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NASA NTRS1986

A Monte Carlo study of Weibull reliability analysis for space shuttle main engine components

The incorporation of a number of additional capabilities into an existing Weibull analysis computer program and the results of Monte Carlo computer simulation study to evaluate the usefulness of the Weibull methods using samples with a very small number of failures and extensive censoring are discussed. Since the censoring mechanism inherent in the Space Shuttle Main Engine (SSME) data is hard to analyze, it was decided to use a random censoring model, generating censoring times from a uniform probability distribution. Some of the statistical techniques and computer programs that are used in the SSME Weibull analysis are described. The methods documented in were supplemented by adding computer calculations of approximate (using iteractive methods) confidence intervals for several parameters of interest. These calculations are based on a likelihood ratio statistic which is asymptotically a chisquared statistic with one degree of freedom. The assumptions built into the computer simulations are described. The simulation program and the techniques used in it are described there also. Simulation results are tabulated for various combinations of Weibull shape parameters and the numbers of failures in the samples.

Abernethy, K.↗

NASA NTRS1994

LES, DNS and RANS for the analysis of high-speed turbulent reacting flows

The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Sep. 1993 - 1 Sep. 1994, we have focused our efforts on two research problems: (1) developments of 'algebraic' moment closures for statistical descriptions of nonpremixed reacting systems, and (2) assessments of the Dirichlet frequency in presumed scalar probability density function (PDF) methods in stochastic description of turbulent reacting flows. This report provides a complete description of our efforts during this past year as supported by the NASA Langley Research Center under Grant NAG1-1122.

Givi, Peyman↗

NASA NTRS1975

Assessment of NDE reliability data

Twenty sets of relevant nondestructive test (NDT) reliability data were identified, collected, compiled, and categorized. A criterion for the selection of data for statistical analysis considerations was formulated, and a model to grade the quality and validity of the data sets was developed. Data input formats, which record the pertinent parameters of the defect/specimen and inspection procedures, were formulated for each NDE method. A comprehensive computer program was written and debugged to calculate the probability of flaw detection at several confidence limits by the binomial distribution. This program also selects the desired data sets for pooling and tests the statistical pooling criteria before calculating the composite detection reliability. An example of the calculated reliability of crack detection in bolt holes by an automatic eddy current method is presented.

Yee, B. G. W.↗

NASA NTRS1972

Application of the QSDC procedure to the formulation of space shuttle design criteria. Volume 1: Study effort

Criteria to determine the probability of aircraft structural failure were statistically established according to the Quantitative Structural Design Criteria by Statistical Methods, the QSDC procedure. Since an Application Guide is needed to use the QSDC procedure, most of the study was directed to the development of this guide. Most of the considerations followed in the development of the Applications Guide and the Guide itself are reported.

Bouton, I.↗

NASA NTRS1972

Application of the QSDC procedure to the formulation of space shuttle design criteria. Volume 2: Applications guide

Criteria to determine the probability of aircraft structural failure were established according to the Quantitative Structural Design Criteria by Statistical Methods, the QSDC Procedure. This criteria method was applied to the design of the space shuttle during this contract. An Applications Guide was developed to demonstrate the utilization of the QSDC Procedure, with examples of the application to a hypothetical space shuttle illustrating the application to specific design problems. Discussions of the basic parameters of the QSDC Procedure: the Limit and Omega Conditions, and the strength scatter, have been included. Available data pertinent to the estimation of the strength scatter have also been included.

Bouton, I.↗

NASA NTRS2012

A Deterministic Annealing Approach to Clustering AIRS Data

We will examine the validity of means and standard deviations as a basis for climate data products. We will explore the conditions under which these two simple statistics are inadequate summaries of the underlying empirical probability distributions by contrasting them with a nonparametric, method called Deterministic Annealing technique

clustering↗

NASA NTRS1994

Application of static and dynamic enclosures for determining dimethyl sulfide and carbonyl sulfide exchange in Sphagnum peatlands: Implications for the magnitude and direction of flux

A static enclosure method was applied to determine the exchange of dimethyl sulfide (DMS) and carbonyl sulfide (OCS) between the surface of Sphagnum peatlands and the atmosphere. Measurements were performed concurrently with dynamic (flow through) enclosure measurements with sulfur-free air used as sweep gas. This latter technique has been used to acquire the majority of available data on the exchange of S gases between the atmosphere and the continental surfaces and has been criticized because it is thought to overestimate the true flux of gases by disrupting natural S gas gradients. DMS emission rates determined by both methods were not statistically different between 4 and greater than 400 nmol/sq m/h, indicating that previous data on emissions of at least DMS are probably valid. However, the increase in DMS in static enclosures was not linear, indicating the potential for a negative feedback of enlosure DMS concentrations on efflux. The dynamic enclosure method measured positive OCS flux rates (emission) at all sites, while data using static enclosures indicated that OCS was consumed from the atmosphere at these same sites at rates of 3.7 to 55 nmol/sq m/h. Measurements using both enclosure techniques at a site devoid of vegetation showed that peat was a source of both DMS and OCS. However, the rate of OCS efflux from decomposing peat was more than counterbalanced by OCS consumption by vegetation, including Sphagnum mosses, and net OCS uptake occurred at all sites. We propose that all wetlands are net sinks for OCS.

De Mello, William Z.↗

NASA NTRS1984

Predicting Solar Deficits

Statistical method uses available long term solar irradiance data at selected sites in United States to predict probable deviations from long term monthly averages. Technique useful in sizing solar collectors and backup storage systems to cover solar deficits.

Ross, R. G., Jr.↗

NASA NTRS2012

Representation of Probability Density Functions from Orbit Determination using the Particle Filter

Statistical orbit determination enables us to obtain estimates of the state and the statistical information of its region of uncertainty. In order to obtain an accurate representation of the probability density function (PDF) that incorporates higher order statistical information, we propose the use of nonlinear estimation methods such as the Particle Filter. The Particle Filter (PF) is capable of providing a PDF representation of the state estimates whose accuracy is dependent on the number of particles or samples used. For this method to be applicable to real case scenarios, we need a way of accurately representing the PDF in a compressed manner with little information loss. Hence we propose using the Independent Component Analysis (ICA) as a non-Gaussian dimensional reduction method that is capable of maintaining higher order statistical information obtained using the PF. Methods such as the Principal Component Analysis (PCA) are based on utilizing up to second order statistics, hence will not suffice in maintaining maximum information content. Both the PCA and the ICA are applied to two scenarios that involve a highly eccentric orbit with a lower apriori uncertainty covariance and a less eccentric orbit with a higher a priori uncertainty covariance, to illustrate the capability of the ICA in relation to the PCA.

Mashiku, Alinda K.↗

NASA NTRS2014

Some Interesting Applications of Probabilistic Techiques in Structural Dynamic Analysis of Rocket Engines

Numerical and Analytical methods developed to determine damage accumulation in specific engine components when speed variation included. Dither Life Ratio shown to be well over factor of 2 for specific example. Steady‐State assumption shown to be accurate for most turbopump cases, allowing rapid calculation of DLR. If hot‐fire speed data unknown, Monte Carlo method developed that uses speed statistics for similar engines. Application of techniques allow analyst to reduce both uncertainty and excess conservatism. High values of DLR could allow previously unacceptable part to pass HCF criteria without redesign. Given benefit and ease of implementation, recommend that any finite life turbomachine component analysis adopt these techniques. Probability Values calculated, compared, and evaluated for several industry‐proposed methods for combining random and harmonic loads. Two new excel macros written to calculate combined load for any specific probability level. Closed form Curve fits generated for widely used 3(sigma) and 2(sigma) probability levels. For design of lightweight aerospace components, obtaining accurate, reproducible, statistically meaningful answer critical.

Brown, Andrew M.↗

NASA NTRS1989

Combining multispectral and ancillary data in remote sensing using interval-valued probabilities

This paper presents a method for classifying multisource data in remote sensing and geographic information systems using interval-valued probabilities. In this method, each data source is considered as an information source which provides a body of statistical evidence. In order to integrate information obtained from multiple data sources, the method adopts Dempster's rule for combining multiple bodies of evidence. Preliminary experiments have been undertaken to illustrate the use of the method in a supervised ground-cover classification on multispectral data combined with digital elevation data. They demonstrate the ability of the method in capturing information provided by inexact and incomplete evidence when there are not enough training samples to estimate statistical parameters.

Kim, H.↗

NASA NTRS1988

An analytic treatment of gravitational microlensing for sources of finite size at large optical depths

Statistical methods are developed for gravitational lensing in order to obtain analytic expressions for the average surface brightness that include the effects of microlensing by stellar (or other compact) masses within the lensing galaxy. The primary advance here is in utilizing a Markoff technique to obtain expressions that are valid for sources of finite size when the surface density of mass in the lensing galaxy is large. The finite size of the source is probably the key consideration for the occurrence of microlensing by individual stars. For the intensity from a particular location, the parameter which governs the importance of microlensing is determined. Statistical methods are also formulated to assess the time variation of the surface brightness due to the random motion of the masses that cause the microlensing.

Deguchi, Shuji↗

NASA NTRS2016

Consistent Practices for the Probability of Detection (POD) of Fracture Critical Metallic Components Project

NASA-STD-5009 requires that successful flaw detection by NDE methods be statistically qualified for use on fracture critical metallic components, but does not standardize practices. This task works towards standardizing calculations and record retention with a web-based tool, the NNWG POD Standards Library or NPSL. Test methods will also be standardized with an appropriately flexible appendix to -5009 identifying best practices. Additionally, this appendix will describe how specimens used to qualify NDE systems will be cataloged, stored and protected from corrosion, damage, or loss.

Hughitt, Brian↗

NASA NTRS1996

Progressive transmission and compression images

We describe an image data compression strategy featuring progressive transmission. The method exploits subband coding and arithmetic coding for compression. We analyze the Laplacian probability density, which closely approximates the statistics of individual subbands, to determine a strategy for ordering the compressed subband data in a way that improves rate-distortion performance. Results are presented for a test image.

Kiely, A. B.↗

NASA NTRS1996

Progressive Transmission and Compression of Images

Kiely, A. B.↗

NASA NTRS2012

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.

Mashiku, Alinda↗

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 NTRS1969

Wave propagation in a random medium

A simple technique is used to derive statistical characterizations of the perturbations imposed upon a wave (plane, spherical or beamed) propagating through a random medium. The method is essentially physical rather than mathematical, and is probably equivalent to the Rytov method. The limitations of the method are discussed in some detail; in general they are restrictive only for optical paths longer than a few hundred meters, and for paths at the lower microwave frequencies. Situations treated include arbitrary path geometries, finite transmitting and receiving apertures, and anisotropic media. Results include, in addition to the usual statistical quantities, time-lagged functions, mixed functions involving amplitude and phase fluctuations, angle-of-arrival covariances, frequency covariances, and other higher-order quantities.

Lee, R. W.↗