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Results for “least-squares regression”

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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35 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1969

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.↗
NASA NTRS1996

Land Surface Temperature Measurements form EOS MODIS Data

We have developed a physics-based land-surface temperature (LST) algorithm for simultaneously retrieving surface band-averaged emissivities and temperatures from day/night pairs of MODIS (Moderate Resolution Imaging Spectroradiometer) data in seven thermal infrared bands. The set of 14 nonlinear equations in the algorithm is solved with the statistical regression method and the least-squares fit method. This new LST algorithm was tested with simulated MODIS data for 80 sets of band-averaged emissivities calculated from published spectral data of terrestrial materials in wide ranges of atmospheric and surface temperature conditions. Comprehensive sensitivity and error analysis has been made to evaluate the performance of the new LST algorithm and its dependence on variations in surface emissivity and temperature, upon atmospheric conditions, as well as the noise-equivalent temperature difference (NE(Delta)T) and calibration accuracy specifications of the MODIS instrument. In cases with a systematic calibration error of 0.5%, the standard deviations of errors in retrieved surface daytime and nighttime temperatures fall between 0.4-0.5 K over a wide range of surface temperatures for mid-latitude summer conditions. The standard deviations of errors in retrieved emissivities in bands 31 and 32 (in the 10-12.5 micrometer IR spectral window region) are 0.009, and the maximum error in retrieved LST values falls between 2-3 K. Several issues related to the day/night LST algorithm (uncertainties in the day/night registration and in surface emissivity changes caused by dew occurrence, and the cloud cover) have been investigated. The LST algorithms have been validated with MODIS Airborne Simulator (MAS) dada and ground-based measurement data in two field campaigns conducted in Railroad Valley playa, NV in 1995 and 1996. The MODIS LST version 1 software has been delivered.

Wan, Zhengming↗
NASA NTRS1993

Analysis of the distribution of pitch angles in model galactic disks - Numerical methods and algorithms

An automated mathematical method capable of successfully isolating the many different features in prototype and observed spiral galaxies and of accurately measuring the pitch angles and lengths of these individual features is developed. The method is applied to analyze the evolution of specific features in a prototype galaxy exhibiting flocculent spiral structure. The mathematical-computational method was separated into two components. Initially, the galaxy was partitioned into dense regions constituting features using two different methods. The results obtained using these two partitioning algorithms were very similar, from which it is inferred that no numerical biasing was evident and that capturing of the features was consistent. Standard least-squares methods underestimated the true slope of the cloud distribution and were incapable of approximating an orientation of 45 deg. The problems were overcome by introducing a superior fit least-squares method, developed with the intention of calculating true orientation rather than a regression line.

Russell, William S.↗
NASA NTRS1986

Rain cell size statistics derived from radar observations at Wallops Island, Virginia

An investigation of two-dimensional rain cell size statistics has analyzed regression relations relating radar-determined rain rates to disdrometer data. This has yielded least-squares fits of radar reflectivity factors, and the application of a contouring program has generated 22,000 contours in which each isopleth belongs to predefined rain-rate intervals. An abundance of total and cell contours were observed belonging to all rain-rate categories. Both the computed number distributions and the conditional cumulative distributions as a function of contour diameter were found to be represented with good approximation by given exponential functions.

Goldhirsh, J.↗
NASA NTRS1985

Identification of pilot dynamics from in-flight tracking data

Data from a representative flight task involving an F-14 'pursuer' aircraft tracking a T-38 'target' aircraft in a 3G wind-up turn and in level flight are processed using a least squares identification technique in an attempt to identify pilot/vehicle dynamics. Comparative identification results are provided by a Fourier coefficient method which requires a carefully designed and implemented input consisting of a sum of sinusoids. The least-squares results compare favorably with those obtained by the Fourier technique. An example of crossover frequency regression is discussed in the light of the conditions of one of the flight configurations.

Hess, R. A.↗
NASA NTRS1991

A case study demonstration of the soil temperature extrema recovery rates after precipitation cooling at 10-cm soil depth

Since the invention of maximum and minimum thermometers in the 18th century, diurnal temperature extrema have been taken for air worldwide. At some stations, these extrema temperatures were collected at various soil depths also, and the behavior of these temperatures at a 10-cm depth at the Tifton Experimental Station in Georgia is presented. After a precipitation cooling event, the diurnal temperature maxima drop to a minimum value and then start a recovery to higher values (similar to thermal inertia). This recovery represents a measure of response to heating as a function of soil moisture and soil property. Eight different curves were fitted to a wide variety of data sets for different stations and years, and both power and exponential curves were fitted to a wide variety of data sets for different stations and years. Both power and exponential curve fits were consistently found to be statistically accurate least-square fit representations of the raw data recovery values. The predictive procedures used here were multivariate regression analyses, which are applicable to soils at a variety of depths besides the 10-cm depth presented.

Welker, Jean Edward↗
NASA NTRS2017

Heuristic Area Cost Estimation for Observational Coverage Schedulers

This paper presents a comparison of heuris- tics used to estimate the amount of time it would take for a spacecraft to image an area using Boustrophedon decomposition (Choset and Pignon 1998). Machine learning tech- niques are used to characterize algorithmic performance of coverage algorithms. It is shown that an ordinary least-squares linear model is among the most accurate in a set of constant and linear order regression models both in terms of memory consumption and schedule duration. These are demonstrated using the ASPEN planning system (Fukunaga et al. 1997) on the Eagle Eye domain.

Knight, Russell↗
NASA NTRS1973

Critical configurations (determinantal loci) for range and range difference satellite networks

The observational modes of Geometric Satellite Geodesy are discussed. The geometrical analysis of the problem yielded a regression model for the adjustment of the observations along with a suitable and convenient metric for the least-squares criterion. The determinantal loci (critical configurations) for range networks are analyzed. An attempt is made to apply elements of the theory of variants for this purpose. The use of continuously measured range differences for loci determination is proposed.

Tsimis, E.↗
NASA NTRS1994

Isostatic compensation of equatorial highlands on Venus

Spherical harmonic models for Venus' global topography and gravity incorporating Magellan data are used to test isostatic compensation models in five 30 deg x 30 deg regions representative of the main classes of equatorial highlands. The power spectral density for the harmonic models obeys a power-law scaling with spectral slope Beta approximately 2 (Brown noise) for the topography and Beta approximately 3 (Kaula's law) for the geoid, similar to what is observed for Earth. The Venus topography spectrum has lower amplitudes than Earth's which reflects the dominant lowland topography on Venus. Observed degree geoid to topography ratios (GTRs) on Venus are significantly smaller than degree GTRs for uncompensated topography, indicative of substantial compensation. Assuming a global Airy compensation, most of the topography is compensated at depths greater than 100 km, suggesting a thick lithosphere on Venus. For each region considered we obtain a regional degree of compensation C from a linear regression of Bouguer anomaly versus Bouguer gravity data. Geoid anomaly (N) versus topography variation (h) data for each sample were compared, in the least-squares sense, to theoretical correlations for Pratt, Airy, and thermal thinning isostasy models yielding regional GTR, zero-elevation crustal thickness (H), and zero elevation thermal lithosphere thickness (y(sub L(sub 0)), respectively. We find the regional compensation to be substantial (C approximately 52-80%), and the h, N data correlations in the chosen areas can be explained by isostasy models applicable on the Earth and involving variations in crustal thickness (Airy) and/or lithospheric (thermal thinning) thickness. However, a thick crust and lithosphere (y(sub L(sub 0)) approximately 300 km) must be assumed for Venus.

Kucinskas, Algis B.↗
NASA NTRS2020

Global Aerodynamic Modeling Using Automated Local Model Networks in Real Time

A novel method is presented for automated real-time global aerodynamic modeling using local model networks, known as Smoothed Partitioning with Localized Trees in Real Time (SPLITR), as part of NASA’s Learn-to-Fly technology development initiative. The global nonlinear aerodynamics are partitioned into several local regions known as cells, with the dimension, location, and timing of each partition automatically selected based on a residual characterization procedure, under the constraints of real-time operation. Regression trees represent the successive partitioning of the global flight envelope and describe the evolution of the cell structure. Recursive equation-error least-squares parameter estimation in the time domain is used to estimate a model that represents the local aerodynamics in each region, so that it can be updated independently with non-contiguous data in the range of each cell over time. A weighted superposition of these piecewise local models across the flight envelope forms a global nonlinear model that also accurately captures the local aerodynamics. The SPLITR approach is demonstrated using both simulation and flight data, and the results are analyzed in terms of model predictive capabilities as well as interpretability. The results show that SPLITR can be used to automatically partition complex nonlinear aerodynamic behavior, produce an accurate model, and provide valuable physical insight into the local and global aerodynamics.

Weinstein, Rose↗
NASA NTRS1981

Microwave scatterometer measurements of oceanic wind vector

Results from Seasat-A scatterometer (SASS) remote sensing of oceanic wind vectors are reviewed, together with the theory of radar backscattering. The SASS was designed to measure the surface wind stress and neutral stability wind vector at 19.5 m altitude. Requirements included windspeeds from 4-24 m/sec to within 2 m/sec or 10%, a 1000 km swath, directions from 0-360 deg to within 20 deg, a 50 km resolution cell, and cross-track and along-track spacing between resolution cells of 100 km. The method was based on Bragg scattering of microwaves from cm-length capillary ocean waves. The strength of the backscatter is proportional to the capillary wave amplitude, which is in equilibrium with the ocean surface wind speed. The measurement grouping, least-squares estimator, and dB deviation model function table for the SASS geophysical algorithm are discussed. Comparisons of SASS, GOASEX, and ground truth wind data are made, and a 0.92 correlation between SASS and ground truth data is determined from regression analysis.

Jones, W. L.↗
NASA NTRS2001

Information Retrieval from SAGE II and MFRSR Multi-Spectral Extinction Measurements

Direct beam spectral extinction measurements of solar radiation contain important information on atmospheric composition in a form that is essentially free from multiple scattering contributions that otherwise tend to complicate the data analysis and information retrieval. Such direct beam extinction measurements are available from the solar occultation satellite-based measurements made by the Stratospheric and Aerosol Gas Experiment (SAGE II) instrument and by ground-based Multi-Filter Shadowband Radiometers (MFRSRs). The SAGE II data provide cross-sectional slices of the atmosphere twice per orbit at seven wavelengths between 385 and 1020 nm with approximately 1 km vertical resolution, while the MFRSR data provide atmospheric column measurements at six wavelengths between 415 and 940 nm but at one minute time intervals. We apply the same retrieval technique of simultaneous least-squares fit to the observed spectral extinctions to retrieve aerosol optical depth, effective radius and variance, and ozone, nitrogen dioxide, and water vapor amounts from the SAGE II and MFRSR measurements. The retrieval technique utilizes a physical model approach based on laboratory measurements of ozone and nitrogen dioxide extinction, line-by-line and numerical k-distribution calculations for water vapor absorption, and Mie scattering constraints on aerosol spectral extinction properties. The SAGE II measurements have the advantage of being self-calibrating in that deep space provides an effective zero point for the relative spectral extinctions. The MFRSR measurements require periodic clear-day Langley regression calibration events to maintain accurate knowledge of instrument calibration.

Lacis, Andrew A.↗
NASA NTRS2001

The Statistical Consulting Center for Astronomy (SCCA)

The process by which raw astronomical data acquisition is transformed into scientifically meaningful results and interpretation typically involves many statistical steps. Traditional astronomy limits itself to a narrow range of old and familiar statistical methods: means and standard deviations; least-squares methods like chi(sup 2) minimization; and simple nonparametric procedures such as the Kolmogorov-Smirnov tests. These tools are often inadequate for the complex problems and datasets under investigations, and recent years have witnessed an increased usage of maximum-likelihood, survival analysis, multivariate analysis, wavelet and advanced time-series methods. The Statistical Consulting Center for Astronomy (SCCA) assisted astronomers with the use of sophisticated tools, and to match these tools with specific problems. The SCCA operated with two professors of statistics and a professor of astronomy working together. Questions were received by e-mail, and were discussed in detail with the questioner. Summaries of those questions and answers leading to new approaches were posted on the Web (www.state.psu.edu/ mga/SCCA). In addition to serving individual astronomers, the SCCA established a Web site for general use that provides hypertext links to selected on-line public-domain statistical software and services. The StatCodes site (www.astro.psu.edu/statcodes) provides over 200 links in the areas of: Bayesian statistics; censored and truncated data; correlation and regression, density estimation and smoothing, general statistics packages and information; image analysis; interactive Web tools; multivariate analysis; multivariate clustering and classification; nonparametric analysis; software written by astronomers; spatial statistics; statistical distributions; time series analysis; and visualization tools. StatCodes has received a remarkable high and constant hit rate of 250 hits/week (over 10,000/year) since its inception in mid-1997. It is of interest to scientists both within and outside of astronomy. The most popular sections are multivariate techniques, image analysis, and time series analysis. Hundreds of copies of the ASURV, SLOPES and CENS-TAU codes developed by SCCA scientists were also downloaded from the StatCodes site. In addition to formal SCCA duties, SCCA scientists continued a variety of related activities in astrostatistics, including refereeing of statistically oriented papers submitted to the Astrophysical Journal, talks in meetings including Feigelson's talk to science journalists entitled "The reemergence of astrostatistics" at the American Association for the Advancement of Science meeting, and published papers of astrostatistical content.

Akritas, Michael↗
NASA NTRS1999

Ventilatory responses to dynamic exercise elicited by intramuscular sensors

PURPOSE: Eight subjects, aged 27.0+/-1.6 yr, performed incremental workload cycling to investigate the contribution of skeletal muscle mechano- and metaboreceptors to ventilatory control during dynamic exercise. METHODS: Each subject performed four bouts of exercise: exercise with no intervention (CON); exercise with bilateral thigh cuffs inflated to 90 mm Hg (CUFF); exercise with application of lower-body positive pressure (LBPP) to 45 torr (PP); and exercise with 90 mm Hg thigh cuff inflation and 45 torr LBPP (CUFF+PP). Ventilatory responses and pulmonary gas exchange variables were collected breath-by-breath with concomitant measurement of leg intramuscular pressure. RESULTS: Ventilation (VE) was significantly elevated from CON during PP and CUFF+PP at workloads corresponding to > or = 60% CON peak oxygen uptake (VO2peak) and during CUFF at workloads > or = 80% CON VO2peak, P < 0.05. The VO2 at which ventilatory threshold occurred was significantly reduced from CON (2.17+/-0.28 L x min(-1)) to 1.60+/-0.19 L x min(-1), 1.45+/-0.15 L x min(-1), and 1.15+/-0.11 L x min(-1) during CUFF, PP, and CUFF+PP, respectively. The slope of the linear regression describing the VE/CO2 output relationship was increased from CON by approximately 22% during CUFF, 40% during PP, and 41% during CUFF+PP. CONCLUSIONS: As intramuscular pressure was significantly elevated immediately upon application of LBPP during PP and CUFF+PP without a concomitant increase in VE, it seems unlikely that LBPP-induced increases in VE can be attributed to activation of the mechanoreflex. These findings suggest that LBPP-induced reductions in perfusion pressure and decreases in venous outflow resulting from inflation of bilateral thigh cuffs may generate a metabolite sensitive intramuscular ventilatory stimulus.

Non-NASA Center↗
NASA NTRS1982

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.↗
NASA NTRS1993

The analytical representation of viscoelastic material properties using optimization techniques

This report presents a technique to model viscoelastic material properties with a function of the form of the Prony series. Generally, the method employed to determine the function constants requires assuming values for the exponential constants of the function and then resolving the remaining constants through linear least-squares techniques. The technique presented here allows all the constants to be analytically determined through optimization techniques. This technique is employed in a computer program named PRONY and makes use of commercially available optimization tool developed by VMA Engineering, Inc. The PRONY program was utilized to compare the technique against previously determined models for solid rocket motor TP-H1148 propellant and V747-75 Viton fluoroelastomer. In both cases, the optimization technique generated functions that modeled the test data with at least an order of magnitude better correlation. This technique has demonstrated the capability to use small or large data sets and to use data sets that have uniformly or nonuniformly spaced data pairs. The reduction of experimental data to accurate mathematical models is a vital part of most scientific and engineering research. This technique of regression through optimization can be applied to other mathematical models that are difficult to fit to experimental data through traditional regression techniques.

Hill, S. A.↗
NASA NTRS2000

Determining a Prony Series for a Viscoelastic Material From Time Varying Strain Data

In this study a method of determining the coefficients in a Prony series representation of a viscoelastic modulus from rate dependent data is presented. Load versus time test data for a sequence of different rate loading segments is least-squares fitted to a Prony series hereditary integral model of the material tested. A nonlinear least squares regression algorithm is employed. The measured data includes ramp loading, relaxation, and unloading stress-strain data. The resulting Prony series which captures strain rate loading and unloading effects, produces an excellent fit to the complex loading sequence.

Tzikang, Chen↗