Results for “applied statistics” — Page 58

NASA NTRS1993

Flow interaction experiment. Volume 1: Aerothermal modeling, phase 2

An experimental and computational study is reported for the flow of a turbulent jet discharging into a rectangular enclosure. The experimental configurations consisting of primary jets only, annular jets only, and a combination of annular and primary jets are investigated to provide a better understanding of the flow field in an annular combustor. A laser Doppler velocimeter is used to measure mean velocity and Reynolds stress components. Major features of the flow field include recirculation, primary and annular jet interaction, and high turbulence. A significant result from this study is the effect the primary jets have on the flow field. The primary jets are seen to create statistically larger recirculation zones and higher turbulence levels. In addition, a technique called marker nephelometry is used to provide mean concentration values in the model combustor. Computations are performed using three levels of turbulence closures, namely k-epsilon model, algebraic second moment (ASM), and differential second moment (DSM) closure. Two different numerical schemes are applied. One is the lower-order power-law differencing scheme (PLDS) and the other is the higher-order flux-spline differencing scheme (FSDS). A comparison is made of the performance of these schemes. The numerical results are compared with experimental data. For the cases considered in this study, the FSDS is more accurate than the PLDS. For a prescribed accuracy, the flux-spline scheme requires a far fewer number of grid points. Thus, it has the potential for providing a numerical error-free solution, especially for three-dimensional flows, without requiring an excessively fine grid. Although qualitatively good comparison with data was obtained, the deficiencies regarding the modeled dissipation rate (epsilon) equation, pressure-strain correlation model, and the inlet epsilon profile and other critical closure issues need to be resolved before one can achieve the degree of accuracy required to analytically design combustion systems.

Nikjooy, M.↗

NASA NTRS1993

Flow interaction experiment. Volume 2: Aerothermal modeling, phase 2

An experimental and computational study is reported for the flow of a turbulent jet discharging into a rectangular enclosure. The experimental configurations consisting of primary jets only, annular jets only, and a combination of annular and primary jets are investigated to provide a better understanding of the flow field in an annular combustor. A laser Doppler velocimeter is used to measure mean velocity and Reynolds stress components. Major features of the flow field include recirculation, primary and annular jet interaction, and high turbulence. A significant result from this study is the effect the primary jets have on the flow field. The primary jets are seen to create statistically larger recirculation zones and higher turbulence levels. In addition, a technique called marker nephelometry is used to provide mean concentration values in the model combustor. Computations are performed using three levels of turbulence closures, namely k-epsilon model, algebraic second moment (ASM), and differential second moment (DSM) closure. Two different numerical schemes are applied. One is the lower-order power-law differencing scheme (PLDS) and the other is the higher-order flux-spline differencing scheme (FSDS). A comparison is made of the performance of these schemes. The numerical results are compared with experimental data. For the cases considered in this study, the FSDS is more accurate than the PLDS. For a prescribed accuracy, the flux-spline scheme requires a far fewer number of grid points. Thus, it has the potential for providing a numerical error-free solution, especially for three-dimensional flows, without requiring an excessively fine grid. Although qualitatively good comparison with data was obtained, the deficiencies regarding the modeled dissipation rate (epsilon) equation, pressure-strain correlation model, and the inlet epsilon profile and other critical closure issues need to be resolved before one can achieve the degree of accuracy required to analytically design combustion systems.

Nikjooy, M.↗

NASA NTRS1999

Probabilistic Analysis of Aircraft Gas Turbine Disk Life and Reliability

Two series of low cycle fatigue (LCF) test data for two groups of different aircraft gas turbine engine compressor disk geometries were reanalyzed and compared using Weibull statistics. Both groups of disks were manufactured from titanium (Ti-6Al-4V) alloy. A NASA Glenn Research Center developed probabilistic computer code Probable Cause was used to predict disk life and reliability. A material-life factor A was determined for titanium (Ti-6Al-4V) alloy based upon fatigue disk data and successfully applied to predict the life of the disks as a function of speed. A comparison was made with the currently used life prediction method based upon crack growth rate. Applying an endurance limit to the computer code did not significantly affect the predicted lives under engine operating conditions. Failure location prediction correlates with those experimentally observed in the LCF tests. A reasonable correlation was obtained between the predicted disk lives using the Probable Cause code and a modified crack growth method for life prediction. Both methods slightly overpredict life for one disk group and significantly under predict it for the other.

Melis, Matthew E.↗

NASA NTRS2008

Generalized Linear Covariance Analysis

We review and extend in two directions the results of prior work on generalized covariance analysis methods. This prior work allowed for partitioning of the state space into "solve-for" and "consider" parameters, allowed for differences between the formal values and the true values of the measurement noise, process noise, and a priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and a priori solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator s anchor time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the "variance sandpile" and the "sensitivity mosaic," and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Carpenter, J. Russell↗

NASA NTRS2014

Generalized Linear Covariance Analysis

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Navagation↗

NASA NTRS2014

Generalized Linear Covariance Analysis

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

n/a↗

NASA NTRS1987

Personal computer (PC) based image processing applied to fluid mechanics research

A PC based image processing system was employed to determine the instantaneous velocity field of a two-dimensional unsteady flow. The flow was visualized using a suspension of seeding particles in water, and a laser sheet for illumination. With a finite time exposure, the particle motion was captured on a photograph as a pattern of streaks. The streak pattern was digitized and processsed using various imaging operations, including contrast manipulation, noise cleaning, filtering, statistical differencing, and thresholding. Information concerning the velocity was extracted from the enhanced image by measuring the length and orientation of the individual streaks. The fluid velocities deduced from the randomly distributed particle streaks were interpolated to obtain velocities at uniform grid points. For the interpolation a simple convolution technique with an adaptive Gaussian window was used. The results are compared with a numerical prediction by a Navier-Stokes commputation.

Cho, Y.-C.↗

NASA NTRS1977

Remote sensing applied to geological mapping; comparative geomorphology and identification of mineral zones of zinc and lead in the region of Vazante, MG

The author has identified the following significant results. Results showed that the black and white aerial photographs and the color infrared transparencies were efficient for mapping of three lithological units of the Paraopeba formation and for mineralized zones identification, respectively. Multispectral transparencies of I2S made it easier to separate dolomites, which were the rocks conditioning zinc and lead mineralization. Statistical analysis of morphometric indexes obtained from black and white photographs and topographic charts showed significant difference among three lithological units of Paraopeba formation which can be defined as Crest, Hilly, and Karstic reliefs.

Nascimento, F. S. D.↗

NASA NTRS1979

A secondary tracer approach to the derivation of galactic cosmic-ray source isotopic abundances

A formalism has been developed for deriving cosmic-ray source isotopic abundances from observed local abundances using a purely secondary nuclide as a tracer of spallation production during propagation. Although the formalism is based on the leaky-box model of cosmic-ray propagation, it is shown that source abundances derived by the tracer technique are reasonably independent of detailed propagation models. The tracer formalism also permits a quantitative evaluation of the effects of observational uncertainties on deduced source abundances. It is shown that statistical errors in the observed abundances and uncertainties in the spallation cross sections are at present the dominant sources of uncertainty. The latter error can be reduced with increased detector size or exposure time, while the former can be minimized by measurements of the relative production cross sections. As a specific example, the tracer technique is applied to the isotopes of sulfur and calcium, and the level of uncertainties which must be achieved to distinguish evolutionary differences between solar-system material and cosmic ray-source material are established.

Stone, E. C.↗

NASA NTRS1985

Fade margin calculation for channels impaired by Rician fading

Excess path loss due to multipath severely restricts the performance of power limited mobile networks such as those using satellite-aided links. To reduce multipath related losses, the higher elevation angle of the spacecraft can be exploited by utilizing mobile antennas which reduce the strength of the multipath reflections in favor of the line-of-sight signal. The presence of a strong and stable path in a fading link will change the envelope statistics of the received waveform from Rayleigh to a more favorable Rician distribution. It is determined that the excess path loss, or fade margin, of a Rician channel when coherent detection of binary phase shift keying (BPSK) or quaternary phase shift keying (QPSK) signals is considered. The results are presented parametrically such that they can be applied to a wide range of propagation characteristics from heavy fading to nonfading situations. Furthermore, similar results are also given for the case where only limited coverage is provided.

Davarian, F.↗

NASA NTRS1987

Phase error statistics of a phase-locked loop synchronized direct detection optical PPM communication system

Receiver timing synchronization of an optical Pulse-Position Modulation (PPM) communication system can be achieved using a phased-locked loop (PLL), provided the photodetector output is suitably processed. The magnitude of the PLL phase error is a good indicator of the timing error at the receiver decoder. The statistics of the phase error are investigated while varying several key system parameters such as PPM order, signal and background strengths, and PPL bandwidth. A practical optical communication system utilizing a laser diode transmitter and an avalanche photodiode in the receiver is described, and the sampled phase error data are presented. A linear regression analysis is applied to the data to obtain estimates of the relational constants involving the phase error variance and incident signal power.

Natarajan, Suresh↗

NASA NTRS1999

Reconstruction of the 1997/1998 El Nino from TOPEX/POSEIDON and TOGA/TAO Data Using a Massively Parallel Pacific-Ocean Model and Ensemble Kalman Filter

Two massively parallel data assimilation systems in which the model forecast-error covariances are estimated from the distribution of an ensemble of model integrations are applied to the assimilation of 97-98 TOPEX/POSEIDON altimetry and TOGA/TAO temperature data into a Pacific basin version the NASA Seasonal to Interannual Prediction Project (NSIPP)ls quasi-isopycnal ocean general circulation model. in the first system, ensemble of model runs forced by an ensemble of atmospheric model simulations is used to calculate asymptotic error statistics. The data assimilation then occurs in the reduced phase space spanned by the corresponding leading empirical orthogonal functions. The second system is an ensemble Kalman filter in which new error statistics are computed during each assimilation cycle from the time-dependent ensemble distribution. The data assimilation experiments are conducted on NSIPP's 512-processor CRAY T3E. The two data assimilation systems are validated by withholding part of the data and quantifying the extent to which the withheld information can be inferred from the assimilation of the remaining data. The pros and cons of each system are discussed.

Keppenne, C. L.↗

NASA NTRS1988

Linear Least Squares for Correlated Data

Throughout the literature authors have consistently discussed the suspicion that regression results were less than satisfactory when the independent variables were correlated. Camm, Gulledge, and Womer, and Womer and Marcotte provide excellent applied examples of these concerns. Many authors have obtained partial solutions for this problem as discussed by Womer and Marcotte and Wonnacott and Wonnacott, which result in generalized least squares algorithms to solve restrictive cases. This paper presents a simple but relatively general multivariate method for obtaining linear least squares coefficients which are free of the statistical distortion created by correlated independent variables.

Dean, Edwin B.↗

NASA NTRS2004

Neural network uncertainty assessment using Bayesian statistics: a remote sensing application

Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land. The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model. The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.

Neural Networks (Computer)↗

NASA NTRS1991

Statistical description of tectonic motions

The behavior of stochastic processes was studied whose power spectra are described by power-law behavior. The details of the analysis and the conclusions that were reached are presented. This analysis was extended to compare detection capabilities of different measurement techniques (e.g., gravimetry and GPS for the vertical, and seismometers and GPS for horizontal), both in general and for the specific case of the deformations produced by a dislocation in a half-space (which applies to seismic of preseismic sources). The time-domain behavior of power-law noises is also investigated.

Agnew, Duncan Carr↗

NASA NTRS1974

Combined bending-torsion fatigue reliability of AISI 4340 steel shafting with K sub t = 2.34

Results generated by three, unique fatigue reliability research machines which can apply reversed bending loads combined with steady torque are presented. Six-inch long, AISI 4340 steel, grooved specimens with a stress concentration factor of 2.34 and R sub C 35/40 hardness were subjected to various combinations of these loads and cycled to failure. The generated cycles-to-failure and stress-to-failure data are statistically analyzed to develop distributional S-N and Goodman diagrams. Various failure theories are investigated to determine which one represents the data best. The effect of the groove and of the various combined bending-torsion loads on the S-N and Goodman diagrams are determined. Three design applications are presented. The third one illustrates the weight savings that may be achieved by designing for reliability.

Kececioglu, D.↗

NASA NTRS2011

CUDA Simulation of Homogeneous, Incompressible Turbulence

We discuss very fast Compute Unified Device Architecture (CUDA) simulations of ideal homogeneous incompressible turbulence based on Fourier models. These models have associated statistical theories that predict that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. Prior numerical simulations have shown that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We review the theoretical basis of this "broken ergodicity" as applied to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence. Our new simulations examine the phenomenon of broken ergodicity through very long time and large grid size runs performed on a state-of-the-art CUDA platform. Results comparing various CUDA hardware configurations and grid sizes are discussed. NS and MHD results are compared.

Morin, Lee↗

NASA NTRS2022

Statistical Distribution of Gear Surface Fatigue Lives at High Reliability

The reliability of gears is important for a wide variety of applications, and the gearing community has a desire for better prediction of fatigue life at very high reliability. To improve predictions, a set of 950 NASA-conducted gear surface fatigue test results were gathered, pooled together using the general standardized Weibull variate, and then fit to a Weibull three-parameter distribution. An iterative fitting method was developed and then applied to the gear fatigue data to determine the values of the distribution parameters. Additional analyses were done using bearing and gear data that demonstrate a trend of increasing minimum life coefficient as correlated to the timeframe of the fatigue testing, and material cleanliness is proposed as a primary explanation for such correlation. It is noted that this observed trend supports published findings from analytical modeling and experimental studies that improvements to material cleanliness improves minimum fatigue life. Further use and study of the three-parameter Weibull distribution is recommended as a tool to quantify fatigue life most accurately in the high reliability regime.

gear↗