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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Back Propagation Neural Networks for Predicting Ultimate Strengths of Unidirectional Graphite/Epoxy Tensile Specimens

The research presented herein demonstrates the feasibility of predicting ultimate strengths in simple composite structures through a neural network analysis of their acoustic emission (AE) amplitude distribution data. A series of eleven ASTM D-3039 unidirectional graphite/epoxy tensile samples were loaded to failure to generate the amplitude distributions for this analysis. A back propagation neural network was trained to correlate the AE amplitude distribution signatures generated during the first 25% of loading with the ultimate strengths of the samples. The network was trained using two sets of inputs: (1) the statistical parameters obtained from a Weibull distribution fit of the amplitude distribution data, and (2) the event frequency (amplitude) distribution itself. The neural networks were able to predict ultimate strengths with a worst case error of -8.99% for the Weibull modeled amplitude distribution data and 3.74% when the amplitude distribution itself was used to train the network. The principal reason for the improved prediction capability of the latter technique lies in the ability of the neural network to extract subtle features from within the amplitude distribution.

Walker, James L.↗
NASA NTRS1983

Establishment of a center of excellence for applied mathematical and statistical research

The state of the art was assessed with regards to efforts in support of the crop production estimation problem and alternative generic proportion estimation techniques were investigated. Topics covered include modeling the greeness profile (Badhwarmos model), parameter estimation using mixture models such as CLASSY, and minimum distance estimation as an alternative to maximum likelihood estimation. Approaches to the problem of obtaining proportion estimates when the underlying distributions are asymmetric are examined including the properties of Weibull distribution.

Woodward, W. A.↗
NASA NTRS2016

The Effect of Roughness Model on Scattering Properties of Ice Crystals.

We compare stochastic models of microscale surface roughness assuming uniform and Weibull distributions of crystal facet tilt angles to calculate scattering by roughened hexagonal ice crystals using the geometric optics (GO) approximation. Both distributions are determined by similar roughness parameters, while the Weibull model depends on the additional shape parameter. Calculations were performed for two visible wavelengths (864 nm and 410 nm) for roughness values between 0.2 and 0.7 and Weibull shape parameters between 0 and 1.0 for crystals with aspect ratios of 0.21, 1 and 4.8. For this range of parameters we find that, for a given roughness level, varying the Weibull shape parameter can change the asymmetry parameter by up to about 0.05. The largest effect of the shape parameter variation on the phase function is found in the backscattering region, while the degree of linear polarization is most affected at the side-scattering angles. For high roughness, scattering properties calculated using the uniform and Weibull models are in relatively close agreement for a given roughness parameter, especially when a Weibull shape parameter of 0.75 is used. For smaller roughness values, a shape parameter close to unity provides a better agreement. Notable differences are observed in the phase function over the scattering angle range from 5deg to 20deg, where the uniform roughness model produces a plateau while the Weibull model does not.

Weibull density functions↗
NASA NTRS1994

A new approach for determining fully empirical altimeter wind speed model functions

A statistical technique is developed for determining fully empirical model functions relating altimeter backscatter (sigma(sub 0)) measurements to near-surface neutral stability wind speed. By assuming that sigma(sub 0) varies monotonically and uniquely with wind speed, the method requires knowledge only of the separate, rather than joint distribution functions of sigma(sub 0) and wind speed. Analytic simplifications result from using a Weibull distribution to approximate the global ocean wind speed distribution; several different wind data sets are used to demonstrate the validity of the Weibull approximation. The technique has been applied to 1 year of Geosat data. Validation of the new and historical model functions using an independent buoy data set demonstrates that the present model function not only has small overall bias and root mean square (RMS) errors, but yields smaller systematic error trends with wind speed and pseudowave age than previously published models. The present analysis suggests that generally accuracte altimeter model functions can be derived without the use of colocated measurements, nor is additional significant wave height information measured by the altimeter necessary.

Freilich, M. H.↗
NASA NTRS1993

Parameter estimation techniques based on optimizing goodness-of-fit statistics for structural reliability

New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell's numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper's nonlinear regression algorithm.

Starlinger, Alois↗
NASA NTRS2003

Resistance of virus to extinction on bottleneck passages: study of a decaying and fluctuating pattern of fitness loss

RNA viruses display high mutation rates and their populations replicate as dynamic and complex mutant distributions, termed viral quasispecies. Repeated genetic bottlenecks, which experimentally are carried out through serial plaque-to-plaque transfers of the virus, lead to fitness decrease (measured here as diminished capacity to produce infectious progeny). Here we report an analysis of fitness evolution of several low fitness foot-and-mouth disease virus clones subjected to 50 plaque-to-plaque transfers. Unexpectedly, fitness decrease, rather than being continuous and monotonic, displayed a fluctuating pattern, which was influenced by both the virus and the state of the host cell as shown by effects of recent cell passage history. The amplitude of the fluctuations increased as fitness decreased, resulting in a remarkable resistance of virus to extinction. Whereas the frequency distribution of fitness in control (independent) experiments follows a log-normal distribution, the probability of fitness values in the evolving bottlenecked populations fitted a Weibull distribution. We suggest that multiple functions of viral genomic RNA and its encoded proteins, subjected to high mutational pressure, interact with cellular components to produce this nontrivial, fluctuating pattern.

Serial Passage↗
NASA NTRS2018

Simulation of Stochastic Mud-Crack Damage Formation in an Environmental Barrier Coating

The integrated Finite Element Analysis–Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program was used to simulate the formation of mudflat-cracks from thermomechanical loading on a multi-layered Environmental Barrier Coating (EBC) system deposited on a ceramic substrate. FEAMAC/CARES combines MAC/GMC multiscale composite micromechanics code with CARES/Life probabilistic multiaxial failure criteria code and Abaqusfinite element analysis. In this work, step function elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio finite elements enabled the depiction of crack boundaries and formation of mudflat patterned damage. Demonstrated examples include finite element models of button–sized disk–shaped 3-D specimen, and a 2-D model of through-the-thickness cross-section. All models were subjected to a progressive cool down from 1300oC to room temperature. Mudflat crack damage in the coating system resulted from the buildup of residual tensile stresses between the individual material constituents from thermal expansion mismatch. A 2-parameter Weibull distribution characterized the coating layer stochastic strength response and the effect of the Weibull modulus on the formation of damage was studied here.

residual tensile stress↗
NASA NTRS2018

Weibull-Based Stochastic Simulation of Mud-Crack Damage Formation in an Environmental Barrier Coating

The integrated Finite Element Analysis Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program was used to simulate the formation of mudflat-cracks from thermomechanical loading on a multi-layered Environmental Barrier Coating (EBC) system deposited on a ceramic substrate. FEAMAC/CARES combines MAC/GMC (Micromechanics Analysis Code/Generalized Method of Cells) multiscale composite micromechanics code with CARES/Life probabilistic multiaxial failure criteria code and Abaqusfinite element analysis. In this work, step function elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio finite elements enabled the depiction of crack boundaries and formation of mudflat patterned damage. Demonstrated examples include finite element models of button-sized disk-shaped 3-D specimen, and a 2-D model of through-the-thickness cross-section. All models were subjected to a progressive cool down from 1300 degrees Centigrade to room temperature. Mudflat crack damage in the coating system resulted from the buildup of residual tensile stresses between the individual material constituents from thermal expansion mismatch. A 2-parameter Weibull distribution characterized the coating layer stochastic strength response and the effect of the Weibull modulus on the formation of damage was studied here.

Residual Tensile Stress↗
NASA NTRS1986

Measurement and application of fault latency

The time interval between the occurrence of a fault and the detection of the error caused by the fault is divided by the generation of that error into two parts: fault latency and error latency. Since the moment of error generation is not directly observable, all related works in the literature have dealt with only the sum of fault and error latencies, thereby making the analysis of their separate effects impossible. To remedy this deficiency, (1) a new methodology for indirectly measuring fault latency is presented; the distribution of fault latency is derived from the methodology; and (3) the knowledge of fault latency is applied to the analysis of two important examples. The proposed methodology has been implemented for measuring fault latency in the Fault-Tolerant Multiprocessor (FTMP) at the NASA Airlab. The experimental results show wide variations in the mean fault latencies of different function circuits within FTMP. Also, the measured distributions of fault latency are shown to have monotone hazard rates. Consequently, Gamma and Weibull distributions are selected for the least-squares fit as the distribution of fault latency.

Shin, K. G.↗
NASA NTRS1972

Scatter factor and reliability of aircraft structures

The concept of time to first failure is utilized to perform a parameter study of scatter factors of aircraft structures. The Weibull distribution is used for estimation of characteristic and certifiable lives. Scatter factors for various Weibull-shaped parameters, fleet sizes and level of reliabilities are calculated. It is concluded that the currently used range of scatter factors (2 through 4) is too narrow for the estimation of a safe life and that a safe and economical design for structural materials with shape parameters less than 2 does not seem feasible except for very small fleet sizes and low levels of reliability.

Schueller, G. I.↗
NASA NTRS1994

Statistical scaling relationships and size effects in the strength and creep rupture of fibrous composites

In this presentation we discuss a new theoretical model and supporting experimental results for the strength and lifetime in creep rupture of unidirectional, carbon fiber/epoxy matrix composites at ambient conditions. First we review the 'standard' Weibull/power-law methodology that has been standard practice. Then we discuss features of a recent model which build on the statistical aspects of fiber strength, micromechanical aspects of stress transfer around fiber breaks, and time-dependent creep of the matrix. The model is applied to 'microcomposites' consisting of seven fibers in a matrix for which strength and creep-rupture data are available. The model yields Weibull distributions in an envelope format for both strength and lifetime. The respective shape, scale and power-law parameters depend on such parameters as the Weibull shape parameter for fiber strength, the exponent for matrix creep, the effective load transfer length (which grows in time due to matrix creep) and the critical cluster size for failed fibers. The experimental results are consistent with the theory, though time-dependent debonding appears to be part of the failure process.

Phoenix, S. Leigh↗
NASA NTRS2024

Effects of Specimen Geometry on Flatwise Tensile Strength

The through-thickness or flatwise strength of a uniaxial polymer matrix composite was investigated with several test specimen geometries and starting plate thicknesses. The use of thinner plates is desirable to save material and lower costs during materials development programs. The various configurations gave similar results with the exception of thin, straight-sided specimens. Thin specimens tended to provide invalid results per ASTM International D7291; however, the addition of a large, shallow radius improved the results. The Weibull distribution provided a good fit to the combined data.

Polymer matrix composite↗
NASA NTRS2002

Generalized Reliability Methodology Applied to Brittle Anisotropic Single Crystals

A generalized reliability model was developed for use in the design of structural components made from brittle, homogeneous anisotropic materials such as single crystals. The model is based on the Weibull distribution and incorporates a variable strength distribution and any equivalent stress failure criteria. In addition to the reliability model, an energy based failure criterion for elastically anisotropic materials was formulated. The model is different from typical Weibull-based models in that it accounts for strength anisotropy arising from fracture toughness anisotropy and thereby allows for strength and reliability predictions of brittle, anisotropic single crystals subjected to multiaxial stresses. The model is also applicable to elastically isotropic materials exhibiting strength anisotropy due to an anisotropic distribution of flaws. In order to develop and experimentally verify the model, the uniaxial and biaxial strengths of a single crystal nickel aluminide were measured. The uniaxial strengths of the <100> and <110> crystal directions were measured in three and four-point flexure. The biaxial strength was measured by subjecting <100> plates to a uniform pressure in a test apparatus that was developed and experimentally verified. The biaxial strengths of the single crystal plates were estimated by extending and verifying the displacement solution for a circular, anisotropic plate to the case of a variable radius and thickness. The best correlation between the experimental strength data and the model predictions occurred when an anisotropic stress analysis was combined with the normal stress criterion and the strength parameters associated with the <110> crystal direction.

Salem, Jonathan A.↗
NASA NTRS1976

Failure rate analysis of Goddard Space Flight Center spacecraft performance during orbital life

Space life performance data on 57 Goddard Space Flight Center spacecraft are analyzed from the standpoint of determining an appropriate reliability model and the associated reliability parameters. Data from published NASA reports, which cover the space performance of GSFC spacecraft launched in the 1960-1970 decade, form the basis of the analyses. The results of the analyses show that the time distribution of 449 malfunctions, of which 248 were classified as failures (not necessarily catastrophic), follow a reliability growth pattern that can be described with either the Duane model or a Weibull distribution. The advantages of both mathematical models are used in order to: identify space failure rates, observe chronological trends, and compare failure rates with those experienced during the prelaunch environmental tests of the flight model spacecraft.

Norris, H. P.↗
NASA NTRS1988

Grain boundary oxidation and low-cycle fatigue at elevated temperatures

Fatigue life consists of fatigue crack nucleation and propagation periods. In order to predict fatigue life accurately, a methodology for the quantitative assessment of these two fatigue damage processes had to be devised. Grain boundary oxidation penetrates faster than does oxidation within a grain. This faster oxidation penetration causes intergranular fatigue failures at elevated temperatures. Grain boundary oxidation accelerates both crack nucleation and propagation. Grain boundary oxidation kinetics and the statistical distribution of grain boundary oxide penetration depth were measured. Quantitative applications of the grain boundary oxidation kinetics to fatigue crack nucleation and propagation were analyzed. A method, based on the Weibull distribution, of extrapolating the laboratory oxidation data measured with small samples to large engineering structures is presented.

Liu, H. W.↗
NASA NTRS1992

Design prediction for long term stress rupture service of composite pressure vessels

Extensive stress rupture studies on glass composites and Kevlar composites were conducted by the Lawrence Radiation Laboratory beginning in the late 1960's and extending to about 8 years in some cases. Some of the data from these studies published over the years were incomplete or were tainted by spurious failures, such as grip slippage. Updated data sets were defined for both fiberglass and Kevlar composite stand test specimens. These updated data are analyzed in this report by a convenient form of the bivariate Weibull distribution, to establish a consistent set of design prediction charts that may be used as a conservative basis for predicting the stress rupture life of composite pressure vessels. The updated glass composite data exhibit an invariant Weibull modulus with lifetime. The data are analyzed in terms of homologous service load (referenced to the observed median strength). The equations relating life, homologous load, and probability are given, and corresponding design prediction charts are presented. A similar approach is taken for Kevlar composites, where the updated stand data do show a turndown tendency at long life accompanied by a corresponding change (increase) of the Weibull modulus. The turndown characteristic is not present in stress rupture test data of Kevlar pressure vessels. A modification of the stress rupture equations is presented to incorporate a latent, but limited, strength drop, and design prediction charts are presented that incorporate such behavior. The methods presented utilize Cartesian plots of the probability distributions (which are a more natural display for the design engineer), based on median normalized data that are independent of statistical parameters and are readily defined for any set of test data.

Robinson, Ernest Y.↗
NASA NTRS1973

Modern methodology of designing target reliability into rotating mechanical components

Experimentally determined distributional cycles-to-failure versus maximum alternating nominal strength (S-N) diagrams, and distributional mean nominal strength versus maximum alternating nominal strength (Goodman) diagrams are presented. These distributional S-N and Goodman diagrams are for AISI 4340 steel, R sub c 35/40 hardness, round, cylindrical specimens 0.735 in. in diameter and 6 in. long with a circumferential groove 0.145 in. radius for a theoretical stress concentration = 1.42 and 0.034 in. radius for a stress concentration = 2.34. The specimens are subjected to reversed bending and steady torque in specially built, three complex-fatigue research machines. Based on these results, the effects on the distributional S-N and Goodman diagrams and on service life of superimposing steady torque on reversed bending are established, as well as the effect of various stress concentrations. In addition a computer program for determining the three-parameter Weibull distribution representing the cycles-to-failure data, and two methods for calculating the reliability of components subjected to cumulative fatigue loads are given.

Kececioglu, D. B.↗