamics (with three principal dependent variables) are thus reduced to a simpler system with a single prognostic equation for temperature - the variable that will be best observed. (This balance system was apparently first derived by Charney as a first-order Rossby number expansion of the equations of motion). Experience with a full primitive equation model of the martian atmosphere indicates that a further simplification is possible: at least for short-term integrations, the model can be linearized about the zonally symmetric basic state.

Houben, Howard C.↗
NASA NTRS1981

Remarks on nonstandard least-squares problems

It is shown that after treating a least-squares problem in the standard fashion, the imposition of stochastic restrictions on certain parameters can be accomplished essentially by inverting a matrix of an order no larger than the total number of restricted parameters, and that generally there is an explicit term for correcting the unrestricted to the restricted solution. In addition, any known type of nonstandard least-squares adjustment problem can be reduced to an equivalent standard linear problem, that is, one in which there is exactly one observation per condition equation and in which the observations are not correlated.

Eichhorn, H.↗
NASA NTRS1996

A Systematic Solution Approach for Neutron Transport Problems in Diffuse Regimes

A systematic solution approach for the neutron transport equation, based on a least-squares finite-element discretization, is presented. This approach includes the theory for the existence and uniqueness of the analytical as well as of the discrete solution, bounds for the discretization error, and guidance for the development of an efficient multigrid solver for the resulting discrete problem. To guarantee the accuracy of the discrete solution for diffusive regimes, a scaling transformation is applied to the transport operator prior to the discretization. The key result is the proof of the V-ellipticity and continuity of the scaled least-squares bilinear form with constants that are independent of the total cross section and the absorption cross section. For a variety of least-squares finite-element discretizations this leads to error bounds that remain valid in diffusive regimes. Moreover, for problems in slab geometry a full multigrid solver is presented with V(1, 1)-cycle convergence rates approximately equal to 0.1, independent of the size of the total cross section and the absorption cross section.

Manteuffel, T. A.↗
DOE OSTI2023

Error Estimates of Residual Minimization Using Neural Networks for Linear PDES

We propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates for both continuous and discrete formulations of residual minimization in strong and weak forms. The formulations cover recently developed physicsinformed neural networks based on strong and variational formulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Quantifying neptunium oxidation states in nitric acid through spectroelectrochemistry and chemometrics

Controlled-potential in situ thin-layer spectropotentiometry was leveraged to generate visible/near-infrared (VIS/NIR) absorption spectral data sets for the development of chemometric models to quantify Np(III/IV/V/VI) oxidation states in HNO 3 . This technology would be valuable in laboratory studies and when monitoring process solutions to guide feed adjustments for radiochemical separations—the performance of which depends on oxidation state. This approach successfully isolated and stabilized Np species in pure (~99%) oxidation states without compromising solution optical properties. Multivariate curve resolution–alternating least squares models were evaluated to resolve spectral and component concentrations from a scan that sequentially produced Np(VI), Np(V), Np(IV), and Np(III) spectra with mixtures of two valences at a time. Although it provided a useful approximation, the method was not able to quantitively resolve each component likely because of rotational ambiguity. Additionally, partial least squares regression models were built from artificial and electrochemically generated VIS/NIR spectral training sets to study the effect of interionic interactions on spectral characteristics. Models built with true Bi-chemical mixtures of coexisting Np oxidation states and spectra generated from additive combinations of pure end points had similar prediction performance. This methodology can be used to directly quantify Np concentration and the ratio of Np oxidation states and other actinides in remote settings such as hot cells.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
NASA NTRS1976

Techniques for obtaining regional radiation budgets from satellite radiometer observations, phase 4 and phase 5

A scheme was developed which divides the earth-atmosphere system into 2060 elemental areas. The regions previously described are defined in terms of these elemental areas which are fixed in size and position as the satellite moves. One method, termed the instantaneous technique, yields values of the radiant emittance (We) and the radiant reflectance (Wr) which the regions have during the time interval of a single satellite pass. The number of observations matches the number of regions under study and a unique solution is obtained using matrix inversion. The other method (termed the best fit technique), yields time averages of We and Wr for large time intervals (e.g., months, seasons). The number of observations in this technique is much greater than the number of regions considered, and an approximate solution is obtained by the method of least squares.

Pina, J. F.↗
NASA NTRS1994

Preliminary solutions for the lunar gravity field from analysis of lunar orbiter tracking data

Knowledge of the gravitation field, in combination with surface topography, provides one of the principal means of inferring the internal structure of a planetary body. Previous analyses of the lunar gravitational field have been based on data from the Lunar Orbiters, the Apollo subsatellites, and the low altitude passes of the Apollo spacecraft. Recently, Konopliv et al. have reanalyzed all available Lunar Orbiter and Apollo subsatellite tracking data, producing a 60th degree and order solution. In preparation for the Clementine Mission to the Moon, we have also initiated a reanalysis of the Lunar Orbiter and Apollo subsatellite data. Our reanalysis takes advantage of advanced force and measurement modeling techniques as well as modern computational facilities. We applied the least squares collocation technique which stabilizes the behavior of the solution and high degree and order. The extension of the size of the field reduces the aliasing coming from the omitted portion of the gravitational field. This is especially important for the analysis of the tracking data from the Lunar Orbiters, as the periapse heights frequently ranged from 50 to 100 km.

Lemoine, F. G.↗
NASA NTRS1994

Theoretical study of the incompressible Navier-Stokes equations by the least-squares method

Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.

Jiang, Bo-Nan↗
DOE OSTI2026

Fast Active-Set Thresholding Method for Nonnegative Least Squares

Nonnegative Least Squares (NNLS) is a fundamental constrained optimization problem encountered in many applications such as image deblurring, signal processing, nonnegative matrix factorization, magnetic microscopy, and hyperspectral imaging. Active-set based methods are a common class of algorithms for solving NNLS which identify the optimal variable set of the NNLS solution. They do so by iteratively solving a series of unconstrained least squares problems, identifying which variables violate the nonnegativity constraints, and then swapping variables in/out of consideration until the optimal set of variables is found. Several variations improving upon this method exist in the literature. In this work, we propose an active-set swap heuristic which further improves upon existing active-set based methods for NNLS. Our optimizations are based upon adding multiple variables to the passive set within a threshold of the smallest gradient value and removing variables within a similar threshold of the closest boundary constraint. We leverage these optimizations to yield a Fast Active-Set Thresholding NNLS (FAST-NNLS) algorithm which significantly outperforms the existing state-of-the-art NNLS algorithms for a wide range of problems. Rigorous convergence guarantees are proven for the proposed method. We demonstrate the effectiveness of our proposed method on multiple synthetic datasets and two realworld text analysis applications. In doing so, we present the most comprehensive NNLS solver comparison in the literature to date.

Cobb, Benjamin [Georgia Institute of Technology]↗
DOE OSTI2020

Faster Johnson–Lindenstrauss transforms via Kronecker products

The Kronecker product is an important matrix operation with a wide range of applications in signal processing, graph theory, quantum computing and deep learning. In this work, we introduce a generalization of the fast Johnson–Lindenstrauss projection for embedding vectors with Kronecker product structure, the Kronecker fast Johnson–Lindenstrauss transform (KFJLT). The KFJLT reduces the embedding cost by an exponential factor of the standard fast Johnson–Lindenstrauss transform’s cost when applied to vectors with Kronecker structure, by avoiding explicitly forming the full Kronecker products. Here, we prove that this computational gain comes with only a small price in embedding power: consider a finite set of $p$ points in a tensor product of $d$ constituent Euclidean spaces $\bigotimes _{k=d}^{1}{\mathbb{R}}^{n_k}$, and let $N = \prod _{k=1}^{d}n_k$. With high probability, a random KFJLT matrix of dimension $m \times N$ embeds the set of points up to multiplicative distortion $(1\pm \varepsilon )$ provided $m \gtrsim \varepsilon ^{-2} \, \log ^{2d - 1} (p) \, \log N$. We conclude by describing a direct application of the KFJLT to the efficient solution of large-scale Kronecker-structured least squares problems for fitting the CP tensor decomposition.

Kronecker structure↗