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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Probabilities and statistics for backscatter estimates obtained by a scatterometer with applications to new scatterometer design data

The values of the Normalized Radar Backscattering Cross Section (NRCS), sigma (o), obtained by a scatterometer are random variables whose variance is a known function of the expected value. The probability density function can be obtained from the normal distribution. Models for the expected value obtain it as a function of the properties of the waves on the ocean and the winds that generated the waves. Point estimates of the expected value were found from various statistics given the parameters that define the probability density function for each value. Random intervals were derived with a preassigned probability of containing that value. A statistical test to determine whether or not successive values of sigma (o) are truly independent was derived. The maximum likelihood estimates for wind speed and direction were found, given a model for backscatter as a function of the properties of the waves on the ocean. These estimates are biased as a result of the terms in the equation that involve natural logarithms, and calculations of the point estimates of the maximum likelihood values are used to show that the contributions of the logarithmic terms are negligible and that the terms can be omitted.

Pierson, Willard J., Jr.↗
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 NTRS1986

The SIMRAND methodology: Theory and application for the simulation of research and development projects

A research and development (R&D) project often involves a number of decisions that must be made concerning which subset of systems or tasks are to be undertaken to achieve the goal of the R&D project. To help in this decision making, SIMRAND (SIMulation of Research ANd Development Projects) is a methodology for the selection of the optimal subset of systems or tasks to be undertaken on an R&D project. Using alternative networks, the SIMRAND methodology models the alternative subsets of systems or tasks under consideration. Each path through an alternative network represents one way of satisfying the project goals. Equations are developed that relate the system or task variables to the measure of reference. Uncertainty is incorporated by treating the variables of the equations probabilistically as random variables, with cumulative distribution functions assessed by technical experts. Analytical techniques of probability theory are used to reduce the complexity of the alternative networks. Cardinal utility functions over the measure of preference are assessed for the decision makers. A run of the SIMRAND Computer I Program combines, in a Monte Carlo simulation model, the network structure, the equations, the cumulative distribution functions, and the utility functions.

Miles, R. F., Jr.↗
NASA NTRS2012

Bounding the Failure Probability Range of Polynomial Systems Subject to P-box Uncertainties

This paper proposes a reliability analysis framework for systems subject to multiple design requirements that depend polynomially on the uncertainty. Uncertainty is prescribed by probability boxes, also known as p-boxes, whose distribution functions have free or fixed functional forms. An approach based on the Bernstein expansion of polynomials and optimization is proposed. In particular, we search for the elements of a multi-dimensional p-box that minimize (i.e., the best-case) and maximize (i.e., the worst-case) the probability of inner and outer bounding sets of the failure domain. This technique yields intervals that bound the range of failure probabilities. The offset between this bounding interval and the actual failure probability range can be made arbitrarily tight with additional computational effort.

Crespo, Luis G.↗
NASA NTRS1984

Crystal gazing. Part 2: Implications of advanced in digital data storage technology

During the next 5-10 years it is likely that the bit density available in digital mass storage systems (magnetic tapes, optical and magnetic disks) will be increased to such an extent that it will greatly exceed that of the conventional photographic emulsions like IIIaJ which are used in astronomy. These developments imply that it will soon be advantageous for astronomers to use microdensitometers to completely digitize all photographic plates soon after they are developed. Distribution of digital copies of sky surveys and the contents of plate vaults will probably become feasible within ten years. Copies of other astronomical archieves (e.g., Space Telescope) could also be distributed with the same techniques. The implications for designers of future microdensitometers are: (1) there will be a continuing need for precision digitization of large-format photographic imagery, and (2) that the need for real-time analysis of the output of microdensitometers will decrease.

Wells, D. C.↗
NASA NTRS1978

Major and trace element chemistry of separated fragments from a hibonite-bearing Allende inclusion

The major and trace elements of separated fragments and a bulk sample from CG-11, a hibonite-bearing inclusion in the Allende meteorite, were analyzed. Major element abundances were used to determine the minerology of separated fragments. The high degree of correlation between Eu/Sm ratios and Lu/Yb ratios for the samples studied indicates that their rare earth element (REE) distributions are governed by two components. One, Lu-, Eu-rich, is probably hibonite; the other, depleted in these elements, seems to be associated with the secondary alteration phases, grossular, nepheline and anorthite. The REE distribution in CG-11 precludes melting events after formation of the secondary alteration phases, but a melting event involving the primary minerals cannot be excluded. The enrichment of Lu with respect to other measured REE in hibonite can be explained by present REE condensation models. Two Hf-bearing components, most likely hibonite and perovskite, are necessary to account for variations in Sc/Hf ratios in the fragments studied. The lithophile volatiles Na, Mn, Fe, Zn, and probably Cr increase in the same order as the amount of secondary alteration minerals; the volatile siderophile elements Co and Au, however, do not.

Davis, A. M.↗
NASA NTRS1989

On the decoder error probability of linear codes

By using coding and combinatorial techniques, an approximate formula for the weight distribution of decodable words of most linear block codes is evaluated. This formula is then used to give an approximate expression for the decoder error probability P(sub E)(u) of linear block codes, given that an error pattern of weight u has occurred. It is shown that P(sub E)(u) approaches the constant Q as u gets large, where Q is the probability that a completely random error pattern will cause decoder error.

Cheung, K.-M.↗
NASA NTRS2017

Analysis of in Vitro Evolution Reveals the Underlying Distribution of Catalytic Activity Among Random Sequences

The emergence of catalytic RNA is believed to have been a key event during the origin of life. Understanding how catalytic activity is distributed across random sequences is fundamental to estimating the probability that catalytic sequences would emerge. Here, we analyze the in vitro evolution of triphosphorylating ribozymes and translate their fitnesses into absolute estimates of catalytic activity for hundreds of ribozyme families. The analysis efficiently identified highly active ribozymes and estimated catalytic activity with good accuracy. The evolutionary dynamics follow Fisher’s Fundamental Theorem of Natural Selection and a corollary, permitting retrospective inference of the distribution of fitness and activity in the random sequence pool for the first time. The frequency distribution of rate constants appears to be log-normal, with a surprisingly steep dropoff at higher activity, consistent with a mechanism for the emergence of activity as the product of many independent contributions.

Abe Pressman↗
NASA NTRS1972

Social impact evaluation : Some implications of the specific decisional context approach for anticipatory project assessment with special reference to available alternatives and to techniques of evaluating the social impacts of the anticipated effects of such alternatives

The implications are explored of the specific decision context approach to anticipatory project assessment. More specifically, it is hypothesized that with respect to any given effect of a proposed project or action (mobility, job opportunities, air pollution, population distribution, etc.) such effect will likely differ in probability and/or magnitude from one decisional context to another; that the social desirability or undesirability of a given effect is a function (will differ with) each specific decisional context; that therefore the social impact of such effect will in all likelihood differ with each specific decisional context; and that the social significance of even the dame social impact of a given effect will vary from one decisional context to another when such social impact interacts with (competes with or reinforces) the social impacts of other effects. It also follows from this analysis that the respective roles of scientific method (demonstrable data) and adversarial system will not only differ with each specific decisional context but with each alternative course of action available to the decisional entity in each specific context.

Mayo, L. H.↗
NASA NTRS1977

Iron - Whence it came, where it went

Determinations of the abundances of iron and related elements in the photosphere, chromosphere, and corona of the sun as well as in solar and galactic cosmic rays are reviewed and compared with abundances derived from meteoritic data. Observed solar system abundances are found to be in accord with predictions of nucleosynthesis under either hydrostatic or explosive conditions but cannot yet be used to define these processes uniquely. The distribution of iron among planets and meteorites can probably be adequately modelled by condensation and fragmentation under equilibrium conditions above about 700 K, but below that temperature it is likely that inhibited solid-state diffusion perturbed attainment of equilibrium. Pertinent factors which are presently unknown include the mechanism responsible for metal-silicate fractionation, the grain size achieved by metallic iron in the nebula, and whether iron-bearing silicate formed prior to accretion.

Kerridge, J. F.↗
NASA NTRS1977

Flight inspection data and crack initiation times

Lockheed C-130 service-flight inspection data is reduced by means of fracture mechanics and statistical analysis into a form from which the probability of time to crack initiation and the distribution of initial flaw sizes for various locations on the aircraft can be determined. Crack sizes are normalized by extrapolating a growing crack backwards from its first recorded size to .03 inches (crack initiation size) yielding the time to crack initiation. In a similar fashion, the crack is grown backwards to a time equal to zero to yield an initial flaw size. In order to perform the discussed computations, crack growth constants were computed for each individual location and were analyzed statistically. Statistical distributions were fitted to times to crack initiation and to initial flaw sizes in order to describe their expected behavior. Weibull and Johnson distributions have been found to fit the data reasonably well but for a better fit convolution integrals of Poisson load distributions and Weibull strength distributions are needed.

Johnson, W. S.↗
NASA NTRS1980

Estimating probabilities of cloud-free fields-of-view from the earth through the atmosphere

The paper is an extension of previous papers by Lund and Shanklin (1972, 1973). It presents probabilities of cloud-free fields-of-view (CFFOV) to supplement probabilities of cloud-free lines-of-sight (CFLOS) contained in the earlier papers. A model is developed for estimating the probability of obtaining a CFFOV as a function of ground-observer-reported total sky cover for earth-to-space applications. The development of the model and examples of its application are described. A comparison of CFFOV and CFLOS results is made. In conclusion, climatic probabilities of CFFOV overhead through the entire atmosphere between the surface of the earth and space can be estimated for any desired geographical location through the use of a specified equation and conditional probabilities contained in the paper, if the frequency distribution of total sky cover categories for the desired location is known.

Lund, I. A.↗
NASA NTRS1982

Far-infrared photometry of optical emission-line stars. II

Far-infared photometry of dust clouds around a sample of eight optically bright stars, five of which are believed to be pre-main-sequence and three of which are probably post-main-sequence, is reported. Energy distributions consistent with the results of an earlier study of eight other stars where a good correlation was found between the existence of cool, far-infrared-emitting dust clouds and the presumed youth of the central star are found. The post-main-sequence objects, as in the previous study, were found to have energy distributions falling steeply from 10 to 100 microns implying very small amounts of cool dust relative to the amount of dust at a few hundred K.

Harvey, P. M.↗
NASA NTRS1984

Software reliability: Additional investigations into modeling with replicated experiments

The effects of programmer experience level, different program usage distributions, and programming languages are explored. All these factors affect performance, and some tentative relational hypotheses are presented. An analytic framework for replicated and non-replicated (traditional) software experiments is presented. A method of obtaining an upper bound on the error rate of the next error is proposed. The method was validated empirically by comparing forecasts with actual data. In all 14 cases the bound exceeded the observed parameter, albeit somewhat conservatively. Two other forecasting methods are proposed and compared to observed results. Although demonstrated relative to this framework that stages are neither independent nor exponentially distributed, empirical estimates show that the exponential assumption is nearly valid for all but the extreme tails of the distribution. Except for the dependence in the stage probabilities, Cox's model approximates to a degree what is being observed.

Nagel, P. M.↗
NASA NTRS1984

Discrimination of coherent features in turbulent boundary layers by the entropy method

Entropy in information theory is defined as the expected or mean value of the measure of the amount of self-information contained in the ith point of a distribution series x sub i, based on its probability of occurrence p(x sub i). If p(x sub i) is the probability of the ith state of the system in probability space, then the entropy, E(X) = - sigma p(x sub i) logp (x sub i), is a measure of the disorder in the system. Based on this concept, a method was devised which sought to minimize the entropy in a time series in order to construct the signature of the most coherent motions. The constrained minimization was performed using a Lagrange multiplier approach which resulted in the solution of a simultaneous set of non-linear coupled equations to obtain the coherent time series. The application of the method to space-time data taken by a rake of sensors in the near-wall region of a turbulent boundary layer was presented. The results yielded coherent velocity motions made up of locally decelerated or accelerated fluid having a streamwise scale of approximately 100 nu/u(tau), which is in qualitative agreement with the results from other less objective discrimination methods.

Corke, T. C.↗
NASA NTRS1986

A stopping theoretic approach to minimal time detection of system parameter change

The problem of minimal time detection of abrupt parameter changes in linear stochastic systems considered. The problem is posed as an optimal stopping problem for the detection in change of the induced probability measure. Under the assumption of a prior distribution for the time of change (or disruption) a stopping rule is given which minimizes the average detection delay when there is knowledge of the new measure after the change. When the new induced measure is unknown, a stopping rule is given, based only on the noisy observations and is shown to be better than the a priori knowlege of the disruption time.

Mazumdar, Ravi R.↗