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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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Superclustering in the explosion scenario

A simple toy model is used to study the spatial distribution of rich clusters in a generic type of explosion scenario. The model, parameterized by the distribution of shell radii and the filling factor, places spherical shells at random and identifies each 'knot' as a cluster. The resulting cluster correlation function is close to a power law extending to the diameter of the largest spheres. Richer clusters form at the intersections of bigger shells and so have stronger correlations. Typical shell radii and filling factors are required to produce the observed number density of clusters. Models with a power-law radius distribution also reproduce the richness distribution of clusters in the Abell catalog. Supercluster multiplicity functions, void probabilities, number counts, topology statistics, and velocity correlations confirm the presence of strong superclustering and quantify the non-Gaussian nature of the model.

Weinberg, David H.↗
NASA NTRS1988

Toward a comprehensive theory for the sweeping of trapped radiation by inert orbiting matter

There is a need to calculate loss rates when trapped Van Allen radiation encounters inert orbiting material such as planetary rings and satellites. An analytic expression for the probability of a hit in a bounce encounter is available for all cases where the absorber is spherical and the particles are gyrotropically distributed on a cylindrical flux tube. The hit probability is a function of the particle's pitch angle, the size of the absorber, and the distance between the flux tube and the absorber when distances are scaled to the gyroradius of a particle moving perpendicular to the magnetic field. Using this expression, hit probabilities in drift encounters were computed for all regimes of particle energies and absorber sizes.

Fillius, Walker↗
NASA NTRS1999

A Probabilistic Approach to Aeropropulsion System Assessment

A probabilistic approach is described for aeropropulsion system assessment. To demonstrate this approach, the technical performance of a wave rotor-enhanced gas turbine engine (i.e. engine net thrust, specific fuel consumption, and engine weight) is assessed. The assessment accounts for the uncertainties in component efficiencies/flows and mechanical design variables, using probability distributions. The results are presented in the form of cumulative distribution functions (CDFs) and sensitivity analyses, and are compared with those from the traditional deterministic approach. The comparison shows that the probabilistic approach provides a more realistic and systematic way to assess an aeropropulsion system.

Tong, Michael T.↗
NASA NTRS2000

A Probabilistic Approach to Aeropropulsion System Assessment

A probabilistic approach is described for aeropropulsion system assessment. To demonstrate this approach, the technical performance of a wave rotor-enhanced gas turbine engine (i.e. engine net thrust, specific fuel consumption, and engine weight) is assessed. The assessment accounts for the uncertainties in component efficiencies/flows and mechanical design variables, using probability distributions. The results are presented in the form of cumulative distribution functions (CDFS) and sensitivity analyses, and are compared with those from the traditional deterministic approach. The comparison shows that the probabilistic approach provides a more realistic and systematic way to assess an aeropropulsion system.

Tong, Michael T.↗
NASA NTRS2000

A Probabilistic Approach to Aeropropulsion System Assessment

A probabilistic approach is described for aeropropulsion system assessment. To demonstrate this approach, the technical performance of a wave rotor-enhanced gas turbine engine (i.e. engine net thrust, specific fuel consumption, and engine weight) is assessed. The assessment accounts for the uncertainties in component efficiencies/flows and mechanical design variables, using probability distributions. The results are presented in the form of cumulative distribution functions (CDFs) and sensitivity analyses, and are compared with those from the traditional deterministic approach. The comparison shows that the probabilistic approach provides a more realistic and systematic way to assess an aeropropulsion system.

Tong, Michael T.↗
NASA NTRS2010

Analytic Development of a Reference Profile for the First Entry in a Skip Atmospheric Entry

This note shows that a feasible reference drag profile for the first entry portion of a skip entry can be generated as a polynomial expression of the velocity. The coefficients of that polynomial are found through the resolution of a system composed of m + 1 equations, where m is the degree of the drag polynomial. It has been shown that a minimum of five equations (m = 4) are required to establish the range and the initial and final conditions on velocity and flight path angle. It has been shown that at least one constraint on the trajectory can be imposed through the addition of one extra equation in the system, which must be accompanied by the increase in the degree of the drag polynomial. In order to simplify the resolution of the system of equations, the drag was considered as being a probability density function of the velocity, with the velocity as a distribution function of the drag. Combining this notion with the introduction of empirically derived constants, it has been shown that the system of equations required to generate the drag profile can be successfully reduced to a system of linear algebraic equations. For completeness, the resulting drag profiles have been flown using the feedback linearization method of differential geometric control as a guidance law with the error dynamics of a second order homogeneous equation in the form of a damped oscillator. Satisfactory results were achieved when the gains in the error dynamics were changed at a certain point along the trajectory that is dependent on the velocity and the curvature of the drag as a function of the velocity. Future work should study the capacity to update the drag profile in flight when dispersions are introduced. Also, future studies should attempt to link the first entry, as presented and controlled in this note, with a more standard control concept for the second entry, such as the Apollo entry guidance, to try to assess the overall skip entry performance. A guidance law that includes an integral feedback term, as is the case in the actual Space Shuttle entry guidance and as is proposed in Ref 29, could be tried in future studies to assess whether its use results in an improvement of the tracking performance, and to evaluate the design needs when determining the control gains.

Garcia-Llama, Eduardo↗
NASA NTRS1966

Log-normal model for microbial survival in heat sterilization

An analytical model is developed for the survival times of organisms in heat sterilization in which the probability of inactivation as a function of exposure time is log-normally distributed. Experimental data is examined relative to this model and it is concluded that the model is valid except during the initial period of heating when an additional interaction between the organisms and their surrounding medium appears to be present. At long heating times, the log-normal model appears more accurate for extrapolating to low survival probabilities than the usual logarithmic survivor curves and is generally more conservative.

SURVIVAL↗
NASA NTRS1981

Effect of long-term intensity variations on pulsar searches and the pulsar luminosity function

Long-term intensity data for five pulsars are used to obtain the probability density distribution of intensities for each pulsar, and it is found that they are described satisfactorily by chi-squared distributions. Based on these distributions, the number of new pulsars expected to be found on repeatedly searching the same region of the sky with the same sensitivity is given. Nearly 25 percent more new pulsars are expected to be found on the first repeat search. It is also shown that the luminosity function deduced from either a single survey or surveys with very different sensitivities is not affected by the omission of flux density variations in the calculation of selection effects. Finally, a method is proposed for deriving the luminosity function by combining the different searches of a given area on the basis of a probabilistic approach to the evaluation of selection effects.

Krishnamohan, S.↗
NASA NTRS2019

Radar Cross Section of Orbital Debris Objects

This discussion is concerned with the radar-data analysis and usage involved in the building of model orbital debris (OD) populations in the near-Earth environment, focusing on radar cross section (RCS). While varying with radar wavelength, physical dimension, material composition, overall shape and structure, the RCS of an irregular object is also strongly dependent on its spatial orientation. The historical records of observed RCSs for cataloged OD objects in the Space Surveillance Network are usually distributed over an RCS range, forming respective characteristic patterns. The National Aeronautics and Space Administration (NASA) Size Estimation Model provides an empirical probability-density function of RCS as a function of “effective diameter” (or “characteristic length”), which makes it feasible to predict possible RCS distributions for a given model OD population and to link data with model from a statistical perspective. The discussion also includes application of the widely used method of moments (MoM) and the Generalized Multi-particle Mie-solution (GMM) in the prediction of the RCS of arbitrarily shaped objects. Theoretical calculation results for an aluminum cube are compared with corresponding experimental measurements.

Xu, Yu-Lin↗
NASA NTRS1990

Equivalence of physically based statistical fracture theories for reliability analysis of ceramics in multiaxial loading

The present comparison of the Batdorf (1974) flaw density and orientation distribution approach with Evans' (1978) elemental strength approach, with a view to identities in fracture criteria and distribution functions, notes that despite their fundamental differences in multiaxial loading fracture probabilities, the two approaches yield identical predictions. Lamon's (1988) assertion to the contrary, in light of different theoretical predictions by the two methods for the case of alumina disks loaded in flexure, is demonstrated to be in error.

Chao, Luen-Yuan↗
NASA NTRS2003

Statistical Evaluation and Improvement of Methods for Combining Random and Harmonic Loads

Structures in many environments experience both random and harmonic excitation. A variety of closed-form techniques has been used in the aerospace industry to combine the loads resulting from the two sources. The resulting combined loads are then used to design for both yield/ultimate strength and high- cycle fatigue capability. This Technical Publication examines the cumulative distribution percentiles obtained using each method by integrating the joint probability density function of the sine and random components. A new Microsoft Excel spreadsheet macro that links with the software program Mathematica to calculate the combined value corresponding to any desired percentile is then presented along with a curve tit to this value. Another Excel macro that calculates the combination using Monte Carlo simulation is shown. Unlike the traditional techniques. these methods quantify the calculated load value with a consistent percentile. Using either of the presented methods can be extremely valuable in probabilistic design, which requires a statistical characterization of the loading. Additionally, since the CDF at high probability levels is very flat, the design value is extremely sensitive to the predetermined percentile; therefore, applying the new techniques can substantially lower the design loading without losing any of the identified structural reliability.

Brown, A. M.↗
NASA NTRS2004

Statistical Comparison and Improvement of Methods for Combining Random and Harmonic Loads

Structures in many environments experience both random and harmonic excitation. A variety of closed-form techniques has been used in the aerospace industry to combine the loads resulting from the two sources. The resulting combined loads are then used to design for both yield ultimate strength and high cycle fatigue capability. This paper examines the cumulative distribution function (CDF) percentiles obtained using each method by integrating the joint probability density function of the sine and random components. A new Microsoft Excel spreadsheet macro that links with the software program Mathematics is then used to calculate the combined value corresponding to any desired percentile along with a curve fit to this value. Another Excel macro is used to calculate the combination using a Monte Carlo simulation. Unlike the traditional techniques, these methods quantify the calculated load value with a Consistent percentile. Using either of the presented methods can be extremely valuable in probabilistic design, which requires a statistical characterization of the loading. Also, since the CDF at high probability levels is very flat, the design value is extremely sensitive to the predetermined percentile; therefore, applying the new techniques can lower the design loading substantially without losing any of the identified structural reliability.

Brown, Andrew M.↗
NASA NTRS2017

Statistical Characterization of 18650-Format Lithium-Ion Cell Thermal Runaway Energy Distributions

Effective thermal management systems, designed to handle the impacts of thermal runaway (TR) and to prevent cell-to-cell propagation, are key to safe operation of lithium-ion (Li-ion) battery assemblies. Critical factors for optimizing these systems include the total energy released during a single cell TR event and the fraction of the total energy that is released through the cell casing vs. through the ejecta material. A unique calorimeter was utilized to examine the TR behavior of a statistically significant number of 18650-format Li-ion cells with varying manufacturers, chemistries, and capacities. The calorimeter was designed to contain the TR energy in a format conducive to discerning the fractions of energy released through the cell casing vs. through the ejecta material. Other benefits of this calorimeter included the ability to rapidly test of large quantities of cells and the intentional minimization of secondary combustion effects. High energy (270 Wh/kg) and moderate energy (200 Wh/kg) 18650 cells were tested. Some of the cells had an imbedded short circuit (ISC) device installed to aid in the examination of TR mechanisms under more realistic conditions. Other variations included cells with bottom vent (BV) features and cells with thin casings (0.22 1/4m). After combining the data gathered with the calorimeter, a statistical approach was used to examine the probability of certain TR behavior, and the associated energy distributions, as a function of capacity, venting features, cell casing thickness and temperature.

Thermal Runaway Energy Distribution↗
NASA NTRS2010

Probabilistic Design Analysis (PDA) Approach to Determine the Probability of Cross-System Failures for a Space Launch Vehicle

Quantifying the probability of significant launch vehicle failure scenarios for a given design, while still in the design process, is critical to mission success and to the safety of the astronauts. Probabilistic risk assessment (PRA) is chosen from many system safety and reliability tools to verify the loss of mission (LOM) and loss of crew (LOC) requirements set by the NASA Program Office. To support the integrated vehicle PRA, probabilistic design analysis (PDA) models are developed by using vehicle design and operation data to better quantify failure probabilities and to better understand the characteristics of a failure and its outcome. This PDA approach uses a physics-based model to describe the system behavior and response for a given failure scenario. Each driving parameter in the model is treated as a random variable with a distribution function. Monte Carlo simulation is used to perform probabilistic calculations to statistically obtain the failure probability. Sensitivity analyses are performed to show how input parameters affect the predicted failure probability, providing insight for potential design improvements to mitigate the risk. The paper discusses the application of the PDA approach in determining the probability of failure for two scenarios from the NASA Ares I project

Shih, Ann T.↗
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 NTRS1974

Long-duration life tests of slip ring capsule assemblies for inertial guidance platforms

Eight slip ring capsules, each having 80 or 100 circuits, were operated for time periods ranging from 14,300 hours to 24,700 hours. The test mode simulated the motion of gimbal axes of the Saturn inertial guidance the platform in an organic free nitrogen environment. Computer-compiled noise data (approximately 45,000 recordings) were graphed as a function of test time and position within the capsules and as extreme probability distributions. Greater than ninety-nine percent of the noise measurements for the capsules with sufficient lubrication were less than 10 milliohms. Capsules with glass dielectrics did not perform significantly differently than those with filled epoxy dielectrics. The initial wear mode of prow formation was followed by rider wear. After 10 to the 8th power wipes, ring wear depth did not exceed the surface finish and the radial rider wear depth was less than 13 microns.

Cole, S. R.↗