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At least 145 records · Page 8

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NASA NTRS1983

Range reference atmosphere models

A description is given of the methods used to establish the statistical parameters and models for wind and various thermodynamic quantities at an altitude of 0-70 km for nine geographical locations. It is noted that wind is modeled as a vector quantity using the bivariate normal probability function. With the five parameters of the bivariate normal distribution, the distribution for wind speed is derived as a generalized Rayleigh distribution. In addition, the frequency of wind direction is derived, and the conditional distribution of wind speed given the wind direction is derived. It is pointed out that these and other wind models are consistent with the rigorous mathematical properties of the bivariate normal probability theory. The thermodynamic quantities are consistent with the hydrostatic equation and the equation of state for the mean values. With these methods, many statistical relationships can be derived.

Smith, O. E.↗

NASA NTRS1974

Simulation techniques for estimating error in the classification of normal patterns

Methods of efficiently generating and classifying samples with specified multivariate normal distributions were discussed. Conservative confidence tables for sample sizes are given for selective sampling. Simulation results are compared with classified training data. Techniques for comparing error and separability measure for two normal patterns are investigated and used to display the relationship between the error and the Chernoff bound.

Whitsitt, S. J.↗

NASA NTRS2004

GPS FOM Chimney Analysis using Generalized Extreme Value Distribution

Many a time an objective of a statistical analysis is to estimate a limit value like 3-sigma 95% confidence upper limit from a data sample. The generalized Extreme Value Distribution method can be profitably employed in many situations for such an estimate. . .. It is well known that according to the Central Limit theorem the mean value of a large data set is normally distributed irrespective of the distribution of the data from which the mean value is derived. In a somewhat similar fashion it is observed that many times the extreme value of a data set has a distribution that can be formulated with a Generalized Distribution. In space shuttle entry with 3-string GPS navigation the Figure Of Merit (FOM) value gives a measure of GPS navigated state accuracy. A GPS navigated state with FOM of 6 or higher is deemed unacceptable and is said to form a FOM 6 or higher chimney. A FOM chimney is a period of time during which the FOM value stays higher than 5. A longer period of FOM of value 6 or higher causes navigated state to accumulate more error for a lack of state update. For an acceptable landing it is imperative that the state error remains low and hence at low altitude during entry GPS data of FOM greater than 5 must not last more than 138 seconds. I To test the GPS performAnce many entry test cases were simulated at the Avionics Development Laboratory. Only high value FoM chimneys are consequential. The extreme value statistical technique is applied to analyze high value FOM chimneys. The Maximum likelihood method is used to determine parameters that characterize the GEV distribution, and then the limit value statistics are estimated.

Ott, Rick↗

NASA NTRS1994

Experiment K-7-21: Effect of Microgravity on 1: Metabolic Enzymes of Type 1 and Type 2 Muscle Fibers, and on 2: Metabolic Enzymes, Neurotransmitter Amino Acids, and Neurotransmitter Associated Enzymes in Selected Regions of the Central Nervous System: The Distribution of Selected Enzymes and Amino Acids in the Hippocampal Formation - Part 2

Six key metabolic enzymes plus glutaminase and glutamate decarboxylase, as well as glutamate, aspartate and GABA, were measured in 11 regions of the hippocampal formation of synchronous, flight and tail suspension rats. Major differences were observed in the normal distribution patterns of each enzyme and amino acid, but no substantive effects of either microgravity or tail suspension on these patterns were clearly demonstrated.

Lowry, O. H.↗

NASA NTRS1998

Role of the Quasi-Biennial Oscillation in the Transport of Aerosols from the Tropical Stratospheric Reservoir to Midlatitudes

The temporal evolution of the stratospheric aerosol distribution in the tropical stratospheric reservoir after the eruption of Mount Pinatubo was observed from 1992 to 1995 by the HALOE instrument on the UARS satellite. Since the spatial gradient of aerosol loading is large at the boundaries of the tropical stratospheric reservoir due to the volcanic aerosols, the effect of the meridional circulation on the distribution is seen clearly. The mechanism for dispersal of aerosol in the lower stratosphere from the tropics into midlatitudes strongly depends on the phase of the equatorial zonal wind. The time-latitude cross sections of the normalized distribution of aerosol on isentropic surfaces are used to observe the equatorial variation as well as change in meridional dispersal during the quasi-biennial period. Observed tropical stratospheric winds are used with a simple analytical dynamical model to examine transport processes of tracers from the tropics during several phases of the quasi-biennial oscillation (QBO) from 1992 to 1995. The Lagrangian meridional circulation in the tropics is consistent with the vertical and meridional velocities correlated with the QBO in the zonal wind. We find that vertical motion plays a crucial role in vertical and subsequent meridional transport. The pattern of meridional divergence derived from the vertical velocity is closely related to the observed HALOE aerosol distributions and their temporal development in the equatorial region. The westerly (easterly) shear phase of the QBO is associated with sinking (rising) motions at the equator and subsequent poleward (equatorward) transport in the lower stratosphere.

Choi, Wookap↗

NASA NTRS2007

Derivation and Application of a Global Albedo yielding an Optical Brightness To Physical Size Transformation Free of Systematic Errors

Orbital object data acquired via optical telescopes can play a crucial role in accurately defining the space environment. Radar systems probe the characteristics of small debris by measuring the reflected electromagnetic energy from an object of the same order of size as the wavelength of the radiation. This signal is affected by electrical conductivity of the bulk of the debris object, as well as its shape and orientation. Optical measurements use reflected solar radiation with wavelengths much smaller than the size of the objects. Just as with radar, the shape and orientation of an object are important, but we only need to consider the surface electrical properties of the debris material (i.e., the surface albedo), not the bulk electromagnetic properties. As a result, these two methods are complementary in that they measure somewhat independent physical properties to estimate the same thing, debris size. Short arc optical observations such as are typical of NASA's Liquid Mirror Telescope (LMT) give enough information to estimate an Assumed Circular Orbit (ACO) and an associated range. This information, combined with the apparent magnitude, can be used to estimate an "absolute" brightness (scaled to a fixed range and phase angle). This absolute magnitude is what is used to estimate debris size. However, the shape and surface albedo effects make the size estimates subject to systematic and random errors, such that it is impossible to ascertain the size of an individual object with any certainty. However, as has been shown with radar debris measurements, that does not preclude the ability to estimate the size distribution of a number of objects statistically. After systematic errors have been eliminated (range errors, phase function assumptions, photometry) there remains a random geometric albedo distribution that relates object size to absolute magnitude. Measurements by the LMT of a subset of tracked debris objects with sizes estimated from their radar cross sections indicate that the random variations in the albedo follow a log-normal distribution quite well. In addition, this distribution appears to be independent of object size over a considerable range in size. Note that this relation appears to hold for debris only, where the shapes and other properties are not primarily the result of human manufacture, but of random processes. With this information in hand, it now becomes possible to estimate the actual size distribution we are sampling from. We have identified two characteristics of the space debris population that make this process tractable and by extension have developed a methodology for performing the transformation.

Mulrooney, Dr. Mark K.↗

NASA NTRS2004

On the Positive Bias of Peak Horizontal Velocity from an Idealized Doppler Profiler

In the presence of 3-D turbulence, peak horizontal velocity estimates from an idealized Doppler profiler are found to be positively biased due to an incomplete specification of the vertical velocity field. The magnitude of the bias was estimated by assuming that the vertical and horizontal velocities can be separated into average and perturbation values and that the vertical and horizontal velocity perturbations are normally distributed. Under these assumptions, properties of the Type-I Extreme Value Distribution for maxima, known as the Gumbel distribution, can be used to obtain an analytical solution of the bias. The bias depends on geometric properties of the profiler configuration, the variance in the horizontal velocity, and the unresolved variance in the vertical velocity. When these variances are normalized by the average horizontal velocity, the bias can be mapped as a simple function of the normalized variances.

Short, David A.↗

NASA NTRS2013

Evaluation of Low-Gravity Smoke Particulate for Spacecraft Fire Detection

Tests were conducted on the International Space Station to evaluate the smoke particulate size from materials and conditions that are typical of those expected in spacecraft fires. Five different materials representative of those found in spacecraft (Teflon, Kapton, cotton, silicone rubber and Pyrell) were heated to temperatures below the ignition point with conditions controlled to provide repeatable sample surface temperatures and air flow. The air flow past the sample during the heating period ranged from quiescent to 8 cm/s. The effective transport time to the measurement instruments was varied from 11 to 800 seconds to simulate different smoke transport conditions in spacecraft. The resultant aerosol was evaluated by three instruments which measured different moments of the particle size distribution. These moment diagnostics were used to determine the particle number concentration (zeroth moment), the diameter concentration (first moment), and the mass concentration (third moment). These statistics were combined to determine the diameter of average mass and the count mean diameter and by assuming a log-normal distribution, the geometric mean diameter and the geometric standard deviations were also calculated. Smoke particle samples were collected on TEM grids using a thermal precipitator for post flight analysis. The TEM grids were analyzed to determine the particle morphology and shape parameters. The different materials produced particles with significantly different morphologies. Overall the majority of the average smoke particle sizes were found to be in the 200 to 400 nanometer range with the quiescent cases and the cases with increased transport time typically producing with substantially larger particles. The results varied between materials but the smoke particles produced in low gravity were typically twice the size of particles produced in normal gravity. These results can be used to establish design requirements for future spacecraft smoke detectors.

Fire Safety↗

NASA NTRS2013

Evaluation of Low-Gravity Smoke Particulate for Spacecraft Fire Detection

Fire↗

NASA NTRS2004

A Preliminary ZEUS Lightning Location Error Analysis Using a Modified Retrieval Theory

The ZEUS long-range VLF arrival time difference lightning detection network now covers both Europe and Africa, and there are plans for further expansion into the western hemisphere. In order to fully optimize and assess ZEUS lightning location retrieval errors and to determine the best placement of future receivers expected to be added to the network, a software package is being developed jointly between the NASA Marshall Space Flight Center (MSFC) and the University of Nevada Las Vegas (UNLV). The software package, called the ZEUS Error Analysis for Lightning (ZEAL), will be used to obtain global scale lightning location retrieval error maps using both a Monte Carlo approach and chi-squared curvature matrix theory. At the core of ZEAL will be an implementation of an Iterative Oblate (IO) lightning location retrieval method recently developed at MSFC. The IO method will be appropriately modified to account for variable wave propagation speed, and the new retrieval results will be compared with the current ZEUS retrieval algorithm to assess potential improvements. In this preliminary ZEAL work effort, we defined 5000 source locations evenly distributed across the Earth. We then used the existing (as well as potential future ZEUS sites) to simulate arrival time data between source and ZEUS site. A total of 100 sources were considered at each of the 5000 locations, and timing errors were selected from a normal distribution having a mean of 0 seconds and a standard deviation of 20 microseconds. This simulated "noisy" dataset was analyzed using the IO algorithm to estimate source locations. The exact locations were compared with the retrieved locations, and the results are summarized via several color-coded "error maps."

Elander, Valjean↗

NASA NTRS1998

Distribution and observed associations of orthostatic blood pressure changes in elderly general medicine outpatients

Factors associated with orthostatic blood pressure change in elderly outpatients were determined by surveying 398 medical clinical outpatients aged 65 years and older. Blood pressure was measured with random-zero sphygmomanometers after patients were 5 minutes in a supine and 5 minutes in a standing position. Orthostatic blood pressure changes were at normally distributed levels with systolic and diastolic pressures dropping an average of 4 mm Hg (standard deviation [SD]=15 mm Hg) and 2 mm Hg (SD=11 mm Hg), respectively. Orthostatic blood pressure changes were unassociated with age, race, sex, body mass, time since eating, symptoms, or other factors. According to multiple linear regression analysis, supine systolic pressure, chronic obstructive pulmonary disease (COPD), and diabetes mellitus were associated with a decrease in systolic pressure on standing. Hypertension, antiarthritic drugs, and abnormal heartbeat were associated with an increase in systolic pressure on standing. For orthostatic diastolic pressure changes, supine diastolic pressure and COPD were associated with a decrease in diastolic pressure on standing. Congestive heart failure was associated with an increase in standing diastolic pressure. Using logistic regression analysis, only supine systolic pressure was associated with a greater than 20-mm Hg drop in systolic pressure (n=53, prevalence=13%). Supine diastolic pressure and COPD were the only variables associated with a greater than 20-mm Hg drop in diastolic pressure (n=16, prevalence=4%). These factors may help physicians in identifying older persons at risk for having orthostatic hypotension.

Non-NASA Center↗

NASA NTRS1966

Log-normal model for microbial survival in heat sterilization

An analytical model is developed for the survival times of organisms in heat sterilization in which the probability of inactivation as a function of exposure time is log-normally distributed. Experimental data is examined relative to this model and it is concluded that the model is valid except during the initial period of heating when an additional interaction between the organisms and their surrounding medium appears to be present. At long heating times, the log-normal model appears more accurate for extrapolating to low survival probabilities than the usual logarithmic survivor curves and is generally more conservative.

SURVIVAL↗

NASA NTRS2012

Particle Morphology and Size Results from the Smoke Aerosol Measurement Experiment-2

Results are presented from the Reflight of the Smoke Aerosol Measurement Experiment (SAME-2) which was conducted during Expedition 24 (July-September 2010). The reflight experiment built upon the results of the original flight during Expedition 15 by adding diagnostic measurements and expanding the test matrix. Five different materials representative of those found in spacecraft (Teflon, Kapton, cotton, silicone rubber and Pyrell) were heated to temperatures below the ignition point with conditions controlled to provide repeatable sample surface temperatures and air flow. The air flow past the sample during the heating period ranged from quiescent to 8 cm/s. The smoke was initially collected in an aging chamber to simulate the transport time from the smoke source to the detector. This effective transport time was varied by holding the smoke in the aging chamber for times ranging from 11 to 1800 s. Smoke particle samples were collected on Transmission Electron Microscope (TEM) grids for post-flight analysis. The TEM grids were analyzed to observe the particle morphology and size parameters. The diagnostics included a prototype two-moment smoke detector and three different measures of moments of the particle size distribution. These moment diagnostics were used to determine the particle number concentration (zeroth moment), the diameter concentration (first moment), and the mass concentration (third moment). These statistics were combined to determine the diameter of average mass and the count mean diameter and, by assuming a log-normal distribution, the geometric mean diameter and the geometric standard deviations can also be calculated. Overall the majority of the average smoke particle sizes were found to be in the 200 nm to 400 nm range with the quiescent cases producing some cases with substantially larger particles.

Urban, David L.↗

NASA NTRS1974

An analysis of fracture trace patterns in areas of flat-lying sedimentary rocks for the detection of buried geologic structure

Two study areas in a cratonic platform underlain by flat-lying sedimentary rocks were analyzed to determine if a quantitative relationship exists between fracture trace patterns and their frequency distributions and subsurface structural closures which might contain petroleum. Fracture trace lengths and frequency (number of fracture traces per unit area) were analyzed by trend surface analysis and length frequency distributions also were compared to a standard Gaussian distribution. Composite rose diagrams of fracture traces were analyzed using a multivariate analysis method which grouped or clustered the rose diagrams and their respective areas on the basis of the behavior of the rays of the rose diagram. Analysis indicates that the lengths of fracture traces are log-normally distributed according to the mapping technique used. Fracture trace frequency appeared higher on the flanks of active structures and lower around passive reef structures. Fracture trace log-mean lengths were shorter over several types of structures, perhaps due to increased fracturing and subsequent erosion. Analysis of rose diagrams using a multivariate technique indicated lithology as the primary control for the lower grouping levels. Groupings at higher levels indicated that areas overlying active structures may be isolated from their neighbors by this technique while passive structures showed no differences which could be isolated.

Podwysocki, M. H.↗

NASA NTRS1980

A hill-sliding strategy for initialization of Gaussian clusters in the multidimensional space

A hill sliding technique was devised to extract Gaussian clusters from the multivariate probability density estimate of sample data for the first step of iterative unsupervised classification. Each cluster was assumed to posses a unimodal normal distribution. A clustering function proposed distinguished elements of a cluster under formation from the rest in the feature space. Initial clusters were extracted one by one according to the hill sliding tactics. A dimensionless cluster compactness parameter was proposed as a universal measure of cluster goodness and used satisfactorily in test runs with LANDSAT multispectral scanner data. The normalized divergence, defined by the cluster divergence divided by the entropy of the entire sample data, was utilized as a general separability measure between clusters. An overall clustering objective function was set forth in terms of cluster covariance matrices, from which the cluster compactness measure could be deduced. Minimal improvement of initial data partitioning was evaluated by this objective function in eliminating scattered sparse data points. The hill sliding clustering technique developed herein has the potential applicability to decomposition any multivariate mixture distribution into a number of unimodal distributions when an appropriate distribution function to the data set is employed.

Park, J. K.↗

NASA NTRS1987

Probabilistic SSME blades structural response under random pulse loading

The purpose is to develop models of random impacts on a Space Shuttle Main Engine (SSME) turbopump blade and to predict the probabilistic structural response of the blade to these impacts. The random loading is caused by the impact of debris. The probabilistic structural response is characterized by distribution functions for stress and displacements as functions of the loading parameters which determine the random pulse model. These parameters include pulse arrival, amplitude, and location. The analysis can be extended to predict level crossing rates. This requires knowledge of the joint distribution of the response and its derivative. The model of random impacts chosen allows the pulse arrivals, pulse amplitudes, and pulse locations to be random. Specifically, the pulse arrivals are assumed to be governed by a Poisson process, which is characterized by a mean arrival rate. The pulse intensity is modelled as a normally distributed random variable with a zero mean chosen independently at each arrival. The standard deviation of the distribution is a measure of pulse intensity. Several different models were used for the pulse locations. For example, three points near the blade tip were chosen at which pulses were allowed to arrive with equal probability. Again, the locations were chosen independently at each arrival. The structural response was analyzed both by direct Monte Carlo simulation and by a semi-analytical method.

Shiao, Michael↗

NASA NTRS1994

Distributions of the interplanetary magnetic field revisited

The adequacy of the power spectrum to characterize the variations of a parameter depends on whether or not the parameter has a Gaussian distribution. We here perform very simple tests of Gaussianity on the distribution. We here perform very simple tests of Gaussianity on the distributions of the magnitudes of the interplanetary magnetic field, and on the distributions of the components; that is, we find the first four cumulants of the distributions (mean, variance, skewness, and kurtosis) and their solar cycle variations. We find, consistent with other recent analyses, that the traditional distributions of the 1-hour averaged magnitude are not distributed normally or lognomally as has often been assumed and the 1-hour averaged z component is found to have a nonzero kurtosis. Thus the power spectrum is insufficient to completely characterize these variations and polyspectra are needed. We have isolated variations in the 1/f frequency region of the spectrum and show that the distributions of the magnitudes have nonzero skewness and kurtosis, the magnitudes are not distributed lognormally, and the distributions of the components have nonzero kurtosis. Thus higher-order spectra are again needed for a full characterization.

Feynman, Joan↗

NASA NTRS2022

Non-Gaussian Distributions of TOA SW Flux as Observed by MISR and CERES

The Top of Atmosphere (TOA) shortwave (SW) flux, converted from Terra Multi angle Imaging‐SpectroRadiometer (MISR) narrow band albedos, is compared with that measured from Clouds and the Earth’s Radiant Energy System (CERES). We describe the probability density function (PDF) of the monthly TOA SW flux and how the statistical third moment, skewness, can impact the quantification of the flux. The PDF of the SW flux is not normally distributed but positively skewed. In both sets of observations, the near-global (80S-80N) median value of the SW flux is ≈3 W/m 2 less than the mean value, due to the positive skewness of the distribution. The near-global mean TOA SW flux converted from MISR is about 7 W/m 2 (≈7%) less than CERES measured flux during the last two decades. Surprisingly, hemispheric asymmetry exists with TOA SW observations from Terra platform. SH reflects 3.92 W/m 2 and 1.15 W/m 2 more mean SW flux than NH, from MISR and CERES Single Scanner Footprint products, respectively. We can infer that the offsetting by morning clouds in the SH is greater than the effect of hemispheric imbalance of SW flux caused by different land masses in two hemispheres. While the characteristics of the two SW fluxes broadly agree with each other, differences in the regional PDF from two different SW fluxes are substantially different over high cloud regions and high altitude regions. Our analysis shows that some parts of the different skewness from two measurements may be attributed to the different calibration of the radiance anisotropy over high cloud scenes.

satellite measurements↗