Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “bivariate”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Statistical study of the correlation of hard X-ray and type III radio bursts in solar flares

A large number of hard X-ray events which occurred during the maximum of solar cycle 21 have been analyzed in order to study their correlation with type III bursts. It is found that the distribution of occurrences of hard X-ray bursts correlated with type III radio bursts is significantly different from the distribution of all hard X-ray bursts. This result is consistent with the assumption that the hard X-ray and type III intensities are somewhat correlated. A bivariate distribution function of the burst intensities is fitted to the data and is used to determine that the typical ratio of X-ray intensity to type II intensity is about 10 and that the ratio of the number of X-ray producing-electrons to type III-producing electrons is about 1000. Three models which have been proposed to explain the relation between the accelerated hard X-ray and type III-producing electrons are examined in the context of these observations.

Hamilton, Russell J.↗
NASA NTRS1990

Linear regression in astronomy. I

Five methods for obtaining linear regression fits to bivariate data with unknown or insignificant measurement errors are discussed: ordinary least-squares (OLS) regression of Y on X, OLS regression of X on Y, the bisector of the two OLS lines, orthogonal regression, and 'reduced major-axis' regression. These methods have been used by various researchers in observational astronomy, most importantly in cosmic distance scale applications. Formulas for calculating the slope and intercept coefficients and their uncertainties are given for all the methods, including a new general form of the OLS variance estimates. The accuracy of the formulas was confirmed using numerical simulations. The applicability of the procedures is discussed with respect to their mathematical properties, the nature of the astronomical data under consideration, and the scientific purpose of the regression. It is found that, for problems needing symmetrical treatment of the variables, the OLS bisector performs significantly better than orthogonal or reduced major-axis regression.

Isobe, Takashi↗
NASA NTRS1991

Attenuation statistics at 20.6, 31.65 and 52.85 GHz derived from emission measurements by ground-based microwave radiometers

Two seasons (December 1987 to February 1988 and July 1988 to September 1988) of thermal emission measurements, taken by a multichannel ground-based microwave radiometer, are used to derive single-station zenith attenuation statistics at 20.6 and 31.65 GHz. For the summer period, statistics are also derived at 52.85 GHz. In addition, data from two radiometers located 50 km apart are used to derive two-station attenuation diversity statistics at 20.6 and 31.65 GHz. The multichannel radiometer was operated at Denver, Colorado, U.S. and the dual-channel device was operated at Platteville, Colorado. The diversity statistics are presented by cumulative distributions and by bivariate frequency distributions. The frequency distributions are analyzed when either one or both stations have liquid clouds.

Fionda, E.↗
NASA NTRS1992

Systematic differences between the field and cluster elliptical galaxies

Multivariate statistical techniques and fundamental plane fits are used here to study possible systematic differences between field ellipticals (FEs) and cluster ellipticals (CEs). The FEs show more intrinsic scatter in their properties, especially when stellar population variables are included. Pairwise correlations for the two samples are different; the correlations are systematically better for the cluster sample, meaning that ellipticals in the two samples populate their fundamental planes in different ways. Bivariate correlations are different for the two samples, implying that they have different fundamental planes. This is especially true for the correlations which include the population variables Mg2 and (B-V), which are sensitive both to the enrichment history and the storm formation history.

De Carvalho, R. R.↗
NASA NTRS1993

Interpretation of gamma-ray burst source count statistics

Ever since the discovery of gamma-ray bursts, the so-called log N-log S relation has been used for determination of their distances and distribution. This task has not been straightforward because of varying thresholds for the detection of bursts. Most of the current analyses of these data are couched in terms of ambiguous distributions, such as the distribution of Cp/Clim, the ratio of peak to threshold photon count rates, or the distribution of V/Vmax = (Cp/Clim) exp -3/2. It is shown that these distributions are not always a true reflection of the log N-log S relation. Some kind of deconvolution is required for obtaining the true log N-log S. Therefore, care is required in the interpretation of results of such analyses. A new method of analysis of these data is described, whereby the bivariate distribution of Cp and Clim is obtained directly from the data.

Petrosian, Vahe↗
NASA NTRS1994

Image quality measures and their performance

A number of quality measures are evaluated for gray scale image compression. They are all bivariate exploiting the differences between corresponding pixels in the original and degraded images. It is shown that although some numerical measures correlate well with the observers' response for a given compression technique, they are not reliable for an evaluation across different techniques. The two graphical measures (histograms and Hosaka plots), however, can be used to appropriately specify not only the amount, but also the type of degradation in reconstructed images.

Eskicioglu, Ahmet M.↗
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 NTRS1995

The fundamental plane correlations for globular clusters

In the parameter space whose axes include a radius (core, or half-light), a surface brightness (central, or average within the half-light radius), and the central projected velocity dispersion, globular clusters lie on a two-dimensional surface (a plane, if the logarithmic quantities are used). This is analogous to the 'fundamental plane' of elliptical galaxies. The implied bivariate correlations are the best now known for globular clusters. The derived scaling laws for the core properties imply that cluster cores are fully virialized, homologous systems, with a constant (M/L) ratio. The corresponding scaling laws on the half-light scale are differrent, but are nearly identical to those derived from the 'fundamental plane' of ellipticals. This may be due to the range of cluster concentrations, which are correlated with other parameters. A similar explanation for elliptical galaxies may be viable. These correlations provide new empirical constraints for models of globular cluster formation and evolution, and may also be usable as rough distance-indicator relations for globular clusters.

Djorgovski, S.↗
NASA NTRS1995

A multiparametric analysis of the Einstein sample of early-type galaxies. 1: Luminosity and ISM parameters

We have conducted bivariate and multivariate statistical analysis of data measuring the luminosity and interstellar medium of the Einstein sample of early-type galaxies (presented by Fabbiano, Kim, & Trinchieri 1992). We find a strong nonlinear correlation between L(sub B) and L(sub X), with a power-law slope of 1.8 +/- 0.1, steepening to 2.0 +/- if we do not consider the Local Group dwarf galaxies M32 and NGC 205. Considering only galaxies with log L(sub X) less than or equal to 40.5, we instead find a slope of 1.0 +/- 0.2 (with or without the Local Group dwarfs). Although E and S0 galaxies have consistent slopes for their L(sub B)-L(sub X) relationships, the mean values of the distribution functions of both L(sub X) and L(sub X)/L(sub B) for the S0 galaxies are lower than those for the E galaxies at the 2.8 sigma and 3.5 sigma levels, respectively. We find clear evidence for a correlation between L(sub X) and the X-ray color C(sub 21), defined by Kim, Fabbiano, & Trinchieri (1992b), which indicates that X-ray luminosity is correlated with the spectral shape below 1 keV in the sense that low-L(sub X) systems have relatively large contributions from a soft component compared with high-L(sub X) systems. We find evidence from our analysis of the 12 micron IRAS data for our sample that our S0 sample has excess 12 micron emission compared with the E sample, scaled by their optical luminosities. This may be due to emission from dust heated in star-forming regions in S0 disks. This interpretation is reinforced by the existence of a strong L(sub 12)-L(sub 100) correlation for our S0 sample that is not found for the E galaxies, and by an analysis of optical-IR colors. We find steep slopes for power-law relationships between radio luminosity and optical, X-ray, and far-IR (FIR) properties. This last point argues that the presence of an FIR-emitting interstellar medium (ISM) in early-type galaxies is coupled to their ability to generate nonthermal radio continuum, as previously argued by, e.g., Walsh et al. (1989). We also find that, for a given L(sub 100), galaxies with larger L(sub X)/L(sub B) tend to be stronger nonthermal radio sources, as originally suggested by Kim & Fabbiano (1990). We note that, while L(sub B) is most strongly correlated with L(sub 6), the total radio luminosity, both L(sub X) and L(sub X)/L(sub B) are more strongly correlated with L(sub 6 CO), the core radio luminosity. These points support the argument (proposed by Fabbiano, Gioia, & Trinchieri 1989) that radio cores in early-type galaxies are fueled by the hot ISM.

Eskridge, Paul B.↗
NASA NTRS1994

Pressure loss modulus correlation for Delta p across uniformly distributed-loss devices

A dimensionless group, called a pressure loss modulus (N(sub PL)), is introduced that, in conjunction with an appropriately defined Reynolds number, is of considerable engineering utility in correlating steady-state Delta p vs flow calibration data and subsequently as a predictor, using the same or a different fluid, in uniformly distributed pressure loss devices. It is particularly useful under operation in the transition regime. Applications of this simple bivariate correlation to three diverse devices of particular interest for small liquid rocket engine fluid systems are discussed: large L/D capillary tube restrictors, packed granular catalyst beds, and stacked vortex-loss disk restrictors.

Nunz, Gregory J.↗
NASA NTRS1996

Prelude to Cycle 23: The Case for a Fast-Rising, Large Amplitude Cycle

For the common data-available interval of cycles 12 to 22, we show that annual averages of sunspot number for minimum years (R(min)) and maximum years (R(max)) and of the minimum value of the aa geomagnetic index in the vicinity of sunspot minimum (aa(min)) are consistent with the notion that each has embedded within its respective record a long-term, linear, secular increase. Extrapolating each of these fits to cycle 23, we infer that it will have R(min) = 12.7 +/- 5.7, R(max) = 176.7 +/- 61.8, and aa(min) = 21.0 +/- 5.0 (at the 95-percent level of confidence), suggesting that cycle 23 will have R(min) greater than 7.0, R(max) greater than 114.9, and aa(min) greater than 16.0 (at the 97.5-percent level of confidence). Such values imply that cycle 23 will be larger than average in size and, consequently (by the Waidmeier effect), will be a fast riser. We also infer from the R(max) and aa(min) records the existence of an even- odd cycle effect, one in which the odd-following cycle is numerically larger in value than the even-leading cycle. For cycle 23, the even-odd cycle effect suggests that R(max) greater than 157.6 and aa(min) greater than 19.0, values that were recorded for cycle 22, the even-leading cycle of the current even-odd cycle pair (cycles 22 and 23). For 1995, the annual average of the aa index measured about 22, while for sunspot number, it was about 18. Because aa(min) usually lags R(min) by 1 year (true for 8 of 11 cycles) and 1996 seems destined to be the year of R(min) for cycle 23, it may be that aa(min) will occur in 1997, although it could occur in 1996 in conjunction with R(min) (true for 3 of 11 cycles). Because of this ambiguity in determining aa(min), no formal prediction based on the correlation of R(max) against aa(min), having r = 0.90, or of R(max) against the combined effects of R(min) and aa(min)-the bivariate technique-having r = 0.99, is possible until 1997, at the earliest.

Wilson, Robert M.↗
NASA NTRS1998

A Compendium of Wind Statistics and Models for the NASA Space Shuttle and Other Aerospace Vehicle Programs

The wind profile with all of its variations with respect to altitude has been, is now, and will continue to be important for aerospace vehicle design and operations. Wind profile databases and models are used for the vehicle ascent flight design for structural wind loading, flight control systems, performance analysis, and launch operations. This report presents the evolution of wind statistics and wind models from the empirical scalar wind profile model established for the Saturn Program through the development of the vector wind profile model used for the Space Shuttle design to the variations of this wind modeling concept for the X-33 program. Because wind is a vector quantity, the vector wind models use the rigorous mathematical probability properties of the multivariate normal probability distribution. When the vehicle ascent steering commands (ascent guidance) are wind biased to the wind profile measured on the day-of-launch, ascent structural wind loads are reduced and launch probability is increased. This wind load alleviation technique is recommended in the initial phase of vehicle development. The vehicle must fly through the largest load allowable versus altitude to achieve its mission. The Gumbel extreme value probability distribution is used to obtain the probability of exceeding (or not exceeding) the load allowable. The time conditional probability function is derived from the Gumbel bivariate extreme value distribution. This time conditional function is used for calculation of wind loads persistence increments using 3.5-hour Jimsphere wind pairs. These increments are used to protect the commit-to-launch decision. Other topics presented include the Shuttle Shuttle load-response to smoothed wind profiles, a new gust model, and advancements in wind profile measuring systems. From the lessons learned and knowledge gained from past vehicle programs, the development of future launch vehicles can be accelerated. However, new vehicle programs by their very nature will require specialized support for new databases and analyses for wind, atmospheric parameters (pressure, temperature, and density versus altitude), and weather. It is for this reason that project managers are encouraged to collaborate with natural environment specialists early in the conceptual design phase. Such action will give the lead time necessary to meet the natural environment design and operational requirements, and thus, reduce development costs.

Smith, O. E.↗
NASA NTRS1997

Areal Distribution of the Oxygen-Isotope Ratio in Greenland

Mean values of the oxygen-isotope ratio relative to standard mean ocean water reported for 46 sites on the Greenland ice sheet are compiled together with data on mean annual surface temperature, latitude, 6180 elevation, and mean annual shortest distance to the open ocean denoted by the 10% sea-ice concentration boundary. Stepwise regression analyses, with 6180 as the dependent variable, define two robust models. In the forward mode at the 99.9% confidence level, only temperature enters the model. In the backward mode at the 95% confidence level, only temperature, latitude, and distance to the open ocean remain in the model. Inversions of the models on the basis of 160 gridpoint locations 100 km apart in the area delimited by the surface equilibrium line produce four contoured distributions of 6"0. Two distributions are based on the bivariate model and two on the multivariate model. The second distribution for each model is obtained substituting mean annual surface-temperature values obtained from the Nimbus-7 Temperature Humidity Infrared Radiometer (THIR) database. All four distributions are considered valid, and differences between them are evaluated using contoured anomaly maps. It is suggested that the inversion of the multivariate model using THIR data provides the more reliable pattern for studies of atmospheric advection or for the derivation of ice-flow adjustments for 6180 series obtained from deep-core or ablation-zone sites.

Zwally, H. Jay↗
NASA NTRS2002

Application of Modern Design of Experiments to CARS Thermometry in a Model Scramjet Engine

We have applied formal experiment design and analysis to optimize the measurement of temperature in a supersonic combustor at NASA Langley Research Center. We used the coherent anti-Stokes Raman spectroscopy (CARS) technique to map the temperature distribution in the flowfield downstream of an 1160 K, Mach 2 freestream into which supersonic hydrogen fuel is injected at an angle of 30 degrees. CARS thermometry is inherently a single-point measurement technique; it was used to map thc flow by translating the measurement volume through the flowfield. The method known as "Modern Design of Experiments" (MDOE) was used to estimate the data volume required, design the test matrix, perform the experiment and analyze the resulting data. MDOE allowed us to match the volume of data acquired to the precision requirements of the customer. Furthermore, one aspect of MDOE, known as response surface methodology, allowed us to develop precise maps of the flowfield temperature, allowing interpolation between measurement points. An analytic function in two spatial variables was fit to the data from a single measurement plane. Fitting with a Cosine Series Bivariate Function allowed the mean temperature to be mapped with 95% confidence interval half-widths of +/- 30 Kelvin, comfortably meeting the confidence of +/- 50 Kelvin specified prior to performing the experiments. We estimate that applying MDOE to the present experiment saved a factor of 5 in data volume acquired, compared to experiments executed in the traditional manner. Furthermore, the precision requirements could have been met with less than half the data acquired.

Danehy, P. M.↗
NASA NTRS2004

Aerodynamic Shape Optimization Based on Free-form Deformation

This paper presents a free-form deformation technique suitable for aerodynamic shape optimization. Because the proposed technique is independent of grid topology, we can treat structured and unstructured computational fluid dynamics grids in the same manner. The proposed technique is an alternative shape parameterization technique to a trivariate volume technique. It retains the flexibility and freedom of trivariate volumes for CFD shape optimization, but it uses a bivariate surface representation. This reduces the number of design variables by an order of magnitude, and it provides much better control for surface shape changes. The proposed technique is simple, compact, and efficient. The analytical sensitivity derivatives are independent of the design variables and are easily computed for use in a gradient-based optimization. The paper includes the complete formulation and aerodynamics shape optimization results.

Samareh, Jamshid A.↗
NASA NTRS2001

Extending unbiased stereology of brain ultrastructure to three-dimensional volumes

OBJECTIVE: Analysis of brain ultrastructure is needed to reveal how neurons communicate with one another via synapses and how disease processes alter this communication. In the past, such analyses have usually been based on single or paired sections obtained by electron microscopy. Reconstruction from multiple serial sections provides a much needed, richer representation of the three-dimensional organization of the brain. This paper introduces a new reconstruction system and new methods for analyzing in three dimensions the location and ultrastructure of neuronal components, such as synapses, which are distributed non-randomly throughout the brain. DESIGN AND MEASUREMENTS: Volumes are reconstructed by defining transformations that align the entire area of adjacent sections. Whole-field alignment requires rotation, translation, skew, scaling, and second-order nonlinear deformations. Such transformations are implemented by a linear combination of bivariate polynomials. Computer software for generating transformations based on user input is described. Stereological techniques for assessing structural distributions in reconstructed volumes are the unbiased bricking, disector, unbiased ratio, and per-length counting techniques. A new general method, the fractional counter, is also described. This unbiased technique relies on the counting of fractions of objects contained in a test volume. A volume of brain tissue from stratum radiatum of hippocampal area CA1 is reconstructed and analyzed for synaptic density to demonstrate and compare the techniques. RESULTS AND CONCLUSIONS: Reconstruction makes practicable volume-oriented analysis of ultrastructure using such techniques as the unbiased bricking and fractional counter methods. These analysis methods are less sensitive to the section-to-section variations in counts and section thickness, factors that contribute to the inaccuracy of other stereological methods. In addition, volume reconstruction facilitates visualization and modeling of structures and analysis of three-dimensional relationships such as synaptic connectivity.

NASA Discipline Neuroscience↗
NASA NTRS1998

Effect of altered sensory conditions on multivariate descriptors of human postural sway

Multivariate descriptors of sway were used to test whether altered sensory conditions result not only in changes in amount of sway but also in postural coordination. Eigenvalues and directions of eigenvectors of the covariance of shnk and hip angles were used as a set of multivariate descriptors. These quantities were measured in 14 healthy adult subjects performing the Sensory Organization test, which disrupts visual and somatosensory information used for spatial orientation. Multivariate analysis of variance and discriminant analysis showed that resulting sway changes were at least bivariate in character, with visual and somatosensory conditions producing distinct changes in postural coordination. The most significant changes were found when somatosensory information was disrupted by sway-referencing of the support surface (P = 3.2 x 10(-10)). The resulting covariance measurements showed that subjects not only swayed more but also used increased hip motion analogous to the hip strategy. Disruption of vision, by either closing the eyes or sway-referencing the visual surround, also resulted in altered sway (P = 1.7 x 10(-10)), with proportionately more motion of the center of mass than with platform sway-referencing. As shown by discriminant analysis, an optimal univariate measure could explain at most 90% of the behavior due to altered sensory conditions. The remaining 10%, while smaller, are highly significant changes in posture control that depend on sensory conditions. The results imply that normal postural coordination of the trunk and legs requires both somatosensory and visual information and that each sensory modality makes a unique contribution to posture control. Descending postural commands are multivariate in nature, and the motion at each joint is affected uniquely by input from multiple sensors.

NASA Discipline Neuroscience↗
NASA NTRS2005

Probabilistic Fracture Mechanics Analysis of the Orbiter's LH2 Feedline Flowliner

Work performed by Southwest Research Institute (SwRI) as part of an Independent Technical Assessment (ITA) for the NASA Engineering and Safety Center (NESC) is summarized. The ITA goal was to establish a flight rationale in light of a history of fatigue cracking due to flow induced vibrations in the feedline flowliners that supply liquid hydrogen to the space shuttle main engines. Prior deterministic analyses using worst-case assumptions predicted failure in a single flight. The current work formulated statistical models for dynamic loading and cryogenic fatigue crack growth properties, instead of using worst-case assumptions. Weight function solutions for bivariant stressing were developed to determine accurate crack "driving-forces". Monte Carlo simulations showed that low flowliner probabilities of failure (POF = 0.001 to 0.0001) are achievable, provided pre-flight inspections for cracks are performed with adequate probability of detection (POD)-specifically, 20/75 mils with 50%/99% POD. Measurements to confirm assumed POD curves are recommended. Since the computed POFs are very sensitive to the cyclic loads/stresses and the analysis of strain gage data revealed inconsistencies with the previous assumption of a single dominant vibrant mode, further work to reconcile this difference is recommended. It is possible that the unaccounted vibrational modes in the flight spectra could increase the computed POFs.

Bonacuse, Peter J.↗