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Results for “Probability Distribution Function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Asymptotic inconsistency of the cumulative algorithm for laser-induced damage probability analysis

The “cumulative algorithm” is a data analysis method that has been proposed to provide an objective, nonparametric determination of laser-induced damage probability as a function of fluence from experimental data that contain both damaged sites and undamaged sites (i.e., 1-on-1 or S-on-1 testing protocols). In this work, the limitations of this approach are explored by considering the asymptotic limit of a large number of test sites. It is shown that the cumulative algorithm does not converge to the true probability distribution and significantly underestimates the damage probability near the damage onset. Here, based on the results of this work, the cumulative algorithm is not recommended for accurate estimation of damage probability.

Computational methods↗
NASA NTRS1991

Statistical-mechanical selection of the shapes of disk galaxies

A new method is proposed for selecting steady state shapes of disk galaxies as 'most probable states' of a large number of stars, given only the total energy and total angular momentum. A partial differential equation is derived for the mean gravitational potential; it is closely related to the 'sinh-Poisson' equation for the mean-field description of a line vortex system or electrostatic guiding-center plasma. A 'water bag' approximation to the distribution function for bound stars renders the equation analytically tractable, but accurate solution of it may require numerical integration, in view of its general nonlinearity.

Montgomery, David↗
NASA NTRS2003

Evidence of Self-Organized Criticality in Dry Sliding Friction

This letter presents experimental results on unlubricated friction, which suggests that stick-slip is described by self-organized criticality (SOC). The data, obtained with a pin-on-disc tribometer examines the variation of the friction force as a function of time-or sliding distance. This is the first time that standard tribological equipment has been used to examine the possibility of SOC. The materials were matching pins and discs of aluminium loaded with 250, 500 and 1000 g masses, and matching M50 steel couples loaded with a 1000 g mass. An analysis of the data shows that the probability distribution of slip sizes follows a power law. We perform a careful analysis of all the properties, beyond the two just mentioned, which are required to imply the presence of SOC. Our data strongly support the existence of SOC for stick-slip in dry sliding friction.

Zypman, Fredy R.↗
DOE OSTI2024

Fixed Source Sensitivity Calculations for Inertial Confinement Fusion Applications

A numerical code library was developed for the radiation transport code MCNP6.3 to calculate generalized response sensitivity coefficients for fixed source neutron transport problems with applications to inertial confinement fusion (ICF) experiments. The new MCNP6.3 dependency is used to generate a novel time convolution response that represents a neutron time-of-flight (nToF) signal. The traditional suite of macroscopic cross-section sensitivities and constrained fixed source probability distribution sensitivities are available for both the standard and the new response tallies in this library. However, novel sensitivity coefficients for the constrained hyperparameters of analytic fixed source probability distributions are emphasized in this work for their connection to ICF neutron transport models. Particularly, advanced Monte Carlo methods are developed for calculating the sensitivity of a nToF signal to perturbations in an ICF plasma’s ion temperature and burn history as well as perturbations in the target liner mass density and the shape parameters of the nToF detector’s impulse response function. Together, these capabilities form an advanced suite of computational tools that can be used to analyze and extract information from any ICF experimental platform.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1982

Design and calibration of a coherent lidar for measurement of atmospheric backscatter

This paper discusses the background requirements for, and the design and calibration of a coherent Doppler lidar which is oriented specifically toward the measurement of low values of atmospheric backscatter at a wavelength of 10.6 microns. The lidar is a compact, continuous wave system which can operate in two modes, multiple particle scattering and single particle scattering. In the multiple scattering mode, the lidar employs an extended focal volume and utilizes a technique similar to Dicke switching to achieve measurement of the volume backscatter. In the single scattering mode, the focal volume is reduced to ensure a high probability of single particle scattering. Measurement of the single particle backscatter as a function of time leads to the formation of signal histogram from which the volume backscatter can be inferred. In addition to providing the atmospheric backscatter value, appropriate data processing algorithms and focal volume calibration allow the single particle mode to yield information on the atmospheric aerosol scattering cross-section distribution.

Jones, W. D.↗
NASA NTRS1993

Specular scattering on a terrestrial playa and implications for planetary surface studies

Multiangle Advanced Solid State Array Spectroradiometer (ASAS) and Portable Apparatus for Rapid Acquisition of Bidirectional Observations of Land and Atmosphere (PARABOLA) visible and near infrared reflectance data covering the Lunar Lake playa, Nevada, were modeled using specular and volume scattering theory. The volume component used to model the data was based on the Hapke (1986) model and the specular scattering component was based on Fresnel reflection from surface facets with a distribution of tilts. Specular scattering was needed to explain the several-fold increase in reflectance observed at high phase angles in the solar principal plane. Results imply single scattering albedos of approximately 0.93 to 0.95, a real index of refraction value of approximately 1.52 (at a wavelength of 0.66 micron), a small imaginary index of refraction and an exponential facet tilt probability function for the playa. Electron micrographs showed th playa surface to consist of ensembles of smooth, micrometer-scale ellipsoidal particles on gently undulating topography at the millimeter to centimeter scale. The exponential probability function is consistent with this observation. Mars and the icy satellites are discussed as possible places to look for a significant specular scattering component.

Shepard, Michael K.↗
NASA NTRS1997

ERBE Geographic Scene and Monthly Snow Data

The Earth Radiation Budget Experiment (ERBE) is a multisatellite system designed to measure the Earth's radiation budget. The ERBE data processing system consists of several software packages or sub-systems, each designed to perform a particular task. The primary task of the Inversion Subsystem is to reduce satellite altitude radiances to fluxes at the top of the Earth's atmosphere. To accomplish this, angular distribution models (ADM's) are required. These ADM's are a function of viewing and solar geometry and of the scene type as determined by the ERBE scene identification algorithm which is a part of the Inversion Subsystem. The Inversion Subsystem utilizes 12 scene types which are determined by the ERBE scene identification algorithm. The scene type is found by combining the most probable cloud cover, which is determined statistically by the scene identification algorithm, with the underlying geographic scene type. This Contractor Report describes how the geographic scene type is determined on a monthly basis.

Coleman, Lisa H.↗
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 NTRS2003

Past, Present and Future Trends for NASA's EEE Parts Program

The foundation of NASA's Electrical, Electronic and Electromechanical (EEE) parts program is standardization. Standardization helps to reduce the number of unknown variables present as a project or program progresses; unknown variables equate to unknown risk. NASA spacecraft are usually 'one-offs' or at least part of a very short run, and every new part that is used represents a risk that has to be understood and mitigated as necessary. This equates directly to time and cost. Standardization of component parts is used to provide a foundation of known, dependable, qualified parts upon which a safe, reliable system can be built. In addition, the evaluation and selection of parts for the standard parts list unifies the activity under one group of experts rather than having engineers on each project overlapping and duplicating efforts. Thus, the project support engineers are able to concentrate on understanding and mitigating the risks for the non standard parts required to meet specific requirements of their project. Rapid technology change is producing conditions that make any form of parts-based standardization increasingly difficult, particularly the use of Commercial Off The Shelf (COTS) parts and assemblies. There are many complications to COTS-based standardization. COTS parts change rapidly and unpredictably, often have different characteristics fiom manufacturer to manufacturer, frequently are only available through distribution, have no universal specification and have variable and unpredictable radiation characteristics. This presentation will discuss some potential approaches to COTS parts standardization. Further into the future, in three to five years perhaps, the use of COTS boards and boxes will be extensive and standardization at these levels of assembly will be necessary. In five to ten years, most major spacecraft functions will probably be performed by COTS boards. How will this be achieved? What role will the parts engineer play, if any? This presentation will borrow from the lessons of the past to suggest some scenarios for the future.

Sampson, Michael J.↗
NASA NTRS2009

Lunar Outpost Life Support Architecture Study Based on a High Mobility Exploration Scenario

As scenarios for lunar surface exploration and habitation continue to evolve within NASA s Constellation program, so must studies of optimal life support system architectures and technologies. This paper presents results of a life support architecture study based on a 2009 NASA scenario known as Scenario 12. Scenario 12 represents a consolidation of ideas from earlier NASA scenarios and includes an outpost near the Lunar South Pole comprised of three larger fixed surface elements and four attached pressurized rovers. The scenario places a high emphasis on surface mobility, with planning assuming that all four crewmembers spend roughly 50% of the time away from the outpost on 3-14 day excursions in two of the pressurized rovers. Some of the larger elements can also be mobilized for longer duration excursions. This emphasis on mobility poses a significant challenge for a regenerative life support system in terms of cost-effective waste collection and resource recovery across multiple elements, including rovers with very constrained infrastructure resources. The current study considers pressurized rovers as part of a distributed outpost life support architecture in both stand-alone and integrated configurations. A range of architectures are examined reflecting different levels of closure and distributed functionality. Different lander propellant scavenging options are also considered involving either initial conversion of residual oxygen and hydrogen propellants to water or initial direct oxygen scavenging. Monte Carlo simulations are used to assess the sensitivity of results to volatile high-impact mission variables, including the quantity of residual lander propellants available for scavenging, the fraction of crew time away from the outpost on excursions, total extravehicular activity hours, and habitat leakage. Architectures are evaluated by estimating surpluses or deficits of water and oxygen per 180-day mission and differences in fixed and 10-year-total equivalent system mass (ESM) relative to a reference case. Results are presented based on current assumptions for Scenario 12 and based on Monte Carlo simulations with assumed probability distributions for the high-impact mission variables. The calculated probability of no water or oxygen resupply from Monte Carlo simulations provides a quantitative measure of system robustness that can be used for cost/benefit analyses to identify leading architecture candidates. Areas of technology improvement that are likely to have a significant impact are also suggested.

Lange, Kevin E.↗
NASA NTRS2023

Analysis of VFR Traffic Uncertainty and its Impact on Uncrewed Aircraft Operational Capacity at Regional Airports

This paper proposes a method to characterize Visual Flight Rules traffic around a regional airport. The applicability of the method is discussed in the context of Uncrewed Aircraft operations at a regional airport. The relation between traffic interaction uncertainty and operational capacity at the runway is also investigated. The spatio-temporal distribution of traffic operating under Visual Flight Rules is analyzed from historical track data and visualized as heat maps generated at different altitudes. These are used to characterize the spatio-temporal uncertainty associated with traffic density, around a given airport, down to the runway. The traffic patterns at the runway are used to compute the runway capacity as a function of the probability of interaction with traffic operating under visual flight rules. Fort Worth Alliance is used as a representative regional airport for the study. Applications of the traffic characterization methods developed in this paper are also discussed.

VFR traffic, uncertainty, air mobility↗
NASA NTRS2023

Analysis of VFR Traffic Uncertainty and its Impact on Uncrewed Aircraft Operational Capacity at Regional Airports

This paper proposes a method to characterize Visual Flight Rules traffic around a regional airport. The applicability of the method is discussed in the context of Uncrewed Aircraft operations at a regional airport. The relation between traffic interaction uncertainty and operational capacity at the runway is also investigated. The spatio-temporal distribution of traffic operating under Visual Flight Rules is analyzed from historical track data and visualized as heat maps generated at different altitudes. These are used to characterize the spatio-temporal uncertainty associated with traffic density, around a given airport, down to the runway. The traffic patterns at the runway are used to compute the runway capacity as a function of the probability of interaction with traffic operating under visual flight rules. Fort Worth Alliance is used as a representative regional airport for the study. Applications of the traffic characterization methods developed in this paper are also discussed.

VFR traffic↗
NASA NTRS1975

On the alleged collisional origin of the Kirkwood Gaps

This paper examines two proposed mechanisms whereby asteroidal collisions and close approaches may have given rise to the Kirkwood Gaps. The first hypothesis is that asteroids in near-resonant orbits have markedly increased collision probabilities and so are preferentially destroyed, or suffer decay in population density, within the resonance zones. A simple order-of-magnitude analysis shows that this hypothesis is untenable since it leads to conclusions which are either unrealistic or not in accord with present understanding of asteroidal physics. The second hypothesis is the Brouwer-Jefferys theory that collisions would smooth an asteroidal distribution function, as a function of Jacobi constant, thus forming resonance gaps. This hypothesis is examined by direct numerical integration of 50 asteroid orbits near the 2:1 resonance, with collisions simulated by random variables. No tendency to form a gap was observed.

Heppenheimer, T. A.↗
NASA NTRS1983

The spatial distribution of fixed mutations within genes coding for proteins

An examination has been conducted of the extensive amino acid sequence data now available for five protein families - the alpha crystallin A chain, myoglobin, alpha and beta hemoglobin, and the cytochromes c - with the goal of estimating the true spatial distribution of base substitutions within genes that code for proteins. In every case the commonly used Poisson density failed to even approximate the experimental pattern of base substitution. For the 87 species of beta hemoglobin examined, for example, the probability that the observed results were from a Poisson process was the minuscule 10 to the -44th. Analogous results were obtained for the other functional families. All the data were reasonably, but not perfectly, described by the negative binomial density. In particular, most of the data were described by one of the very simple limiting forms of this density, the geometric density. The implications of this for evolutionary inference are discussed. It is evident that most estimates of total base substitutions between genes are badly in need of revision.

Holmquist, R.↗
NASA NTRS2005

Probabilistic Parameter Uncertainty Analysis of Single Input Single Output Control Systems

The current standards for handling uncertainty in control systems use interval bounds for definition of the uncertain parameters. This approach gives no information about the likelihood of system performance, but simply gives the response bounds. When used in design, current methods of m-analysis and can lead to overly conservative controller design. With these methods, worst case conditions are weighted equally with the most likely conditions. This research explores a unique approach for probabilistic analysis of control systems. Current reliability methods are examined showing the strong areas of each in handling probability. A hybrid method is developed using these reliability tools for efficiently propagating probabilistic uncertainty through classical control analysis problems. The method developed is applied to classical response analysis as well as analysis methods that explore the effects of the uncertain parameters on stability and performance metrics. The benefits of using this hybrid approach for calculating the mean and variance of responses cumulative distribution functions are shown. Results of the probabilistic analysis of a missile pitch control system, and a non-collocated mass spring system, show the added information provided by this hybrid analysis.

Smith, Brett A.↗
NASA NTRS2005

Probabilistic Design of a Wind Tunnel Model to Match the Response of a Full-Scale Aircraft

approach is presented for carrying out the reliability-based design of a plate-like wing that is part of a wind tunnel model. The goal is to design the wind tunnel model to match the stiffness characteristics of the wing box of a flight vehicle while satisfying strength-based risk/reliability requirements that prevents damage to the wind tunnel model and fixtures. The flight vehicle is a modified F/A-18 aircraft. The design problem is solved using reliability-based optimization techniques. The objective function to be minimized is the difference between the displacements of the wind tunnel model and the corresponding displacements of the flight vehicle. The design variables control the thickness distribution of the wind tunnel model. Displacements of the wind tunnel model change with the thickness distribution, while displacements of the flight vehicle are a set of fixed data. The only constraint imposed is that the probability of failure is less than a specified value. Failure is assumed to occur if the stress caused by aerodynamic pressure loading is greater than the specified strength allowable. Two uncertain quantities are considered: the allowable stress and the thickness distribution of the wind tunnel model. Reliability is calculated using Monte Carlo simulation with response surfaces that provide approximate values of stresses. The response surface equations are, in turn, computed from finite element analyses of the wind tunnel model at specified design points. Because the response surface approximations were fit over a small region centered about the current design, the response surfaces were refit periodically as the design variables changed. Coarse-grained parallelism was used to simultaneously perform multiple finite element analyses. Studies carried out in this paper demonstrate that this scheme of using moving response surfaces and coarse-grained computational parallelism reduce the execution time of the Monte Carlo simulation enough to make the design problem tractable. The results of the reliability-based designs performed in this paper show that large decreases in the probability of stress-based failure can be realized with only small sacrifices in the ability of the wind tunnel model to represent the displacements of the full-scale vehicle.

Mason, Brian H.↗
NASA NTRS2011

Reliability Based Design for a Raked Wing Tip of an Airframe

A reliability-based optimization methodology has been developed to design the raked wing tip of the Boeing 767-400 extended range airliner made of composite and metallic materials. Design is formulated for an accepted level of risk or reliability. The design variables, weight and the constraints became functions of reliability. Uncertainties in the load, strength and the material properties, as well as the design variables, were modeled as random parameters with specified distributions, like normal, Weibull or Gumbel functions. The objective function and constraint, or a failure mode, became derived functions of the risk-level. Solution to the problem produced the optimum design with weight, variables and constraints as a function of the risk-level. Optimum weight versus reliability traced out an inverted-S shaped graph. The center of the graph corresponded to a 50 percent probability of success, or one failure in two samples. Under some assumptions, this design would be quite close to the deterministic optimum solution. The weight increased when reliability exceeded 50 percent, and decreased when the reliability was compromised. A design could be selected depending on the level of risk acceptable to a situation. The optimization process achieved up to a 20-percent reduction in weight over traditional design.

Patnaik, Surya N.↗
NASA NTRS1987

Observations on the magnitude-frequency distribution of Earth-crossing asteroids

During the past decade, discovery of Earth-crossing asteroids has continued at the pace of several per year; the total number of known Earth crossers reached 70 as of September, 1986. The sample of discovered Earth crossers has become large enough to provide a fairly strong statistical basis for calculations of mean probabilities of asteroid collision with the Earth, the Moon, and Venus. It is also now large enough to begin to address the more difficult question of the magnitude-frequency distribution and size distribution of the Earth-crossing asteroids. Absolute V magnitude, H, was derived from reported magnitudes for each Earth crosser on the basis of a standard algorithm that utilizes a physically realistic phase function. The derived values of H range from 12.88 for (1627) Ivar to 21.6 for the Palomar-Leiden object 6344, which is the faintest and smallest asteroid discovered.

Shoemaker, Eugene M.↗