SEARCH · Engineering Papers

Results for “lognormal 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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

All sources NASA NTRS DOE OSTI

NASA NTRS1998

Statistical Treatment of Earth Observing System Pyroshock Separation Test Data

The Earth Observing System (EOS) AM-1 spacecraft for NASA's Mission to Planet Earth is scheduled to be launched on an Atlas IIAS vehicle in June of 1998. One concern is that the instruments on the EOS spacecraft are sensitive to the shock-induced vibration produced when the spacecraft separates from the launch vehicle. By employing unique statistical analysis to the available ground test shock data, the NASA Lewis Research Center found that shock-induced vibrations would not be as great as the previously specified levels of Lockheed Martin. The EOS pyroshock separation testing, which was completed in 1997, produced a large quantity of accelerometer data to characterize the shock response levels at the launch vehicle/spacecraft interface. Thirteen pyroshock separation firings of the EOS and payload adapter configuration yielded 78 total measurements at the interface. The multiple firings were necessary to qualify the newly developed Lockheed Martin six-hardpoint separation system. Because of the unusually large amount of data acquired, Lewis developed a statistical methodology to predict the maximum expected shock levels at the interface between the EOS spacecraft and the launch vehicle. Then, this methodology, which is based on six shear plate accelerometer measurements per test firing at the spacecraft/launch vehicle interface, was used to determine the shock endurance specification for EOS. Each pyroshock separation test of the EOS spacecraft simulator produced its own set of interface accelerometer data. Probability distributions, histograms, the median, and higher order moments (skew and kurtosis) were analyzed. The data were found to be lognormally distributed, which is consistent with NASA pyroshock standards. Each set of lognormally transformed test data produced was analyzed to determine if the data should be combined statistically. Statistical testing of the data's standard deviations and means (F and t testing, respectively) determined if data sets were significantly different at a 95-percent confidence level. If two data sets were found to be significantly different, these families of data were not combined for statistical purposes. This methodology produced three separate statistical data families of shear plate data. For each population, a P99.1/50 (probability/confidence) per-separation-nut firing level was calculated. By using the binomial distribution, Lewis researchers determined that this pernut firing level was equivalent to a P95/50 per-flight confidence level. The overall envelope of the per-flight P95/50 levels led to Lewis' recommended EOS interface shock endurance specification. A similar methodology was used to develop Lewis' recommended EOS mission assurance levels. The available test data for the EOS mission are significantly larger than for a normal mission, thus increasing the confidence level in the calculated expected shock environment. Lewis significantly affected the EOS mission by properly employing statistical analysis to the data. This analysis prevented a costly requalification of the spacecraft's instruments, which otherwise would have been exposed to significantly higher test levels.

McNelis, Anne M.↗

NASA NTRS1995

Soot Aerosol In The Atmosphere: Pole-to-Pole Distribution And Contributions by Aircraft

Interest in the distribution of black carbon (soot) aerosol (BCA) in the atmosphere is warranted for the following reasons: (1) BCA has the highest absorption cross section of any compound known, thus it can absorb solar radiation to cause atmospheric warming; (2) BCA is a strong adsorber of gases, thus it can catalyze heterogeneous chemical reactions to modify the chemical composition of the atmosphere; (3) If aircraft emission is the major source of atmospheric BCA, it can serve as an atmospheric tracer of aircraft exhaust. We collect BCA particles greater than or equal to 0.02 micrometer diameter by wires mounted on both the DC-8 and ER-2 aircraft. After return to the laboratory, the wires are examined with a field emission scanning electron microscope to identify BCA particles by their characteristic morphology. Typically, BCA exists in the atmosphere as small particles of complex morphology. The particle sizes at the source are measured in tens of Angstrom units; after a short residence time in the atmosphere, individual particles coalesce to loosely packed agglomerates of typical dimensions 0.01 to 0.1 micrometer. We approximate the size of each BCA aggregate by that of a sphere of equivalent volume. This is done by computing the volume of a sphere whose diameter is the mean between averaged minimum and maximum dimensions of the BCA particle. While this procedure probably underestimates the actual surface area, it permits us to compare BCA size distributions among themselves and with other types of aerosols. When statistically justified, we fit lognormal distributions to the data points to determine number concentrations, geometric mean radii, standard deviations, BCA surface areas and volumes. Results to date permit the following conclusions: (1) BCA concentration in the northern stratosphere averages 0.6 ng per cubic meters. This amount is one part in 10(exp 4) after a volcanic eruption (e.g., Pinatubo) increasing to about one percent during volcanic quiescence. In the northern troposphere, BCA concentration averages 3.2 ng per cubic meters, or 0.3 percent of the background aerosol. (2) Applying an BCA emission index EI(BCA)=5 x 10(exp -5), measured in the exhaust wake of a Concorde supersonic jet aircraft, to realistic estimates of fuel burnt by the current and projected fleets permits us to conclude that: (i) Most BCA in the northern stratosphere results from aircraft emissions; (ii) Most BCA in the northern troposphere results from other sources than aircraft; (iii) A projected supersonic fleet will increase the northern stratospheric BCA concentration by one order of magnitude, unless the emission index is substantially reduced. (3) A strong gradient between the northern and southern hemispheres indicates that mixing across the equator is greatly inhibited in relation to atmospheric residence times of BCA. (4) The single scatter albedo of BCA/"background" aerosol mixtures suggests a cooling effect for most of the globe; an exemption is the Arctic because of the high surface albedo of the snow/ice covered earth's surface.

Pueschel, R. F.↗

DOE OSTI2025

Diagenesis is key to unlocking outcrop fracture data suitable for quantitative extrapolation to geothermal targets

Exceptionally large, well-exposed sandstone outcrops in New York provide insights into folds, deformation bands, and fractures that could influence permeability, heat exchange, and stimulation outcomes of geothermal reservoir targets. Cambrian Potsdam Sandstone with <5% porosity contains decimeter-scale open, angular-limbed monoclines <0.5 km apart with associated low-porosity mm-wide cataclastic deformation bands. Crossing and abutting relationships among sub-vertical opening-mode fractures show four chronological Sets A–D, striking NNW, NE, NW, and ENE, respectively. Fracture lengths and heights range from millimeters to tens of meters. Sets A and C macro-fractures, and possibly B and D, contain quartz deposits. All sets have abundant associated quartz cemented microfractures that also record set orientations and crosscutting relations. Quartz cement deposits—evidence of diagenesis—are the key to identifying attributes of outcrop fractures suitable for extrapolation to geothermal targets in sandstones because they show which fractures formed in the subsurface. Set A fluid inclusion homogenization temperatures (120°C–129°C) are compatible with fracture at >3 km depth. Fractures are stiff and those ≥0.05 mm (Set C) and ≥0.1 mm (Set A) are open and potentially conducive to flow. Sets A and D are abundant in outcrops with close fracture spacing—0.18 m and 0.68 m, respectively—and define a rectangular connectivity network dominated by crossing and abutting X and Y nodes. Set A aperture distributions follow a power law with slope –0.8 up to 0.15 mm; other sets have lognormal distributions. Set A and D microfractures are weakly clustered, while macro-fractures commonly have 1D anticlustered (regular or periodic) arrangements at shorter length scales (<0.2 m). Sub-horizontal fractures are barren and may have formed near the surface. Fracture heights, lengths, and spatial arrangements show good trace connectivity but low open connectivity. For geothermal applications, outcrop results predict low initial well-test permeabilities owing to quartz disconnecting open fractures, but stimulation of closely spaced microfractures and partly open macro-fractures could yield high surface area for heat exchange. Quantitative extrapolation of key fracture attributes like abundance, orientation, spatial arrangement, length, and open fracture connectivity is possible from outcrops to fractured reservoirs if differing thermal histories and diagenesis are accounted for.

02 PETROLEUM↗

NASA NTRS1993

A study of the threshold method utilizing raingage data

The threshold method for estimation of area-average rain rate relies on determination of the fractional area where rain rate exceeds a preset level of intensity. Previous studies have shown that the optimal threshold level depends on the climatological rain-rate distribution (RRD). It has also been noted, however, that the climatological RRD may be composed of an aggregate of distributions, one for each of several distinctly different synoptic conditions, each having its own optimal threshold. In this study, the impact of RRD variations on the threshold method is shown in an analysis of 1-min rainrate data from a network of tipping-bucket gauges in Darwin, Australia. Data are analyzed for two distinct regimes: the premonsoon environment, having isolated intense thunderstorms, and the active monsoon rains, having organized convective cell clusters that generate large areas of stratiform rain. It is found that a threshold of 10 mm/h results in the same threshold coefficient for both regimes, suggesting an alternative definition of optimal threshold as that which is least sensitive to distribution variations. The observed behavior of the threshold coefficient is well simulated by assumption of lognormal distributions with different scale parameters and same shape parameters.

Short, David A.↗

NASA NTRS1999

Statistical Properties of SGR 1900+14 Bursts

We study the statistics of soft gamma repeater (SGR) bursts using a database of 187 events detected with BATSE and 837 events detected with the Rossi X-Ray Timing Explorer Proportional Counter Array: all events are from SGR 1900+14 during its 1998-1999 active phase. We find that the fluence or energy distribution of bursts is consistent with a power law of index 1.66, over 4 orders of magnitude. This scale-free distribution resembles the Gutenberg-Richter law for earthquakes and gives evidence for self-organized criticality in SGRS. The distribution of time intervals between successive bursts from SGR 1900+14 is consistent with a lognormal distribution. There is no correlation between burst intensity and the waiting times till the next burst, but there is some evidence for a correlation between burst intensity and the time elapsed since the previous burst. We also find a correlation between the duration and the energy of the bursts, but with significant scatter. In all these statistical properties, SGR bursts resemble earthquakes and solar flares more closely than they resemble any known accretion-powered or nuclear-powered phenomena. Thus, our analysis lends support to the hypothesis that the energy source for SGR bursts is internal to the neutron star and plausibly magnetic.

Gogus, Ersin↗

NASA NTRS1999

Pyroshock Environments Characterized for Spacecraft Missions

Pyrotechnic shock, or pyroshock, is the transient response of a structure to loading induced by the ignition of pyrotechnic (explosive or propellant activated) devices. These devices are typically used to separate structural systems (e.g., separate a spacecraft from a launch vehicle) and deploy appendages (e.g., solar panels). Pyroshocks are characterized by high peak acceleration, high-frequency content, and short duration. Because of their high acceleration and high-frequency, pyroshocks can cause spaceflight hardware to fail. Verifying by test that spaceflight hardware can withstand the anticipated shock environment is considered essential to mission success. The Earth Observing System (EOS) AM-1 spacecraft for NASA's Mission to Planet Earth is scheduled to be launched on an Atlas IIAS vehicle in 1999, and the NASA Lewis Research Center is the launch vehicle integrator for this NASA Goddard Space Flight Center spacecraft. The EOS spacecraft was subjected to numerous ground shock tests to verify that its scientific instruments and avionics components will withstand the shock-induced vibration produced when the spacecraft separates from the launch vehicle. Shock test data from these tests represent the third largest available pyroshock database in the United States. Future spacecraft missions will directly benefit from the knowledge gained from these tests. The payload separation system used for EOS is a new system that operates by firing six separation nuts. This system was tested to verify its functional operation and to characterize the resulting shock levels. The launch vehicle contractor (Lockheed Martin Astronautics) and spacecraft contractor (Lockheed Martin Missiles & Space) completed 16 separation test firings. This resulted in an unusually large amount of pyroshock data. Typically, only one or two pyroshock test firings are performed for a spacecraft mission. Because of the size of this separation system shock database, engineers were able to perform unique statistical analyses to characterize the distribution of the test data. For example, it was proven that the shock data follow a lognormal distribution, a concept often assumed but rarely proven. The test-to-test repeatability of the shock source level was analyzed, and the effects of various test configurations and separation nut production lots were examined and quantified. Engineers investigated the change in shock level as the shock traveled from the spacecraft separation interface to the avionics components of the upper stage and analyzed the effects of the structural fidelity (simulator versus real) of the components and their weight on vibrational response. In addition, the shock attenuation with distance and across joints was quantified and compared with concepts originally generated in 1970, and the effects of separation nut preload and firing sequences effects were examined. Because of this EOS shock testing and the analyses performed at NASA Lewis, a significant amount of new information on pyroshock and its characteristics is now available to the aerospace industry. We hope that this information will help future spacecraft test planners to perform better and cheaper spacecraft separation shock tests and to better understand their test data.

Hughes, William O.↗

DOE OSTI2026

Statistical Uncertainty of Inhalation Dose Coefficients: Impact of Particle Deposition in ICRP 66 Human Respiratory Tract Model

Inhaled radioactive materials can pose a long-term health concern, as the material can be incorporated into the body’s metabolic pathways and remain in organs and tissues for extended durations. During the retention period, the radioactive material may localize in a source organ and irradiate adjacent target organs and tissues. Distribution of these materials changes over time, requiring biokinetic modeling to evaluate their movement through various tissues and organs. The evolving distribution depends on multiple inputs characterizing the inhaled material, such as particle size and size distribution, particle density, aspect ratio, specific radionuclide, the chemical form, and solubility. In addition, biological parameters such as breathing rate, breathing type (nasal or nasal/oral), respiratory system morphometry, tidal volume, functional residual capacity, and anatomical dead space all influence material transport. These aerosol properties and physiological characteristics of the respiratory tract jointly define a range of initial conditions that influence the time-dependent distribution of radioactive material. To evaluate both uncertainty in the initial conditions of inhalation exposure and the final output (committed effective dose) from biokinetic models, a Python-based software tool, Radiological Exposure Dose Calculator (REDCAL), was developed to propagate uncertainty within the human respiratory tract model. Focusing on deposition fraction uncertainty, the primary objective was to characterize the initial activity distribution across respiratory regions as a function of anticipated particle sizes and distributions. The impact of the deposition fraction uncertainty was propagated to committed effective dose coefficients for selected radionuclides in a companion publication. For each particle size, a lognormal distribution, characterized by its geometric mean as defined within ICRP Publication 66, serves as the basis for introducing uncertainty into the physical processes governing deposition in various lung regions. Finally, this study addresses the deposition process and examines how uncertainty in deposition mechanisms affects activity distribution in the airways, ultimately presenting the expected range and standard deviation of deposited activity as a function of particle size.

International Commission on Radiological Protectio↗

NASA NTRS1992

Linear velocity fields in non-Gaussian models for large-scale structure

Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.

Scherrer, Robert J.↗

NASA NTRS1991

Particle size distributions in polar mesospheric clouds derived from solar mesosphere explorer measurements

Data from the visible and UV spectrometers on the Solar Mesosphere Explorer are used to derive the color ratios of the reflectance at 265, 296, and 393 nm of light scattered from polar mesospheric cloud particles. This analysis extends the spectral coverage into the visible region of the spectrum. The data reduction technique compared the cloud brightness to the brightness scattered from the background atmosphere at the same wavelength. The ratios determined in this way are independent of systematic errors in instrument radiometric calibration. The data are analyzed using theoretical determinations of the color ratios from the Mie theory of small particle scattering, assuming a lognormal distribution for the particle size dispersion. Here 'size' means the average radius of the sphere having the same ice volume. The present results confirm earlier findings that the effective sizes of polar mesospheric cloud particles are less than 70 nm. Still, there exists a small number of measurements which result in particle sizes of the order of 80 nm. Even for these large particle sizes the required vertical column content of water vapor does not exceed limits imposed by the available atmospheric water vapor concentrations.

Rusch, D. W.↗

NASA NTRS1980

Rate statistics for radio noise from lightning

Radio frequency noise from lightning was measured at several frequencies in the HF - VHF range at the Kennedy Space Center, Florida. The data were examined to determine flashing rate statistics during periods of strong activity from nearby storms. It was found that the time between flashes is modeled reasonably well by a random variable with a lognormal distribution.

Levine, D. M.↗

NASA NTRS1981

Accelerated life testing and reliability of high K multilayer ceramic capacitors

The reliability of one lot of high K multilayer ceramic capacitors was evaluated using accelerated life testing. The degradation in insulation resistance was characterized as a function of voltage and temperature. The times to failure at a voltage-temperature stress conformed to a lognormal distribution with a standard deviation approximately 0.5.

Minford, W. J.↗

NASA NTRS1983

Stillwater anorthosites - A lunar analog?

Samples of anorthosite from Stillwater complex units AN-I and AN-II have been studied by instrumental neutron activation analysis for FeO, CaO, Na2O, REE, and other trace elements, and the results are discussed. No systematic variations of chemical composition with stratigraphic position were observed. The major and trace compositions of both units appear to be identical, with plagioclase compositions virtually constant throughout both. Thus, there is almost no evidence for evolution of parent magma composition during the genesis of these units. The bulk of the anorthosites appear to consist of cumulus-adcumulus plagioclase and pyroxene. Very little trapped liquid component was found. The chemical elements are not normally or lognormally distributed among samples taken from either anorthosite unit. The irregular distribution of pyroxene oikocrysts indicates that interstitial melt migrated substantially prior to final consolidation of the rock.

Salpas, P. A.↗

NASA NTRS1986

Satellite rainfall retrieval by logistic regression

The potential use of logistic regression in rainfall estimation from satellite measurements is investigated. Satellite measurements provide covariate information in terms of radiances from different remote sensors.The logistic regression technique can effectively accommodate many covariates and test their significance in the estimation. The outcome from the logistical model is the probability that the rainrate of a satellite pixel is above a certain threshold. By varying the thresholds, a rainrate histogram can be obtained, from which the mean and the variant can be estimated. A logistical model is developed and applied to rainfall data collected during GATE, using as covariates the fractional rain area and a radiance measurement which is deduced from a microwave temperature-rainrate relation. It is demonstrated that the fractional rain area is an important covariate in the model, consistent with the use of the so-called Area Time Integral in estimating total rain volume in other studies. To calibrate the logistical model, simulated rain fields generated by rainfield models with prescribed parameters are needed. A stringent test of the logistical model is its ability to recover the prescribed parameters of simulated rain fields. A rain field simulation model which preserves the fractional rain area and lognormality of rainrates as found in GATE is developed. A stochastic regression model of branching and immigration whose solutions are lognormally distributed in some asymptotic limits has also been developed.

Chiu, Long S.↗

NASA NTRS1989

Scattering of light by stochastically rough particles

The single particle phase function and the linear polarization for large stochastically deformed spheres have been calculated by Monte Carlo simulation using the geometrical optics approximation. The radius vector of a particle is assumed to obey a bivariate lognormal distribution with three free parameters: mean radius, its standard deviation and the coherence length of the autocorrelation function. All reflections/refractions which include sufficient energy have been included. Real and imaginary parts of the refractive index can be varied without any restrictions. Results and comparisons with some earlier less general theories are presented. Applications of this theory to the photometric properties of atmosphereless bodies and interplanetary dust are discussed.

Peltoniemi, Jouni I.↗

NASA NTRS1991

Statistical properties of shock-accelerated ions in the outer heliosphere

Reported here are statistical studied of interplanetary protons (about 0.5-1.5 MeV) as measured by the Voyager 2 spacecraft in the outer heliosphere between about 1 and 22 AU. The acceleration processes which produce the fluctuations in intensity of the protons throughout the interval studied are caused by solar flare-generated shock waves and corotating shock structures in the solar wind. It is found that the proton count rates can be represented by a lognormal distribution, independent of the phase of the solar cycle in which the measurements were made. Power spectra of the logarithm of the counts show that for frequencies in the range of about 0.02-0.5 cycles per day, the spectra can be characterized as about f exp -2. At lower frequencies, the spectra turn over and flatten. Over the entire frequency range studied, about 0.002-0.5 cycles per day, the spectra are therefore nonfractal. The rollover in the spectra at about 100 days probably represents the reorganization time for solar wind streams within the coronal source at the sun.

Lanzeroti, L. J.↗

NASA NTRS1993

Optimal thresholds for the estimation of area rain-rate moments by the threshold method

Optimization of the threshold method, achieved by determination of the threshold that maximizes the correlation between an area-average rain-rate moment and the area coverage of rain rates exceeding the threshold, is demonstrated empirically and theoretically. Empirical results for a sequence of GATE radar snapshots show optimal thresholds of 5 and 27 mm/h for the first and second moments, respectively. Theoretical optimization of the threshold method by the maximum-likelihood approach of Kedem and Pavlopoulos (1991) predicts optimal thresholds near 5 and 26 mm/h for lognormally distributed rain rates with GATE-like parameters. The agreement between theory and observations suggests that the optimal threshold can be understood as arising due to sampling variations, from snapshot to snapshot, of a parent rain-rate distribution. Optimal thresholds for gamma and inverse Gaussian distributions are also derived and compared.

Short, David A.↗

NASA NTRS1992

Generation of magnetic fields by chaotic fluid convection - The fast dynamo problem

In the kinematic fast dynamo problem, the underlying nonlinear dynamics of the flow play a critical role in the behavior of a dynamo field. It is presently noted that the two important facets of the problem are the approximately lognormal distribution of vector lengths, and the presence of partial cancellation. It is suggested that these features may be reflected in the magnetic fields observed on the sun.

Finn, John M.↗

NASA NTRS1993

Mixing in a stratified shear flow: Energetics and sampling

Direct numerical simulations of the time evolution of homogeneous stably stratified shear flows have been performed for Richardson numbers from 0 to 1 and for Prandtl numbers between 0.1 and 2. The results indicate that mixing efficiency R(sub f) varies with turbulent Froude number in a manner consistent with laboratory experiments performed with Prandtl numbers of 0.7 and 700. However, unlike the laboratory results, for a particular Froude number, the simulations do not show a clear dependence on the magnitude of R(sub f) on Pr. The observed maximum value of R(sub f) is 0.25. When averaged over vertical length scales of an order of magnitude greater than either the overturning or Ozmidov scales of the flow, the simulations indicate that the dissipation rate epsilon is only weakly lognormally distributed with an intermittency of about 0.01 whereas estimated values in the ocean are 3 to 7.

Ivey, G. N.↗