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Results for “least-squares method”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Crustal interpretation of the MAGSAT data in the continental United States

The processing of MAGSAT scalar data to construct a crustal magnetic anomaly map over the continental U.S. involves removal of the reference field model, a path-by-path subtraction of a low order polynomial through a least-squares fit to reduce orbital offset errors, and a two dimensional spectral filtering to mitigate the spectral bias induced by the path-by-path orbital correction scheme. The resultant anomaly map shows reasonably good correlations with an aeromagnetic map derived from the project MAGNET. Prominent satellite magnetic anomalies are identified in terms of geological provinces and age boundaries. An inversion method was applied to MAGSAT data which produces both the Curie depth topography and laterally varying magnetic susceptibility of the crust. A contoured Curie depth map thus derived shows general agreements with a crustal thickness map based on seismic data.

Won, I. J.↗
NASA NTRS1988

Development of the NASA/FLAGRO computer program

A preliminary version of a new computer program has been developed for calculating crack propagation in cyclically loaded structures. The new program, titled NASA/FLAGRO, has numerous enhanced features over previous programs used for safe life analysis on space systems. The essential features of the new program consist of modular design, promptive input using a cathode ray tube terminal, improved crack growth rate analytical methods, many new crack case solutions, and incorporation of user-defined files for material properties and fatigue spectrums. Also, five options made available in the program are to compute: (1) safe life of a part with a preexisting crack; (2) critical crack size for a specified stress level; (3) stress-intensity factor numerical values for making comparisons or checks of solutions; (4) least-squares fit of growth rate equations to crack growth rate data; and (5) the conversion of a versus N data to Delta K versus da/dN.

Forman, Royce G.↗
NASA NTRS1986

Parameter estimation and error analysis in environmental modeling and computation

A method for the estimation of parameters and error analysis in the development of nonlinear modeling for environmental impact assessment studies is presented. The modular computer program can interactively fit different nonlinear models to the same set of data, dynamically changing the error structure associated with observed values. Parameter estimation techniques and sequential estimation algorithms employed in parameter identification and model selection are first discussed. Then, least-square parameter estimation procedures are formulated, utilizing differential or integrated equations, and are used to define a model for association of error with experimentally observed data.

Kalmaz, E. E.↗
NASA NTRS1987

State-space formulation of multi-shaker modal analysis

As modal testing techniques have improved in recent years, the demands placed on the accuracy of modal test results have increased. This paper describes a new multi-input, multi-output modal parameter estimation algorithm suitable for the identification of reduced-order models of structures. The method described is a frequency-domain method based on excitation and response spectra. The principal features of the algorithm are: (1) applicability to general linear, time-invariant systems, (2) direct use of multiple input and multiple response data, (3) identification of reduced-order models with minimum user interaction through the use of two automatic model-reduction techniques, (4) identification of a consistent set of modal parameters through the use of numerically stable least-squares techniques, and (5) complete user documentation.

Craig, Roy R., Jr.↗
NASA NTRS1986

Hierarchial implicit dynamic least-square solution algorithm

This paper develops an implicit type transient solution strategy which possesses hierarchial levels of application. In particular, due to the manner of formulation, stiffness updating, assembly inversion, solution constraint, as well as iteration are all performed at a localized level. The level of iterative calculations depends on the type of hierarchial partitioning employed, namely degree of freedom, nodal, elemental, material/nonlinear group, substructural, and so on. Since the iterative solution process and application of constraints are applied at a local level, the resulting so-called hierarchial implicit solution algorithm possesses very stable and efficient numerical properties and is highly storage efficient. To demonstrate the scheme, the results of several benchmark examples are presented. These enable comparisons with the Newton-Raphson solved implicit transient solution method. Overall the comparisons illustrate the superior stability and efficiency of the hierarchial scheme.

Padovan, J.↗
NASA NTRS1981

Simulation of the magnetic structure of the inner heliosphere by means of non-spherical source surface

A new method for mapping the Sun's magnetic field B from the photosphere through the corona and interplanetary space is presented. The method entails the derivation of B from a scalar potential within a current-free annular volume bounded inside by photosphere and outside by a prescribed nonspherical source surface to which B is made (as nearly as possible) perpendicular. As usual we obtain the potential for the part of B that arises from currents inside the Sun by fitting an expansion to the observed line-of-sight component of B at the photosphere. A second least-squares fit is introduced to obtain the part of B that arises from currents outside the source surface. Comparisons are made between this model and observed coronal and interplanetary structures. There is evidence that observation data underestimate the strength of photospheric polar magnetic fields.

Levine, R. H.↗
NASA NTRS1982

X-ray observations of Abell 2218 and implications for the Sunyaev-Zel'dovich effect

The Einstein Observatory was used to obtain a high-resolution X-ray image and an X-ray flux measurement of the galaxy cluster Abell 2218. The combined system of intracluster medium and galaxies is modeled as a gas in hydrostatic equilibrium in a common gravitational potential with an isothermal galaxy component. This model is then fitted in the least-squares sense to the X-ray surface brightness distribution and to the optically determined galaxy surface density profile to determine model parameters. The gas is found to be nominally isothermal, moderately dense, and very hot (10-30 keV); these conditions are consistent with the Sunyaev-Zel'dovich effect, i.e., the diminution in the cosmic microwave background radiation intensity in the direction of this cluster. It is noted that the considerable imprecision inherent in the method of distance measurement based on the combination of microwave measurements with X-ray and optical data makes it impossible to make a definitive statement about the distance to Abell 2218.

Boynton, P. E.↗
NASA NTRS1982

Errors in fixed and moving frame of references - Applications for conventional and Doppler radar analysis

Techniques for the correction of errors in Doppler radar scans due to advection effects are presented. A moving frame of reference is shown to be useful in least-squares estimates with stationary observations expressed in scalars or Cartesian coordinates. For non-Cartesian coordinates, such as the deduction of radial velocities from triple Doppler radar data, an integral is defined for accounting for advection effects and consequent coordinate transformations. The multiple radars are necessary for unambiguous characterization of the horizontal wind velocity. A scale analysis is employed to estimate errors with and without the error correction procedure. Improvements in correlations between scans are demonstrated when the error correction method is used.

Tzvi, G.-C.↗
NASA NTRS1974

Curve fits of predicted inviscid stagnation-point radiative heating rates, cooling factors, and shock standoff distances for hyperbolic earth entry

Curve-fit formulas are presented for the stagnation-point radiative heating rate, cooling factor, and shock standoff distance for inviscid flow over blunt bodies at conditions corresponding to high-speed earth entry. The data which were curve fitted were calculated by using a technique which utilizes a one-strip integral method and a detailed nongray radiation model to generate a radiatively coupled flow-field solution for air in chemical and local thermodynamic equilibrium. The range of free-stream parameters considered were altitudes from about 55 to 70 km and velocities from about 11 to 16 km.sec. Spherical bodies with nose radii from 30 to 450 cm and elliptical bodies with major-to-minor axis ratios of 2, 4, and 6 were treated. Powerlaw formulas are proposed and a least-squares logarithmic fit is used to evaluate the constants. It is shown that the data can be described in this manner with an average deviation of about 3 percent (or less) and a maximum deviation of about 10 percent (or less). The curve-fit formulas provide an effective and economic means for making preliminary design studies for situations involving high-speed earth entry.

Suttles, J. T.↗
NASA NTRS1975

Consolidation of fatigue and fatigue-crack-propagation data for design use

Analytical methods developed for consolidation of fatigue and fatigue-crack-propagation data for use in design of metallic aerospace structural components are evaluated. A comprehensive file of data on 2024 and 7075 aluminums, Ti-6Al-4V alloy, and 300M steel was established by obtaining information from both published literature and reports furnished by aerospace companies. Analyses are restricted to information obtained from constant-amplitude load or strain cycling of specimens in air at room temperature. Both fatigue and fatigue-crack-propagation data are analyzed on a statistical basis using a least-squares regression approach. For fatigue, an equivalent strain parameter is used to account for mean stress or stress ratio effects and is treated as the independent variable; cyclic fatigue life is considered to be the dependent variable. An effective stress-intensity factor is used to account for the effect of load ratio on fatigue-crack-propagation and treated as the independent variable. In this latter case, crack-growth rate is considered to be the dependent variable. A two term power function is used to relate equivalent strain to fatigue life, and an arc-hyperbolic-tangent function is used to relate effective stress intensity to crack-growth rate.

Rice, R. C.↗
NASA NTRS1984

Doppler line profile analysis for a multichannel Fabry-Perot interferometer

A new method of instrument calibration and data analysis is presented for single-etalon interferometric measurements of winds, temperatures, and emission line intensities. The technique has been developed for the multichannel Fabry-Perot interferometer on the Dynamics Explorer spacecraft. A numerical representation of the instrumental transfer function is used based on a truncated Fourier series with empirically determined coefficients. The numerical form is compared with the conventional analytic form. The Fourier coefficients describing the instrument function are generated at the wavelength of a stable He-Ne laser and are translated to other wavelengths using an interpolation technique for both phase and power. A quasi-linear least-squares fitting process involving matrices provides for a rapid and accurate data reduction.

Killeen, T. L.↗
NASA NTRS1983

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed.

Rodriguez, G.↗
NASA NTRS1983

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal esimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed. While this paper focuses on theoretical developments, applications arising in the area of large structure static shape determination are contained in a closely related paper (Rodriguez and Scheid, 1982).

Rodriguez, G.↗
NASA NTRS1974

Surface fitting three-dimensional bodies

The geometry of general three-dimensional bodies is generated from coordinates of points in several cross sections. Since these points may not be smooth, they are divided into segments and general conic sections are curve fit in a least-squares sense to each segment of a cross section. The conic sections are then blended in the longitudinal direction by fitting parametric cubic-spline curves through coordinate points which define the conic sections in the cross-sectional planes. Both the cross-sectional and longitudinal curves may be modified by specifying particular segments as straight lines and slopes at selected points. Slopes may be continuous or discontinuous and finite or infinite. After a satisfactory surface fit has been obtained, cards may be punched with the data necessary to form a geometry subroutine package for use in other computer programs. At any position on the body, coordinates, slopes and second partial derivatives are calculated. The method is applied to a blunted 70 deg delta wing, and it was found to generate the geometry very well.

Dejarnette, F. R.↗
NASA NTRS1971

Development of techniques for measuring pilot workload

An objective method of assessing information workload based on physiological measurements was developed. Information workload, or reserve capacity, was measured using a visual discrimination secondary task and subjective rating of task difficulty. The primary task was two axis (pitch and roll) tracking, and the independent variables in this study were aircraft pitch dynamics and wind gust disturbances. The study was structured to provide: (1) a sensitive, nonloading measure of reserve capacity, and (2) an unencumbering reliable measurement of the psychophysiological state. From these, a measured workload index (MWI) and physiological workload index (PWI) were extracted. An important measure of the success of this study was the degree to which the MWI and PWI agreed across the 243 randomly-presented, four-minute trials (9 subjects X 9 tasks X 3 replications). The electrophysiological data collected included vectorcardiogaram, respiration, electromyogram, skin impedance, and electroencephalogram. Special computer programs were created for the analysis of each physiological variable. The digital data base then consisted of 82 physiological features for each of the 243 trials. A prediction of workload based on physiological observations was formulated as a simultaneous least-squares prediction problem. A best subset of 10 features was chosen to predict the three measures of reserve capacity. The cannonical correlation coefficient was .754 with a chi squared value of 91.3 which allows rejection of the null hypothesis with p of .995.

Spyker, D. A.↗