Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “least-squares analysis”

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 127 records · Page 7

Simultaneous elastic and photoelastic calibration of birefringent orthotropic model materials

Transmission photoelastic analysis of composite models has been shown in recent years to be a viable stress analysis method for composite structures. However, difficulties in the fabrication of the model materials require the development of efficient mechanical and optical calibration procedures. In this paper, the methods for measuring elastic and photoelastic constants of composites are briefly reviewed. Then a new method, utilizing a relatively small calibration specimen, is described. In this method, electrical resistance strain gauges are mounted at selected points of a half-plane model and photoelastic measurements and strain readings are simultaneously taken. The data are processed by a least-squares procedure to yield the elastic and photoelastic constants. Comparison of results obtained by the proposed method with the results from conventional tests shows good agreement.

Prabhakaran, R.↗

Seasat orbit refinement for altimetry application

This paper describes the use of stochastic differential correction models in refining the Seasat orbit based on post-flight analysis of tracking data. The objective is to obtain orbital-height precision that is commensurate with the inherent Seasat altimetry data precision level of 10 cms. Local corrections to a mean ballistic arc, perturbed principally by atmospheric drag variations and local gravitational anomalies, are obtained by the introduction of stochastic dynamical models in conjunction with optimal estimation/smoothing techniques. Assessment of the resulting orbit with 'ground truth' provided by Seasat altimetry data shows that the orbital height precision is improved by 32% when compared to a conventional least-squares solution using the same data set. The orbital height precision realized by employing stochastic differential correction models is in the range of 73 cms to 208 cms rms.

Mohan, S. N.↗

Correction factors for on-line microprobe analysis of multielement alloy systems

An on-line correction technique was developed for the conversion of electron probe X-ray intensities into concentrations of emitting elements. This technique consisted of off-line calculation and representation of binary interaction data which were read into an on-line minicomputer to calculate variable correction coefficients. These coefficients were used to correct the X-ray data without significantly increasing computer core requirements. The binary interaction data were obtained by running Colby's MAGIC 4 program in the reverse mode. The data for each binary interaction were represented by polynomial coefficients obtained by least-squares fitting a third-order polynomial. Polynomial coefficients were generated for most of the common binary interactions at different accelerating potentials and are included. Results are presented for the analyses of several alloy standards to demonstrate the applicability of this correction procedure.

Unnam, J.↗

On the determination and investigation of the terrestrial ionospheric refractive indices using GEOS-3/ATS-6 satellite-to-satellite tracking data

An analysis of the shortening and lengthening of the phase of satellite-to-satellite (SST) data that passed within 40-700 km above the earth surface during its ATS-6 to GEOS-3 to ATS-6 path resulted in refractivity vs height profiles. The SST Doppler data were used directly to adjust the GEOS-3 orbit. Perturbations from the moon, sun, and a 15th-order/degree earth gravity field were included in the orbit solution. This orbit was continued through the occulation period and a model ionosphere was estimated by a least-squares adjustment of the Chapman ionosphere parameters from the SST data residuals. The refractivity profile obtained by this model ionosphere was compared to a refractivity profile obtained by a direct integral inversion of the SST data residuals. Systematic differences between the two methods were caused by orbital errors, which propagated into the solution.

Liu, A. S.↗

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.↗

On the determination and investigation of the terrestrial ionospheric refractive indices using GEOS-3/ATS-6 satellite-to-satellite tracking data

When the radio link between two satellites (GEOS-3/ATS-6) is intercepted by the earth's ionosphere and neutral atmosphere, a change in the Doppler frequency results. Travel through the atmosphere causes the Doppler phase to be advanced in the ionosphere's portion and retarded in the neutral portion of the atmosphere. Analysis of the shortening and lengthening of the phase of the Satellite-to-Satellite Tracking (SST) data that passed within 40-700 km above the earth's surface during its ATS-6 to GEOS-3 to ATS-6 path, caused by the atmosphere, results in refractivity versus height profiles. The SST Doppler data were used directly to adjust the GEOS-3 orbit. Perturbation from the Moon, Sun and a 15th order/degree earth gravity field were included in the orbit solution. This orbit was continued through the occultation period and a model ionosphere was estimated by a least-square adjustment of the Chapman ionosphere parameters from the SST data residuals. The refractivity profile obtained by this model ionosphere was compared to a refractivity profile obtained by a direct integral inversion of the SST data residuals. Systematic differences between the 2 methods were caused by orbital errors, which propagated into the solution. The SST data yielded refractive index profiles in a novel economical manner because no additional or special on-board equipment were required.

Liu, A. S.↗

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.↗

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.↗

Center of mass estimation in closed vortices - A verification in principle and practice

The problem of tracking closed mesoscale vortices using center of mass estimation techniques is studied. Three estimators are evaluated using data from a warm core Gulf Stream ring. The comparisons show that a method based on the intersection of perpendicular bisectors and one using a least-squares fit of a conic section perform comparably. The perpendicular bisector algorithm is used in conjunction with a Gaussian ring model and a star-shaped survey pattern to produce an expected error curve as a function of vortex translation, survey speed and vortex size. For typical ring parameters, center estimation is usually possible to within + or - 5 km. The feasibility of using differing data sets to construct a history of ring motion based on a coordinate system moving with the ring is also investigated. In this way, the validity of using satellite-derived data and drifter trajectories to estimate the center of mass of a mesoscale feature is assessed. The results of the analysis demonstrate that the location of the deeper structure of the ring and the surface expression are sufficiently well correlated to permit dynamically relevant calculations based on surface measurements. It is shown that satellite-derived data can be used to approximate the center of mass trajectory to within the error in the individual center estimates for the period analyzed. The Lagrangian-drifter-derived centers are offset from the center of mass trajectory in a manner consistent with kinematic arguments.

Hooker, S. B.↗

Line-frequency measurements and analysis of N2O between 900 and 4700/cm

The N2O infrared spectrum from 900 to 4700/cm has been studied with a high-resolution Fourier-transform spectrometer. Measurements were made of line frequencies of several N2O isotopes for several ground-state and hot bands. These bands include the 1530-0330, 2330-0330, 0441-0440, 0441-0330, 0531-0330, and 1331-0330 bands of (N-14)2(O-16). Also, perturbation-enhanced transitions in the 0710-0110 and 0730-0110 bands were assigned and measured. The frequencies have been analyzed to obtain a unique set of effective vibration-rotation parameters for each vibrational state. The results obtained from this research are of high accuracy for the ground-state, and the first-excited-state bands of (N-14)2(O-16), in which the computed frequencies derived from the least-squares fits, are known to an absolute uncertainty of only +/-4 x 10 exp -5 for nonperturbed transitions.

Toth, Robert A.↗

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.↗

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.↗

DFW microburst model based on AA-539 data

Analysis of the August 2, 1985 crash for an L-1011 jumbo jet (DL-191) on approach to the Dallas-Ft. Worth International Airport (DFW) in a thunderstorm indicates that the severe windshear microburst that caused the crash was composed not only of a strong downflow and outflow but also included several large-scale vortex rings entrained in the flowfield. This paper presents a detailed two-dimensional model of the DFW microburst based on data from the MD-80 (AA-539) that followed behind DL-191 and flew through the microburst about two minutes after the crash of DL-191. The model was developed using wind-vector and flight-path data reconstructed by NASA Ames Research Center and a combination of interactive graphics and least-squares error best fit between the modeled and measured wind vectors along the AA-539 flight path. The model indicates that the flowfield contains some significant elements and vortices not previously reported. The alternating direction of rotation of the vortices in the model suggests a microburst structure based on a von Karman vortex street rather than on a Kelvin-Helmholtz instability. The model also indicates that the reconstructed wind-vector data contain a time lag of at least one second in the horizontal winds.

Grantham, Walter J.↗

The relationship between IR, optical, and UV extinction

An analysis is presented for the variability of absolute IR, optical, and UV extinction, A(sub lambda), derived through the ratio of total-to-selective extinction, R, for 31 lines of sight for which reliable UV extinction parameters were derived. These data sample a wide range of environments and are characterized by 2.5 is less than or equal to R is less than or equal to 6.0. It was found that there is a strong linear dependence between extinction expressed as A(sub lambda)/A(sub V) and 1/R for 1.25 micron is less than or equal to lambda is less than or equal to 0.12 micron. Differences in the general shape of extinction curves are largely due to variations in shape of optical/near-UV extinction corresponding to changes in R, with A(sub lambda)/A(sub V) decreasing for increasing R. From a least-squares fit of the observed R-dependence as a function of wavelength for 0.8/micron is less than or greater than 1/lambda is less than or equal to 8.3/micron, an analytic expression was generated from which IR, optical, and UV extinction curves of the form A(sub lambda)/A(sub V) can be reproduced with reasonable accuracy from a knowledge of R. It was also found that the absolute bump strength normalized to A(sub V) shows a general decrease with increasing R, suggesting that some fraction of bump grains may be selectively incorporated into coagulated grains. Finally, it was found that absolute extinction normalized by suitably chosen color indices results in a minimization of the R-dependence of portions of the UV curve, allowing A(sub lambda) to be estimated for these wavelengths independent of R.

Cardelli, Jason A.↗

An airborne study of microwave surface sensing and boundary layer heat and moisture fluxes for Project FIFE

This is the third semiannual status report describing the University of Wyoming participation in project FIFE, under NASA Grant NAG 5-913. The reader is referred to the first and second semiannual status reports for this grant for descriptions of University of Wyoming participation in the field operations of 1987. This report is concerned with continuing analysis of field data. Most of the instrument calibration effort has concentrated on interpretation and use of the high-rate water vapor measurements with the University of Wyoming Lyman-alpha device. In addition, fluxes of water vapor have been corrected for sensible heat flux, and all the high-rate (10 Hz for the Wyoming King Air) data have been filtered before the flux calculations. For each flight the Lyman-alpha data (10 Hz) are calibrated against the Cambridge dew-point hygrometer (1 Hz), by using data from the take-off sounding. The reasoning here is that the takeoff sounding (held to 500 fpm rate-of-climb specifically for the calibration) covers the widest range of humidity conditions of any sequence of the flight. For each takeoff sounding, then, the Lyman-alpha data, averaged to 1 Hz, are matched to the dewpoint data with a second-order least-squares fit. The resulting quadratic equation is then used in all subsequent analyses to convert the Lyman-alpha voltages to vapor desities for that specific flight. An alternative method is to use the range of fluctuation for the same two devices from horizontal passes to establish the calibration function. However, since the Lyman-alpha data are used only in the flux calculations, i.e., only the fluctuation and not the absolute values are used, this method is thought unnecessary.

Kelly, Robert D.↗

Least-squares sequential parameter and state estimation for large space structures

This paper presents the formulation of simultaneous state and parameter estimation problems for flexible structures in terms of least-squares minimization problems. The approach combines an on-line order determination algorithm, with least-squares algorithms for finding estimates of modal approximation functions, modal amplitudes, and modal parameters. The approach combines previous results on separable nonlinear least squares estimation with a regression analysis formulation of the state estimation problem. The technique makes use of sequential Householder transformations. This allows for sequential accumulation of matrices required during the identification process. The technique is used to identify the modal prameters of a flexible beam.

Thau, F. E.↗

Optimal focal-plane restoration

Image restoration can be implemented efficiently by calculating the convolution of the digital image and a small kernel during image acquisition. Processing the image in the focal-plane in this way requires less computation than traditional Fourier-transform-based techniques such as the Wiener filter and constrained least-squares filter. Here, the values of the convolution kernel that yield the restoration with minimum expected mean-square error are determined using a frequency analysis of the end-to-end imaging system. This development accounts for constraints on the size and shape of the spatial kernel and all the components of the imaging system. Simulation results indicate the technique is effective and efficient.

Reichenbach, Stephen E.↗