Search NASA⌕ Search

SEARCH · Search NASA

Results for “Alternating 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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Fourier domain target transformation analysis in the thermal infrared

Remote sensing uses of principal component analysis (PCA) of multispectral images include band selection and optimal color selection for display of information content. PCA has also been used for quantitative determination of mineral types and abundances given end member spectra. The preliminary results of the investigation of target transformation PCA (TTPCA) in the fourier domain to both identify end member spectra in an unknown spectrum, and to then calculate the relative concentrations of these selected end members are presented. Identification of endmember spectra in an unknown sample has previously been performed through bandmatching, expert systems, and binary classifiers. Both bandmatching and expert system techniques require the analyst to select bands or combinations of bands unique to each endmember. Thermal infrared mineral spectra have broad spectral features which vary subtly with composition. This makes identification of unique features difficult. Alternatively, whole spectra can be used in the classification process, in which case there is not need for an expert to identify unique spectra. Use of binary classifiers on whole spectra to identify endmember components has met with some success. These techniques can be used, along with a least squares fit approach on the endmembers identified, to derive compositional information. An alternative to the approach outlined above usese target transformation in conjunction with PCA to both identify and quantify the composition of unknown spectra. Preprocessing of the library and unknown spectra into the fourier domain, and using only a specific number of the components, allows for significant data volume reduction while maintaining a linear relationship in a Beer's Law sense. The approach taken here is to iteratively calculate concentrations, reducing the number of endmember components until only non-negative concentrations remain.

Anderson, D. L.↗
NASA NTRS1976

Velocity dispersions in galaxies. V - The nuclei of M31 and M32

Stigmatic spectra between 4160 and 4385 A of the central regions of M31 and M32 as well as the K0 III star 51 Ori are presented which were obtained using a SEC-vidicon integrating television tube and the coude spectrograph of the Hale telescope. Line-of-sight velocity dispersions of approximately 130 and 55 km/s are determined for the nuclei of M31 and M32, respectively, by directly comparing their spectra with Gaussian-broadened spectra of 51 Ori. The analytical techniques are outlined, and alternative methods for estimating velocity dispersions are evaluated, including least-squares fitting of intensities and division of Fourier transforms. It is noted that the broadened spectrum of 51 Ori fits the nucleus of M32 and the bulge of M31 much better than the nucleus of M31 in the region between 4180 and 4370 A.

Morton, D. C.↗
DOE OSTI2020

A Dynamic Trajectory Fit to Multisensor Fireball Observations

Meteorites with known orbital origins are key to our understanding of solar system formation and the source of life on Earth. Fireball networks have been developed globally in a unified effort to record and ultimately retrieve these cosmic samples. However, the accuracy of the determined orbit and the likelihood of meteorite recovery depend directly on the accuracy of the chosen meteoroid triangulation method. There are three leading techniques for meteoroid triangulation discussed in the literature: the method of planes, the straight-line least-squares method, and the multiparameter fit method. Here we describe an alternative method to meteoroid triangulation, called the dynamic trajectory fit. This approach uses the meteoroid’s 3D dynamic equations of motion to fit a realistic trajectory directly to multisensor line-of-sight observations. This method has the ability to resolve fragmentation events, fit systematic observatory timing offsets, and determine mass estimates of the meteoroid along its observable trajectory. Through a comprehensive Monte Carlo analysis of over 100,000 trajectory simulations, we find this new method to more accurately estimate meteoroid trajectories of slow entry events (<25 km s{sup −1}) and events observed from low convergence angles (<10°) compared to existing meteoroid triangulation techniques. Additionally, we triangulate an observed fireball event with visible fragmentation using the various triangulation methods to show that the proposed dynamic trajectory fit implementing fragmentation to best match the captured multisensor line-of-sight data.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1995

Prediction of pressurant mass requirements for axisymmetric liquid hydrogen tanks

Experimental data from several test series are compared to an existing correlation that predicts the amount of pressurant gas mass required to expel liquid hydrogen from axisymmetric tanks. It was necessary to use an alternate definition of the tank equivalent diameter to accommodate thermal mass in the tank wall that is initially warm and to accommodate liquid residuals in the tank after expulsion is stopped. With this modification, the existing correlation predicted mass requirements to within 14 percent of experimental results. Revision of the correlation constants using a nonlinear least-squares fit of the current experimental data has a minor effect, thus supporting the validity of the original correlation's form, its fitted constants, and the alternate definition of the tank equivalent diameter.

Vandresar, N. T.↗
NASA NTRS1984

Exploring the use of structural models to improve remote sensing agricultural estimates

Satellite estimates of agricultural characteristics often are not sufficiently precise for reliable use in small geographical regions. The precision of estimates of agricultural characteristics such as crop proportions and leaf area indexes can be increased by modeling ground observations as a function of satellite estimates. Linear regression models using least squares estimators of the model parameters are most often advocated as an appropriate methodology; however, least squares estimation requires that the predictor variables are measured without error, an unreasonable assumption for this application. An alternative estimation methodology which assumes that both the response variables (ground observations) and the predictor variables (satellite estimates) are measured with error involves the use of linear structural models. The application of linear structural models to the estimation of agricultural characteristics using satellite spectral measurements is examined.

Gunst, R. F.↗
DOE OSTI2020

Algorithms in Diffraction Profile Analysis

This chapter introduces several approaches to crystallographic structure refinement from diffraction profile data including the Rietveld method, global optimization methods, and Bayesian modeling. First, the Rietveld method and related nonlinear least squares approaches to analyzing diffraction profiles are briefly discussed. We then review the most common algorithms within global optimization as alternative methods of structure solution: grid search, simulated annealing, and genetic algorithms. As the Rietveld method is the standard tool for analyzing diffraction profile data, we catalogue its challenges and limitations. A Bayesian approach to diffraction profile analysis is presented as an alternative, along with several sampling algorithms including Gibbs sampling, variants of Metropolis sampling, Hamiltonian Monte Carlo, and approximate Bayesian computing. These sampling algorithms are applied to the fitting of a neutron diffraction profile from a National Institute of Standards and Technology silicon standard reference material, and their results are compared.

Singh, Susheela↗
NASA NTRS1973

Pole and zero placement in multivariable control systems

A method is proposed for designing multivariable systems based on an alternate derivation of Davison's theorem on pole placement and the solution of the nonlinear equations for the feedback gains by the least square error method. Output feedback is used to control a complex dynamical system. The freedom in design, after allocating poles, is used to place zeros and/or satisfy other design objectives. This method results in algorithms which are computationally attractive. However, this is done at a considerable sacrifice in terms of the design freedom available. For a system with m inputs and p outputs only m + p variables are available instead of mp variables.

Sridhar, B.↗
DOE OSTI2026

Two-Level Sketching Alternating Anderson Acceleration for Complex Physics Applications

We present a novel two-level sketching extension of the Alternating Anderson–Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multiphysics simulations governed by discretized PDEs. Our approach combines a static, physics-based projection that reduces the least-squares (LS) problem to the most informative field (e.g., via Schur-complement insight) with a dynamic, algebraic sketching stage driven by a backward stability analysis under Lipschitz continuity. We introduce inexpensive estimators for stability thresholds and cache-aware randomized selection strategies to balance computational cost against memory access overhead. The resulting algorithm solves reduced LS systems in place, minimizes memory footprints, and seamlessly alternates between low-cost Picard updates and Anderson mixing. Implemented in Julia, our two-level sketching AAP achieves up to 50% time-to-solution reductions compared to standard Anderson acceleration—without degrading convergence rates—on benchmark problems including Stokes, 𝑝-Laplacian, bidomain, and Navier–Stokes formulations at varying problem sizes. These results demonstrate the method’s robustness, scalability, and potential for integration into high-performance scientific computing frameworks. Our implementation is available open source in the AAP.jl library.

Barnafi, Nicolas [University of Chile, Santiago]↗
NASA NTRS1989

The moments of inertia of Mars

The mean moment of inertia of Mars is, at present, very poorly constrained. The generally accepted value of 0.365 M(R-squared) is obtained by assuming that the observed second degree gravity field can be decomposed into a hydrostatic oblate spheroid and a nonhydrostatic prolate spheroid with an equatorial axis of symmetry. An alternative decomposition is advocated in the present analysis. If the nonhydrostatic component is a maximally triaxial ellipsoid (intermediate moment exactly midway between greatest and least), the hydrostatic component is consistent with a mean moment of 0.345 M(R-squared). The plausibility of this decomposition is supported by statistical arguments and comparison with the earth, moon and Venus.

Bills, Bruce G.↗
NASA NTRS1990

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.↗
DOE OSTI2026

What Shapes Transportation Charging Infrastructure Availability? Evidence from Tennessee

This study examines how community, travel, and freight characteristics relate to public charging infrastructure availability across Tennessee ZIP codes. We link Alternative Fuels Data Center station locations with traffic, socioeconomic, demographic, commuting, and freight employment data to build a ZIP code-level dataset. Ordinary least squares regression captures variation in chargers per 10,000 residents (R2=0.311). Quantile regressions at the 25th, 50th, and 75th percentiles, with pseudo R2 values up to 0.099, show that the determinants of infrastructure availability differ across low-, medium-, and high-availability areas. Percent female, percent car commuters, average household size, and median age are negatively associated with charging availability across much of the distribution. Truck traffic is positively associated only in lower-availability ZIP codes, while vehicle miles traveled shifts from a negative association at the lower end of the distribution to a positive association at the upper end. The results provide insight into how public charging deployment aligns with community characteristics, mobility demand, and freight activity across Tennessee. Future work can distinguish charger types and power levels, incorporate land-use and temporal rollout patterns, and examine how charging infrastructure needs differ across urban and rural contexts.

Calderón, Oriana [University of Tennessee, Knoxvil↗
NASA NTRS1988

Absolute intensities of CO2 lines in the 3140-3410/cm spectral region

Absolute intensities for 430 transitions belonging to eleven rotation-vibration bands of (C-12)(O-16)2, (C-13)(O-16)2, and (O-16)(C-18)(O-18) in the 3140-3410/cm spectral region have been determined by analyzing spectra recorded at 0.01/cm resolution with the Fourier transform spectrometer in the McMath solar telescope complex at the National Solar Observatory on Kitt Peak. The data were recorded at room temperature and low pressures (less than 10 torr) using a natural sample of carbon dioxide. Intensities were derived using a nonlinear least-squares spectral fitting procedure, and the values obtained for each band have been analyzed to determine the vibrational band intensity and nonrigid rotor coefficients. An alternative mathematical formulation is shown in the case of bands for which the Coriolis effect is large and the Q-branch line intensities were not determinable either because they were severely blended or absent from the spectra. Comparison are made between the results obtained in this study and other published values.

Benner, D. Chris↗
NASA NTRS1989

Optimized resolved rate control of seven-degree-of-freedom Laboratory Telerobotic Manipulator (LTM) with application to three-dimensional graphics simulation

The Laboratory Telerobotic Manipulator (LTM) is a seven-degree-of-freedom robot arm. Two of the arms were delivered to Langley Research Center for ground-based research to assess the use of redundant degree-of-freedom robot arms in space operations. Resolved-rate control equations for the LTM are derived. The equations are based on a scheme developed at the Oak Ridge National Laboratory for computing optimized joint angle rates in real time. The optimized joint angle rates actually represent a trade-off, as the hand moves, between small rates (least-squares solution) and those rates which work toward satisfying a specified performance criterion of joint angles. In singularities where the optimization scheme cannot be applied, alternate control equations are devised. The equations developed were evaluated using a real-time computer simulation to control a 3-D graphics model of the LTM.

Barker, L. Keith↗
NASA NTRS2008

Jet Mixing Noise Scaling Laws SHJAR Data Vs. Predictions

High quality jet noise spectral data measured at the anechoic dome at the NASA Glenn Research Center is used to examine a number of jet noise scaling laws. Configurations considered in the present study consist of convergent as well as convergent-divergent axisymmetric nozzles. The spectral measurements are shown in narrow band and cover 8193 equally spaced points in a typical Strouhal number range of (0.01 10.0). Measurements are reported as lossless (i.e. atmospheric attenuation is added to as-measured data), and at 24 equally spaced angles (50deg to 165deg) on a 100-diameter arc. Following the work of Viswanathan [Ref. 1], velocity power laws are derived using a least square fit on spectral power density as a function of jet temperature and observer angle. The goodness of the fit is studied at each angle, and alternative relationships are proposed to improve the spectral collapse when certain conditions are met. On the application side, power laws are extremely useful in identifying components from various noise generation mechanisms. From this analysis, jet noise prediction tools can be developed with physics derived from the different spectral components.

Khavaran, Abbas↗
NASA NTRS1979

The application of finite element techniques to acoustic transmission in lined ducts with flow

The finite element method (FEM) is used to analyze the propagation of sound in two-dimensional nonuniform ducts carrying a compressible subsonic mean flow. Galerkin and residual least squares (RLS) methods with natural and forced boundary conditions are considered. The accuracy of FEM results for the eigenvalue and transmission problems is assessed by comparison with alternative numerical schemes for nonuniform ducts. The results presented and those from associated investigations indicate that modal coupling is a significant feature of the acoustic field, especially at high Mach numbers. A multimodal model therefore appears to be essential if any reliable conclusions are to be drawn in the context of turbofan inlet regions. Improvements to the eigenvalue scheme following the implementation of higher-order Hermitian elements indicate a similar modification for the transmission problem.

Astley, R. J.↗
NASA NTRS1989

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.↗
DOE OSTI2020

Improving air leakage prediction of buildings using the fan pressurization method with the Weighted Line of Organic Correlation

In many countries, the fan pressurization method is the most frequently chosen approach for measuring the air leakage of houses. The measurements are usually performed at pressures that far exceed pressures to which buildings are exposed to under normal conditions. A fit of these tests to the power-law formulation allows an extrapolation to data points outside the measured pressure range. With the Ordinary Least Square (OLS) fitting method, the pressure exponent and flow coefficient can be determined. However, the measurement results are highly sensitive to uncertainties induced by external factors like changing wind conditions during the tests, which is neglected by OLS. This may lead to errors in the prediction of flows at lower pressures. The Weighted Line of Organic Correlation (WLOC) is an alternative approach and takes measurement uncertainty into account. In this paper, a statistical analysis of an extensive data set of pressurization measurements has been performed. Both regression techniques have been compared for almost 7500 fan pressurization measurements of six houses in 109 different house leak configurations. The variability in predicting pressure exponent and flow coefficient for both WLOC and OLS regression was analyzed using probability density functions. It was found that the Weighted Line of Organic Correlation significantly decreases the uncertainty in predicting pressure exponent, flow coefficient, and other low-pressure air leakage metrics compared to the Ordinary Least Square fitting. Here, the authors highly recommend the implementation of WLOC in current measurement standards and test equipment.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Fast-RF-Shimming: Accelerate RF shimming in 7T MRI using deep learning

Ultrahigh field (UHF) Magnetic Resonance Imaging (MRI) offers an elevated signal-to-noise ratio (SNR), enabling exceptionally high spatial resolution that benefits both clinical diagnostics and advanced research. However, the jump to higher fields introduces complications, particularly transmit radiofrequency (RF) field ($B^{+}_{1}$) inhomogeneities, manifesting as uneven flip angles and image intensity irregularities. These artifacts can degrade image quality and impede broader clinical adoption. Traditional RF shimming methods, such as Magnitude Least Squares (MLS) optimization, effectively mitigate $B^{+}_{1}$ inhomogeneity, but remain time-consuming. Recent machine learning approaches, including RF Shim Prediction by Iteratively Projected Ridge Regression and other deep learning architectures, suggest alternative pathways. Although these approaches show promise, challenges such as extensive training periods, limited network complexity, and practical data requirements persist. In this paper, we introduce a holistic learning-based framework called Fast-RF-Shimming, which achieves a 5000 ​× ​speed-up compared to the traditional MLS method. In the initial phase, we employ random-initialized Adaptive Moment Estimation (Adam) to derive the desired reference shimming weights from multi-channel $B^{+}_{1}$ fields. Next, we train a Residual Network (ResNet) to map $B^{+}_{1}$ fields directly to the ultimate RF shimming outputs, incorporating the confidence parameter into its loss function. Finally, we design Non-uniformity Field Detector (NFD), an optional post-processing step, to ensure the extreme non-uniform outcomes are identified. Comparative evaluations with standard MLS optimization underscore notable gains in both processing speed and predictive accuracy, which indicates that our technique shows a promising solution for addressing persistent inhomogeneity challenges.

Deep learning↗