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NASA NTRS1973

Statistical properties of two sine waves in Gaussian noise.

A detailed study is presented of some statistical properties of a stochastic process that consists of the sum of two sine waves of unknown relative phase and a normal process. Since none of the statistics investigated seem to yield a closed-form expression, all the derivations are cast in a form that is particularly suitable for machine computation. Specifically, results are presented for the probability density function (pdf) of the envelope and the instantaneous value, the moments of these distributions, and the relative cumulative density function (cdf).

Esposito, R.↗

NASA NTRS1983

Approximation to the Probability Density at the Output of a Photmultiplier Tube

The probability density of the integrated output of a photomultiplier tube (PMT) is approximated by the Gaussian, Rayleigh, and Gamma probability densities. The accuracy of the approximations depends on the signal energy alpha: the Gamma distribution is accurate for all alpha, the Raleigh distribution is accurate for small alpha (approximate or less than 1 photon) and the Gaussian distribution is accurate for large alpha (approximate or greater than 10 photons).

Stokey, R. J.↗

NASA NTRS1985

SCARE: A post-processor program to MSC/NASTRAN for the reliability analysis of structural ceramic components

A computer program was developed for calculating the statistical fast fracture reliability and failure probability of ceramic components. The program includes the two-parameter Weibull material fracture strength distribution model, using the principle of independent action for polyaxial stress states and Batdorf's shear-sensitive as well as shear-insensitive crack theories, all for volume distributed flaws in macroscopically isotropic solids. Both penny-shaped cracks and Griffith cracks are included in the Batdorf shear-sensitive crack response calculations, using Griffith's maximum tensile stress or critical coplanar strain energy release rate criteria to predict mixed mode fracture. Weibull material parameters can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and fracture data. The reliability prediction analysis uses MSC/NASTRAN stress, temperature and volume output, obtained from the use of three-dimensional, quadratic, isoparametric, or axisymmetric finite elements. The statistical fast fracture theories employed, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.

Gyekenyesi, J. P.↗

NASA NTRS1986

SCARE - A postprocessor program to MSC/NASTRAN for reliability analysis of structural ceramic components

Gyekenyesi, J. P.↗

NASA NTRS1991

Theoretical temperature-dependent branching ratios and laser thresholds of the 3F4 to 3H6 levels of Tm(3+) in ten garnets

The calculated energy levels, the branching ratios, and the estimated thresholds for thulium operating on the 3F4 to 3H6 transitions are reported. Garnet materials with the general formula A3B2C3O12 are evaluated. Calculations are performed for the A side under the assumption of D2 symmetry. X-ray data available in the literature are used to evaluate the crystal-field components, A sub nm. Even-n components are employed to calculate the crystal-field splittings within the manifold. Thermal occupation factors are determined in a straightforward manner using a Boltzmann distribution for the respective manifolds. Odd-n components are applied to calculate the transition probabilities for electric field transitions. It is determined that the magnetic dipole contributions to the transition probability are comparable to the electric dipole contributions in some cases. Thresholds as a function of the density of thulium atoms are calculated.

Filer, Elizabeth D.↗

NASA NTRS1992

Comets as a possible source of prebiotic molecules

Prebiotic molecules derive from abiotic organic molecules, radicals, and ions that pervade the universe at temperatures as high as several 1000 K. Here we review the role of organic molecules that condensed at low temperatures before or during comet formation in the early history of the Solar System. Recent spacecraft encounters and ground-based observations of carbon-rich volatile and dust components of comet comae provide a broad database for the investigation of these organic molecules. New laboratory data for some potential cometary organics are presented. Probable icy organic constituents of the nucleus and CHON particles as likely candidates for the distributed sources of gas-phase organic species in the coma are discussed. There is broad agreement that many organic molecules observed in the coma originate from the dust that must have existed in the solar nebula at the time and place of comet formation. We conclude that complex organic molecules found in comets may be a source of prebiotic molecules that led to the origins of life.

Huebner, W. F.↗

NASA NTRS2005

Toward Question-Asking Machines: The Logic of Questions and the Inquiry Calculus

For over a century, the study of logic has focused on the algebra of logical statements. This work, first performed by George Boole, has led to the development of modern computers, and was shown by Richard T. Cox to be the foundation of Bayesian inference. Meanwhile the logic of questions has been much neglected. For our computing machines to be truly intelligent, they need to be able to ask relevant questions. In this paper I will show how the Boolean lattice of logical statements gives rise to the free distributive lattice of questions thus defining their algebra. Furthermore, there exists a quantity analogous to probability, called relevance, which quantifies the degree to which one question answers another. I will show that relevance is not only a natural generalization of information theory, but also forms its foundation.

Knuth,Kevin H.↗

NASA NTRS2007

Probabilistic Modeling of Space Shuttle Debris Impact

On Feb 1, 2003, the Shuttle Columbia was lost during its return to Earth. As a result of the conclusion that debris impact caused the damage to the left wing of the Columbia Space Shuttle Vehicle (SSV) during ascent, the Columbia Accident Investigation Board recommended that an assessment be performed of the debris environment experienced by the SSV during ascent. A flight rationale based on probabilistic assessment is used for the SSV return-to-flight. The assessment entails identifying all potential debris sources, their probable geometric and aerodynamic characteristics, and their potential for impacting and damaging critical Shuttle components. A probabilistic analysis tool, based on the SwRI-developed NESSUS probabilistic analysis software, predicts the probability of impact and damage to the space shuttle wing leading edge and thermal protection system components. Among other parameters, the likelihood of unacceptable damage depends on the time of release (Mach number of the orbiter) and the divot mass as well as the impact velocity and impact angle. A typical result is visualized in the figures below. Probability of impact and damage, as well as the sensitivities thereof with respect to the distribution assumptions, can be computed and visualized at each point on the orbiter or summarized per wing panel or tile zone.

Huyse, Luc J.↗

NASA NTRS2007

Reliability and Creep/Fatigue Analysis of a CMC Component

High temperature ceramic matrix composites (CMC) are being explored as viable candidate materials for hot section gas turbine components. These advanced composites can potentially lead to reduced weight and enable higher operating temperatures requiring less cooling; thus leading to increased engine efficiencies. There is a need for convenient design tools that can accommodate various loading conditions and material data with their associated uncertainties to estimate the minimum predicted life as well as the failure probabilities of a structural component. This paper presents a review of the life prediction and probabilistic analyses performed for a CMC turbine stator vane. A computer code, NASALife, is used to predict the life of a 2-D woven silicon carbide fiber reinforced silicon carbide matrix (SiC/SiC) turbine stator vane due to a mission cycle which induces low cycle fatigue and creep. The output from this program includes damage from creep loading, damage due to cyclic loading and the combined damage due to the given loading cycle. Results indicate that the trends predicted by NASALife are as expected for the loading conditions used for this study. In addition, a combination of woven composite micromechanics, finite element structural analysis and Fast Probability Integration (FPI) techniques has been used to evaluate the maximum stress and its probabilistic distribution in a CMC turbine stator vane. Input variables causing scatter are identified and ranked based upon their sensitivity magnitude. Results indicate that reducing the scatter in proportional limit strength of the vane material has the greatest effect in improving the overall reliability of the CMC vane.

Murthy, Pappu L. N.↗

NASA NTRS2011

The Effect on the Lunar Exosphere of a Coroual Mass Ejection Passage

Solar wind bombardment onto exposed surfaces in the solar system produces an energetic component to the exospheres about those bodies. The solar wind energy and composition are highly dependent on the origin of the plasma. Using the measured composition of the slow wind, fast wind, solar energetic particle (SEP) population, and coronal mass ejection (CME), broken down into their various components, we have estimated the total sputter yield for each type of solar wind. We show that the heavy ion component, especially the He++ and 0+7 can greatly enhance the total sputter yield during times when the heavy ion population is enhanced. Folding in the flux, we compute the source rate for several species during different types of solar wind. Finally, we use a Monte Carlo model developed to simulate the time-dependent evolution of the lunar exosphere to study the sputtering component of the exosphere under the influence of a CME passage. We simulate the background exosphere of Na, K, Ca, and Mg. Simulations indicate that sputtering increases the mass of those constituents in the exosphere a few to a few tens times the background values. The escalation of atmospheric density occurs within an hour of onset The decrease in atmospheric density after the CME passage is also rapid, although takes longer than the increase, Sputtered neutral particles have a high probability of escaping the moon,by both Jeans escape and photo ionization. Density and spatial distribution of the exosphere can be tested with the LADEE mission.

Killen, R. M.↗

NASA NTRS2019

Uncertainty Quantification of Modeled Electron Backstreaming Failure for the NEXT Ion Thruster

Excessive electron back streaming is one of the primary life-limiting failure modes for gridded ion thrusters. Physics-based modeling of the optics grid erosion and electron back streaming margins is augmented with statistical uncertainty quantification techniques to generate a life expectancy distribution of this particular failure mechanism for the NEXT ion thruster. Generation of distributions instead of a single point estimate provide a more comprehensive picture of thruster failure probabilities and life expectation for various mission applications.

Yim, John T.↗

NASA NTRS1987

Optical communication with semiconductor laser diodes

A 25 megabit/sec direct detection optical communication system that used Q=4 PPM signalling was constructed and its performance measured under laboratory conditions. The system used a single-mode AlGaAs laser diode transmitter and low noise silicon avalanche photodiode (APD) photodetector. Comparison of measured performance with the theoretical revealed that modeling the APD output as a Gaussian process under conditions of negligible background radiation and low (less than 10 to the -12 power A) APD bulk leakage currents leads to substantial underestimates of optimal APD gain to use and overestimates of system bit error probability. A procedure is given to numerically compute system performance which uses the more accurate Webb's Approximation of the exact Conradi distribution for the APD ouput signal that does not require excessive amounts of computer time (a few minutes of VAX 8600 CPU time per system operating point). Examples are given which illustrate the breakdown of the Gaussian approximation in assessing system performance. This system achieved a bit error probability of 10 to the -6 power at a received signal energy corresponding to an average of 60 absorbed photons/bit and optimal APD gain of 700.

Davidson, F.↗

NASA NTRS1992

Uncertainties in obtaining high reliability from stress-strength models

There has been a recent interest in determining high statistical reliability in risk assessment of aircraft components. The potential consequences are identified of incorrectly assuming a particular statistical distribution for stress or strength data used in obtaining the high reliability values. The computation of the reliability is defined as the probability of the strength being greater than the stress over the range of stress values. This method is often referred to as the stress-strength model. A sensitivity analysis was performed involving a comparison of reliability results in order to evaluate the effects of assuming specific statistical distributions. Both known population distributions, and those that differed slightly from the known, were considered. Results showed substantial differences in reliability estimates even for almost nondetectable differences in the assumed distributions. These differences represent a potential problem in using the stress-strength model for high reliability computations, since in practice it is impossible to ever know the exact (population) distribution. An alternative reliability computation procedure is examined involving determination of a lower bound on the reliability values using extreme value distributions. This procedure reduces the possibility of obtaining nonconservative reliability estimates. Results indicated the method can provide conservative bounds when computing high reliability. An alternative reliability computation procedure is examined involving determination of a lower bound on the reliability values using extreme value distributions. This procedure reduces the possibility of obtaining nonconservative reliability estimates. Results indicated the method can provide conservative bounds when computing high reliability.

Neal, Donald M.↗

NASA NTRS1979

Mercury - A post-Mariner 10 assessment

The paper reviews the analyses of the imagery since the Mariner 10 flight, and considers the implications for the surface evolution of the terrestrial planets. Mercury is probably differentiated into a large iron-rich core and a thin silicate mantle. It differs from the moon by having (1) large areas of old intercrater plains, (2) a wide-spread distribution of lobate scarps, and (3) a similar albedo between young smooth plains and the older mercurian highlands. The origin of Mercury's plains and lobate scarps is discussed, and it is concluded that the crater diameter density distribution on the moon, Mars, and Mercury indicates that all the terrestrial planets experienced intense bombardment early in their histories, and that the objects responsible for this bombardment probably belonged to the same population(s).

Storm, R. G.↗

NASA NTRS1997

The Galim LL/EH Polymict Breccia: Evidence for Impact-Induced Exchange Between Reduced and Oxidized Meteoritic Material

Galim is a polymict breccia consisting of a heavily shocked (shock stage S6) LL6 chondrite, Galim (a), and an impact-melted EH chondrite, Galim (b). Relict chondrules in Galim (b) served as nucleation sites for euhedral enstatite grains crystallizing from the impact melt. Many of the reduced phases typical of EH chondrites (e.g., Si-bearing metallic Fe-Ni; Ti-bearing troilite) are absent. Galim (b) was probably shock-melted while in contact with a more oxidized source, namely, Galim (a); during this event, Si was oxidized from the metal and Ti was oxidized from troilite. Galim (a) contains shock veins and recrystallized, unzoned olivine. The absence of evidence for reduction in Galim (a) may indicate that the amount of LL material greatly exceeded that of EH material; shock metamorphism may have taken place on the LL parent body. Shock-induced redox reactions such as those inferred for the Galim breccia appear to be restricted mainly to asteroids because the low-end tail of their relative-velocity distribution permits mixing of intact disparate materials (including accretion of projectiles of different oxidation states), whereas the peak of the distribution leads to high equilibration shock pressures (allowing impact-induced exchange between previously accreted, disequilibrated materials). Galim probably formed by a two-stage process: (I) accretion to the LL parent body of an intact EH projectile at low relative velocities, and (2) shock metamorphism of the assemblage by the subsequent impact of another projectile at significantly higher relative velocities.

Rubin, Alan E.↗

NASA NTRS2004

Joint-probability Analysis of the Natural Variability of Tropical Oceanic Precipitation

Data projects pertaining to KWAJEX are described.Data sets delivered to the Goddard Distributed Active Archive Center (DAAC): 1) Kwajalein Experiment (KWAJEX) S-band calibrated, quality-controlled radar data, 1221 1 files of 3D volume data and 6832 files of 2D low-level reflectivity. 2) Raw and quality-control- processed versions of University of Washington Joss-Waldvogel disdrometer measurements obtained during KWAJEX. 3) A time series of synoptic-scale gif images of the Geostationary Meteorological Satellite (GMS) IR data for the KWAJEX period. The GMS satellite data set for the KWAJEX period was obtained from the University of Wisconsin and reprocessed into format amenable for comparison with radar data.Aircraft microphysics flight-leg definitions for all aircraft and all missions during KWAJEX were completed to facilitate microphysics data processing.

Yuter, Sandra E.↗

NASA NTRS2018

Development of a Detailed Surface Chemistry Framework in DSMC

A generalized finite-rate surface chemistry framework incorporating a comprehensive list of reaction mechanisms is developed and implemented into the Direct Simulation Monte Carlo (DSMC) solver SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer). The various mechanisms include adsorption, desorption, Eley-Rideal (ER), and several types of Langmuir-Hinshelwood (LH) mechanisms. The approach is to stochastically model the various competing reactions occurring on a set of active sites. Both gas-surface (e.g., adsorption, ER) and pure-surface (e.g., desorption) reaction mechanisms are incorporated, and the framework also includes catalytic or surface altering mechanisms involving the participation of the bulk-phase species (e.g., bulk carbon atoms). Marschall and MacLean developed a general formulation in which multiple phases and surface sites are used and a similar convention is adopted in the current work. Expressions for the microscopic parameters of reaction probabilities (for gas-surface reactions) and frequencies (for pure-surface reactions) that are required for DSMC are derived from the surface properties and macroscopic parameters such as rate constants, sticking coefficients, etc. The energy and angular distributions of the products are specified according to the reaction type and input parameters. This framework also presents physically consistent procedures to accurately compute the reaction probabilities and frequencies in the case of multiple reactions. The result is a modeling tool with a wide variety of surface reactions characterized via user-specified reaction rate constants, surface properties and parameters.

Surface Chemistry↗

NASA NTRS1992

Detecting change as it occurs

Traditionally climate changes have been detected from long series of observations and long after they have happened. Our 'inverse sequential' procedure, for detecting change as soon as it occurs, describes the existing or most recent data by their frequency distribution. Its parameter(s) are estimated both from the existing set of observations and from the same set augmented by 1,2,....j new observations. Individual-value probability products ('likelihoods') are used to form ratios which yield two probabilities for erroneously accepting the existing parameter(s) as valid for the augmented data set, and vice versa. A genuine parameter change is signaled when these probabilities (or a more stable compound probability) show a progressive decrease. New parameter values can then be estimated from the new observations alone using standard statistical techniques. The inverse sequential procedure will be illustrated for global annual mean temperatures (assumed normally distributed), and for annual numbers of North Atlantic hurricanes (assumed to represent Poisson distributions). The procedure was developed, but not yet tested, for linear or exponential trends, and for chi-squared means or degrees of freedom, a special measure of autocorrelation.

Radok, Uwe↗