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At least 1,099 records · Page 61

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NASA NTRS2019

A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus

This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.

stochastic calculus↗

NASA NTRS1992

Quantifying parameters for Bayesian prior assumptions when estimating the probability of failure of software

Software reliability has become increasingly important, especially in life-critical situations. The ability to measure the results of testing and to quantify software reliability is needed. If this is accomplished, a certain minimum amount of reliability for a piece of software can be specified, and testing and/or other analysis may be done until that minimum number has been attained. There are many models for estimating software reliability. The accuracy of these models has been challenged and many revisions for the models and recalibration techniques have been devised. Of particular interest is the method of estimating the probability of failure of software when no failures have yet occurred in its current version as described by Miller. This model uses black box testing with formulae based on Bayesian estimation. The focus is on three interrelated issues: estimating the probability of failure when testing has revealed no errors; modifying this estimation when the input use distribution does not match the test distribution; and combining the results from random testing with other relevant information to obtain a possibly more accurate estimate of the probability of failure. Obtaining relevant information about the software and combining the results for a better estimate for the Miller model are discussed.

Long, Jacquelyn E.↗

NASA NTRS2001

Distribution functions of probabilistic automata

Each probabilistic automaton M over an alphabet A defines a probability measure Prob sub(M) on the set of all finite and infinite words over A. We can identify a k letter alphabet A with the set {0, 1,..., k-1}, and, hence, we can consider every finite or infinite word w over A as a radix k expansion of a real number X(w) in the interval [0, 1]. This makes X(w) a random variable and the distribution function of M is defined as usual: F(x) := Prob sub(M) { w: X(w) < x }. Utilizing the fixed-point semantics (denotational semantics), extended to probabilistic computations, we investigate the distribution functions of probabilistic automata in detail. Automata with continuous distribution functions are characterized. By a new, and much more easier method, it is shown that the distribution function F(x) is an analytic function if it is a polynomial. Finally, answering a question posed by D. Knuth and A. Yao, we show that a polynomial distribution function F(x) on [0, 1] can be generated by a prob abilistic automaton iff all the roots of F'(x) = 0 in this interval, if any, are rational numbers. For this, we define two dynamical systems on the set of polynomial distributions and study attracting fixed points of random composition of these two systems.

Denotational semantics↗

NASA NTRS1976

Interactions of satellite-speed helium atoms with satellite surfaces. 2: Energy distributions of reflected helium atoms

Energy transfer in collisions of satellite-speed (7,000 m/sec) helium atoms with a cleaned 6061-T6 satellite-type aluminum surface was investigated using the molecular-beam technique. The amount of energy transferred was determined from the measured energy of the molecular-beam and the measured spatial and energy distributions of the reflected atoms. Spatial distributions of helium atoms scattered from a 6061-T6 aluminum surface were measured. The scattering pattern exhibits a prominent backscattering, probably due to the gross surface roughness and/or the relative lattice softness of the aluminum surface. Energy distributions of reflected helium atoms from the same surface were measured for six different incidence angles. For each incidence angle, distributions were measured at approximately sixty scattering positions. At a given scattering position, the energy spectra of the reflected helium atoms and the background gas were obtained using the retarding-field energy analyzer.

Liu, S. M.↗

NASA NTRS1983

Eolian intracrater deposits on Mars - Physical properties and global distribution

It is noted that more than one-fourth of all craters larger than 25 km in diameter between -50 deg S and 50 deg N have localized deposits of coarse material on the floor which are associated with the dark 'splotches' that are seen visually. If homogeneous, unconsolidated materials are assumed, the measured thermal inertias of these deposits imply effective grain sizes that range from 0.1 mm to 1 cm, with a modal value of 0.9 mm. Even though these deposits are coarser and darker than the surrounding terrains and the greater part of the Martian surface, they are not compositionally distinct from materials with similar albedos. It is thought most likely that these features were formed by entrapment of marginally mobile material that can be transported into, but not out of, crater depressions by the wind. Most of the 'splotch' deposits are coarser than the dune-forming materials occurring in the north polar region and inside extreme southern latitude craters; they probably form low, broad zibar dunes or lag deposits. The distribution of intracrater deposits is seen as suggesting that the intracrater features have been buried in the interior of Arabia and that the dust deposit is less extensive at the margins and may currently be expanding.

Christensen, P. R.↗

NASA NTRS1990

Closed-form solution of decomposable stochastic models

Markov and semi-Markov processes are increasingly being used in the modeling of complex reconfigurable systems (fault tolerant computers). The estimation of the reliability (or some measure of performance) of the system reduces to solving the process for its state probabilities. Such a model may exhibit numerous states and complicated transition distributions, contributing to an expensive and numerically delicate solution procedure. Thus, when a system exhibits a decomposition property, either structurally (autonomous subsystems), or behaviorally (component failure versus reconfiguration), it is desirable to exploit this decomposition in the reliability calculation. In interesting cases there can be failure states which arise from non-failure states of the subsystems. Equations are presented which allow the computation of failure probabilities of the total (combined) model without requiring a complete solution of the combined model. This material is presented within the context of closed-form functional representation of probabilities as utilized in the Symbolic Hierarchical Automated Reliability and Performance Evaluator (SHARPE) tool. The techniques adopted enable one to compute such probability functions for a much wider class of systems at a reduced computational cost. Several examples show how the method is used, especially in enhancing the versatility of the SHARPE tool.

Sjogren, Jon A.↗

NASA NTRS1985

An APL program for the distribution of energy deposition by charged particles passing through thin absorbers

An APL program which numerically evaluates the probability density function (PDF) for the energy deposited in a thin absorber by a charged particle is proposed, with application to the construction, pointing, and control of spacecraft. With this program, the PDF of the restricted energy loss distribution of Watts (1973) is derived, and Vavilov's (1957) distribution is obtained by proper parameter selection. The method is demonstrated with the example of the effect of charged particle induced radiation on the Hubble Space Telescope (HST) pointing accuracy. A Monte Carlo study simulates the photon noise caused by charged particles passing through the photomultiplier tube window, and the stochastic variation of energy loss is introduced into the simulation by generating random energy losses from a power law distribution. The program eliminates annoying loop procedures, and model parameter sensitivity can be studied using the graphical output.

Howell, L. W.↗

NASA NTRS1972

Distribution of error in least-squares solution of an overdetermined system of linear simultaneous equations

Probability density functions were derived for errors in the evaluation of unknowns by the least squares method in system of nonhomogeneous linear equations. Coefficients of the unknowns were assumed correct and computational precision were also assumed. A vector space was used, with number of dimensions equal to the number of equations. An error vector was defined and assumed to have uniform distribution of orientation throughout the vector space. The density functions are shown to be insensitive to the biasing effects of the source of the system of equations.

Miller, C. D.↗

NASA NTRS1988

Parallel discrete event simulation using shared memory

With traditional event-list techniques, evaluating a detailed discrete-event simulation-model can often require hours or even days of computation time. By eliminating the event list and maintaining only sufficient synchronization to ensure causality, parallel simulation can potentially provide speedups that are linear in the numbers of processors. A set of shared-memory experiments, using the Chandy-Misra distributed-simulation algorithm, to simulate networks of queues is presented. Parameters of the study include queueing network topology and routing probabilities, number of processors, and assignment of network nodes to processors. These experiments show that Chandy-Misra distributed simulation is a questionable alternative to sequential-simulation of most queueing network models.

Reed, Daniel A.↗

NASA NTRS2019

Probability Index of Low Stratus and Fog at Dawn using Dual Geostationary Satellite Observations from COMS and FY-2D near the Korean Peninsula

We developed a new remote sensing method for detecting low stratus and fog (LSF) at dawn in terms of probability index (PI) of LSF from simultaneous stereo observations of two geostationary-orbit satellites; the Korean Communication, Ocean, and Meteorological Satellite (COMS; 128.2°E); and the Chinese FengYun satellite (FY-2D; 86.5°E). The algorithm was validated near the Korean Peninsula between the months of April and August from April 2012 to June 2015, by using surface observations at 45 meteorological stations in South Korea. The optical features of LSF were estimated by using satellite retrievals and simulated data from the radiative transfer model. The PI was calculated using the combination of three satellite-observed variables: 1) the reflectance at 0.67 μm (R(0.67)) from COMS, and 2) the FY-2D R(0.67) minus the COMS R(0.67) (△R(0.67)) and (3) the FY-2D-COMS difference in the brightness temperature difference between 3.7 and 11.0 μm (ΔBTD(3.7-11)). The three variables, adopted from the top three probability of detection (POD) scores for their fog detection thresholds: △R(0.67) (0.82) > ΔBTD(3.7-11) (0.73) > R(0.67) (0.70) > BTD(3.7-11) (0.51). The LSF PI for this algorithm was significantly better in the two case studies compared to that using COMS only (i.e., R(0.67) or BTD(3.7-11)), so that this improvement was due to △R(0.67) and ΔBTD(3.7-11). Overall, PI in the LSF spatial distribution has the merits of a high detection rate, a specific probability display, and a low rate of seasonality and variability in detection accuracy. Therefore, PI would be useful for monitoring LSF in near-real-time, and to further its forecast ability, using next-generation satellites.

fog↗

NASA NTRS1986

Optical techniques to feed and control GaAs MMIC modules for phased array antenna applications

A complex signal distribution system is required to feed and control GaAs monolithic microwave integrated circuits (MMICs) for phased array antenna applications above 20 GHz. Each MMIC module will require one or more RF lines, one or more bias voltage lines, and digital lines to provide a minimum of 10 bits of combined phase and gain control information. In a closely spaced array, the routing of these multiple lines presents difficult topology problems as well as a high probability of signal interference. To overcome GaAs MMIC phased array signal distribution problems optical fibers interconnected to monolithically integrated optical components with GaAs MMIC array elements are proposed as a solution. System architecture considerations using optical fibers are described. The analog and digital optical links to respectively feed and control MMIC elements are analyzed. It is concluded that a fiber optic network will reduce weight and complexity, and increase reliability and performance, but higher power will be required.

Bhasin, K. B.↗

NASA NTRS1986

Optical techniques to feed and control GaAs MMIC modules for phased array antenna applications

Bhasin, K. B.↗

NASA NTRS2015

A Metric to Quantify Shared Visual Attention in Two-Person Teams

Introduction: Critical tasks in high-risk environments are often performed by teams, the members of which must work together efficiently. In some situations, the team members may have to work together to solve a particular problem, while in others it may be better for them to divide the work into separate tasks that can be completed in parallel. We hypothesize that these two team strategies can be differentiated on the basis of shared visual attention, measured by gaze tracking. 2) Methods: Gaze recordings were obtained for two-person flight crews flying a high-fidelity simulator (Gontar, Hoermann, 2014). Gaze was categorized with respect to 12 areas of interest (AOIs). We used these data to construct time series of 12 dimensional vectors, with each vector component representing one of the AOIs. At each time step, each vector component was set to 0, except for the one corresponding to the currently fixated AOI, which was set to 1. This time series could then be averaged in time, with the averaging window time (t) as a variable parameter. For example, when we average with a t of one minute, each vector component represents the proportion of time that the corresponding AOI was fixated within the corresponding one minute interval. We then computed the Pearson product-moment correlation coefficient between the gaze proportion vectors for each of the two crew members, at each point in time, resulting in a signal representing the time-varying correlation between gaze behaviors. We determined criteria for concluding correlated gaze behavior using two methods: first, a permutation test was applied to the subjects' data. When one crew member's gaze proportion vector is correlated with a random time sample from the other crewmember's data, a distribution of correlation values is obtained that differs markedly from the distribution obtained from temporally aligned samples. In addition to validating that the gaze tracker was functioning reasonably well, this also allows us to compute probabilities of coordinated behavior for each value of the correlation. As an alternative, we also tabulated distributions of correlation coefficients for synthetic data sets, in which the behavior was modeled as a first-order Markov process, and compared correlation distributions for identical processes with those for disparate processes, allowing us to choose criteria and estimate error rates. 3) Discussion: Our method of gaze correlation is able to measure shared visual attention, and can distinguish between activities involving different instruments. We plan to analyze whether pilots strategies of sharing visual attention can predict performance. Possible measurements of performance include expert ratings from instructors, fuel consumption, total task time, and failure rate. While developed for two-person crews, our approach can be applied to larger groups, using intra-class correlation coefficients instead of the Pearson product-moment correlation.

Gontar, Patrick↗

NASA NTRS1998

On Estimating Provenances of Lunar Highland Materials

That even relatively small impacts can spread material across the face of the Moon is evident from the rays of Tycho. Tycho ejecta triggered the landslide that produced the light mantle deposit at Apollo 17 and perhaps excavated the Central Valley craters there. Basin-sized impacts appear to follow the same scaling laws as smaller impacts, as indicated by the satisfaction of a geophysical model. These giant impacts rearranged huge amounts of premare material, complicating the determination of provenance of materials collected from the highlands. We have developed a model to estimate the probability that material at a particular location might derive from a given basin or large crater. This model is based on crater scaling laws, and effects of secondary cratering. Because it accounts for the volume of primary ejecta from the basin-forming transient craters and the excavating and mixing effects of these ejecta with the substrate onto which they fall, it gives much thicker deposits than an early work. Our modeling takes into account the distribution of sizes of primary ejecta fragments (PriFrags) to obtain the probability at a given site for a deposit of a particular thickness and with a fraction of PriFrags.

Haskin, Larry A.↗

NASA NTRS2007

A Simple Stochastic Model for Generating Broken Cloud Optical Depth and Top Height Fields

A simple and fast algorithm for generating two correlated stochastic twodimensional (2D) cloud fields is described. The algorithm is illustrated with two broken cumulus cloud fields: cloud optical depth and cloud top height retrieved from Moderate Resolution Imaging Spectrometer (MODIS). Only two 2D fields are required as an input. The algorithm output is statistical realizations of these two fields with approximately the same correlation and joint distribution functions as the original ones. The major assumption of the algorithm is statistical isotropy of the fields. In contrast to fractals and the Fourier filtering methods frequently used for stochastic cloud modeling, the proposed method is based on spectral models of homogeneous random fields. For keeping the same probability density function as the (first) original field, the method of inverse distribution function is used. When the spatial distribution of the first field has been generated, a realization of the correlated second field is simulated using a conditional distribution matrix. This paper is served as a theoretical justification to the publicly available software that has been recently released by the authors and can be freely downloaded from http://i3rc.gsfc.nasa.gov/Public codes clouds.htm. Though 2D rather than full 3D, stochastic realizations of two correlated cloud fields that mimic statistics of given fields have proved to be very useful to study 3D radiative transfer features of broken cumulus clouds for better understanding of shortwave radiation and interpretation of the remote sensing retrievals.

Prigarin, Sergei M.↗

NASA NTRS1979

Characteristics of the inverted-V event

An attempt is made to determine the origin of the inverted-V precipitating electrons and mechanisms that could create the inverted-V structure. The energy and pitch angle structures are compared with predictions from several theories that have been proposed to explain the origin of inverted-V events. Data from the AE-D satellite indicate that the origin of the inverted-V precipitating electrons is in the magnetosphere, the most probable regions being the plasma sheet and the neutral sheet. The energy and pitch angle distributions show that electrons are trapped between the mirror points and the electric field potential. The observations suggest that field-aligned precipitating electrons have been heated, probably when they were accelerated by the parallel electric field. Qualitatively, the detailed structures of the inverted-V events favor the theory of anomalous resistivity.

Lin, C. S.↗

NASA NTRS1991

Probabilistic micromechanics and macromechanics of polymer matrix composites

A probabilistic evaluation of an eight ply graphite-epoxy quasi-isotropic laminate was completed using the Integrated Composite Analyzer (ICAN) in conjunction with Monte Carlo simulation and Fast Probability Integration (FPI) techniques. Probabilistic input included fiber and matrix properties, fiber misalignment, fiber volume ratio, void volume ratio, ply thickness and ply layup angle. Cumulative distribution functions (CDFs) for select laminate properties are given. To reduce the number of simulations, a Fast Probability Integration (FPI) technique was used to generate CDFs for the select properties in the absence of fiber misalignment. These CDFs were compared to a second Monte Carlo simulation done without fiber misalignment effects. It was found that FPI requires fewer simulations to obtain the cumulative distribution functions as opposed to Monte Carlo simulation techniques. Furthermore, FPI provides valuable information regarding the sensitivities of composite properties to the constituent properties, fiber volume ratio and void volume ratio.

Mase, G. T.↗

NASA NTRS1991

Probabilistic micromechanics and macromechanics of polymer matrix composites

Mase, G. T.↗