Search NASA⌕ Search

SEARCH · Search NASA

Results for “standard normal variate”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Rolling Bearing Life Prediction-Past, Present, and Future

Comparisons were made between the life prediction formulas of Lundberg and Palmgren, Ioannides and Harris, and Zaretsky and full-scale ball and roller bearing life data. The effect of Weibull slope on bearing life prediction was determined. Life factors are proposed to adjust the respective life formulas to the normalized statistical life distribution of each bearing type. The Lundberg-Palmgren method resulted in the most conservative life predictions compared to Ioannides and Harris, and Zaretsky methods which produced statistically similar results. Roller profile can have significant effects on bearing life prediction results. Roller edge loading can reduce life by as much as 98 percent. The resultant predicted life not only depends on the life equation used but on the Weibull slope assumed, the least variation occurring with the Zaretsky equation. The load-life exponent p of 10/3 used in the American National Standards Institute (ANSI)/American Bearing Manufacturers Association (ABMA)/International Organization for Standardization (ISO) standards is inconsistent with the majority roller bearings designed and used today.

Zaretsky, E V↗
NASA NTRS2009

A Comparison Study of Normal-Incidence Acoustic Impedance Measurements of a Perforate Liner

The eduction of the acoustic impedance for liner configurations is fundamental to the reduction of noise from modern jet engines. Ultimately, this property must be measured accurately for use in analytical and numerical propagation models of aircraft engine noise. Thus any standardized measurement techniques must be validated by providing reliable and consistent results for different facilities and sample sizes. This paper compares normal-incidence acoustic impedance measurements using the two-microphone method of ten nominally identical individual liner samples from two facilities, namely 50.8 mm and 25.4 mm square waveguides at NASA Langley Research Center and the University of Florida, respectively. The liner chosen for this investigation is a simple single-degree-of-freedom perforate liner with resonance and anti-resonance frequencies near 1.1 kHz and 2.2 kHz, respectively. The results show that the ten measurements have the most variation around the anti-resonance frequency, where statistically significant differences exist between the averaged results from the two facilities. However, the sample-to-sample variation is comparable in magnitude to the predicted cross-sectional area-dependent cavity dissipation differences between facilities, providing evidence that the size of the present samples does not significantly influence the results away from anti-resonance.

Schultz, Todd↗
NASA NTRS1993

Mixing noise reduction for rectangular supersonic jets by nozzle shaping and induced screech mixing

Two methods of mixing noise modification were studied for supersonic jets flowing from rectangular nozzles with an aspect ratio of about five and a small dimension of about 1.4 cm. The first involves nozzle geometry variation using either single (unsymmetrical) or double bevelled (symmetrical) thirty degree cutbacks of the nozzle exit. Both converging (C) and converging-diverging (C-D) versions were tested. The double bevelled C-D nozzle produced a jet mixing noise reduction of about 4 dB compared to a standard rectangular C-D nozzle. In addition all bevelled nozzles produced an upstream shift in peak mixing noise which is conducive to improved attenuation when the nozzle is used in an acoustically treated duct. A large increase in high frequency noise also occurred near the plane of the nozzle exit. Because of near normal incidence, this noise can be easily attenuated with wall treatment. The second approach uses paddles inserted on the edge of the two sides of the jet to induce screech and greatly enhance the jet mixing. Although screech and mixing noise levels are increased, the enhanced mixing moves the source locations upstream and may make an enclosed system more amenable to noise reduction using wall acoustic treatment.

Rice, Edward J.↗
NASA NTRS1993

Analysis of communication in the standard versus automated aircraft

Past research has shown crew communication patterns to be associated with overall crew performance, recent flight experience together, low-and high-error crew performance and personality variables. However, differences in communication patterns as a function of aircraft type and level of aircraft automation have not been fully addressed. Crew communications from ten MD-88 and twelve DC-9 crews were obtained during a full-mission simulation. In addition to large differences in overall amount of communication during the normal and abnormal phases of flight (DC-9 crews generating less speech than MD-88 crews), differences in specific speech categories were also found. Log-linear analyses also generated speaker-response patterns related to each aircraft type, although in future analyses these patterns will need to account for variations due to crew performance.

Veinott, Elizabeth S.↗
NASA NTRS1999

The ISO View of Star Forming Galaxies

ISO studies of normal galaxies in the local Universe have revealed basic new properties whose significant implications for the star formation process and cosmology are only starting to be understood. This review will touch on the general results of a statistical nature, and provide a quick summary of the profusion of exciting results on individual objects. In the mid-infrared, PHT-S has established that the spectra of star forming galaxies between 6 and-13microns are dominated by the Aromatic Features in Emission (AFE), and show little variation as a function of the heating intensity. The Carriers of the AFE (CAFE) are thus a universal component of dust with standard properties, and contribute between 10 and 25% of the total dust luminosity. In addition to AFE, the spectra show a low-level continuum detectable at wavelengths longer than 3.5microns whose origin is still under investigation. The mid-infrared colors formed as the ratio of flux densities in the 6.75micron and the 15micron bands of ISO-CAM remain essentially constant and near unity for quiescent and mildly active galaxies. As dust heating increases further, the 15micron flux increases steeply compared to 6.75microns, indicating that dust heated to 100K<T<200K becomes a significant component. Such hot dust is presumably located within or just outside HII regions. At the other end of the spectrum, photometry at 120-200microns using ISO-PHOT is starting to constrain the distribution of dust temperatures at the low end of the temperature scale. From LWS data, the far-infrared fine-structure lines of [CII] and [OI], which provide most of the cooling for warm atomic gas, show variations that have remained controversial in their interpretation. In particular, as the galaxy become more active in star formation, its [CII] flux weakens relative to total dust emission while the [OI] does not. This behavior has attracted much interest because it extrapolates to the most active galaxies, making them weaker in [CII] than previously expected. Several explanations for the effect have been advanced, and will be discussed in this review. Spectroscopy with SWS has measured molecular hydrogen in galaxies, providing a powerful handle on the warm molecular gas content. SWS and CAM-CVF studies targeting ionic fine-structure lines have demonstrated their value as diagnostics of the radiation field.

Helou, George↗
NASA NTRS2003

A statistical model of diurnal variation in human growth hormone

The diurnal pattern of growth hormone (GH) serum levels depends on the frequency and amplitude of GH secretory events, the kinetics of GH infusion into and clearance from the circulation, and the feedback of GH on its secretion. We present a two-dimensional linear differential equation model based on these physiological principles to describe GH diurnal patterns. The model characterizes the onset times of the secretory events, the secretory event amplitudes, as well as the infusion, clearance, and feedback half-lives of GH. We illustrate the model by using maximum likelihood methods to fit it to GH measurements collected in 12 normal, healthy women during 8 h of scheduled sleep and a 16-h circadian constant-routine protocol. We assess the importance of the model components by using parameter standard error estimates and Akaike's Information Criterion. During sleep, both the median infusion and clearance half-life estimates were 13.8 min, and the median number of secretory events was 2. During the constant routine, the median infusion half-life estimate was 12.6 min, the median clearance half-life estimate was 11.7 min, and the median number of secretory events was 5. The infusion and clearance half-life estimates and the number of secretory events are consistent with current published reports. Our model gave an excellent fit to each GH data series. Our analysis paradigm suggests an approach to decomposing GH diurnal patterns that can be used to characterize the physiological properties of this hormone under normal and pathological conditions.

Non-NASA Center↗
NASA NTRS2019

Turbulent Axial Odometer Model

A Galilean-invariant field equation is proposed and tested on standard turbulence model test cases. The field equation provides an additional non-dimensional outer scale which allows the turbulence models to reproduce the axial normal stress increase with Re seen in high Reynolds numbers experiments. The field equation provides a Reynolds number for every point based on the length of turbulent flow upstream of that point in the domain. This outer scale equation can be considered an odometer that gives a length scale conjectured to be related to the large streamwise structures that are seen in turbulent flow and that require run length to develop. A new RANS model using this additional scale is able to match the Reynolds number variation of the normal stresses seen at high Reynolds number. Furthermore, the good attached flow prediction capabilities of current RANS models appears to be attained. Using this scale equation, the entire Reynolds-stress state appears to be predicted correctly, over a large run length Reynolds number range such as experienced in aircraft design.

Olsen, Michael E.↗
NASA NTRS2019

Turbulent Axial Odometer Model

A Galilean-invariant field equation is proposed and tested on standard turbulence model test cases. The field equation provides an additional non-dimensional outer scale which allows the turbulence models to reproduce the axial normal stress increase with Re seen in high Reynolds numbers experiments. The field equation provides a Reynolds number for every point based on the length of turbulent flow upstream of that point in the domain. This outer scale equation can be considered an odometer that gives a length scale conjectured to be related to the large stream wise structures that are seen in turbulent flow and that require run length to develop. A new RANS model using this additional scale is able to match the Reynolds number variation of the normal stresses seen at high Reynolds number. Furthermore, the good attached flow prediction capabilities of current RANS models appears to be attained. Using this scale equation, the entire Reynolds-stress state appears to be predicted correctly, over a large run length Reynolds number range such as experienced in aircraft design.

Olsen, Michael E.↗
NASA NTRS1973

On the normality and accuracy of simulated random processes.

Efficient methods of simulating stationary and nonstationary random processes and envelopes, by using a series of sine or cosine functions or by using the fast Fourier transform, have been proposed previously. Without applying the central limit theorem, it is shown in this paper that the simulated random processes are asymptotically Gaussian processes as the number of terms, N, of sine or cosine functions approaches infinity. The accuracy of the first-order probability densities of the simulated random processes is investigated by using the fast Fourier transform. Numerical results are computed with respect to the variation of the number of terms, N, of sine or cosine functions used for simulation. It is shown that within the practical range of N, such as 500, the accuracy is remarkably satisfactory even outside the region of 3 standard deviations.

Yang, J.-N.↗
NASA NTRS2019

Quantifying the Storm Time Thermospheric Neutral Density Variations Using Model and Observations

Accurate determination of thermospheric neutral density holds crucial importance for satellited rag calculations. The problem is twofold and involves the correct estimation of the quiet time climatology and storm time variations. In this work, neutral density estimations from two empirical and threephysics based models of the ionosphere thermosphere are compared with the neutral densities along the Challenging MicroSatellite Payload satellite track for six geomagnetic storms. Storm time variations are extracted from neutral density by (1) subtracting the mean difference between model and observation (bias),(2) setting climatological variations to zero, and (3) multiplying model data with the quiet time ratio between the model and observation. Several metrics are employed to evaluate the model performances. We find that the removal of bias or climatology reveals actual performance of the model in simulating the storm time variations. When bias is removed, depending on event and model, storm time errors in neutral density can decrease by an amount of 113% or can increase by an amount of 12% with respect to error in models with quiet time bias. It is shown that using only average and maximum values of neutral density to determine the model performances can be misleading since a model can estimate the averages fairly well but may not capture the maximum value or vice versa. Since each of the metrics used for determining model performances provides different aspects of the error, among these, we suggest employing mean absolute error, prediction efficiency, and normalized root mean square error together as a standard set ofmetrics for the neutral density.

Eyiguler, E. Ceren Kalafatoglu↗
DOE OSTI2024

Forest carbon sequestration on the west coast, USA: Role of species, productivity, and stockability

Forest ecosystems store large amounts of carbon and can be important sources, or sinks, of the atmospheric carbon dioxide that is contributing to global warming. Understanding the carbon storage potential of different forests and their response to management and disturbance events are fundamental to developing policies and scenarios to partially offset greenhouse gas emissions. Projections of live tree carbon accumulation are handled differently in different models, with inconsistent results. We developed growth-and-yield style models to predict stand-level live tree carbon density as a function of stand age in all vegetation types of the coastal Pacific region, US (California, Oregon, and Washington), from 7,523 national forest inventory plots. We incorporated site productivity and stockability within the Chapman-Richards equation and tested whether intensively managed private forests behaved differently from less managed public forests. We found that the best models incorporated stockability in the equation term controlling stand carrying capacity, and site productivity in the equation terms controlling the growth rate and shape of the curve. RMSEs ranged from 10 to 137 Mg C/ha for different vegetation types. There was not a significant effect of ownership over the standard industrial rotation length (~50 yrs) for the productive Douglas-fir/western hemlock zone, indicating that differences in stockability and productivity captured much of the variation attributed to management intensity. Our models suggest that doubling the rotation length on these intensively managed lands from 35 to 70 years would result in 2.35 times more live tree carbon stored on the landscape. These findings are at odds with some studies that have projected higher carbon densities with stand age for the same vegetation types, and have not found an increase in yields (on an annual basis) with longer rotations. We suspect that differences are primarily due to the application of yield curves developed from fully-stocked, undisturbed, single-species, “normal” stands without accounting for the substantial proportion of forests that don’t meet those assumptions. The carbon accumulation curves developed here can be applied directly in growth-and-yield style projection models, and used to validate the predictions of ecophysiological, cohort, or single-tree style models being used to project carbon futures for forests in the region. Our approach may prove useful for developing robust models in other forest types.

Chisholm, Paul J. (ORCID:0000000238784707)↗
NASA NTRS2010

Global Patterns of Lightning Properties Derived by LIS

The Lightning Imaging Sensor LIS aboard the TRMM satellite provides unmatched empirical data of the global lightning distribution (up to approx.35deg S/N) since end of 1997. Climatological flash rate densities derived from LIS are standard references, e.g. for flash rate parameterizations used in GCMs. It is known that flash characteristics are quite variable, and that various quantities (like the flash energy or the NOx production per flash) vary considerably, statistically as well as systematically on regional and seasonal scales. LIS provides information beyond flash counts, in particular radiance and flash footprint. Here we present an analysis of global patterns of various lightning properties derived from LIS, in relation to the number of flashes. These normalized flash characteristics show consistent spatial patterns of regions with "strong" versus regions with "weak" lightning. Most striking is a clear land-ocean contrast, with oceanic flashes being "stronger" than continental flashes. But also over continents, flash strength shows systematic variations. Highest continental values are found over the US, while values over South America and India are quite low. These regional variations cannot be simply parameterized as function of latitude. Information on spatial patterns of mean flash "strength", though rather qualitative up to now, is potentially a valuable input for improving empirical parameterizations based on flash counts (like precipitation or lightning NOx). Further investigation is in progress to come to a more physical and quantitative understanding of the spatial patterns of the different LIS properties. In particular, it has to be checked how far they could be related to established lightning properties (like energy or the fraction of intra-cloud to cloud-to-ground flashes) or to meteorological quantities (like CAPE).

Beirle, S.↗
NASA NTRS2010

Development of an Uncertainty Model for the National Transonic Facility

This paper introduces an uncertainty model being developed for the National Transonic Facility (NTF). The model uses a Monte Carlo technique to propagate standard uncertainties of measured values through the NTF data reduction equations to calculate the combined uncertainties of the key aerodynamic force and moment coefficients and freestream properties. The uncertainty propagation approach to assessing data variability is compared with ongoing data quality assessment activities at the NTF, notably check standard testing using statistical process control (SPC) techniques. It is shown that the two approaches are complementary and both are necessary tools for data quality assessment and improvement activities. The SPC approach is the final arbiter of variability in a facility. Its result encompasses variation due to people, processes, test equipment, and test article. The uncertainty propagation approach is limited mainly to the data reduction process. However, it is useful because it helps to assess the causes of variability seen in the data and consequently provides a basis for improvement. For example, it is shown that Mach number random uncertainty is dominated by static pressure variation over most of the dynamic pressure range tested. However, the random uncertainty in the drag coefficient is generally dominated by axial and normal force uncertainty with much less contribution from freestream conditions.

Walter, Joel A.↗
NASA NTRS1997

Experimental Investigation of Unsteady Shock Wave Turbulent Boundary Layer Interactions About a Blunt Fin

A series of experiments were performed to investigate the effects of Mach number variation on the characteristics of the unsteady shock wave/turbulent boundary layer interaction generated by a blunt fin. A single blunt fin hemicylindrical leading edge diameter size was used in all of the experiments which covered the Mach number range from 2.0 to 5.0. The measurements in this investigation included surface flow visualization, static and dynamic pressure measurements, both on centerline and off-centerline of the blunt fin axis. Surface flow visualization and static pressure measurements showed that the spatial extent of the shock wave/turbulent boundary layer interaction increased with increasing Mach number. The maximum static pressure, normalized by the incoming static pressure, measured at the peak location in the separated flow region ahead of the blunt fin was found to increase with increasing Mach number. The mean and standard deviations of the fluctuating pressure signals from the dynamic pressure transducers were found to collapse to self-similar distributions as a function of the distance perpendicular to the separation line. The standard deviation of the pressure signals showed initial peaked distribution, with the maximum standard deviation point corresponding to the location of the separation line at Mach number 3.0 to 5.0. At Mach 2.0 the maximum standard deviation point was found to occur significantly upstream of the separation line. The intermittency distributions of the separation shock wave motion were found to be self-similar profiles for all Mach numbers. The intermittent region length was found to increase with Mach number and decrease with interaction sweepback angle. For Mach numbers 3.0 to 5.0 the separation line was found to correspond to high intermittencies or equivalently to the downstream locus of the separation shock wave motion. The Mach 2.0 tests, however, showed that the intermittent region occurs significantly upstream of the separation line. Power spectral densities measured in the intermittent regions were found to have self-similar frequency distributions when compared as functions of a Strouhal number for all Mach numbers and interaction sweepback angles. The maximum zero-crossing frequencies were found to correspond with the peak frequencies in the power spectra measured in the intermittent region.

Barnhart, Paul J.↗
DOE OSTI2025

Thermal oxidation of nuclear graphite and pyrolytic carbon coatings

The oxidation of pyrolytic carbon (PyC) deposited via fluidized bed chemical vapor deposition was characterized and compared with that of standard nuclear-grade graphite. The materials were heated at 700 to 1000 °C in a thermogravimetric analysis system under 20% v/v O 2 flow, allowing for direct comparison of dynamic oxidative mass change in each material. Further, three different PyC samples fabricated under different conditions exhibited variation in total mass loss and mass loss rate, varying by as much as 709 mg/cm 2 in total mass loss and 14.2 (mg/cm 2 )/min in mass loss rate at a single temperature. These variations highlight the correlation between PyC microstructure/defect density and oxidation susceptibility. Additionally, changes in the microstructure and composition between PyC and graphite were characterized via scanning electron microscopy and correlated to the mass loss results. The results of this work have implications toward the safety of tristructural isotropic (TRISO) and other coated particle fuels, especially under off-normal conditions, given the limited information that exists about the oxidation behavior of PyC.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Variability of prediction of maximal oxygen concumption on the cycle ergometer using standard equations

Several investigations within the Exercise Countermeasures Project at the NASA Johnson Space Center focused on the assessment of maximum oxygen consumption (VO2(sub max)) within the Astronaut Corps pre- and postspace flight. Investigations during the Apollo era suggested that there was a significant decrease in postflight VO2(sub max) when compared to preflight values, and current studies have documented that this trend continues in the Space Shuttle era. It is generally accepted and was confirmed in our laboratory that VO2(sub max) can be predicted from submaximal measures taken during graded exercise tests on the cycle ergometer with respect to populations. However, previous work had not examined the effect of day-to-day variations in the physiologic responses that might alter these predictions for individuals. Stability of individual submaximal data over serial tests is important so that predicted changes in VO2(sub max) are reflective of actual VO2(sub max) changes. Therefore, the purpose of this investigation was to determine which of the accepted equations to predict VO2(sub max) would be less affected by normal daily physiologic changes.

Greenisen, Michael C.↗
DOE OSTI2025

Analyzing the Quantum Approximate Optimization Algorithm: Ansätze, Symmetries, and Lie Algebras

The quantum approximate optimization algorithm (QAOA) has been proposed as a method to obtain approximate solutions for combinatorial optimization tasks. In this work, we study the underlying algebraic properties of three QAOA ansätze for the maximum-cut problem on connected graphs, while focusing on the generated Lie algebras as well as their invariant subspaces. Specifically, we analyze the standard QAOA ansatz as well as the orbit and multiangle ansätze. We are able to fully characterize the Lie algebras of the multiangle ansatz across arbitrary connected graphs, finding that they only fall into one of just six families. Aside from the cycle and path graphs, the Lie dimensions for every graph are exponentially large in the system size, meaning that multiangle ansätze are extremely prone to exhibiting barren plateaus. Then, a similar quasi-graph-independent Lie-algebraic characterization beyond the multiangle ansatz is impeded as the circuit exhibits additional “hidden” symmetries besides those naturally arising from a certain parity-superselection operator and all automorphisms of the considered graph. Disregarding the “hidden” symmetries, we can upper bound the dimensions of the orbit and the standard Lie algebras, and the dimensions of the associated invariant subspaces are determined via explicit character formulas. To finish, we conjecture that (for most graphs) the standard Lie algebras have only components that are either exponential or that grow, at most, polynomially with the system size. This would imply that the QAOA is either prone to barren plateaus or classically simulable. More generally, our work provides a symmetry framework and tools to analyze any desired variational quantum algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1996

Heat and Momentum Transfer Studies in High Reynolds Number Wavy Films at Normal and Reduced Gravity Conditions

We examined the effect of the gas flow on the liquid film when the gas flows in the countercurrent direction in a vertical pipe at normal gravity conditions. The most dramatic effect of the simultaneous flow of gas and liquid in pipes is the greatly increased transport rates of heat, mass, and momentum. In practical situations this enhancement can be a benefit or it can result in serious operational problems. For example, gas-liquid flow always results in substantially higher pressure drop and this is usually undesirable. However, much higher heat transfer coefficients can be expected and this can obviously be of benefit for purposes of design. Unfortunately, designers know so little of the behavior of such two phase systems and as a result these advantages are not utilized. Due to the complexity of the second order boundary model as well as the fact that the pressure variation across the film is small compared to the imposed gas phase pressure, the countercurrent gas flow affect was studied for the standard boundary layer model. A different stream function that can compensate the shear stress affect was developed and this stream function also can predict periodic solutions. The discretized model equations were transformed to a traveling wave coordinate system. A stability analysis of these sets of equations showed the presence of a Hopf bifurcation for certain values of the traveling wave velocity and the shear stress. The Hopf celerity was increased due to the countercurrent shear. For low flow rate the increases of celerity are more than for the high flow rate, which was also observed in experiments. Numerical integration of a traveling wave simplification of the model also predicts the existence of chaotic large amplitude, nonperiodic waves as observed in the experiments. The film thickness was increased by the shear.

Balakotaiah, V.↗