Search NASA⌕ Search

SEARCH · Search NASA

Results for “Normal Distribution”

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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Monte Carlo simulation of wave sensing with a short pulse radar

A Monte Carlo simulation is used to study the ocean wave sensing potential of a radar which scatters short pulses at small off-nadir angles. In the simulation, realizations of a random surface are created commensurate with an assigned probability density and power spectrum. Then the signal scattered back to the radar is computed for each realization using a physical optics analysis which takes wavefront curvature and finite radar-to-surface distance into account. In the case of a Pierson-Moskowitz spectrum and a normally distributed surface, reasonable assumptions for a fully developed sea, it has been found that the cumulative distribution of time intervals between peaks in the scattered power provides a measure of surface roughness. This observation is supported by experiments.

Levine, D. M.↗
NASA NTRS1977

Landsat-D thematic mapper simulation using aircraft multispectral scanner data

A simulation of imagery from the upcoming Landsat-D Thematic Mapper was accomplished by using selected channels of aircraft 24-channel multispectral scanner data. The purpose was to simulate Thematic Mapper 30-meter resolution imagery, to compare its spectral quality with the original aircraft MSS data, and to determine changes in thematic classification accuracy for the simulated imagery. The original resolution of approximately 7.5 meters IFOV and simulated resolution of 15, 30, and 60 meters were used to indicate the trend of spectral quality and classification accuracy. The study was based in a 6.5 square kilometer area of urban Los Angeles having a diversity of land use. The original imagery was reduced in resolution by two related methods: pixel matrix averaging, and matrix smoothing with a unity box filter, followed by matrix averaging. Thematic land use classification using training sites and a Bayesian maximum-likelihood algorithm was performed at three levels of standard deviation - 1.0, 2.0, and 3.0 sigma. Plots of relative standard deviation showed that for larger training sites with a normal distribution of data, as the resolution decreased, the distribution range of density values decreased. Also, the classification accuracies for three levels of standard deviation increased as resolution decreased. However, the indication is that a point of diminishing returns had been reached, and 30 meters IFOV should be the best for multispectral classification of urban scenes.

Clark, J.↗
NASA NTRS1979

A model for the microwave emissivity of the ocean's surface as a function of wind speed

A quanitative model is presented which describes the ocean surface as a ensemble of flat facets with a normal distribution of slopes. The variance of the slope distribution is linearly related to frequency up to 35 GHz and constant at higher frequencies. These facets are partially covered with an absorbing nonpolarized foam layer. Experimental evidence is presented for this model.

Wilheit, T. T.↗
NASA NTRS1978

The CLASSY clustering algorithm: Description, evaluation, and comparison with the iterative self-organizing clustering system (ISOCLS)

A clustering method, CLASSY, was developed, which alternates maximum likelihood iteration with a procedure for splitting, combining, and eliminating the resulting statistics. The method maximizes the fit of a mixture of normal distributions to the observed first through fourth central moments of the data and produces an estimate of the proportions, means, and covariances in this mixture. The mathematical model which is the basic for CLASSY and the actual operation of the algorithm is described. Data comparing the performances of CLASSY and ISOCLS on simulated and actual LACIE data are presented.

Lennington, R. K.↗
NASA NTRS1979

A multi-disciplinary approach to structural design for stochastic loads

The development of aircraft gust design techniques is reviewed with emphasis on those techniques applicable to large scale multidisciplinary closed-loop optimization methods. An overall view is presented of the optimization methodology utilized. An analysis is presented wherein the bivariate normal distribution function for a particular loading condition is considered. By use of maximization techniques, functions are derived for stress components along equal probability contours which allow for directionality and auto-correlation effects to be considered. These functions are then applied to the problem being considered and the effects on the structural sizing and weight penalties evaluated against more conventional methods.

Gross, D. W.↗
NASA NTRS1979

Stresses from arbitrary loads on a circular crack

An inclusive theory is developed for stresses and displacements due to arbitrarily distributed normal and tangential loads acting on a circular crack in an infinite body. The representation chosen for the boundary conditions leads to solutions expressed as series of Bessel-function integrals of a class quite susceptible to further analysis and to rapid evaluation on modern computers. The load coefficients which appear in all the solution series bear intelligible interpretation, and stress intensity factors are related to them by simple formulas. The inclusiveness and tractability of the solutions qualify this theory to be a useful part of analyses for cracks in finite bodies in which the effective crack loads can assume many patterns.

Bell, J. C.↗
NASA NTRS1979

Modeling the Earth's radiation belts. A review of quantitative data based electron and proton models

The evolution of quantitative models of the trapped radiation belts is traced to show how the knowledge of the various features has developed, or been clarified, by performing the required analysis and synthesis. The Starfish electron injection introduced problems in the time behavior of the inner zone, but this residue decayed away, and a good model of this depletion now exists. The outer zone electrons were handled statistically by a log normal distribution such that above 5 Earth radii there are no long term changes over the solar cycle. The transition region between the two zones presents the most difficulty, therefore the behavior of individual substorms as well as long term changes must be studied. The latest corrections to the electron environment based on new data are outlined. The proton models have evolved to the point where the solar cycle effect at low altitudes is included. Trends for new models are discussed; the feasibility of predicting substorm injections and solar wind high-speed streams make the modeling of individual events a topical activity.

Vette, J. I.↗
NASA NTRS1980

Second moments of optical degradation due to a thin turbulent layer

The effect of thin turbulent layers, including boundary layers and shear layers, on light propagation is examined from a theoretical point of view. In particular, a mathematical model is developed to describe the interaction between the aerodynamic or, more precisely, the density fluctuations and the electromagnetic field. It is assumed that the turbulence induces a normally distributed phase aberration which is a homogeneous random function in the plane of the aperture. Hypotheses concerning the density fluctuations in the layer sufficient to guarantee such a phase aberration are exhibited. The optical degradation is described in terms of the optical transfer function (OTF) and the Strehl ratio (I/I O ) which are random. Expressions for the first and second moments of these two parameters are developed from the definitions. Asymptotic ("large" aperture) approximations to these expressions are derived and discussed. Finally, the exact and approximate results are compared for several "typical" values of the ratios of aperture diameter to scale of density fluctuations and rms phase aberration to wave length respectively.

W J Steinmetz↗
NASA NTRS1980

Confidence regions of planar cardiac vectors

A method for plotting the confidence regions of vectorial data obtained in electrocardiology is presented. The 90%, 95% and 99% confidence regions of cardiac vectors represented in a plane are obtained in the form of an ellipse centered at coordinates corresponding to the means of a sample selected at random from a bivariate normal distribution. An example of such a plot for the frontal plane QRS mean electrical axis for 80 horses is also presented.

Dubin, S.↗
NASA NTRS1979

A model for the microwave emissivity of the ocean's surface as a function of wind speed

A quantitative model is presented, which describes the ocean surface as an ensemble of flat facets with a normal distribution of slopes. The variance of the slope distribution is linearly related to frequency up to 35 GHz and constant at higher frequencies. These facets are partially covered with an absorbing nonpolarized foam layer. Experimental evidence is presented for this model.

Wilheit, T. T., Jr.↗
NASA NTRS1980

An analysis of short pulse and dual frequency radar techniques for measuring ocean wave spectra from satellites

Scanning beam microwave radars were used to measure ocean wave directional spectra from satellites. In principle, surface wave spectral resolution in wave number can be obtained using either short pulse (SP) or dual frequency (DF) techniques; in either case, directional resolution obtains naturally as a consequence of a Bragg-like wave front matching. A four frequency moment characterization of backscatter from the near vertical using physical optics in the high frequency limit was applied to an analysis of the SP and DF measurement techniques. The intrinsic electromagnetic modulation spectrum was to the first order in wave steepness proportional to the large wave directional slope spectrum. Harmonic distortion was small and was a minimum near 10 deg incidence. NonGaussian wave statistics can have an effect comparable to that in the second order of scattering from a normally distributed sea surface. The SP technique is superior to the DF technique in terms of measurement signal to noise ratio and contrast ratio.

Jackson, F. C.↗
NASA NTRS1981

Assessment of variations in thermal cycle life data of thermal barrier coated rods

An analysis of thermal cycle life data for 22 thermal barrier coated (TBC) specimens was conducted. The Zr02-8Y203/NiCrAlY plasma spray coated Rene 41 rods were tested in a Mach 0.3 Jet A/air burner flame. All specimens were subjected to the same coating and subsequent test procedures in an effort to control three parametric groups; material properties, geometry and heat flux. Statistically, the data sample space had a mean of 1330 cycles with a standard deviation of 520 cycles. The data were described by normal or log-normal distributions, but other models could also apply; the sample size must be increased to clearly delineate a statistical failure model. The statistical methods were also applied to adhesive/cohesive strength data for 20 TBC discs of the same composition, with similar results. The sample space had a mean of 9 MPa with a standard deviation of 4.2 MPa.

Hendricks, R. C.↗
NASA NTRS1981

Improved version of the split routine for CLASSY

The theoretical basis for a new version of the SPLIT routine for CLASSY is developed. (The SPLIT routine is used to guess the positions of the parts of a cluster which is not normally distributed.) The proposed routine would be a faster, more accurate replacement for the existing SPLIT routine, which was developed on an ad hoc basis.

Rassbach, M. E.↗
NASA NTRS1981

Assessment of variations in thermal cycle life data of thermal barrier coated rods

The reported study had the purpose to examine variations in cyclic life and in adhesive/cohesive coating strength. Possible effects of heating rate, stress reversal, temperature level, and ceramic deposition methods on coating life were also investigated. Life cycle data for 22 thermal barrier coated rods were examined and found to be statistically modeled by normal or log-normal distributions. The sample mean was 1330 cycles with a standard deviation of 520 cycles. Adhesive/cohesive pulloff strength data for 20 thermal barrier coated flat head piston specimens were taken. The average pulloff stress was 9 MPa with a standard deviation of 4.2 MPa. It was found that variations in heating rate can produce significant variations in the life cycle data.

Hendricks, R. C.↗
NASA NTRS1981

Development of design, qualification, screening, and application requirements for plastic encapsulated solid-state devices for space applications

Test data were collected on 1035 plastic encapsulated devices and 75 hermetically scaled control group devices that were purchased from each of five different manufacturers in the categories of (1) low power Schottsky TTL (bipolar) digital circuits; (2) CMOS digital circuits; (3) operational amplifier linear circuits; and (4) NPN transistors. These parts were subjected to three different initial screening conditions, then to extended life testing, to determine any possible advantages or trends for any particular screen. Several tests were carried out in the areas of flammability testing, humidity testing, high pressure steam (auroclave) testing, and high temperature storage testing. Test results are presented. Procurement and application considerations for use of plastic encapsulated semiconductors are presented and a statistical analysis program written to study the log normal distributions resulting from life testing is concluded.

Source record↗
NASA NTRS1982

Fundamental studies of the solid-particle erosion of silicon

The predictions of the theories of solid-particle erosion of brittle materials are compared to experimental results of studies in which angular Al2O3 particles with mean diameters D of 23 to 270 microns are used to erode (111) surfaces of silicon single crystals at impact angles alpha from 20 to 90 deg and velocities v from 30 to 150 m/s. The description of the steady state erosion rate by a power law, delta W varies directly as (v sin alpha)(n)D(m) must be modified to include threshold and plasticity effects. Furthermore the velocity exponent n depends on D. Results using abrasives of different sizes mixed together can be explained using a logarithmic-normal distribution. The results of transient experiments can be used to explain the synergistic effects which are observed using a biomodal distribution of abrasives.

Routbort, J. L.↗
NASA NTRS1982

Predicting the required number of training samples

A criterion which measures the quality of the estimate of the covariance matrix of a multivariate normal distribution is developed. Based on this criterion, the necessary number of training samples is predicted. Experimental results which are used as a guide for determining the number of training samples are included.

Kalayeh, H. M.↗