Engineering Papers⌕ Search

SEARCH · Engineering Papers

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Statistics for ionospherically diffracted VHF/UHF signals.

In this paper, a general characterization of the statistics for an ionospherically diffracted, monochromatic plane wave is presented. The main results are restricted to weak scatter, although two possible extensions that accommodate large phase perturbations and multiple scatter are discussed. A detailed discussion of the first-order statistics of amplitude is given. The general Gaussian distribution is discussed together with its Nakagami-distribution approximation and the log-normal distribution. By using a segment of ATS-3 satellite data recorded at Lima, Peru, we show equally good fits to Gaussian and log-normal distributions at least for the limited dynamic range available. The Nakagami distribution provides only a poor approximation.

Rino, C. L.↗
NASA NTRSDate not supplied

Nonnormality of Sonic Boom Loudness Metrics in the Turbulent Atmospheric Boundary Layer at Large Lateral Distances from the Flight Path

Atmospheric boundary layer (ABL) turbulence causes variability of the sonic boom waveform at the ground. Recent numerical investigations of sonic boom propagation through kinematic velocity fluctuations indicate that loudness metric distributions are positively skewed relative to a normal distribution. This skewness depends on the propagation distance and turbulence intensity. Propagation simulations of N-waves and shaped booms through inhomogeneous ABL turbulence are presented. Meteorological conditions are varied to examine different daytime ABL conditions and their effect on sonic boom loudness distributions. Two outcomes are observed: 1) the loudness metric distributions become increasingly positively skewed as the propagation distance through the ABL increases, and 2) the distributions become increasingly positively skewed at the same lateral distance from the flight path as the convection level of the daytime ABL is increased. Thus, results indicate that ground level measurements of sonic boom loudness from flight tests performed at large lateral distances from the flight path may not be normally distributed, due to turbulence present in the ABL. (This research is supported by the Commercial Supersonic Technology Project of the National Aeronautics and Space Administration under Grant No. 80NSSC19K1685.)

sonic boom↗
NASA NTRS2005

A Posteriori Correction of Forecast and Observation Error Variances

Proposed method of total observation and forecast error variance correction is based on the assumption about normal distribution of "observed-minus-forecast" residuals (O-F), where O is an observed value and F is usually a short-term model forecast. This assumption can be accepted for several types of observations (except humidity) which are not grossly in error. Degree of nearness to normal distribution can be estimated by the symmetry or skewness (luck of symmetry) a(sub 3) = mu(sub 3)/sigma(sup 3) and kurtosis a(sub 4) = mu(sub 4)/sigma(sup 4) - 3 Here mu(sub i) = i-order moment, sigma is a standard deviation. It is well known that for normal distribution a(sub 3) = a(sub 4) = 0.

Rukhovets, Leonid↗
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 NTRS1939

Tests of Two Full-Scale Propellers with Different Pitch Distributions, at Blade Angles up to 60 Degrees

Two 3-blade 10-foot propellers were operated in front of a liquid-cooled engine nacelle. The propellers differed only in pitch distribution; one had normal distribution (nearly constant pitch for a blade angle of 15 degrees at 0.75 radius), and the other had the pitch of the tip sections decreased with respect to that for the shank sections (blade angle of 35 degrees for nearly constant pitch distribution). Propeller blade angles at 0.75r from 15 degrees to sixty degrees, corresponding to design speeds up to 500 miles per hour, were investigated. Propeller blade angles at 0.75r from 15 degrees to 60 degrees, corresponding to design speeds up to 500 miles per hour, were investigated. The results indicated that the propulsive efficiency at a blade angle of 60 degrees was about 9 percent less than the maximum value of 86 percent, which occurred at blade angle of about 30 degrees. The efficiency at a blade angle of 60 degrees was increased about 7 percent by correcting for the effect of a spinner and, at a blade angle of 30 degrees about 3 percent. The peak efficiencies for the propeller having the washed-out pitch distribution were slightly less than for the normal propeller but the take-off efficiency was generally higher.

Biermann, David↗
NASA NTRS1980

An approximation to student's t-distribution

Three equations relate Student's t-distribution to standard normal distribution with maximum error of less than 0.8 percent. First equation, used for degrees of freedom (v) greater than 2, expresses t variable in terms of standard normal variable z. For v=1 and 2, second and third equations express t exactly in terms of probability P.

Rummler, D. R.↗
DOE OSTI2024

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. As a result, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem.

Lei, Jinlong↗
NASA NTRS2011

Distribution Functions of Sizes and Fluxes Determined from Supra-Arcade Downflows

The frequency distributions of sizes and fluxes of supra-arcade downflows (SADs) provide information about the process of their creation. For example, a fractal creation process may be expected to yield a power-law distribution of sizes and/or fluxes. We examine 120 cross-sectional areas and magnetic flux estimates found by Savage & McKenzie for SADs, and find that (1) the areas are consistent with a log-normal distribution and (2) the fluxes are consistent with both a log-normal and an exponential distribution. Neither set of measurements is compatible with a power-law distribution nor a normal distribution. As a demonstration of the applicability of these findings to improved understanding of reconnection, we consider a simple SAD growth scenario with minimal assumptions, capable of producing a log-normal distribution.

McKenzie, D.↗
NASA NTRS1987

Statistical analysis of the 70 meter antenna surface distortions

Statistical analysis of surface distortions of the 70 meter NASA/JPL antenna, located at Goldstone, was performed. The purpose of this analysis is to verify whether deviations due to gravity loading can be treated as quasi-random variables with normal distribution. Histograms of the RF pathlength error distribution for several antenna elevation positions were generated. The results indicate that the deviations from the ideal antenna surface are not normally distributed. The observed density distribution for all antenna elevation angles is taller and narrower than the normal density, which results in large positive values of kurtosis and a significant amount of skewness. The skewness of the distribution changes from positive to negative as the antenna elevation changes from zenith to horizon.

Kiedron, K.↗
NASA NTRS1990

Estimation of area-averaged rainfall over tropical oceans from microwave radiometry - A single channel approach

This paper presents a new simple retrieval algorithm for estimating area-time averaged rain rates over tropical oceans by using single channel microwave measurements from satellites. The algorithm was tested by using the Nimbus-5 Electrically Scanning Microwave Radiometer and a simple microwave radiative transfer model to retrieve seasonal 5-deg x 5-deg area averaged rainrate over the tropical Atlantic and Pacific from December 1973 to November 1974. The brightness temperatures were collected and analyzed into histograms for each season and in each grid box from December 1973 to November 1974. The histograms suggest a normal distribution of background noise plus a skewed rain distribution at the higher brightness temperatures. By using a statistical estimation procedure based upon normally distributed background noise, the rain distribution was separated from the raw histogram. The radiative transfer model was applied to the rain-only distribution to retrieve area-time averaged rainrates throughout the tropics. Despite limitations of single channel information, the retrieved seasonal rain rates agree well in the open ocean with expectations based upon previous estimates of tropical rainfall over the oceans.

Shin, Kyung-Sup↗
NASA NTRS1981

Statistical distribution of mechanical properties for three graphite-epoxy material systems

Graphite-epoxy composites are playing an increasing role as viable alternative materials in structural applications necessitating thorough investigation into the predictability and reproducibility of their material strength properties. This investigation was concerned with tension, compression, and short beam shear coupon testing of large samples from three different material suppliers to determine their statistical strength behavior. Statistical results indicate that a two Parameter Weibull distribution model provides better overall characterization of material behavior for the graphite-epoxy systems tested than does the standard Normal distribution model that is employed for most design work. While either a Weibull or Normal distribution model provides adequate predictions for average strength values, the Weibull model provides better characterization in the lower tail region where the predictions are of maximum design interest. The two sets of the same material were found to have essentially the same material properties, and indicate that repeatability can be achieved.

Reese, C.↗
NASA NTRS1976

Determination of statistics for any rotation of axes of a bivariate normal elliptical distribution

Transformation of statistics from a dimensional set to another dimensional set involves linear functions of the original set of statistics. Similarly, linear functions will transform statistics within a dimensional set such that the new statistics are relevant to a new set of coordinate axes. A restricted case of the latter is the rotation of axes in a coordinate system involving any two correlated random variables. A special case is the transformation for horizontal wind distributions. Wind statistics are usually provided in terms of wind speed and direction (measured clockwise from north) or in east-west and north-south components. A direct application of this technique allows the determination of appropriate wind statistics parallel and normal to any preselected flight path of a space vehicle. Among the constraints for launching space vehicles are critical values selected from the distribution of the expected winds parallel to and normal to the flight path. These procedures are applied to space vehicle launches at Cape Kennedy, Florida.

Falls, L. W.↗
NASA NTRS2008

Analysis of Regolith Simulant Ejecta Distributions from Normal Incident Hypervelocity Impact

The National Aeronautics and Space Administration (NASA) has established the Constellation Program. The Constellation Program has defined one of its many goals as long-term lunar habitation. Critical to the design of a lunar habitat is an understanding of the lunar surface environment; of specific importance is the primary meteoroid and subsequent ejecta environment. The document, NASA SP-8013 'Meteoroid Environment Model Near Earth to Lunar Surface', was developed for the Apollo program in 1969 and contains the latest definition of the lunar ejecta environment. There is concern that NASA SP-8013 may over-estimate the lunar ejecta environment. NASA's Meteoroid Environment Office (MEO) has initiated several tasks to improve the accuracy of our understanding of the lunar surface ejecta environment. This paper reports the results of experiments on projectile impact into powdered pumice and unconsolidated JSC-1A Lunar Mare Regolith simulant targets. Projectiles were accelerated to velocities between 2.45 and 5.18 km/s at normal incidence using the Ames Vertical Gun Range (AVGR). The ejected particles were detected by thin aluminum foil targets strategically placed around the impact site and angular ejecta distributions were determined. Assumptions were made to support the analysis which include; assuming ejecta spherical symmetry resulting from normal impact and all ejecta particles were of mean target particle size. This analysis produces a hemispherical flux density distribution of ejecta with sufficient velocity to penetrate the aluminum foil detectors.

Edwards, David L.↗
NASA NTRS1998

Bell-Curve Based Evolutionary Optimization Algorithm

The paper presents an optimization algorithm that falls in the category of genetic, or evolutionary algorithms. While the bit exchange is the basis of most of the Genetic Algorithms (GA) in research and applications in America, some alternatives, also in the category of evolutionary algorithms, but use a direct, geometrical approach have gained popularity in Europe and Asia. The Bell-Curve Based Evolutionary Algorithm (BCB) is in this alternative category and is distinguished by the use of a combination of n-dimensional geometry and the normal distribution, the bell-curve, in the generation of the offspring. The tool for creating a child is a geometrical construct comprising a line connecting two parents and a weighted point on that line. The point that defines the child deviates from the weighted point in two directions: parallel and orthogonal to the connecting line, the deviation in each direction obeying a probabilistic distribution. Tests showed satisfactory performance of BCB. The principal advantage of BCB is its controllability via the normal distribution parameters and the geometrical construct variables.

Sobieszczanski-Sobieski, J.↗
NASA NTRS1979

Extreme Mean and Its Applications

Extreme value statistics obtained from normally distributed data are considered. An extreme mean is defined as the mean of p-th probability truncated normal distribution. An unbiased estimate of this extreme mean and its large sample distribution are derived. The distribution of this estimate even for very large samples is found to be nonnormal. Further, as the sample size increases, the variance of the unbiased estimate converges to the Cramer-Rao lower bound. The computer program used to obtain the density and distribution functions of the standardized unbiased estimate, and the confidence intervals of the extreme mean for any data are included for ready application. An example is included to demonstrate the usefulness of extreme mean application.

Swaroop, R.↗
NASA NTRS2008

Comparison of Ejecta Distributions from Normal Incident Hypervelocity Impact on Lunar Regolith Simulant

The National Aeronautics and Space Administration (NASA) is progressing toward long-term lunar habitation. Critical to the design of a lunar habitat is an understanding of the lunar surface environment; of specific importance is the primary meteoroid and subsequent ejecta environment. The document, NASA SP-8013, was developed for the Apollo program and is the latest definition of the ejecta environment. There is concern that NASA SP-8013 may over-estimate the lunar ejecta environment. NASA's Meteoroid Environment Office (MEO) has initiated several tasks to improve the accuracy of our understanding of the lunar surface ejecta environment. This paper reports the results of experiments on projectile impact into powered pumice and unconsolidated JSC-1A Lunar Mare Regolith stimulant (JSC-1A) targets. The Ames Vertical Gun Range (AVGR) was used to accelerate projectiles to velocities in excess of 5 km/s and impact the targets at normal incidence. The ejected particles were detected by thin aluminum foil targets placed around the impact site and angular distributions were determined for ejecta. Comparison of ejecta angular distribution with previous works will be presented. A simplistic technique to characterize the ejected particles was formulated and improvements to this technique will be discussed for implementation in future tests.

Edwards, David L.↗
NASA NTRSDate not supplied

Analysis of Pull Force Test Results for Crimped Connections

Crimped electrical contacts are reliable when strict process controls are followed during manufacturing and accompanied by continuous process verification through pull force testing. Cable and wire harness assemblies’ standards are developed and refined over time to provide the minimum pull force that a crimp contact must meet before it breaks from the wire. However, in practice the failures occur at a much higher tensile strength than the minimum required. The first section of this paper reviewed 780 pull force test results provided by NASA Centers were collected and analyzed to determine how the data compares to NASA’s pre-existing requirements from the cable/harness standards NASA-STD-8739.4 and IPC/WHMA-A-620B-S. The measured tensile strength of most of the contact/conductor pairs (i.e. Contact/Wires or C/W) exceeded the minimum pull force values of NASA-STD-8739.4 and IPC/WHMA-A-620 standards by at least 100 %. The tensile strength samples of the C/W pairs values followed a normal distribution with an average tensile strength value that was at least 182 % of the minimum requirement, and all the samples analyzed passed the pull force testing. In addition, the 95 % confidence interval of the average tensile strength distributions for several C/W pairs was determined and plotted as error bars to show that there is good likelihood to observe C/W pair normal distribution with a 95 % confidence interval that will meet and surpass the standard requirements. The frequency of pull force testing can be problematic for projects because of the cost and availability of spare contacts for the destructive test. It could be possible to reduce the frequency of pull force testing if at the beginning of the production run, the conditions of the crimp tool and materials are verified, and the settings of the tool remain unchanged throughout the process. However, the project must evaluate the impact to risk from reducing the frequency of testing.

Crimped connections↗