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NASA NTRS1981

Masses of neutron stars in X-ray binary systems

Methods and assumptions used in determining masses of neutron stars in binary X-ray pulsar systems are discussed. The determination of the neutron star masses requires a knowledge of the orbital elements of the systems, which can be measured by tracking the pulse arrival times over a suitably long time interval. A method to estimate orbital inclination angle when the source exhibits X-ray eclipses is presented, in which the photospheric radius of the companion star in units of the orbital separation can be simply related by geometry to the inclination angle and eclipse angle. Probability distributions for 4 neutron star masses are presented, which have a 95% confidence limit.

Kelley, R. L.↗

NASA NTRS1982

Generation of pseudo-random numbers

Practical methods for generating acceptable random numbers from a variety of probability distributions which are frequently encountered in engineering applications are described. The speed, accuracy, and guarantee of statistical randomness of the various methods are discussed.

Howell, L. W.↗

NASA NTRS1980

Sensor failure and multivariable control for airbreathing propulsion systems

A new sensor/actuator failure analysis technique for turbofan jet engines was developed. Three phases of failure analysis, namely detection, isolation, and accommodation are considered. Failure detection and isolation techniques are developed by utilizing the concept of Generalized Likelihood Ratio (GLR) tests. These techniques are applicable to both time varying and time invariant systems. Three GLR detectors are developed for: (1) hard-over sensor failure; (2) hard-over actuator failure; and (3) brief disturbances in the actuators. The probability distribution of the GLR detectors and the detectability of sensor/actuator failures are established. Failure type is determined by the maximum of the GLR detectors. Failure accommodation is accomplished by extending the Multivariable Nyquest Array (MNA) control design techniques to nonsquare system designs. The performance and effectiveness of the failure analysis technique are studied by applying the technique to a turbofan jet engine, namely the Quiet Clean Short Haul Experimental Engine (QCSEE). Single and multiple sensor/actuator failures in the QCSEE are simulated and analyzed and the effects of model degradation are studied.

Behbehani, K.↗

NASA NTRS1983

FUNSTAT and statistical image representations

General ideas of functional statistical inference analysis of one sample and two samples, univariate and bivariate are outlined. ONESAM program is applied to analyze the univariate probability distributions of multi-spectral image data.

Parzen, E.↗

NASA NTRS1982

Computer program for solving laminar, transitional, or turbulent compressible boundary-layer equations for two-dimensional and axisymmetric flow

A numerical algorithm and computer program are presented for solving the laminar, transitional, or turbulent two dimensional or axisymmetric compressible boundary-layer equations for perfect-gas flows. The governing equations are solved by an iterative three-point implicit finite-difference procedure. The software, program VGBLP, is a modification of the approach presented in NASA TR R-368 and NASA TM X-2458, respectively. The major modifications are: (1) replacement of the fourth-order Runge-Kutta integration technique with a finite-difference procedure for numerically solving the equations required to initiate the parabolic marching procedure; (2) introduction of the Blottner variable-grid scheme; (3) implementation of an iteration scheme allowing the coupled system of equations to be converged to a specified accuracy level; and (4) inclusion of an iteration scheme for variable-entropy calculations. These modifications to the approach presented in NASA TR R-368 and NASA TM X-2458 yield a software package with high computational efficiency and flexibility. Turbulence-closure options include either two-layer eddy-viscosity or mixing-length models. Eddy conductivity is modeled as a function of eddy viscosity through a static turbulent Prandtl number formulation. Several options are provided for specifying the static turbulent Prandtl number. The transitional boundary layer is treated through a streamwise intermittency function which modifies the turbulence-closure model. This model is based on the probability distribution of turbulent spots and ranges from zero to unity for laminar and turbulent flow, respectively. Several test cases are presented as guides for potential users of the software.

Harris, J. E.↗

NASA NTRS1983

A probabilistic analysis of silicon cost

Silicon materials costs represent both a cost driver and an area where improvement can be made in the manufacture of photovoltaic modules. The cost from three processes for the production of low-cost silicon being developed under the U.S. Department of Energy's (DOE) National Photovoltaic Program is analyzed. The approach is based on probabilistic inputs and makes use of two models developed at the Jet Propulsion Laboratory: SIMRAND (SIMulation of Research ANd Development) and IPEG (Improved Price Estimating Guidelines). The approach, assumptions, and limitations are detailed along with a verification of the cost analyses methodology. Results, presented in the form of cumulative probability distributions for silicon cost, indicate that there is a 55% chance of reaching the DOE target of $16/kg for silicon material. This is a technically achievable cost based on expert forecasts of the results of ongoing research and development and do not imply any market prices for a given year.

Reiter, L. J.↗

NASA NTRS1983

A development of logistics management models for the Space Transportation System

A new analytic queueing approach was described which relates stockage levels, repair level decisions, and the project network schedule of prelaunch operations directly to the probability distribution of the space transportation system launch delay. Finite source population and limited repair capability were additional factors included in this logistics management model developed specifically for STS maintenance requirements. Data presently available to support logistics decisions were based on a comparability study of heavy aircraft components. A two-phase program is recommended by which NASA would implement an integrated data collection system, assemble logistics data from previous STS flights, revise extant logistics planning and resource requirement parameters using Bayes-Lin techniques, and adjust for uncertainty surrounding logistics systems performance parameters. The implementation of these recommendations can be expected to deliver more cost-effective logistics support.

Carrillo, M. J.↗

NASA NTRS1984

Slant path rain attenuation and path diversity statistics obtained through radar modeling of rain structure

Single and joint terminal slant path attenuation statistics at frequencies of 28.56 and 19.04 GHz have been derived, employing a radar data base obtained over a three-year period at Wallops Island, VA. Statistics were independently obtained for path elevation angles of 20, 45, and 90 deg for purposes of examining how elevation angles influences both single-terminal and joint probability distributions. Both diversity gains and autocorrelation function dependence on site spacing and elevation angles were determined employing the radar modeling results. Comparisons with other investigators are presented. An independent path elevation angle prediction technique was developed and demonstrated to fit well with the radar-derived single and joint terminal radar-derived cumulative fade distributions at various elevation angles.

Goldhirsh, J.↗

NASA NTRS1983

Spline approximation of quantile functions

The study reported here explored the development and utility of a spline representation of the sample quantile function of a continuous probability distribution in providing a functional description of a random sample and a method of generating random variables. With a spline representation, the random samples are generated by transforming a sample of uniform random variables to the interval of interest. This is useful, for example, in simulation studies in which a random sample represents the only known information about the distribution. The spline formulation considered here consists of a linear combination of cubic basis splines (B-splines) fit in a least squares sense to the sample quantile function using equally spaced knots. The following discussion is presented in five parts. The first section highlights major results realized from the study. The second section further details the results obtained. The methodology used is described in the third section, followed by a brief discussion of previous research on quantile functions. Finally, the results of the study are evaluated.

Schiess, J. R.↗

NASA NTRS1984

A performability solution method for degradable nonrepairable systems

The present performability model-solving algorithm identifies performance with 'reward', representing the state behavior of a system S by a finite-state stochastic process and determining reward by means of reward rates that are associated with the states of the base model. A general method is obtained for determining the probability distribution function of the performance (reward) variable, and therefore the performability, of the corresponding system. This is done for bounded utilization periods, and the result is an integral expression which is either analytically or numerically solvable.

Furchtgott, D. G.↗

NASA NTRS1984

Spatial estimation from remotely sensed data via empirical Bayes models

Multichannel satellite image data, available as LANDSAT imagery, are recorded as a multivariate time series (four channels, multiple passovers) in two spatial dimensions. The application of parametric empirical Bayes theory to classification of, and estimating the probability of, each crop type at each of a large number of pixels is considered. This theory involves both the probability distribution of imagery data, conditional on crop types, and the prior spatial distribution of crop types. For the latter Markov models indexed by estimable parameters are used. A broad outline of the general theory reveals several questions for further research. Some detailed results are given for the special case of two crop types when only a line transect is analyzed. Finally, the estimation of an underlying continuous process on the lattice is discussed which would be applicable to such quantities as crop yield.

Hill, J. R.↗

NASA NTRS1984

Starbursts in Galaxies: Implications of Molecular and Far-infrared Observations

Starburst galaxies are defined in several ways (colors, optical spectroscopic signatures, and excess radio flux), and observational evidence indicating that episodes of rapid star formation occur in many galaxies with active nuclei is presented. There is a good correlation of 100 micron luminosity with CO emission, and of both quantities with excess nonthermal radio flux. This fact requires some linkage between central and global star formation rates. In addition, the presence of starbusts distorts the appearance of the molecular gas in which they occur. Using far infrared color temperatures and comparisons of CO isotopes, it is shown that the strong (12)CO emission in these galaxies does not accurately trace the H2 distribution, probably because the starburst raises the avearage temperature of the cloud ensemble.

Rickard, L. J.↗

NASA NTRS1985

Monte Carlo lattice models for adsorbed polymer conformation

The adhesion between a polymer film and a metal surface is of great technological interest. However, the prediction of adhesion and wear properties of polymer coated metals is quite difficult because a fundamental understanding of the polymer surface interaction does not yet exist. A computer model for the conformation of a polymer molecule adsorbed on a surface is discussed. The chain conformation is assumed to be described by a partially directed random walk on a three dimensional simple cubic lattice. An attractive surface potential is incorporated into the model through the use of a random walk step probability distribution that is anisotropic in the direction normal to the attractive surface. The effects of variations in potential characteristics are qualitatively included by varying both the degree of anisotropy of the step distribution and the range of the anisotropy. Polymer conformation is characterized by the average end to end distance, average radius of gyration, and average number of chain segments adsorbed on the surface.

Good, B. S.↗

NASA NTRS1985

Areal coverage of storm precipitation

The probability distributions of the spatial distribution of precipitation from storms of different types were studied. The occurrence of wetted rainstorm area within a catchment was modeled as a Poisson arrival process in which each storm is composed of stationary, nonoverlapping, independent random cell clusters whose centers are Poisson-distributed as through fractals. The portion of a catchment covered by a stationary rainstorm was modeled by the common area of two overlapping circles. The first two moments of the distribution of the common area were derived from purely geometrical considerations. The spatial structure of the depth of rainfall from a stationary rainstorm was investigated using point process techniques. Total storm rainfall at the center of each cell is a random variable, and rainfall is distributed around the center specified by a spread function that may incorporate random parameters.

Eagleson, P. S.↗

NASA NTRS1984

On the spatial correlations of Abell clusters

If rich clusters formed where the primordial density enhancement, when averaged over an appropriate volume, was unusually large, then they give a biased measure of the large-scale density correlation function determiend by the probability distribution of the density fluctuations on a rich cluster mass scale. If this distribution was Gaussian, the correlation function is amplified. The amplification for rich clusters is estimated to be eaual about ten and predicted trend of amplification with richness agrees qualitatively with that observed. Some implications of these results for the large-scale density correlations are discussed.

Kaiser, N.↗

NASA NTRS1985

Composite statistical method for modeling wind gusts for aircraft simulation

This paper discusses the application of three statistical methods in combination to model wind gusts for use in aircraft flight simulation. The approach combines principal components analysis, time series analysis and probability distribution model to analyze and simulate wind gust components. Comparisons are given between wind gust components generated by the model and components measured onboard an aircraft.

Schiess, J. R.↗

NASA NTRS1985

The atmospheric effect on the separability of field classes measured from satellites

The atmospheric effect on the upward radiance emerging from the atmosphere above a nonuniform surface results in a reduction of the separability between the surface classes by broadening the radiance probability distribution of each class, while narrowing the total radiance range. The atmospheric modulation transfer function (MTF) is used in Fourier transform analyses to simulate the atmospheric effect on the imagery of a nonuniform surface and to demonstrate the atmospheric effect on separability of field classes.

Kaufman, Y. J.↗

NASA NTRS1986

Digital Pseudonoise Generator

Architecture developed for noise generator based on pseudorandom number sequence. Concept involves no additions or multiplications; outputs of set of feedback shift registers combined, bit-by-bit, in accordance with desired probability distribution. Digital, pseudorandom number output fed to digital-to-analog converter to generate pseudonoise signal suitable for testing broadband amplifiers.

Knoebel, A.↗