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NASA NTRS1986

The statistics of peaks of Gaussian random fields

A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of 'upcrossing' points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima.

Bardeen, J. M.↗

NASA NTRS1986

Optimal estimation for the satellite attitude using star tracker measurements

An optimal estimation scheme is presented, which determines the satellite attitude using the gyro readings and the star tracker measurements of a commonly used satellite attitude measuring unit. The scheme is mainly based on the exponential Fourier densities that have the desirable closure property under conditioning. By updating a finite and fixed number of parameters, the conditional probability density, which is an exponential Fourier density, is recursively determined. Simulation results indicate that the scheme is more accurate and robust than extended Kalman filtering. It is believed that this approach is applicable to many other attitude measuring units. As no linearization and approximation are necessary in the approach, it is ideal for systems involving high levels of randomness and/or low levels of observability and systems for which accuracy is of overriding importance.

Lo, J. T.-H.↗

NASA NTRS1989

On-orbit Metrology and Calibration Requirements for Space Station Activities Definition Study

The Space Station is the focal point for the commercial development of space. The long term routine operation of the Space Station and the conduct of future commercial activities suggests the need for in-space metrology capabilities analogous when possible to those on-Earth. The ability to perform periodic calibrations and measurements with proper traceability is imperative for the routine operation of the Space Station. An initial review, however, indicated a paucity of data related to metrology and calibration requirements for in-space operations. This condition probably exists because of the highly developmental aspect of space activities to date, their short duration, and nonroutine nature. The on-orbit metrology and calibration needs of the Space Station were examined and assessed. In order to achieve this goal, the following tasks were performed: an up-to-date literature review; identification of on-orbit calibration techniques; identification of sensor calibration requirements; identification of calibration equipment requirements; definition of traceability requirements; preparation of technology development plans; and preparation of the final report. Significant information and major highlights pertaining to each task is presented. In addition, some general (generic) conclusions/observations and recommendations that are pertinent to the overall in-space metrology and calibration activities are presented.

Cotty, G. M.↗

NASA NTRS1990

Tornadogenesis via squall line and supercell interaction revisited - The 15 November 1989 Huntsville tornado

A case study analyzing the environmental setting and storm system morphology that provides observational evidence of a mechanism involving the interaction of a gust front with a preexisting mesocyclone is presented. This case serves to reemphasize the existence of a high conditional probability of tornado occurrence, given the merger of a gust front (or storm outflow) with a moderate to strong thunderstorm ahead of it. The resultant data serve to illustrate some important unresolved issues relevant to the severe weather warning system that involve the present and planned local warning and network radars, and future algorithms that might intelligently integrate other data sources and models with the radar data.

Goodman, Steven J.↗

NASA NTRS1993

Hidden Markov models for fault detection in dynamic systems

The invention is a system failure monitoring method and apparatus which learns the symptom-fault mapping directly from training data. The invention first estimates the state of the system at discrete intervals in time. A feature vector x of dimension k is estimated from sets of successive windows of sensor data. A pattern recognition component then models the instantaneous estimate of the posterior class probability given the features, p(w(sub i) perpendicular to x), 1 less than or equal to i is less than or equal to m. Finally, a hidden Markov model is used to take advantage of temporal context and estimate class probabilities conditioned on recent past history. In this hierarchical pattern of information flow, the time series data is transformed and mapped into a categorical representation (the fault classes) and integrated over time to enable robust decision-making.

Smyth, Padhraic J.↗

NASA NTRS1994

Regional and seasonal estimates of fractional storm coverage based on station precipitation observations

Simulated climates using numerical atmospheric general circulation models (GCMs) have been shown to be highly sensitive to the fraction of GCM grid area assumed to be wetted during rain events. The model hydrologic cycle and land-surface water and energy balance are influenced by the parameter bar-kappa, which is the dimensionless fractional wetted area for GCM grids. Hourly precipitation records for over 1700 precipitation stations within the contiguous United States are used to obtain observation-based estimates of fractional wetting that exhibit regional and seasonal variations. The spatial parameter bar-kappa is estimated from the temporal raingauge data using conditional probability relations. Monthly bar-kappa values are estimated for rectangular grid areas over the contiguous United States as defined by the Goddard Institute for Space Studies 4 deg x 5 deg GCM. A bias in the estimates is evident due to the unavoidably sparse raingauge network density, which causes some storms to go undetected by the network. This bias is corrected by deriving the probability of a storm escaping detection by the network. A Monte Carlo simulation study is also conducted that consists of synthetically generated storm arrivals over an artificial grid area. It is used to confirm the bar-kappa estimation procedure and to test the nature of the bias and its correction. These monthly fractional wetting estimates, based on the analysis of station precipitation data, provide an observational basis for assigning the influential parameter bar-kappa in GCM land-surface hydrology parameterizations.

Gong, Gavin↗

NASA NTRS1994

H2-rich interstellar grain mantles: An equilibrium description

Experiments simulating the codeposition of molecular hydrogen and water ice on interstellar grains demonstrate that amorphous water ice at 12 K can incorporate a substantial amount of H2, up to a mole ratio of H2/H2O = 0.53. We find that the physical behavior of approximately 80% of the hydrogen can be explained satisfactorily in terms of an equilibrium population, thermodynamically governed by a wide distribution of binding site energies. Such a description predicts that gas phase accretion could lead to mole fractions of H2 in interstellar grain mantles of nearly 0.3; for the probable conditions of WL5 in the rho Ophiuchi cloud, an H2 mole fraction of between 0.05 and 0.3 is predicted, in possible agreement with the observed abundance reported by Sandford, Allamandola, & Geballe. Accretion of gas phase H2 onto grain mantles, rather than photochemical production of H2 within the ice, could be a general explanation for frozen H2 in interstellar ices. We speculate on the implications of such a composition for grain mantle chemistry and physics.

Dissly, Richard W.↗

NASA NTRS1995

Hidden Markov models for fault detection in dynamic systems

The invention is a system failure monitoring method and apparatus which learns the symptom-fault mapping directly from training data. The invention first estimates the state of the system at discrete intervals in time. A feature vector x of dimension k is estimated from sets of successive windows of sensor data. A pattern recognition component then models the instantaneous estimate of the posterior class probability given the features, p(w(sub i) (vertical bar)/x), 1 less than or equal to i isless than or equal to m. Finally, a hidden Markov model is used to take advantage of temporal context and estimate class probabilities conditioned on recent past history. In this hierarchical pattern of information flow, the time series data is transformed and mapped into a categorical representation (the fault classes) and integrated over time to enable robust decision-making.

Smyth, Padhraic J.↗

NASA NTRS1996

Quantifying Danger To Spacecraft Crews From Orbital Debris

MSCSurv computer program designed to quantify conditional probability of losing one or more crew members following remote likelihood of penetration of orbital debris into cluster of spacecraft modules containing crew members. Contributions to probability of losing one or more crew members quantified from three significant penetration-induced hazards: rupture of pressure wall (explosive decompression), injuries induced by fragments, and "slow" depressurization. Uses Monte Carlo-style subroutine to simulate penetration of thousands of orbital debris particles of various sizes, velocities, and angles of approach into spacecraft of selected exterior geometry. Written in FORTRAN 77.

Williamsen, Joel↗

NASA NTRS1996

Improved Closed-Loop Carrier-Phase Synchronization In BPSK

Scheme motivated by maximum-likelihood approach offers advantages over other well-known schemes. Proposed signal-processing system generates error signal proportional to derivative of conditional probability density function with respect to estimated carrier phase. Signal serves as feedback signal in carrier-phase-tracking loop.

Simon, Marvin K.↗

NASA NTRS1996

A Comparison of Single-Cycle Versus Multiple-Cycle Proof Testing Strategies

Single-cycle and multiple-cycle proof testing (SCPT and MCPT) strategies for reusable aerospace propulsion system components are critically evaluated and compared from a rigorous elastic-plastic fracture mechanics perspective. Earlier MCPT studies are briefly reviewed. New J-integral estimation methods for semi-elliptical surface cracks and cracks at notches are derived and validated. Engineering methods are developed to characterize crack growth rates during elastic-plastic fatigue crack growth (FCG) and the tear-fatigue interaction near instability. Surface crack growth experiments are conducted with Inconel 718 to characterize tearing resistance, FCG under small-scale yielding and elastic-plastic conditions, and crack growth during simulated MCPT. Fractography and acoustic emission studies provide additional insight. The relative merits of SCPT and MCPT are directly compared using a probabilistic analysis linked with an elastic-plastic crack growth computer code. The conditional probability of failure in service is computed for a population of components that have survived a previous proof test, based on an assumed distribution of initial crack depths. Parameter studies investigate the influence of proof factor, tearing resistance, crack shape, initial crack depth distribution, and notches on the MCPT vs. SCPT comparison. The parameter studies provide a rational basis to formulate conclusions about the relative advantages and disadvantages of SCPT and MCPT. Practical engineering guidelines are proposed to help select the optimum proof test protocol in a given application.

McClung, R. C.↗

NASA NTRS1996

A Comparison of Single-Cycle Versus Multiple-Cycle Proof Testing Strategies

McClung, R. C.↗

NASA NTRS1997

Algorithms for Multiple Fault Diagnosis With Unreliable Tests

In this paper, we consider the problem of constructing optimal and near-optimal multiple fault diagnosis (MFD) in bipartite systems with unreliable (imperfect) tests. It is known that exact computation of conditional probabilities for multiple fault diagnosis is NP-hard. The novel feature of our diagnostic algorithms is the use of Lagrangian relaxation and subgradient optimization methods to provide: (1) near optimal solutions for the MFD problem, and (2) upper bounds for an optimal branch-and-bound algorithm. The proposed method is illustrated using several examples. Computational results indicate that: (1) our algorithm has superior computational performance to the existing algorithms (approximately three orders of magnitude improvement), (2) the near optimal algorithm generates the most likely candidates with a very high accuracy, and (3) our algorithm can find the most likely candidates in systems with as many as 1000 faults.

Shakeri, Mojdeh↗

NASA NTRS1999

A Comparison of Single-Cycle Versus Multiple-Cycle Proof Testing Strategies

Single-cycle and multiple-cycle proof testing (SCPT and MCPT) strategies for reusable aerospace propulsion system components are critically evaluated and compared from a rigorous elastic-plastic fracture mechanics perspective. Earlier MCPT studies are briefly reviewed. New J-integral estimation methods for semielliptical surface cracks and cracks at notches are derived and validated. Engineering methods are developed to characterize crack growth rates during elastic-plastic fatigue crack growth (FCG) and the tear-fatigue interaction near instability. Surface crack growth experiments are conducted with Inconel 718 to characterize tearing resistance, FCG under small-scale yielding and elastic-plastic conditions, and crack growth during simulated MCPT. Fractography and acoustic emission studies provide additional insight. The relative merits of SCPT and MCPT are directly compared using a probabilistic analysis linked with an elastic-plastic crack growth computer code. The conditional probability of failure in service is computed for a population of components that have survived a previous proof test, based on an assumed distribution of initial crack depths. Parameter studies investigate the influence of proof factor, tearing resistance, crack shape, initial crack depth distribution, and notches on the MCPT versus SCPT comparison. The parameter studies provide a rational basis to formulate conclusions about the relative advantages and disadvantages of SCPT and MCPT. Practical engineering guidelines are proposed to help select the optimum proof test protocol in a given application.

McClung, R. C.↗

NASA NTRS1999

Can Kelvin-Helmholtz Instabilites of Jet-Like Structures and Plumes Cause Solar Wind Fluctuations at 1 AU?

The long high-latitude sampling of Ulysses provides the opportunity to study fine structures. At latitudes poleward of about -60 degrees the solar wind had fluctuations in velocity gradients which were attributed to "microstreams." The data also suggested fluctuations characterized by magnetic plus thermal pressure balance structures ('PBS'). At higher frequencies, MHD turbulence was observed and found to be less evolved than it is in the ecliptic but essentially independent of heliographic latitude. It is argued here that microstreams, PBS, and MHD turbulence could all be the remnants of mixing due to shear instabilities associated with plumes and other filamentary structures ("jets") in coronal holes. To show this, we simulate a plume-like jet in the presence of an ambient magnetic field. We find that the presence of the ambient field reduces the growth rate of the instability, but the shear between a jet and its ambient still becomes unstable to the MHD Kelvin-Helmholtz instability when the shear speed is larger than the largest local magnetosonic speed, a condition probably satisfied for plumes.

Parhi, S.↗

NASA NTRS1998

Can Kelvin-Helmholtz Instabilities of Jet-Like Structures and Plumes Cause Solar Wind Fluctuations at 1 AU?

The long high latitude sampling of Ulysses provides the opportunity to study fine structures. At latitudes poleward of approx. -60 deg, the solar wind had fluctuations in velocity gradients which were attributed to "microstreams". The data also suggested fluctuations characterized by magnetic plus thermal pressure balance structures ("PBS"). At higher frequencies, MHD turbulence was observed and found to be less evolved than in the ecliptic, but essentially independent of heliographic latitude. It is argued here that microstreams, PBS, and MHD turbulence could all be the remnants of mixing due to shear instabilities associated with plumes and other filamentarystructures ("jets") in coronal holes. To show this we simulate a plume-like jet in the presence of an ambient magnetic field. We find the presence of the ambient field reduces the growth rate of the instability, but the shear between a jet and its ambient still becomes unstable to the MHD Kelvin-Helmholtz ("KH") instability when the shear speed is larger than the largest local magnetosonic speed - a condition probably satisfied for plumes.

Shyamsundar, Parhi↗

NASA NTRS1999

Remote Sensing of Rain

The first problem addressed concerns passive-microwave rain retrievals. Most current approaches start by building off-line a cloud-model-derived database. Given data, the retrieval algorithms search the database for the microwave temperatures "closest" to the observed data, then after some fine-tuning (performed in different ways by different implementations) the rain is estimated to be that which corresponds to the selected (and fine-tuned) set of database temperatures. These approaches have three drawbacks: they cannot properly take into account the ambiguities which arise from the fact that several rain scenarios can produce the same observed temperatures; they are quite inefficient since they require manipulating a large database along with often complex "fine-tuning" procedures; and they cannot refine their estimates if additional data is available. This past year we have derived closed formulae relating observed microwave brightness temperatures, T(sub b), and the underlying rain rates, R: average T(sub b) =f (rain) and average rain = g (T(sub b)), along with the corresponding covariance matrices. These results are sufficient to describe the conditional probabilities p(R/T(sub b)) and p(T(sub b)/R) to second order. Progress has also been made towards deriving a robust description of the rain drop size distribution (DSD). The widespread approach consisting in parameterizing the DSD as a gamma-distribution in terms of the drop diameter D suffers from the facts that, in reality, the DSD is not a smooth function of D and that the largely arbitrary Gamma model imposes unintended behavior, which has implications on any quantities derived from the DSD model. We have therefore developed a non-parametric yet practical description of the DSD, which is particularly well-suited for use in remote-sensing applications. The diagram on the left shows a comparison between an actual DSD sample and the truncated non-parametric representation. One figure shows the relation between radar reflectivity and rain rate derived using this representation. Validation of the Tropical Rainfall Measuring Mission (TRMM) radar-radiometer combined R and DSD algorithm is underway. This algorithm was designed to make optimal use of the instantaneous reflectivity profiles measured by the TRMM radar and the microwave brightness temperatures measured by the TRMM passive radiometer. So far, it appears to be the most reliable TRMM rain algorithm.

Haddad, Ziad S.↗

NASA NTRS2007

Using Latent Sleepiness to Evaluate an Important Effect of Promethazine

Astronauts often use promethazine (PMZ) to counteract space motion sickness; however PMZ may cause drowsiness, which might impair cognitive function. In a NASA ground study, subjects received PMZ and their cognitive performance was then monitored over time. Subjects also reported sleepiness using the Karolinska Sleepiness Score (KSS), which ranges from 1 - 9. A problem arises when using KSS to establish an association between true sleepiness and performance because KSS scores tend to overly concentrate on the values 3 (fairly awake) and 7 (moderately tired). Therefore, we defined a latent sleepiness measure as a continuous random variable describing a subject s actual, but unobserved true state of sleepiness through time. The latent sleepiness and observed KSS are associated through a conditional probability model, which when coupled with demographic factors, predicts performance.

Feiveson, Alan H.↗