Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Probability distribution”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Modified Spectral Fatigue Methods for S-N Curves With MIL-HDBK-5J Coefficients

The rainflow method is used for counting fatigue cycles from a stress response time history, where the fatigue cycles are stress-reversals. The rainflow method allows the application of Palmgren-Miner's rule in order to assess the fatigue life of a structure subject to complex loading. The fatigue damage may also be calculated from a stress response power spectral density (PSD) using the semi-empirical Dirlik, Single Moment, Zhao-Baker and other spectral methods. These methods effectively assume that the PSD has a corresponding time history which is stationary with a normal distribution. This paper shows how the probability density function for rainflow stress cycles can be extracted from each of the spectral methods. This extraction allows for the application of the MIL-HDBK-5J fatigue coefficients in the cumulative damage summation. A numerical example is given in this paper for the stress response of a beam undergoing random base excitation, where the excitation is applied separately by a time history and by its corresponding PSD. The fatigue calculation is performed in the time domain, as well as in the frequency domain via the modified spectral methods. The result comparison shows that the modified spectral methods give comparable results to the time domain rainflow counting method.

Irvine, Tom↗
NASA NTRSDate not supplied

Interval Predictor Models for Robust System Identification

This paper proposes a framework for the identification and uncertainty quantification of plant models according to multivariable data. The only restriction imposed upon such models is for their outputs to depend continuously on their parameters. An Interval Predictor Model (IPM) prescribes the parameters of a computational model as a path-connected set thereby making each predicted output an interval-valued function of its inputs. The formulation proposed seeks the parameter set for which the predicted outputs tightly enclose the data. This set, which is modeled as a semi-algebraic set of low-degree polynomials, enables the characterization of possibly strong parameter dependencies commonly found in practice. This uncertainty characterization makes the resulting plant model amenable to robust control approaches using polynomial optimization. Furthermore, we use non-convex scenario theory to assess the reliability of the resulting IPM. This assessment yields a distribution-free upper bound on the probability that future data will fall outside the predicted intervals.

interval↗
NASA NTRSDate not supplied

Quantum-Accelerated Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees

We present two algorithms in the Quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability; One for producing an approximately optimal Steiner Tree, and one for producing an exact Minimum Directed Spanning tree. These use O(n1/4) rounds of communication and O(n9/4) messages, leading to a quantum speedup in round and message complexity compared to any known algorithms in the classical CONGEST-CLIQUE model (vs O(n1/3) and O(n7/3)). At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. Further, these problems can not be sped up in the CONGEST (non-clique) setting, and we characterize the constants involved.

Phillip Kerger↗
NASA NTRS1989

Size distribution of dust grains: A problem of self-similarity

Distribution functions describing the results of natural processes frequently show the shape of power laws, e.g., mass functions of stars and molecular clouds, velocity spectrum of turbulence, size distributions of asteroids, micrometeorites and also interstellar dust grains. It is an open question whether this behavior is a result simply coming about by the chosen mathematical representation of the observational data or reflects a deep-seated principle of nature. The authors suppose the latter being the case. Using a dust model consisting of silicate and graphite grains Mathis et al. (1977) showed that the interstellar extinction curve can be represented by taking a grain radii distribution of power law type n(a) varies as a(exp -p) with 3.3 less than or equal to p less than or equal to 3.6 (example 1) as a basis. A different approach to understanding power laws like that in example 1 becomes possible by the theory of self-similar processes (scale invariance). The beta model of turbulence (Frisch et al., 1978) leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot's (1977) fractal dimension. In the frame of this beta model, it is supposed that on each stage of a cascade the system decays to N clumps and that only the portion beta N remains active further on. An important feature of this model is that the active eddies become less and less space-filling. In the following, the authors assume that grain-grain collisions are such a scale-invarient process and that the remaining grains are the inactive (frozen) clumps of the cascade. In this way, a size distribution n(a) da varies as a(exp -(D+1))da (example 2) results. It seems to be highly probable that the power law character of the size distribution of interstellar dust grains is the result of a self-similarity process. We can, however, not exclude that the process leading to the interstellar grain size distribution is not fragmentation at all. It could be, e.g., diffusion-limited growth discussed by Sander (1986), who applied the theory of fractal geometry to the classification of non-equilibrium growth processes. He received D=2.4 for diffusion-limited aggregation in 3d-space.

Henning, TH.↗
NASA NTRS1988

A survey of IRAS data on 41 classical novae

The IRAS database has been searched for detections of 41 classical novae using coadditions of survey scans; 15 were detected. IRAS temporal observations of novae in outburst are discussed. The observed long-wavelength infrared distributions of DQ Her, and possibly HR Del, can be explained by emission from small (a of about 0.1 microns) dust grains heated by the central object. An alternative explanation for the energy distributions of DQ Her and HR Del is emission from fine-structure lines. FH Ser and LW Ser display energy distributions that have color temperatures much too hot to be due to heating of dust by the central source in any plausible scenario. Line emission is probably the best explanation of their observed energy distributions. The novae NQ Vul and LV Vul have energy distributions that may be contaminated by emission from galactic cirrus. The unusual object PL 1547.3-5612 exhibits an energy distribution that does not resemble those of planetary nebulae or other novae detected in this sample. An IRAS low-resolution spectrum of RR Tel shows the 10-micron silicate emission feature.

Harrison, T. E.↗
NASA NTRS1974

The problem of the structure of the surface of the lunar maria

The results are described of geological and morphological interpretation of large-scale photographs of the surface of lunar maria. A morphological classification is proposed for small craters. It is shown that the classification of a crater in a given morphological category, reflecting the degree of its morphological maturity, is determined by the age of the given crater. A check on the nature of distribution of small craters, as done on the basis of the nearest neighbor method, show that the distribution is governed by a near-random law. It is found that variations of the probability density function for the craters conform to a normal distribution law. An empirical relation is found for the coefficient of variation as a function of crater diameter and the dimensions of the area on which the counts are made. The rockfalls near craters of various morphological classes are described.

Florenskiy, K. P.↗
NASA NTRS1973

A determination of meteor mass distribution from meteor echoes

Meteor counts from observations at four magnitudes in the range of about +9 to +15 in the visual scale were used to determine the exponent of the mass distribution law under certain assumptions. Since for these data no range measures were available, and since the pattern of the transmitting/receiving antennas was very broad, the same range and radiant distribution were assumed for all counts within the same half hour during which individual counts at different magnitudes were obtained. These echo counts, covering in five successive days 24 hr with overlapping periods, yielded for the exponent a value of 1.95 + or - 0.02, close to other determinations. Individual values, however, presented a considerable scatter, probably reflecting changes in radiant and mass distribution over the year. From the same data, it appeared that the mass exponent changed during the day, yielding generally a higher value for the evening hours.

Forti, G.↗
NASA NTRS2003

Coupled Multi-Disciplinary Optimization for Structural Reliability and Affordability

A computational simulation method is presented for Non-Deterministic Multidisciplinary Optimization of engine composite materials and structures. A hypothetical engine duct made with ceramic matrix composites (CMC) is evaluated probabilistically in the presence of combined thermo-mechanical loading. The structure is tailored by quantifying the uncertainties in all relevant design variables such as fabrication, material, and loading parameters. The probabilistic sensitivities are used to select critical design variables for optimization. In this paper, two approaches for non-deterministic optimization are presented. The non-deterministic minimization of combined failure stress criterion is carried out by: (1) performing probabilistic evaluation first and then optimization and (2) performing optimization first and then probabilistic evaluation. The first approach shows that the optimization feasible region can be bounded by a set of prescribed probability limits and that the optimization follows the cumulative distribution function between those limits. The second approach shows that the optimization feasible region is bounded by 0.50 and 0.999 probabilities.

Abumeri, Galib H.↗
NASA NTRS1985

Influence of meteorological conditions on aerosol vertical distribution and composition off the northeast American coastline

The size distribution and composition of lower tropospheric aerosols were measured off the northeast American coastline under clear air and disturbed meteorological conditions. Under the clear air conditions observed on 5 August 1982, with air flow from west to east, sulfate-rich stratified layers are the dominant feature of aerosol distribution in the lowest 3000 m of the troposphere. The encroachment of a warm frontal system over the study area on 9 August 1982 resulted in dramatic changes in aerosol distribution and composition prior to any precipitation, probably due to increased vertical mixing and dilution of pollutant aerosols. Chloride becomes the dominant water soluble anion in the lower 3000 m, primarily due to a several fold decrease in sulfate. Although these results are limited to only two sets of measurements, the data indicate the variability which can occur in the tropospheric vertical aerosol distributions at remote locations. A knowledge of the structure and stability of these stratified layers is of particular importance to studies of the ocean-troposphere chemistry problem.

Sebacher, D. I.↗
NASA NTRS1990

An analytical approach to gravitational lensing by an ensemble of axisymmetric lenses

The problem of gravitational lensing by an ensemble of identical axisymmetric lenses randomly distributed on a single lens plane is considered and a formal expression is derived for the joint probability density of finding shear and convergence at a random point on the plane. The amplification probability for a source can be accurately estimated from the distribution in shear and convergence. This method is applied to two cases: lensing by an ensemble of point masses and by an ensemble of objects with Gaussian surface mass density. There is no convergence for point masses whereas shear is negligible for wide Gaussian lenses.

Lee, Man Hoi↗
NASA NTRS2014

The Effect of General Statistical Fiber Misalignment on Predicted Damage Initiation in Composites

A micromechanical method is employed for the prediction of unidirectional composites in which the fiber orientation can possess various statistical misalignment distributions. The method relies on the probability-weighted averaging of the appropriate concentration tensor, which is established by the micromechanical procedure. This approach provides access to the local field quantities throughout the constituents, from which initiation of damage in the composite can be predicted. In contrast, a typical macromechanical procedure can determine the effective composite elastic properties in the presence of statistical fiber misalignment, but cannot provide the local fields. Fully random fiber distribution is presented as a special case using the proposed micromechanical method. Results are given that illustrate the effects of various amounts of fiber misalignment in terms of the standard deviations of in-plane and out-of-plane misalignment angles, where normal distributions have been employed. Damage initiation envelopes, local fields, effective moduli, and strengths are predicted for polymer and ceramic matrix composites with given normal distributions of misalignment angles, as well as fully random fiber orientation.

Micromechanical↗
NASA NTRS1989

Linear canonical transformations of coherent and squeezed states in the Wigner phase space. II - Quantitative analysis

It is possible to calculate expectation values and transition probabilities from the Wigner phase-space distribution function. Based on the canonical transformation properties of the Wigner function, an algorithm is developed for calculating these quantities in quantum optics for coherent and squeezed states. It is shown that the expectation value of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable. Parallel-axis theorems are established for the photon number and its variant. It is also shown that the transition probability between two squeezed states can be reduced to that of the transition from one squeezed state to vacuum.

Han, D.↗
NASA NTRS1998

Development of a Probabilistic Dynamic Synthesis Method for the Analysis of Nondeterministic Structures

Accounting for the statistical geometric and material variability of structures in analysis has been a topic of considerable research for the last 30 years. The determination of quantifiable measures of statistical probability of a desired response variable, such as natural frequency, maximum displacement, or stress, to replace experience-based "safety factors" has been a primary goal of these studies. There are, however, several problems associated with their satisfactory application to realistic structures, such as bladed disks in turbomachinery. These include the accurate definition of the input random variables (rv's), the large size of the finite element models frequently used to simulate these structures, which makes even a single deterministic analysis expensive, and accurate generation of the cumulative distribution function (CDF) necessary to obtain the probability of the desired response variables. The research presented here applies a methodology called probabilistic dynamic synthesis (PDS) to solve these problems. The PDS method uses dynamic characteristics of substructures measured from modal test as the input rv's, rather than "primitive" rv's such as material or geometric uncertainties. These dynamic characteristics, which are the free-free eigenvalues, eigenvectors, and residual flexibility (RF), are readily measured and for many substructures, a reasonable sample set of these measurements can be obtained. The statistics for these rv's accurately account for the entire random character of the substructure. Using the RF method of component mode synthesis, these dynamic characteristics are used to generate reduced-size sample models of the substructures, which are then coupled to form system models. These sample models are used to obtain the CDF of the response variable by either applying Monte Carlo simulation or by generating data points for use in the response surface reliability method, which can perform the probabilistic analysis with an order of magnitude less computational effort. Both free- and forced-response analyses have been performed, and the results indicate that, while there is considerable room for improvement, the method produces usable and more representative solutions for the design of realistic structures with a substantial savings in computer time.

Brown, A. M.↗
NASA NTRS2007

Implementation of a Collision Probability Prediction Technique for Constellation Maneuver Planning

On March 22, 2006, the Space Technology 5 (ST5) constellation spacecraft were successfully delivered to orbit by a Pegasus XI, launch vehicle. An unexpected relative motion experienced by the constellation after orbit insertion brought about a problem. Soon after launch the observed relative position of the inert rocket body was between the leading and the middle spacecraft within the constellation. The successful planning and execution of an orbit maneuver that would create a fly-by of the rocket body was required to establish the.formation. This maneuver would create a close approach that needed to conform to predefined collision probability requirements. On April 21, 2006, the ST5 "155" spacecraft performed a large orbit maneuver and successfully passed the inert Pegasus 3rd Stage Rocket Body on April 30, 2006 15:20 UTC at a distance of 2.55 km with a Probability of Collision of less than 1.0E-06. This paper will outline the technique that was implemented to establish the safe planning and execution of the fly-by maneuver. The method makes use of Gaussian distribution models of state covariance to determine underlying probabilities of collision that arise under low velocity encounters. Specific numerical examples used for this analysis are discussed in detail. The mechanics of this technique are explained to foster deeper understanding of the concepts presented and to improve existing processes for use in future constellation maneuver planning.

Concha, Marco a.↗
NASA NTRS1991

Incorporating finite element analysis into component life and reliability

A method for calculating a component's design survivability by incorporating finite element analysis and probabilistic material properties was developed. The method evaluates design parameters through direct comparisons of component survivability expressed in terms of Weibull parameters. The analysis was applied to a rotating disk with mounting bolt holes. The highest probability of failure occurred at, or near, the maximum shear stress region of the bolt holes. Distribution of failure as a function of Weibull slope affects the probability of survival. Where Weibull parameters are unknown for a rotating disk, it may be permissible to assume Weibull parameters, as well as the stress-life exponent, in order to determine the disk speed where the probability of survival is highest.

August, Richard↗
NASA NTRS2009

A Monte-Carlo Model for the Formation of Radiation-induced Chromosomal Aberrations

Purpose: To simulate radiation-induced chromosome aberrations in mammalian cells (e.g., rings, translocations, and dicentrics) and to calculate their frequency distributions following exposure to DNA double strand breaks (DSBs) produced by high-LET ions. Methods: The interphase genome was assumed to be comprised of a collection of 2 kbp rigid-block monomers following the random-walk geometry. Additional details for the modeling of chromosomal structure, such as chromosomal domains and chromosomal loops, were included. A radial energy profile for heavy ion tracks was used to simulate the high-LET pattern of induced DSBs. The induced DSB pattern depended on the ion charge and kinetic energy, but always corresponded to the DSB yield of 25 DSBs/cell/Gy. The sum of all energy contributions from Poisson-distributed particle tracks was taken to account for all possible one-track and multi-track effects. The relevant output of the model was DNA fragments produced by DSBs. The DSBs, or breakpoints, were defined by (x, y, z, l) positions, where x, y, z were the Euclidian coordinates of a DSB, and where l was the relative position along the genome. Results: The code was used to carry out Monte Carlo simulations for DSB rejoinings at low doses. The resulting fragments were analyzed to estimate the frequencies of specific types of chromosomal aberrations. Histograms for relative frequencies of chromosomal aberrations and P.D.F.s (probability density functions) of a given aberration type were produced. The relative frequency of dicentrics to rings was compared to empirical data to calibrate rejoining probabilities. Of particular interest was the predicted distribution of ring sizes, irrespective of their frequencies relative to other aberrations. Simulated ring sizes were . 4 kbp, which are far too small to be observed experimentally (i.e., by microscopy) but which, nevertheless, are conjectured to exist. Other aberrations, for example, inversions, translocations, as well as multi-centrics were also recorded. Conclusion: High-LET DNA damage affects the frequencies of chromosomal aberrations. The ratio of rings to dicentrics is correct for the genomic size cut-offs corresponding to available experimental data. The present work predicts a relative abundance of small rings following irradiation by heavy ions.

Ponomarev, Artem L.↗
NASA NTRS1979

Collisional evolution of asteroids - Populations, rotations, and velocities

The collisional evolution of various initial populations of asteroids is simulated numerically and compared with the present asteroid size-frequency distribution to find those populations which collisionally relax to the present belt. Both orbital and size distributions are treated, as well as the simultaneous evolution of two collisionally interacting populations with different physical properties. If the initial belt distribution was a power law, the initial belt population at the time when the present high-collision speed was established was probably only modestly larger than the present population. However, other distributions allow a more massive early belt. The rotational evolution due to collisions of asteroids with power-law distributions is also examined and compared with observations, leading to conclusions generally in agreement with those of size evolution. The high-collision speed in the present belt is likely due to Jupiter. Gravitational stirring by massive Jupiter-scattered planetesimals or secular resonances sweeping through the belt are the most probable mechanisms.

Davis, D. R.↗
NASA NTRS2005

What Does Reflection from Cloud Sides Tell Us About Vertical Distribution of Cloud Droplet Sizes?

Cloud development, the onset of precipitation and the effect of aerosol on clouds depend on the structure of the cloud profiles of droplet size and phase. Aircraft measurements of cloud profiles are limited in their temporal and spatial extent. Satellites were used to observe cloud tops not cloud profiles with vertical profiles of precipitation-sized droplets anticipated from Cloudsat. The recently proposed CLAIM-3D satellite mission (cloud aerosol interaction mission in 3D) suggests to measure profiles of cloud microphysical properties by retrieving them from the solar and infrared radiation reflected or emitted from cloud sides. Inversion of measurements from the cloud sides requires rigorous understanding of the 3-dimensional (3D) properties of clouds. Here we discuss the reflected sunlight from the cloud sides and top at two wavelengths: one nonabsorbing to solar radiation (0.67 micrometers) and one with liquid water efficient absorption of solar radiation (2.1 micrometers). In contrast to the plane-parallel approximation, a conventional approach to all current operational retrievals, 3D radiative transfer is used for interpreting the observed reflectances. General properties of the radiation reflected from the sides of an isolated cloud are discussed. As a proof of concept, the paper shows a few examples of radiation reflected from cloud fields generated by a simple stochastic cloud model with the prescribed vertically resolved microphysics. To retrieve the information about droplet sizes, we propose to use the probability density function of the droplet size distribution and its first two moments instead of the assumption about fixed values of the droplet effective radius. The retrieval algorithm is based on the Bayesian theorem that combines prior information about cloud structure and microphysics with radiative transfer calculations.

Marshak, Alexander↗