Search NASA⌕ Search

SEARCH · Search NASA

Results for “least-squares”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

Computation of solar wind parameters from the OGO-5 plasma spectrometer data using Hermite polynomials

The method used to calculate the velocity, temperature, and density of the solar wind plasma is presented from spectra obtained by attitude-stabilized plasma detectors on the earth satellite OGO 5. The method, which used expansions in terms of Hermite polynomials, is very inexpensive to implement on an electronic computer compared to the least-squares and other iterative methods often used for similar problems.

Neugebauer, M.↗

A program for identification of linear systems

A program has been written for the identification of parameters in certain linear systems. These systems appear in biomedical problems, particularly in compartmental models of pharmacokinetics. The method presented here assumes that some of the state variables are regularly modified by jump conditions. This simulates administration of drugs following some prescribed drug regime. Parameters are identified by a least-square fit of the linear differential system to a set of experimental observations. The method is especially suited when the interval of observation of the system is very long.

Buell, J.↗

Determination of stability derivatives from flight data using a Newton-Raphson minimization technique

A modified Newton-Raphson or quasilinearization minimization technique for determining stability derivatives from flight data was developed and compared with simple-equations, analog-matching, least-squares, and Shinbrot methods of analysis. For the data analyzed, the solutions computed by using the estimates obtained from the Newton-Raphson technique fit the data and determined coefficients adequately. A further modification to include a priori information was found to be useful. A model statistically similar to the flight data was analyzed using the same methods (excluding analog matching), and the Newton-Raphson technique was found to yield superior estimates. An approximate Cramer-Rao bound was compared with the error covariance matrix of the model and was found to provide information about the reliability of the individual estimates obtained. The technique was successfully applied to data obtained from a light airplane, a large supersonic airplane, and a lifting body vehicle. It was shown that the reliability of the estimates of a given coefficient obtained from these vehicles depends upon the data analyzed.

Iliff, K. W.↗

A computer program for Moessbauer data processing

A computer program to analyze Mossbauer data is presented in detail. The least-squares curve fitting techniques described apply to single line spectra, single hyperfine spectra, or when the constituent spectra are separated well enough to let the individual absorption peaks stand alone. The present program is not adapted for complex spectra resulting from the existence of several local environments in the absorber iron alloy. Sample problems are presented to aid the user in setting up and running the program. The program is written in FORTRAN 4 language for the Control Data 6000 series digital computer with the SCOPE 3.0 operating system and requires approximately 115,000 octal locations of core storage. A typical case with one absorption peak runs in 20 seconds, and a typical problem with six absorption peaks requires 50 seconds.

Howser, L. M.↗

Strapdown platforms using redundant two-degree-of-freedom gyros

A new concept of high reliability strapdown attitude sensing systems for space vehicles is presented. Each system utilizes a set of redundant two-degree-of-freedom gyros. An optimum system configuration is obtained for maximum system reliability and the best measurement accuracy. Improved accuracy of the final data is obtained by using the least-square data reduction technique. Each system possesses a sensor performance management feature which is capable of failure detection, faulty gyro identification, system reconfiguration, and possibly, sensor recalibration. Improvement in reliability as compared to other types of strapdown systems is demonstrated. Details of the development are described in terms of a system containing four gyros.

Hung, J. C.↗

Neutron die-away experiment for remote analysis of the surface of the moon and the planets, phase 3

Continuing work on the two die-away measurements proposed to be made in the combined pulsed neutron experiment (CPNE) for analysis of lunar and planetary surfaces is described. This report documents research done during Phase 3. A general exposition of data analysis by the least-squares method and the related problem of the prediction of variance is given. A data analysis procedure for epithermal die-away data has been formulated. In order to facilitate the analysis, the number of independent material variables has been reduced to two: the hydrogen density and an effective oxygen density, the latter being determined uniquely from the nonhydrogeneous elemental composition. Justification for this reduction in the number of variables is based on a set of 27 new theoretical calculations. Work is described related to experimental calibration of the epithermal die-away measurement. An interim data analysis technique based solely on theoretical calculations seems to be adequate and will be used for future CPNE field tests.

Mills, W. R.↗

In-plane, flexural, twisting and thickness-shear coefficients for stiffness and damping of a monolayer filamentary composite, part 1

Elastic and damping analyses resulting in determinations of the various stiffnesses and associated loss tangents for the complete characterization of the elastic and damping behavior of a monofilament composite layer are presented. For the determination of the various stiffnesses, either an elementary mechanics-of-materials formulation or a more rigorous mixed-boundary-value elasticity formulation is used. The solution for the latter formulation is obtained by means of the boundary-point least-square error technique. Kimball-Lovell type damping is assumed for each of the constituent materials. For determining the loss tangents associated with the various stiffnesses, either the viscoelastic correspondence principle or an energy analysis based on the appropriate elastic stress distribution is used.

Bert, C. W.↗

The production rate of Al/26/ from target elements in the Bruderheim chondrite.

A specimen of the Bruderheim chondrite was subjected to magnetic and heavy-liquid mineral separation procedures, resulting in a number of chemically distinct samples. These samples were analyzed for cosmogenic Al(26) by nondestructive gamma-gamma coincidence counting. The observed Al(26) specific activities were correlated with the chemical composition of potential target elements by a weighted least-squares fitting technique. The calculated Al(26) production rates from Al, Si, S, Mg, and Ca are presented. Most meteorite classes are shown to have a distribution of observed Al(26) vs calculated Al(26) primarily between 0.80 and 1.10, with the only exception of the eucrites. Two Apollo 12 samples, from mean depths of 15-20 cm, have approximately 0.78 of the Al(26) activities calculated for their chemical composition. A depletion in Al(26) in lunar samples shielded from solar radiation is in accord with a reduced cosmic-ray flux near the earth's orbit, relative to that experienced by most meteorites.

Cressy, P. J., Jr.↗

Zeeman effect of As II.

Spectrograms of As electrodeless-discharge tubes operated in a field of 24,025 G have given Zeeman patterns for 232 As II spectral lines from 2361 to 10,556 A and yielded 80 Lande g factors, of which more than half are new. There is agreement between these and the g values calculated by least-squares fitting for single configurations or for multiconfigurations, where configuration interaction is noticeable. All of the measured g values as well as the energy levels are used in the fitting process.

Li, H.↗

Linear restoration of incoherently radiating objects.

Light from an incoherently radiating object and background light are focused onto a photosensitive mosaic, the currents from whose elements constitute the data on which is based a least-squares linear estimate of the radiance at points in the object. By comparison of the mean-square error with that given by Wiener filtering theory, the equivalent noise spectral density for use in the latter is shown to consist of a shot-noise term and a term due to the random fluctuations of the incoherent light; the former predominates under most circumstances. Turbulent distortion of the image after passage of the rays through a random-phase screen is also treated from this standpoint.

Helstrom, C. W.↗

Thermal conductivity of Apollo 12 fines at intermediate density.

The thermal conductivity of an Apollo 12 fines sample (12001,19) was measured under vacuum conditions over a temperature range of 200 to 400 K for a density of 1640 kg/cu m. It was found to vary from approximately .0012 to about .0026 W/m-K. A least-squares curve was found to represent the data satisfactorily.

Cremers, C. J.↗

Influence of thermal anisotropy on best-fit estimates of shock normals.

This paper deals with the influence of thermal anisotropy on least-squares estimates of interplanetary shock parameters and the associated normals by using the Rankine-Hugoniot equations. A practical theorem is given for quantitatively correcting for anisotropic effects by weighting the before and after magnetic fields by the same 'anisotropy parameter' h. The quantity h depends only on the thermal anisotropies before and after the shock and on the angles between the magnetic fields and the shock normal. It is shown that, for fast shocks and for a liberal range of realistic conditions, the quantity h lies in the range from 0.90 to 1.22. The theorem can also be applied to most slow shocks, but in those instances h usually should be lower and sometimes markedly lower than unity.

Lepping, R. P.↗

Comments on the figure of the moon from Apollo landmark tracking.

The selenographic positions of the observed lunar features are solved for, or estimated directly from, angular measurements made from the orbiting spacecraft (Apollo missions 8, 10, 11, 12, 14, and 15) to the landmark, using least-squares techniques. It appears that the radius values derived from the Apollo landmark data provide some proof of the existence of a displacement between the center of figure and center of mass of the moon along the earth-moon line. In addition, all three components of the estimated crater locations should be useful toward establishing a selenodetic reference system for interpreting or reducing earth-based observation data.

Wollenhaupt, W. R.↗

A two-spacecraft test of a single spacecraft method of estimating shock normals

By assuming the validity of a subset of the Rankine-Hugoniot conservation relations for interplanetary (IP) shocks in an isotropic medium it has been demonstrated, in principle, that improved shock normals can be calculated by using a least-squares technique on combined magnetic field and plasma data from a single spacecraft. The scheme uses those six conservation relations not involving pressure and temperature. This paper deals with a test of the scheme by examining in detail a shock across which the magnetic field changed direction by a small amount (approximately 10 deg). On January 26, 1968 at about 1430 UT this shock was observed by the plasma and magnetic field instruments in Explorers 33 and 35. The spacecraft were 76.6 and 56.9 R sub E sunward of the earth, respectively (and 43.5 R sub E from each other), and therefore well outside the earth's bow shock region, a necessary condition for a valid test.

Lepping, R. P.↗

Probabilistic-graphical and phenomenological analysis of combined bending-torsion fatigue reliability data

Fatigue data generated by three combined bending-torsion fatigue reliability research machines at The University of Arizona are probabilistic-graphically and phenomenologically analyzed. Distributions that are applicable to fatique life and static strength data are discussed. Phenomenological justifications for the use of these distributions are presented. It is found that the normal distribution represents the cycles-to-failure data at the highest stress levels best. The lognormal distribution appears to fit the cycles-to-failure data at the lower stress levels best and quite well at all stress levels including the highest. A regression analysis and least-squares goodness-of-fit test was performed for normal and lognormal plots. In most cases, the correlation coefficient gave a better fit to the data using the normal distribution, but the difference between the two was so slight that positive discrimination could not be made.

Kececioglu, D.↗

Elastostatic stress analysis of orthotropic rectangular center-cracked plates

A mapping-collocation method was developed for the elastostatic stress analysis of finite, anisotropic plates with centrally located traction-free cracks. The method essentially consists of mapping the crack into the unit circle and satisfying the crack boundary conditions exactly with the help of Muskhelishvili's function extension concept. The conditions on the outer boundary are satisfied approximately by applying the method of least-squares boundary collocation. A parametric study of finite-plate stress intensity factors, employing this mapping-collocation method, is presented. It shows the effects of varying material properties, orientation angle, and crack-length-to-plate-width and plate-height-to-plate-width ratios for rectangular orthotropic plates under constant tensile and shear loads.

Gyekenyesi, G. S.↗

Refinement of the gravity field by satellite-to-satellite Doppler tracking.

The question of what resolution of the gravity field can be obtained from satellite-to-satellite Doppler tracking was investigated by performing least-squares adjustments of simulated Doppler data, solving for parameters describing the anomalous gravity field in various sized blocks. By examining the correlation between the adjusted parameters describing neighboring blocks, it was possible to judge whether a given set of data was capable of resolving blocks of a given size. Two concepts of satellite-to-satellite tracking are considered: the first involves two satellites near together in very low orbits, while the second uses geostationary satellites to track a single very low satellite. In either case, blocks 500 km on a side can be satisfactorily resolved from an orbital altitude of 700 km. From an altitude of 200 km, blocks 200 km on a side can be resolved. Because of the lower limit on altitude imposed by the presence of the earth's atmosphere, it does not appear that satellite-to-satellite Doppler tracking will be able to resolve features smaller than 200 km on a side.

Schwarz, C. R.↗

Satellite material contaminant optical properties

The Air Force Wright Research and Development Center and the Arnold Engineering Development Center are continuing a program for measuring optical effects of satellite material outgassing products on cryo-optic surfaces. Presented here are infrared (4000 to 700 cm(-1)) transmittance data for contaminant films condensed on a 77 K geranium window. From the transmittance data, the contaminant film refractive and absorptive indices (n, k) were derived using an analytical thin-film interference model with a nonlinear least-squares algorithm. To date 19 materials have been studied with the optical contents determined for 13 of those. The materials include adhesives, paints, composites, films, and lubricants. This program is continuing and properties for other materials will be available in the future.

Wood, B. E.↗