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A condition for the Gateaux differentiability of the probability of misclassification as a function of a feature selection matrix B, assuming a maximum likelihood classifier and normally distributed populations, is given. It is also shown that if the probability of error has a local minimum at B then it is differentiable at B.
A top priority of any launch vehicle is to insert as much mass into the desired orbit as possible. This requirement must be traded against vehicle capability in terms of dynamic control, thermal constraints, and structural margins. The vehicle is certified to specific structural limits which will yield certain performance characteristics of mass to orbit. Some limits cannot be certified generically and must be checked with each mission design. The most sensitive limits require an assessment on the day-of-launch. To further minimize vehicle loads while maximizing vehicle performance, a day-of-launch trajectory can be designed. This design is optimized according to that day s wind and atmospheric conditions, which increase the probability of launch. The day-of-launch trajectory design and verification process is critical to the vehicle s safety. The Day-Of-Launch I-Load Update (DOLILU) is the process by which the National Aeronautics and Space Administration's (NASA) Space Shuttle Program tailors the vehicle steering commands to fit that day s environmental conditions and then rigorously verifies the integrated vehicle trajectory s loads, controls, and performance. This process has been successfully used for almost twenty years and shares many of the same elements with other launch vehicles that execute a day-of-launch trajectory design or day-of-launch trajectory verification. Weather balloon data is gathered at the launch site and transmitted to the Johnson Space Center s Mission Control. The vehicle s first stage trajectory is then adjusted to the measured wind and atmosphere data. The resultant trajectory must satisfy loads and controls constraints. Additionally, these assessments statistically protect for non-observed dispersions. One such dispersion is the change in the wind from the last measured balloon to launch time. This process is started in the hours before launch and is repeated several times as the launch count proceeds. Should the trajectory design not meet all constraint criteria, Shuttle would be No-Go for launch. This Shuttle methodology is very similar to other unmanned launch vehicles. By extension, this method would likely be employed for any future NASA launch vehicle. This paper will review the Shuttle s day-of-launch trajectory optimization and verification operations as an example of a more generic application of day-of-launch design and validation. With Shuttle s retirement, it is fitting to document the current state of this critical process and capture lessons learned to benefit current and future launch vehicle endeavors.
A paper presents further results of continuing research reported in several previous NASA Tech Briefs articles, the two most recent being Stochastic Representations of Chaos Using Terminal Attractors (NPO-41519), [Vol. 30, No. 5 (May 2006), page 57] and Physical Principle for Generation of Randomness (NPO-43822) [Vol. 33, No. 5 (May 2009), page 56]. This research focuses upon a mathematical formalism for describing post-instability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism involves fictitious control forces that couple the equations of motion of the system with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These stabilizing forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in configuration space (ordinary three-dimensional space as commonly perceived) is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. As a result, the post-instability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable.
The probability of collision between a spacecraft and another object is calculated for various altitude and orbit conditions, and factors affecting the probability are discussed. It is shown that a collision can only occur when the spacecraft is located at an altitude which is between the perigee and apogee altitudes of the object and that the probability per unit time is largest when the orbit of the object is nearly circular. However, at low altitudes, the atmospheric drag causes changes with time of the perigee and the apogee, such that circular orbits have a much shorter lifetime than many of the elliptical orbits. Thus, when the collision probability is integrated over the lifetime of the orbiting object, some elliptical orbits are found to have much higher total collision probability than circular orbits. Rocket bodies used to boost payloads from low earth orbit to geosynchronous orbit are an example of objects in these elliptical orbits.
A method of linear feature selection for n dimensional observation vectors which belong to one of m populations is presented. Each population has a known apriori probability and is described by a known multivariate normal density function. Specifically we consider the problem of finding a k x n matrix B of rank k (k n) for which the transformed probability of misclassification is minimized. Providing that the transformed a posterior probabilities are distinct theoretical results are obtained which, for the case k = l, give rise to a numerically tractable formula for the derivative of the probability of misclassification. It is shown that for the two population problem this condition is also necessary. The dependence of the minimum probability of error on the a priori probabilities is investigated. The minimum probability of error satisfies a uniform Lipschitz condition with respect to the a priori probabilities.
A cost-effective approach for Mars exploration is to use available resources, such as water and atmospheric gases. Nitrogen (N2) and argon (Ar) are available and could form the inert gas component of a habitat atmosphere at 8.0, 9.0, or 10.0 pounds per square inch (psia). The habitat and space suit are designed as an integrated system: a comfortable living environment about 85% of the time and a safe working environment about 15% of the time. A goal is to provide a system that permits unrestricted exploration of Mars, but the risk of decompression sickness (DCS) during the extravehicular activity in a 3.75-psia suit, after exposure to any of the three habitat conditions, may limit unrestricted exploration. I evaluate here the risk of DCS since a significant proportion of a trinary breathing gas in the habitat might contain Ar. I draw on past experience and published information to extrapolate into untested, multivariable conditions to evaluate risk. A rigorous assessment of risk as a probability of DCS for each habitat condition is not yet possible. Based on many assumptions about Ar in hypobaric decompressions, I conclude that the presence of Ar significantly increases the risk of DCS. The risk is significant even with the best habitat option: 2.56 psia oxygen, 3.41 psia N2, and 2.20 psia Ar. Several hours of prebreathing 100% 02, a higher suit pressure, or a combination of other important variables such as limited exposure time on the surface or exercise during prebreathe would be necessary to reduce the risk of DCS to an acceptable level. The acceptable level for DCS risk on Mars has not yet been determined. Mars is a great distance from Earth and therefore from primary medical care. The acceptable risk would necessarily be defined by the capability to treat DCS in the Rover vehicle, in the habitat, or both.
The impact parameter method and the sudden approximation are applied to determine the total probability of inelastic rotational transitions arising from a collision of an atom and a homonuclear diatomic molecule at large impact parameters. An analytical approximation to this probability is found for conditions where the electron exchange or overlap forces dominate the scattering. An approximate upper bound to the range of impact parameters for which rotational scattering can be important is determined. In addition, an estimate of the total inelastic cross section is found at conditions for which a statistical model describes the scattering well. The results of this analysis are applied to Ar-O2 collisions and may be readily applied to other combinations of atoms and molecules.
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Results of studies aimed at clarifying the failure of gramicidin A (GA) to sediment in early experiments are analyzed. In the present work, no sedimentation was observed in pure pentanol or ethanol, while normal sedimentation was observed in ethanol-water mixtures. It is concluded that GA exists in two conformations that differ in volume. Since the apparent specific volume in absolute ethanol sinks to its lowest values on increasing concentration, the GA molecule probably unfolds completely in conditions favorable for dimerization.
The Forest Pest Management Division (FPMD) of the Pennsylvania Bureau of Forestry has the responsibility for conducting annual surveys of the State's forest lands to accurately detect, map, and appraise forest insect infestations. A standardized, timely, and cost-effective method of accurately surveying forests and their condition should enhance the probability of suppressing infestations. The repetitive and synoptic coverage provided by LANDSAT (formerly ERTS) makes such satellite-derived data potentially attractive as a survey medium for monitoring forest insect damage over large areas. Forest Pest Management Division personnel have expressed keen interest in LANDSAT data and have informally cooperated with NASA/Goddard Space Flight Center (GSFC) since 1976 in the development of techniques to facilitate their use. The results of this work indicate that it may be feasible to use LANDSAT digital data to conduct annual surveys of insect defoliation of hardwood forests.
The sedimentation and diffusion of a nonneutrally buoyant Brownian particle in vertical fluid-filled cylinder of finite length which is instantaneously inverted at regular intervals are investigated analytically. A one-dimensional convective-diffusive equation is derived to describe the temporal and spatial evolution of the probability density; a periodicity condition is formulated; the applicability of Fredholm theory is established; and the parameter-space regions are determined within which the existence and uniqueness of solutions are guaranteed. Numerical results for sample problems are presented graphically and briefly characterized.
Hubble Space Telescope (HST) observations of the eclipsing dwarf nova OY Car in its quiescent state are used to isolate the ultraviolet spectrum (1150-2500 A at 9.2 A Full Width at Half Maximum (FWHM) resolution) of the white dwarf, the accretion disk, and the bright spot. The white dwarf spectrum has a Stark-broadened photospheric L(alpha) absorption, but is veiled by a forest of blended Fe II features that we attribute to absorption by intervening disk material. A fit gives T(sub w) approx. = 16.5 x 10(exp 3) K for the white dwarf with a solar-abundance, log g = 8 model atmosphere, and T approx. = 10(exp 4) K, n(sub e) approx. = 10(exp 13)/cu cm, N(sub H) approx. = 10(exp 22) sq cm, and velocity dispersion delta V approx. = 60 km/s for the veil of homogeneous solar-abundance local thermodynamic equilibrium (LTE) gas. The veil parameters probably measure characteristic physical conditions in the quiescent accretion disk or its chromosphere. The large velocity dispersion is essential for a good fit; it lowers (chi square)/778 from 22 to 4. Keplerian shear can produce the velocity dispersion if the veiling gas is located at R approx. = 5 R(sub W) with (delta R)/R approx. = 0.3, but this model leaves an unobscured view to the upper hemisphere of the white dwarf, incompatible with absorptions that are up to 80% deep. The veiling gas may be in the upper atmosphere of the disk near its outer rim, but we then require supersonic (Mach approx. = 6) but sub-Keplerian (delta V/V(sub Kep) approx. = 0.07) velocity disturbances in this region to produce both the observed radial velocity dispersion and vertical motions sufficient to elevate the gas to z/R = cos i = 0.12. Such motions might be driven by the gas stream, since it may take several Kepler periods to reestablish the disk's vertical hydrostatic equilibrium. The temperature and column density of the gas we see as Fe II absorption in the ultraviolet are similar to what is required to produce the strong Balmer jump and line emissions seen in optical spectra of OY Car and similar quiescent dwarf novae. The outer accretion disk is detected at mid-eclipse with a spectrum that rises from 0.05 to 0.3 mJy between 2000 and 2500 A, consistent with combinations of cool blackbodies, blended Fe II emission lines, and Balmer continuum emission. The total disk flux density is 0.5 mJy at 2500 A, and this shallow disk eclipse implies a roughly flat surface brightness distribution. The bright spot, somewhat bluer than the disk, has a flux density rising from 0.05 to 0.15 mJy between 1600 and 2500 A. The C IV emission line has a broad shallow eclipse, but the radial velocity variations observed during the eclipse do not clearly distinguish between a disk or wind origin. The only possible indications of boundary layer emission are fast UV flares that appear to arise from near the central object -- not from the bright spot.
This report summarizes information on State-sponsored 'Centers of Excellence' gathered during a survey of State programs in the Fall of 1987. For the purposes of this catalog, 'Centers of Excellence' refers to organizations or activities with the following characteristics: institutionalized, focused, cooperative Research and Development (R&D) programs; supported in part by State governments, in addition to universities, industry and (in some cases) Federal agencies; performed by teams that may include both industry and university employees; and concentrated on relatively specific R&D agendas, usually with near term commercial or governmental applicability. Most of these activities involve state-of-the-art advancement of new technologies under conditions leading to early practical applications. Not included in this catalog are project-level matching grant programs. The principal purpose of this catalog is to help NASA program management, at all levels. to identify and where appropriate, to initiate relationships with other technology-developing organizations. These State-sponsored programs should be of particular interest, because: they present an opportunity to leverage NASA's R&D investments; they are concentrated at the frontier, yet have a concern for practical applications; and they involve industrial participation under conditions that increase the probability of prompt, widespread dissemination in the form of new or enhanced commercial products, processes, or services.
Schedule Risk Assessment (SRA) determines the probability of finishing on or before a given point in time. This viewgraph presentation introduces the prerequisites, probability distribution curves, special conditions, calculations, and results analysis for SRA.
Movements of the celestial bodies in our solar system inspired Isaac Newton to work out his profound laws of gravitation and motion; with one or two notable exceptions, all of those objects move as Newton said they would. But normally harmonious orbital motion is accompanied by the risk of collision, which can be cataclysmic. The Earth s moon is thought to have been produced by such an event, and we recently witnessed magnificent bombardments of Jupiter by several pieces of what was once Comet Shoemaker-Levy 9. Other comets or asteroids may have met the Earth with such violence that dinosaurs and other forms of life became extinct; it is this possibility that causes us to ask how the human species might avoid a similar catastrophe, and the answer requires a thorough understanding of orbital motion. The two red square flags with black square centers displayed are internationally recognized as a warning of an impending hurricane. Mariners and coastal residents who know the meaning of this symbol and the signs evident in the sky and ocean can act in advance to try to protect lives and property; someone who is unfamiliar with the warning signs or chooses to ignore them is in much greater jeopardy. Although collisions between Earth and large comets or asteroids occur much less frequently than landfall of a hurricane, it is imperative that we learn to identify the harbingers of such collisions by careful examination of an object s path. An accurate determination of the orbit of a comet or asteroid is necessary in order to know if, when, and where on the Earth s surface a collision will occur. Generally speaking, the longer the warning time, the better the chance of being able to plan and execute action to prevent a collision. The more accurate the determination of an orbit, the less likely such action will be wasted effort or, what is worse, an effort that increases rather than decreases the probability of a collision. Conditions necessary for a collision to occur are discussed, and warning times for long-period comets and near-Earth asteroids are presented.
GRCop-84 (Cu-8 at.% Cr-4 at.% Nb) has excellent strength, creep resistance, low cycle fatigue (LCF) life and stability at elevated temperatures. It suffers in comparison to many commercially available precipitation-strengthened alloys below 500 C (932 F). It was observed that the addition of Zr consistently improved the mechanical properties of Cu-based alloys especially below 500 C. In an effort to improve the low temperature properties of GRCop-84, 0.35 wt.% Zr was added to the alloy. Limited tensile, creep, and LCF testing was conducted to determine if improvements occur. The results showed some dramatic increases in the tensile and creep properties at the conditions tested with the probability of additional improvements being possible through cold working. LCF testing at room temperature did not show an improvement, but improvements might occur at elevated temperatures.
Fast, continuous detection of a wide range of hazardous substances simultaneously is needed to achieve improved safety for personnel working with hypergolic fuels and oxidizers, as well as other hazardous substances, with a requirement for such detection systems to warn personnel immediately upon the sudden advent of hazardous conditions, with a high probability of detection and a low false alarm rate. The primary purpose of this software is to read the voltage outputs from voltage dividers containing carbon nano - tube sensors as a variable resistance leg, and to recognize quickly when a leak has occurred through recognizing that a generalized pattern change in resistivity of a carbon nanotube sensor has occurred upon exposure to dangerous substances, and, further, to identify quickly just what substance is present through detailed pattern recognition of the shape of the response provided by the carbon nanotube sensor.
Numerical analysis has shown that the SLS nozzle environmental barrier (nozzle plug) design is inadequate for the prelaunch condition, which consists of two dominant loads: 1) the main engines startup pressure and 2) an environmentally induced pressure. Efforts to reduce load conservatisms included a dynamic analysis which showed a 31% higher safety factor compared to the standard static analysis. The environmental load is typically approached with a deterministic method using the worst possible combinations of pressures and temperatures. An alternate probabilistic approach, utilizing the distributions of pressures and temperatures, resulted in a 54% reduction in the environmental pressure load. A Monte Carlo simulation of environmental load that used five years of historical pressure and temperature data supported the results of the probabilistic analysis, indicating the probabilistic load is reflective of a 3-sigma condition (1 in 370 probability). Utilizing the probabilistic load analysis eliminated excessive conservatisms and will prevent a future overdesign of the nozzle plug. Employing a similar probabilistic approach to other design and analysis activities can result in realistic yet adequately conservative solutions.