Results for “Probability Distribution Function” — Page 32

NASA NTRS2010

An High Resolution Near-Earth Objects Population Enabling Next-Generation Search Strategies

Over the past decade, the dedicated search for kilometer-size near-Earth objects (NEOs), potentially hazardous objects (PHOs), and potential Earth impactors has led to a boost in the rate of discoveries of these objects. The catalog of known NEOs is the fundamental ingredient used to develop a model for the NEOs population, either by assessing and correcting for the observational bias (Jedicke et al., 2002), or by evaluating the migration rates from the NEOs source regions (Bottke et al., 2002). The modeled NEOs population is a necessary tool used to track the progress in the search of large NEOs (Jedicke et al., 2003) and to try to predict the distribution of the ones still undiscovered, as well as to study the sky distribution of potential Earth impactors (Chesley & Spahr, 2004). We present a method to model the NEOs population in all six orbital elements, on a finely grained grid, allowing us the design and test of targeted and optimized search strategies. This method relies on the observational data routinely reported to the Minor Planet Center (MPC) by the Catalina Sky Survey (CSS) and by other active NEO surveys over the past decade, to determine on a nightly basis the efficiency in detecting moving objects as a function of observable quantities including apparent magnitude, rate of motion, airmass, and galactic latitude. The cumulative detection probability is then be computed for objects within a small range in orbital elements and absolute magnitude, and the comparison with the number of know NEOs within the same range allows us to model the population. When propagated to the present epoch and projected on the sky plane, this provides the distribution of the missing large NEOs, PHOs, and potential impactors.

Tricaico, Pasquale↗

NASA NTRS2012

Probability and Confidence Trade-space (PACT) Evaluation: Accounting for Uncertainty in Sparing Assessments

There are two general shortcomings to the current annual sparing assessment: 1. The vehicle functions are currently assessed according to confidence targets, which can be misleading- overly conservative or optimistic. 2. The current confidence levels are arbitrarily determined and do not account for epistemic uncertainty (lack of knowledge) in the ORU failure rate. There are two major categories of uncertainty that impact Sparing Assessment: (a) Aleatory Uncertainty: Natural variability in distribution of actual failures around an Mean Time Between Failure (MTBF) (b) Epistemic Uncertainty : Lack of knowledge about the true value of an Orbital Replacement Unit's (ORU) MTBF We propose an approach to revise confidence targets and account for both categories of uncertainty, an approach we call Probability and Confidence Trade-space (PACT) evaluation.

Anderson, Leif↗

NASA NTRS1993

Structured adaptive grid generation using algebraic methods

The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration of points to the grid redistribution scheme. The evaluation of the weighting mesh is accomplished by utilizing the weight function representing the solution variation and the equidistribution law. The selection of the weight function plays a key role in grid adaptation. A new weight function utilizing a properly weighted boolean sum of various flowfield characteristics is defined. The redistribution scheme is developed utilizing Non-Uniform Rational B-Splines (NURBS) representation. The application of NURBS representation results in a well distributed smooth grid by maintaining the fidelity of the geometry associated with boundary curves. Several algebraic methods are applied to smooth and/or nearly orthogonalize the grid lines. An elliptic solver is utilized to smooth the grid lines if there are grid crossings. Various computational examples of practical interest are presented to demonstrate the success of these methods.

Yang, Jiann-Cherng↗

NASA NTRS1983

The ISPM dust experiment

The ISPM Dust Experiment observes particulate matter with masses between 10 to the minus 19th power and 10 to the minus 10th power kg in the solar system; investigates its physical and dynamical properties as a function of ecliptic latitude and heliocentric distance; and studies its interaction with solar radiation, the solar wind, and the interplanetary magnetic field. Measurement of the three dimensional spatial distribution of cosmic dust particles and their dynamics allows the relative significance of their probable sources (comets, asteroids and interstellar dust) to be determined. An instrument that measures the mass, speed, flight direction and electric charge of individual dust particles is used. It is a multicoincidence detector with a sensitivity 100,000 times higher than that of previous experiments. The instrument weighs 3.750 kg, consumes 2.0 W, and has a normal data transmission rate of 8 bit/sec in spacecraft tracking mode.

Gruen, E.↗

NASA NTRS1987

The unusual dust-scattering properties in the reflection nebula CED 201

Spectrophotometric data available from ground-based and IUE observations of the reflection nebula CED 201 and its illuminating star BD + 69.1231 deg are analyzed to deduce the most likely star-nebula geometry and the wavelength dependence of the scattering characteristics of the nebular grains. The dust albedo is found to decline from 0.72 at V to probably less than 0.2 at lambda less than 2000 A, explaining the unusual red color of this reflection nebula. The wavelength dependence of the optical depth and of the phase function asymmetry in the visible suggests the existence of a narrow size distribution of grains, skewed toward larger than normal particle sizes. CED 201 is one of two reflection nebulae with positive evidence for enhanced scattering in the long-wavelength wing of the 2175 A dust extinction feature, also pointing toward larger than average grains.

Witt, A. N.↗

NASA NTRS1996

Electromagnetic Compatibility Testing Studies

This report discusses the results on analytical models and measurement and simulation of statistical properties from a study of microwave reverberation (mode-stirred) chambers performed at Texas Tech University. Two analytical models of power transfer vs. frequency in a chamber, one for antenna-to-antenna transfer and the other for antenna to D-dot sensor, were experimentally validated in our chamber. Two examples are presented of the measurement and calculation of chamber Q, one for each of the models. Measurements of EM power density validate a theoretical probability distribution on and away from the chamber walls and also yield a distribution with larger standard deviation at frequencies below the range of validity of the theory. Measurements of EM power density at pairs of points which validate a theoretical spatial correlation function on the chamber walls and also yield a correlation function with larger correlation length, R(sub corr), at frequencies below the range of validity of the theory. A numerical simulation, employing a rectangular cavity with a moving wall shows agreement with the measurements. The determination that the lowest frequency at which the theoretical spatial correlation function is valid in our chamber is considerably higher than the lowest frequency recommended by current guidelines for utilizing reverberation chambers in EMC testing. Two suggestions have been made for future studies related to EMC testing.

Trost, Thomas F.↗

NASA NTRS1999

CARES/Life Ceramics Durability Evaluation Software Enhanced for Cyclic Fatigue

The CARES/Life computer program predicts the probability of a monolithic ceramic component's failure as a function of time in service. The program has many features and options for materials evaluation and component design. It couples commercial finite element programs--which resolve a component's temperature and stress distribution--to reliability evaluation and fracture mechanics routines for modeling strength-limiting defects. The capability, flexibility, and uniqueness of CARES/Life have attracted many users representing a broad range of interests and has resulted in numerous awards for technological achievements and technology transfer. Recent work with CARES/Life was directed at enhancing the program s capabilities with regards to cyclic fatigue. Only in the last few years have ceramics been recognized to be susceptible to enhanced degradation from cyclic loading. To account for cyclic loads, researchers at the NASA Lewis Research Center developed a crack growth model that combines the Power Law (time-dependent) and the Walker Law (cycle-dependent) crack growth models. This combined model has the characteristics of Power Law behavior (decreased damage) at high R ratios (minimum load/maximum load) and of Walker law behavior (increased damage) at low R ratios. In addition, a parameter estimation methodology for constant-amplitude, steady-state cyclic fatigue experiments was developed using nonlinear least squares and a modified Levenberg-Marquardt algorithm. This methodology is used to give best estimates of parameter values from cyclic fatigue specimen rupture data (usually tensile or flexure bar specimens) for a relatively small number of specimens. Methodology to account for runout data (unfailed specimens over the duration of the experiment) was also included.

Nemeth, Noel N.↗

NASA NTRS2015

The Integrated Medical Model: A Probabilistic Simulation Model Predicting In-Flight Medical Risks

The Integrated Medical Model (IMM) is a probabilistic model that uses simulation to predict mission medical risk. Given a specific mission and crew scenario, medical events are simulated using Monte Carlo methodology to provide estimates of resource utilization, probability of evacuation, probability of loss of crew, and the amount of mission time lost due to illness. Mission and crew scenarios are defined by mission length, extravehicular activity (EVA) schedule, and crew characteristics including: sex, coronary artery calcium score, contacts, dental crowns, history of abdominal surgery, and EVA eligibility. The Integrated Medical Evidence Database (iMED) houses the model inputs for one hundred medical conditions using in-flight, analog, and terrestrial medical data. Inputs include incidence, event durations, resource utilization, and crew functional impairment. Severity of conditions is addressed by defining statistical distributions on the dichotomized best and worst-case scenarios for each condition. The outcome distributions for conditions are bounded by the treatment extremes of the fully treated scenario in which all required resources are available and the untreated scenario in which no required resources are available. Upon occurrence of a simulated medical event, treatment availability is assessed, and outcomes are generated depending on the status of the affected crewmember at the time of onset, including any pre-existing functional impairments or ongoing treatment of concurrent conditions. The main IMM outcomes, including probability of evacuation and loss of crew life, time lost due to medical events, and resource utilization, are useful in informing mission planning decisions. To date, the IMM has been used to assess mission-specific risks with and without certain crewmember characteristics, to determine the impact of eliminating certain resources from the mission medical kit, and to design medical kits that maximally benefit crew health while meeting mass and volume constraints.

Risk Analysis↗

NASA NTRS2015

The Integrated Medical Model: A Probabilistic Simulation Model for Predicting In-Flight Medical Risks

The Integrated Medical Model (IMM) is a probabilistic model that uses simulation to predict mission medical risk. Given a specific mission and crew scenario, medical events are simulated using Monte Carlo methodology to provide estimates of resource utilization, probability of evacuation, probability of loss of crew, and the amount of mission time lost due to illness. Mission and crew scenarios are defined by mission length, extravehicular activity (EVA) schedule, and crew characteristics including: sex, coronary artery calcium score, contacts, dental crowns, history of abdominal surgery, and EVA eligibility. The Integrated Medical Evidence Database (iMED) houses the model inputs for one hundred medical conditions using in-flight, analog, and terrestrial medical data. Inputs include incidence, event durations, resource utilization, and crew functional impairment. Severity of conditions is addressed by defining statistical distributions on the dichotomized best and worst-case scenarios for each condition. The outcome distributions for conditions are bounded by the treatment extremes of the fully treated scenario in which all required resources are available and the untreated scenario in which no required resources are available. Upon occurrence of a simulated medical event, treatment availability is assessed, and outcomes are generated depending on the status of the affected crewmember at the time of onset, including any pre-existing functional impairments or ongoing treatment of concurrent conditions. The main IMM outcomes, including probability of evacuation and loss of crew life, time lost due to medical events, and resource utilization, are useful in informing mission planning decisions. To date, the IMM has been used to assess mission-specific risks with and without certain crewmember characteristics, to determine the impact of eliminating certain resources from the mission medical kit, and to design medical kits that maximally benefit crew health while meeting mass and volume constraints.

Risk Analysis↗

NASA NTRS1995

GPS integrity monitoring and multipath error distributions

The ability to perform integrity monitoring of a differential Global Positioning System (DGPS) precision approach system is dependent upon the form of monitor used and the various noise sources acting on the reference station, the monitor, and the approaching aircraft. This paper focuses on how multipath and assumptions about its probability density function (pdf) affect the availability of the integrity monitoring function. Also discussed is a technique specified as code/carrier integrity monitoring which can be used to greatly improve integrity monitoring availability over methods employing conventional C/A-code operations.

Skidmore, Trent A.↗

NASA NTRS1974

An empirical analysis of the distribution of the duration of overshoots in a stationary gaussian stochastic process

This analysis utilizes computer simulation and statistical estimation. Realizations of stationary gaussian stochastic processes with selected autocorrelation functions are computer simulated. Analysis of the simulated data revealed that the mean and the variance of a process were functionally dependent upon the autocorrelation parameter and crossing level. Using predicted values for the mean and standard deviation, by the method of moments, the distribution parameters was estimated. Thus, given the autocorrelation parameter, crossing level, mean, and standard deviation of a process, the probability of exceeding the crossing level for a particular length of time was calculated.

Parrish, R. S.↗

NASA NTRS1976

Recent decametric and hectometric observations of Jupiter

Observational results on Jupiter's high-frequency radiation, for the range 1-35 MHz (10 to 100 m), obtained over the past six years with the aid of orbited telescopes, are surveyed. Spectral distributions, periodic effects, burst waveforms and dynamic spectra of storms, polarization effects, high-resolution interferometry, and possible correlations with solar activity are discussed. Related spacecraft experiments are described. Close attention is given to long-term accumulation of occurrence probability data as functions of time and frequency (synoptic monitoring) on Jovian HF emission, and to dominating effects of the Jovian satellite Io, as well as modulation of periodicities by the 11.9-year orbital motion period of Jupiter. Possible effects of the other four Jovian satellites immersed in the Jovian magnetosphere are also taken into consideration. Absence of a Jovian Faraday effect and polarization of fine burst structure are discussed.

Carr, T. D.↗

NASA NTRS1982

A Markov chain model for reliability growth and decay

A mathematical model is developed to describe a complex system undergoing a sequence of trials in which there is interaction between the internal states of the system and the outcomes of the trials. For example, the model might describe a system undergoing testing that is redesigned after each failure. The basic assumptions for the model are that the state of the system after a trial depends probabilistically only on the state before the trial and on the outcome of the trial and that the outcome of a trial depends probabilistically only on the state of the system before the trial. It is shown that under these basic assumptions, the successive states form a Markov chain and the successive states and outcomes jointly form a Markov chain. General results are obtained for the transition probabilities, steady-state distributions, etc. A special case studied in detail describes a system that has two possible state ('repaired' and 'unrepaired') undergoing trials that have three possible outcomes ('inherent failure', 'assignable-cause' 'failure' and 'success'). For this model, the reliability function is computed explicitly and an optimal repair policy is obtained.

Siegrist, K.↗

NASA NTRS1987

First-order Fermi acceleration in the two-stream limit

A study of the first-order Fermi mechanism for accelerating cosmic-rays at relativistic and nonrelativistic shocks is carried out by using the two-stream approximation. Exact steady-state analytic solutions illustrating the shock acceleration process in the test-particle limit in which monoenergetic (relativistic) seed particles enter the shock through an upstream free-escape boundary are obtained. The momentum spectrum of the shock accelerated particles consists of a series of Dirac delta distributions corresponding to particles that have undergone an integral number of acceleration cycles. Since particles in the model have a finite fixed escape probability from the shock and the particle momenta p are equally spaced in log p, the envelope of the delta functions series is a power law in momentum. The solutions are used to discuss time-dependent aspects of the shock acceleration process in terms of the finite cycle time, escape probability, and momentum change per cycle that can be deduced from the steady-state model. The length-scale over which the accelerated particles extend upstream of the shock is shown to depend upon the particle energy, with the higher energy particles extending further upstream. This effect is shown to be intimately related to the kinematic threshold requirement that the particle speed exceed the fluid speed in order for particles to swim upstream of the shock and participate in the shock acceleration process.

Bogdan, T. J.↗

NASA NTRS1989

On the structure of pressure fluctuations in simulated turbulent channel flow

Pressure fluctuations in a turbulent channel flow are investigated by analyzing a database obtained from a direct numerical simulation. Detailed statistics associated with the pressure fluctuations are presented. Characteristics associated with the rapid (linear) and slow (nonlinear) pressure are discussed. It is found that the slow pressure fluctuations are larger than the rapid pressure fluctuations throughout the channel except very near the wall, where they are about the same magnitude. This is contrary to the common belief that the nonlinear source terms are negligible compared to the linear source terms. Probability density distributions, power spectra, and two-point correlations are examined to reveal the characteristics of the pressure fluctuations. The global dependence of the pressure fluctuations and pressure-strain correlations are also examined by evaluating the integral associated with Green's function representations of them. In the wall region where the pressure-strain terms are large, most contributions to the pressure-strain terms are from the wall region (i.e., local), whereas away from the wall where the pressure-strain terms are small, contributions are global. Structures of instantaneous pressure and pressure gradients at the wall and the corresponding vorticity field are examined.

Kim, John↗

NASA NTRS1989

On the structure of pressure fluctuations in simulated turbulent channel flow

Pressure fluctuations in a turbulent channel flow are investigated by analyzing a database obtained from a direct numerical simulation. Detailed statistics associated with the pressure fluctuations are presented. Characteristics associated with the rapid (linear) and slow (nonlinear) pressure are discussed. It is found that the slow pressure fluctuations are larger than the rapid pressure fluctuations throughout the channel except very near the wall, where they are about the same magnitude. This is contrary to the common belief that the nonlinear source terms are negligible compared to the linear source terms. Probability density distributions, power spectra, and two-point correlations are examined to reveal the characteristics of the pressure fluctuations. The global dependence of the pressure fluctuations and pressure-strain correlations are also examined by evaluating the integral associated with Green's function representations of them. In the wall region where the pressure-strain terms are large, most contributions to the pressure-strain terms are from the wall region (i.e., local), whereas away from the wall where the pressure-strain terms are small, contributions are global. Structures of instantaneous pressure and pressure gradients at the wall and the corresponding vorticity field are examined.

Kim, John↗

NASA NTRS1991

Building a generalized distributed system model

A modeling tool for both analysis and design of distributed systems is discussed. Since many research institutions have access to networks of workstations, the researchers decided to build a tool running on top of the workstations to function as a prototype as well as a distributed simulator for a computing system. The effects of system modeling on performance prediction in distributed systems and the effect of static locking and deadlocks on the performance predictions of distributed transactions are also discussed. While the probability of deadlock is considerably small, its effects on performance could be significant.

Mukkamala, Ravi↗

NASA NTRS1979

A comparison of computer architectures for the NASA demonstration advanced avionics system

The paper compares computer architectures for the NASA demonstration advanced avionics system. Two computer architectures are described with an unusual approach to fault tolerance: a single spare processor can correct for faults in any of the distributed processors by taking on the role of a failed module. It was shown the system must be used from a functional point of view to properly apply redundancy and achieve fault tolerance and ultra reliability. Data are presented on complexity and mission failure probability which show that the revised version offers equivalent mission reliability at lower cost as measured by hardware and software complexity.

Seacord, C. L.↗