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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 91 records · Page 5
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NASA NTRS1993

Enhanced data reduction of the velocity data on CETA flight experiment

A newly developed technique for enhanced data reduction provides an improved procedure that allows least squares minimization to become possible between data sets with an unequal number of data points. This technique was applied in the Crew and Equipment Translation Aid (CETA) experiment on the STS-37 Shuttle flight in April 1991 to obtain the velocity profile from the acceleration data. The new technique uses a least-squares method to estimate the initial conditions and calibration constants. These initial conditions are estimated by least-squares fitting the displacements indicated by the Hall-effect sensor data to the corresponding displacements obtained from integrating the acceleration data. The velocity and displacement profiles can then be recalculated from the corresponding acceleration data using the estimated parameters. This technique, which enables instantaneous velocities to be obtained from the test data instead of only average velocities at varying discrete times, offers more detailed velocity information, particularly during periods of large acceleration or deceleration.

Finley, Tom D.↗
NASA NTRS1989

Least-squares finite element method for fluid dynamics

An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.

Jiang, Bo-Nan↗
NASA NTRS1989

Least-squares finite element method for fluid dynamics

An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.

Jiang, Bo-Nan↗
NASA NTRS1988

Performance comparison of five frequency domain system identification techniques for helicopter higher harmonic control

This paper presents the results of a computer simulation comparing the performance of five system identification techniques currently proposed for use with helicopter, frequency domain, higher harmonic vibration control algorithms. The system identification techniques studied were: (1) the weighted least squares method in moving block format, (2) the classical Kalman filter, (3) a generalized Kalman filter, (4) the classical least mean square (LMS) filter, and (5) a generalized LMS filter. The generalized Kalman and LMS filters were derived by allowing for multistep operation, rather than the single-step update approach used by their classical versions. Both open-loop and closed-loop (vibration control mode) identification results are presented in the paper. The algorithms are evaluated in terms of their accuracy, stability, convergence properties, computation speeds, and the relative ease with which these techniques may be directly applied to the helicopter vibration control problem.

Jacklin, Stephen A.↗
NASA NTRS1984

Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing

An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

Park, J. H.↗
NASA NTRS1985

Separation of core and crustal magnetic field sources

Fluid motions in the electrically conducting core and magnetized crustal rocks are the two major sources of the magnetic field observed on or slightly above the Earth's surface. The exact separation of these two contributions is not possible without imposing a priori assumptions about the internal source distribution. Nonetheless models like these were developed for hundreds of years Gauss' method, least squares analysis with a truncated spherical harmonic expansion was the method of choice for more than 100 years although he did not address separation of core and crustal sources, but rather internal versus external ones. Using some arbitrary criterion for appropriate truncation level, we now extrapolate downward core field models through the (approximately) insulating mantle. Unfortunately our view can change dramatically depending on the degree of truncation for describing core sources.

Shure, L.↗
NASA NTRS1987

Robust statistical methods for automated outlier detection

The computational challenge of automating outlier, or blunder point, detection in radio metric data requires the use of nonstandard statistical methods because the outliers have a deleterious effect on standard least squares methods. The particular nonstandard methods most applicable to the task are the robust statistical techniques that have undergone intense development since the 1960s. These new methods are by design more resistant to the effects of outliers than standard methods. Because the topic may be unfamiliar, a brief introduction to the philosophy and methods of robust statistics is presented. Then the application of these methods to the automated outlier detection problem is detailed for some specific examples encountered in practice.

Jee, J. R.↗
NASA NTRS2012

Comparisons of a Constrained Least Squares Model Versus Human-in-the-Loop for Spectral Unmixing to Determine Material Type of GEO Debris

Spectral reflectance data through the visible regime was collected at Las Campanas Observatory in Chile using an imaging spectrograph on one of the twin 6.5-m Magellan telescopes. The data were obtained on 1-2 May 2012 on the 'Landon Clay' telescope with the LDSS3 (Low Dispersion Survey Spectrograph 3). Five pieces of Geosynchronous Orbit (GEO) or near-GEO debris were identified and observed with an exposure time of 30 seconds on average. In addition, laboratory spectral reflectance data was collected using an Analytical Spectral Device (ASD) field spectrometer at California Polytechnic State University in San Luis Obispo on several typical common spacecraft materials including solar cells, circuit boards, various Kapton materials used for multi-layer insulation, and various paints. The remotely collected data and the laboratory-acquired data were then incorporated in a newly developed model that uses a constrained least squares method to unmix the spectrum in specific material components. The results of this model are compared to the previous method of a human-in-the-loop (considered here the traditional method) that identifies possible material components by varying the materials and percentages until a spectral match is obtained. The traditional model was found to match the remotely collected spectral data after it had been divided by the continuum to remove the space weathering effects, or a "reddening" of the materials. The constrained least-squares model also used the de-reddened spectra as inputs and the results were consistent with those obtained through the traditional method. For comparison, a first-order examination of including reddening effects into the constrained least-squares model will be explored and comparisons to the remotely collected data will be examined. The identification of each object's suspected material component will be discussed herein.

Rapp, Jason↗
NASA NTRS2013

Comparisons of a Constrained Least Squares Model versus Human-in-the-Loop for Spectral Unmixing to Determine Material Type of GEO Debris

Spectral reflectance data through the visible regime was collected at Las Campanas Observatory in Chile using an imaging spectrograph on one of the twin 6.5-m Magellan telescopes. The data were obtained on 1-2 May 2012 on the 'Landon Clay' telescope with the LDSS3 (Low Dispersion Survey Spectrograph 3). Five pieces of Geosynchronous Orbit (GEO) or near-GEO debris were identified and observed with an exposure time of 30 seconds on average. In addition, laboratory spectral reflectance data was collected using an Analytical Spectral Device (ASD) field spectrometer at California Polytechnic State University (Cal Poly) in San Luis Obispo on several typical common spacecraft materials including solar cells, circuit boards, various Kapton materials used for multi-layer insulation, and various paints. The remotely collected data and the laboratory-acquired data were then incorporated in a newly developed model that uses a constrained least squares method to unmix the spectrum in specific material components. The results of this model are compared to the previous method of a human-in-the-loop (considered here the traditional method) that identifies possible material components by varying the materials and percentages until a spectral match is obtained. The traditional model was found to match the remotely collected spectral data after it had been divided by the continuum to remove the space weathering effects, or a reddening of the materials. The constrained least-squares model also used the de-reddened spectra as inputs and the results were consistent with those obtained through the traditional method. For comparison, a first-order examination of including reddening effects into the constrained least-squares model will be explored and comparisons to the remotely collected data will be examined. The identification of each object s suspected material component will be discussed herein.

Abercromby, Kira J.↗
NASA NTRS1996

First-Order System Least Squares for Velocity-Vorticity-Pressure Form of the Stokes Equations, with Application to Linear Elasticity

In this paper, we study the least-squares method for the generalized Stokes equations (including linear elasticity) based on the velocity-vorticity-pressure formulation in d = 2 or 3 dimensions. The least squares functional is defined in terms of the sum of the L(exp 2)- and H(exp -1)-norms of the residual equations, which is weighted appropriately by by the Reynolds number. Our approach for establishing ellipticity of the functional does not use ADN theory, but is founded more on basic principles. We also analyze the case where the H(exp -1)-norm in the functional is replaced by a discrete functional to make the computation feasible. We show that the resulting algebraic equations can be uniformly preconditioned by well-known techniques.

Cai, Zhiqiang↗
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 NTRS1990

Vertical structure and characteristics of 23-60 day (zonal) oscillations over the tropical latitudes during the winter months of 1986 - Results of equatorial wave campaign-II

Results are presented of the equatorial wave campaign-II, a meteorological rocket study which was part of the Indian Middle Atmosphere Program. The equatorial wave campaign-II was conducted from Shar, India (13.7 deg N, 80.2 deg E) from January 15-February 28, 1986. By means of high altitude balloon and the RH-200 meteorological rocket, winds were measured from ground level up to 60 km altitude once each day during the 45-day period. The oscillation frequencies of the deviations in the east-west component of the winds from their mean at each 1-km height interval are obtained by the maximum entropy method. The phases and amplitudes of these frequencies are determined by use of the least squares method on the wind variation time series. Enhanced wave activity is shown to take place in the troposphere and lower mesosphere. The tropospheric waves observed suggest themselves to be Rossby waves of extratropical origin penetrating to tropical latitudes. The observed stratospheric/mesospheric waves appear to emanate from a source around the stratopause.

Raghavarao, R.↗
NASA NTRS1994

The least-squares finite element method for low-mach-number compressible viscous flows

The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

Yu, Sheng-Tao↗
NASA NTRS1998

Flow Applications of the Least Squares Finite Element Method

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Jiang, Bo-Nan↗
NASA NTRS1998

Development of Least-Squares Finite Element Method

The main purpose of this final report is to study the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications.

Jiang, Bo-Nan↗
NASA NTRS1990

Least-squares finite element methods for compressible Euler equations

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Jiang, Bo-Nan↗