Search NASA⌕ Search

SEARCH · Search NASA

Results for “non-Gaussian 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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Simulation of flight maneuver-load distributions by utilizing stationary, non-Gaussian random load histories

Random numbers were generated with the aid of a digital computer and transformed such that the probability density function of a discrete random load history composed of these random numbers had one of the following non-Gaussian distributions: Poisson, binomial, log-normal, Weibull, and exponential. The resulting random load histories were analyzed to determine their peak statistics and were compared with cumulative peak maneuver-load distributions for fighter and transport aircraft in flight.

Leybold, H. A.↗
NASA NTRS1979

A comparison of theoretical and experimental video compression designs

This paper compares theoretical and experimental picture compression designs, for images processed in 8 x 8 blocks using the Walsh-Hadamard transform (WHT). The optimum picture compression design is well known, if the mean-square error (mse) is used as the measure of distortion, and if it is assumed that the video process is a stationary first-order Markov process with a Gaussian distribution. This theoretical design gives useful results when the transform processing is done on full pictures, but gives inferior results (relative to empirical design) when transform processing is done on small 8 x 8 blocks. The use of non-Gaussian distributions for the transform components fails to improve this poor performance, which is due to the nonstationary nature of the video process. An experimentally based design procedure, which considers nonstationarity, yields significantly improved mse and subjective performance.

Jones, H. W., Jr.↗
NASA NTRS1973

Effects of vibration and shock on the performance of gas-bearing space-power Brayton cycle turbomachinery. Part 3: Sinusoidal and random vibration data reduction and evaluation, and random vibration probability analysis

The random vibration response of a gas bearing rotor support system has been experimentally and analytically investigated in the amplitude and frequency domains. The NASA Brayton Rotating Unit (BRU), a 36,000 rpm, 10 KWe turbogenerator had previously been subjected in the laboratory to external random vibrations, and the response data recorded on magnetic tape. This data has now been experimentally analyzed for amplitude distribution and magnetic tape. This data has now been experimentally analyzed for amplitude distribution and frequency content. The results of the power spectral density analysis indicate strong vibration responses for the major rotor-bearing system components at frequencies which correspond closely to their resonant frequencies obtained under periodic vibration testing. The results of amplitude analysis indicate an increasing shift towards non-Gaussian distributions as the input level of external vibrations is raised. Analysis of axial random vibration response of the BRU was performed by using a linear three-mass model. Power spectral densities, the root-mean-square value of the thrust bearing surface contact were calculated for specified input random excitation.

Tessarzik, J. M.↗
NASA NTRS1982

A study of the feasibility of statistical analysis of airport performance simulation

The feasibility of conducting a statistical analysis of simulation experiments to study airport capacity is investigated. First, the form of the distribution of airport capacity is studied. Since the distribution is non-Gaussian, it is important to determine the effect of this distribution on standard analysis of variance techniques and power calculations. Next, power computations are made in order to determine how economic simulation experiments would be if they are designed to detect capacity changes from condition to condition. Many of the conclusions drawn are results of Monte-Carlo techniques.

Myers, R. H.↗
NASA NTRS1972

On the application of Rice's exceedance statistics to atmospheric turbulence.

Discrepancies produced by the application of Rice's exceedance statistics to atmospheric turbulence are examined. First- and second-order densities from several data sources have been measured for this purpose. Particular care was paid to each selection of turbulence that provides stationary mean and variance over the entire segment. Results show that even for a stationary segment of turbulence, the process is still highly non-Gaussian, in spite of a Gaussian appearance for its first-order distribution. Data also indicate strongly non-Gaussian second-order distributions. It is therefore concluded that even stationary atmospheric turbulence with a normal first-order distribution cannot be considered a Gaussian process, and consequently the application of Rice's exceedance statistics should be approached with caution.

Chen, W. Y.↗
NASA NTRS1980

An experimental study of the surface elevation probability distribution and statistics of wind-generated waves

Laboratory experiments were performed to measure the surface elevation probability density function and associated statistical properties for a wind-generated wave field. The laboratory data along with some limited field data were compared. The statistical properties of the surface elevation were processed for comparison with the results derived from the Longuet-Higgins (1963) theory. It is found that, even for the highly non-Gaussian cases, the distribution function proposed by Longuet-Higgins still gives good approximations.

Huang, N. E.↗
NASA NTRS1977

Analysis of low altitude atmospheric turbulence data measured in flight

All three components of turbulence were measured simultaneously in flight at each wing tip of a Beech D-18 aircraft. The flights were conducted at low altitude, 30.5 - 61.0 meters (100-200 ft.), over water in the presence of wind driven turbulence. Statistical properties of flight measured turbulence were compared with Gaussian and non-Gaussian turbulence models. Spatial characteristics of the turbulence were analyzed using the data from flight perpendicular and parallel to the wind. The probability density distributions of the vertical gusts show distinctly non-Gaussian characteristics. The distributions of the longitudinal and lateral gusts are generally Gaussian. The power spectra compare in the inertial subrange at some points better with the Dryden spectrum, while at other points the von Karman spectrum is a better approximation. In the low frequency range the data show peaks or dips in the power spectral density. The cross between vertical gusts in the direction of the mean wind were compared with a matched non-Gaussian model. The real component of the cross spectrum is in general close to the non-Gaussian model. The imaginary component, however, indicated a larger phase shift between these two gust components than was found in previous research.

Ganzer, V. M.↗
NASA NTRS1976

A non-gaussian model of continuous atmospheric turbulence for use in aircraft design

A non-Gaussian model of atmospheric turbulence is presented and analyzed. The model is restricted to the regions of the atmosphere where the turbulence is steady or continuous, and the assumptions of homogeneity and stationarity are justified. Also spatial distribution of turbulence is neglected, so the model consists of three independent, stationary stochastic processes which represent the vertical, lateral, and longitudinal gust components. The non-Gaussian and Gaussian models are compared with experimental data, and it is shown that the Gaussian model underestimates the number of high velocity gusts which occur in the atmosphere, while the non-Gaussian model can be adjusted to match the observed high velocity gusts more satisfactorily. Application of the proposed model to aircraft response is investigated, with particular attention to the response power spectral density, the probability distribution, and the level crossing frequency. A numerical example is presented which illustrates the application of the non-Gaussian model to the study of an aircraft autopilot system. Listings and sample results of a number of computer programs used in working with the model are included.

Reeves, P. M.↗
NASA NTRS1979

Higher-order skewness and excess coefficients of some probability distributions applicable to optical propagation phenomena

Expressions are derived for higher-order skewness and excess coefficients using central moments and cumulants up to 8th order. These coefficients are then calculated for three probability distributions: (1) Log-normal, (2) Rice-Nakagami, and (3) Gamma distributions. Curves are given to shown the variation of skewness with excess coefficients for these distributions. These curves are independent of the particular distribution parameters. This method is useful for studying fluctuating phenomena, which obey non-Gaussian statistics.

Majumdar, A. K.↗
NASA NTRS1980

Narrow-band nonlinear sea waves

Probabilistic description of nonlinear waves with a narrow-band spectrum is simplified to a form in which each realization of the surface displacement becomes an amplitude-modulated Stokes wave with a mean frequency and random phase. Under appropriate conditions this simplification provides a convenient yet rigorous means of describing nonlinear effects on sea surface properties in a semiclosed or closed form. In particular, it is shown that surface displacements are non-Gaussian and skewed, as was previously predicted by the Gram-Charlier approximation; that wave heights are Rayleigh distributed, just as in the linear case; and that crests are non-Rayleigh.

Tayfun, M. A.↗
NASA NTRS1975

A mathematical examination of the press model for atmospheric turbulence

The random process used to model atmospheric turbulence in aircraft response problems is examined. The first, second, and higher order probability density and characteristic functions were developed. The concepts of the Press model lead to an approximate procedure for the analysis of the response of linear dynamic systems to a class of non-Gaussian random processes. The Press model accounts for both the Gaussian and non-Gaussian forms of measured turbulence data. The nonstationary aspects of measured data are explicitly described by the transition properties of the random process. The effects of the distribution of the intensity process upon calculated exceedances are examined. It is concluded that the press model with a Gaussian intensity distribution gives a conservative prediction of limit load values.

Sidwell, K.↗
NASA NTRS1979

The reflection of impulses from a nonlinear random sea

A model of the reflection of radar impulses from the sea at near-vertical incidence is used to account for non-Gaussian ocean waves statistics. The joint probability density function (pdf), of wave height and slope, is calculated according to the theory of Longuet-Higgins (1963) on the distribution of variables in a 'weakly nonlinear' random era. The long-crested approximation is made, a Phillips wave spectrum is assumed, and the Gram-Charlier series is truncated after skewness terms. It is found that the height and height-slope skewness coefficients bear the ratio 1:2 and that the derived impulse response and conditional cross section versus wave height are in excellent agreement with previous observations. Finally, it is suggested that the empirically determined and theoretically predicted sea state bias be corrected for in the routine processing of satellite radar altimeter data.

Jackson, F. C.↗
NASA NTRS1975

Induced anisotropy of thermal conductivity of polymer solids under large strains

A simple analytical form of induced anisotropy of heat conductivity of initially isotropic polymer solids results from employing the simplified theory of the three-chain model of the non-Gaussian network. The analytical form appears to be valid up to a stretch ratio of 2.65, which is the limit of existing experimental data. The effect of induced anisotropy on the temperature distribution, due to the large deformations, is illustrated for a highly expanded spherical shell and a cylindrical tube under a steady-state heat flow using the derived analytical form of the strain-dependent heat conductivity.

Peng, S. T. J.↗
NASA NTRS1979

A cosmological redshift-distance square law

This paper directly examines the claims of Segal (1976) that the (m,z) Hubble diagram is fitted best by a square law z = Kr-squared rather than by the traditional Hubble law z = Hr in the low-redshift range, z no more than about 0.01, corresponding to galaxies brighter than 14th mag. Segal attempts to fit a distance relation to the (m,z) scatter diagram in which each individual galaxy is plotted. The exact relation between the mean redshift for all galaxies in a small magnitude interval and the apparent magnitude is calculated. This relation is independent of luminosity function and peculiar velocity distribution about the general expansion, and is not affected by sample incompleteness as a function of apparent magnitude or the clustering of galaxies in the sample. Segal's method is affected by all of these and requires a highly sophisticated statistical analysis to deal with the non-Gaussian pointwise scatter. The present analysis favors the Hubble law and conclusively rules out the square law for the small redshift region.

Soneira, R. M.↗
NASA NTRS1975

A non-Gaussian model of continuous atmospheric turbulence proposed for use in aircraft design

This paper describes a statistical model proposed for use in forecasting vehicle responses to stationary continuous atmospheric turbulence. The model is suggested by the observed patchy character of turbulence, and differs from models now in use in that it does not assume the gust velocity to be a Gaussian process. For simplicity only the vertical gust component is considered here. The validity of the proposed model is established through comparison with published data. This comparison shows that the model is in better agreement with observed gust velocity probability distributions and exceedance frequencies than is the widely used Gaussian model, especially insofar as high velocity gusts are concerned. A method of applying the proposed model to the determination of vehicle responses is developed. It is shown that response probability distributions as well as exceedance frequencies can be derived from the eigenvalues and eigenfunction of certain unsymmetric kernels.

Reeves, P. M.↗