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NASA NTRS1986

The statistics of peaks of Gaussian random fields

A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of 'upcrossing' points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima.

Bardeen, J. M.↗

NASA NTRS2008

Pharmacokinetics of Acetaminophen in Hind Limbs Unloaded Mice: A Model System Simulating the Effects of Low Gravity on Astronauts in Space

The pharmacokinetics (PK) of medications administered to astronauts could be altered by the conditions in Space. Low gravity and free floating (and associated hemodynamic changes) could affect the absorption, distribution, metabolism and excretion of the drugs. Knowledge of these alterations is essential for adjusting the dosage and the regimen of drug administration in astronauts. Acquiring of such knowledge has inherent difficulties due to limited opportunities for experimenting in Space. One of the approaches is to use model systems that simulate some of the Space conditions on Earth. In this study we used hind limbs unloaded mice (HLU) to investigate the possible changes in PK of acetaminophen, a widely used analgesic with high probability of use by astronauts. The HLU is recognized as an appropriate model for simulating the effects of low gravity on hemodynamic parameters. Mice were tail suspended (n = 24) for 24-96 hours prior to introduction of acetaminophen (150 - 300 mg/kg). The drug (in aqueous solution containing 10% ethyl alcohol by volume) was given orally by a gavage procedure and after the administration of acetaminophen mice were additionally suspended for 30 min, 1 and 2 hours. Control mice (n = 24) received the same dose of acetaminophen and were kept freely all the time. Blood specimens were obtained either from retroorbital venous sinuses or from heart. Acetaminophen concentration was measured in plasma by the fluorescent polarization immunoassay and the AxSYM analyzer (Abbott Laboratories). In control mice peak acetaminophen concentration was achieved at 30 min. By 1 hour the concentration decreased to less than 50% of the peak level and at 2 hours the drug was almost undetectable in the serum. HLU for 24 hours significantly altered the acetaminophen pharmacokinetic: at 30 min the acetaminophen concentrations were significantly (both statistically and medically significant) lower than in control mice. The concentrations also reduced less significantly after 1 and 2 hours. At 2 hours approximately 20% of the drug still remained in the circulation. After 96 hrs of HLU the changes in acetaminophen PK were less prominent. These data indicate that short term HLU causes significant changes in acetaminophen PK most likely associated with HUL-related hemodynamic changes. However, after 96 hour these changes diminished. This suggests hemodynamic adaptation to the HUL conditions that possibly occurs also in real space conditions.

Peterson, Amanda↗

NASA NTRS2019

TURBOMAT: A Probabilistic Turbomachinery Aeroelastic Analysis Tool

An integration of aeroelastic analysis procedures with probabilistic analysis methods enables us to design safe reliable engines with quantified reliability. Towards this goal, a graphical user interface (GUI) based tool that integrates the codes Aeroelastic analysis of propfans (ASTROP2) and Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) is developed. The tool entitled TURBOMachinery Aeroelastic Analysis Tool (TURBOMAT), is developed utilizing the MATrix Laboratory (Matlab) Guide (Graphical User Interface Development) tool box. TURBOMAT provides a user friendly computational environment for rapid assessment of Turbomachinery blades flutter characteristics, subjected to uncertain loading conditions with variability in material and aerodynamic properties. The tool is seen as an education tool for new students and young engineers starting their careers in structural Aeroelasticity who want to learn and understand aeroelastic aspects of turbomachinery components, fans, compressors and turbines, including uncertainties in loading and material properties.A typical fan blade configuration geometry was chosen to demonstrate the tool. The results are presented in the form of probabilistic density function (PDF), the cumulative distribution function (CDF) and sensitivity factors. Both first order fast probability integration (FPI) and the Monto Carlo (MC) techniques are used in the analysis and compared. The tool enabled us to quantify blade flutter reliability as well as the ranking of uncertain variables and their importance to blade flutter response.

Aeroelastic Analysis↗

NASA NTRS2004

Integrity of Ceramic Parts Predicted When Loads and Temperatures Fluctuate Over Time

Brittle materials are being used, and being considered for use, for a wide variety of high performance applications that operate in harsh environments, including static and rotating turbine parts for unmanned aerial vehicles, auxiliary power units, and distributed power generation. Other applications include thermal protection systems, dental prosthetics, fuel cells, oxygen transport membranes, radomes, and microelectromechanical systems (MEMS). In order for these high-technology ceramics to be used successfully for structural applications that push the envelope of materials capabilities, design engineers must consider that brittle materials are designed and analyzed differently than metallic materials. Unlike ductile metals, brittle materials display a stochastic strength response because of the combination of low fracture toughness and the random nature of the size, orientation, and distribution of inherent microscopic flaws. This plus the fact that the strength of a component under load may degrade over time because of slow crack growth means that a probabilistic-based life-prediction methodology must be used when the tradeoffs of failure probability, performance, and useful life are being optimized. The CARES/Life code (which was developed at the NASA Glenn Research Center) predicts the probability of ceramic components failing from spontaneous catastrophic rupture when these components are subjected to multiaxial loading and slow crack growth conditions. Enhancements to CARES/Life now allow for the component survival probability to be calculated when loading and temperature vary over time.

Nemeth, Noel N.↗

NASA NTRS1986

Aerothermal tests of spherical dome protuberances on a flat plate at a Mach number of 6.5

Aerothermal tests were conducted in the Langley 8-Foot High-Temperature Tunnel at a Mach number of 6.5 on a series of spherical dome protuberances mounted on a flat-plate test apparatus. Detailed surface pressure and heating-rate distributions were obtained for various dome heights and diameters submerged in both laminar and turbulent boundary layers including a baseline geometric condition representing a thermally bowed metallic thermal protection system (TPS) tile. The present results indicated that the surface pressures on the domes were increased on the windward surface and reduced on the leeward surface as predicted by linearized small-perturbation theory, and the distributions were only moderately affected by boundary-layer variations. Surface heating rates for turbulent flow increased on the windward surface and decreased on the leeward surface similar to the pressure; but for laminar boundary layers, the heating rates remained high on the leeward surface, probably due to local transition. Transitional flow effects cause heat load augmentation to increase by 30 percent for the maximum dome height in a laminar boundary layer. However, the corresponding augmentation for a dome with a height of 0.1 in. and a diameter of 14 in. representative of a bowed TPS tile was 14 percent or less for either a laminar or turbulent boundary layer.

Glass, C. E.↗

NASA NTRS1990

Measurements of tropospheric nitric acid over the Western United States and Northeastern Pacific Ocean

Over 240 measurements of nitric acid (HNO3) were made in the free troposphere as well as in the boundary layer. Marine HNO3 measurement results were strikingly similar to results from GAMETAG and other past atmospheric field experiments. The marine boundary layer HNO3 average, 62 parts-per-trillion by volume (pptv), was 1/3 lower than the marine free tropospheric average, 108 pptv, suggesting that the boundary layer is a sink for tropospheric nitric acid, probably by dry deposition. Nitric acid measurements on a nighttime continental flight gave a free tropospheric average of 218 pptv, substantially greater than the daytime continental free tropospheric 5-flight average of 61 pptv. However, the nighttime results may be influenced by highly convective conditions that existed from thunderstorms in the vicinity during that night flight. The continental boundary layer HNO3 average of 767 pptv is an order of magnitude greater than the free tropospheric average, indicating that the boundary layer is a source of free tropospheric HNO3. The distribution of continental boundary layer HNO3 data, from averages of 123 over rural Nevada and Utah to 1057 pptv in the polluted San Joaquin Valley of California suggest a close tie between boundary layer HNO3 and anthropogenic activity.

Lebel, P. J.↗

NASA NTRS2005

Probabilistic Parameter Uncertainty Analysis of Single Input Single Output Control Systems

The current standards for handling uncertainty in control systems use interval bounds for definition of the uncertain parameters. This approach gives no information about the likelihood of system performance, but simply gives the response bounds. When used in design, current methods of m-analysis and can lead to overly conservative controller design. With these methods, worst case conditions are weighted equally with the most likely conditions. This research explores a unique approach for probabilistic analysis of control systems. Current reliability methods are examined showing the strong areas of each in handling probability. A hybrid method is developed using these reliability tools for efficiently propagating probabilistic uncertainty through classical control analysis problems. The method developed is applied to classical response analysis as well as analysis methods that explore the effects of the uncertain parameters on stability and performance metrics. The benefits of using this hybrid approach for calculating the mean and variance of responses cumulative distribution functions are shown. Results of the probabilistic analysis of a missile pitch control system, and a non-collocated mass spring system, show the added information provided by this hybrid analysis.

Smith, Brett A.↗

NASA NTRSDate not supplied

Role of PHM in Autonomous Decision-Making: Aerospace applications

There is an increased need for onboard decision-making capabilities in cyber-physical systems be it in energy, automotive, aviation, space, or other industries as they aim for increased efficiency, resiliency, and mission assurance capabilities. Emerging next-gen technologies such as multi-rover planetary missions, distributed satellites, unmanned ground and aerial vehicle operations and smart grid systems rely on in-time risk assessment and autonomous decision-making. One critical piece of the autonomy puzzle is reliable prediction of system behavior under time-varying and potentially uncertain environmental conditions. Further, if agent states change during operation such as initiation of faults or degradation, reliable diagnostic tools need to be investigated. In this tutorial, we will revise approaches that integrates existing physics-based and data-driven models of agents interacting with probability models of the environment and component operation state. Role of existing PHM methodologies as they feed into decision-making under uncertainty will be studied. Balancing critical trade-offs between high-fidelity prognostic models, prediction time-horizons and the computational requirements for in-time cost-effective decision-making will be discussed through the implementation of surrogate models. Finally, the audience will be introduced to a real-time application of in-time trajectory planning of an unmanned aerial system (UAS) based on its PHM assessments under uncertain and varying wind conditions.

decision-making↗

NASA NTRS1988

The cryptoendolithic microbial environment in the Ross Desert of Antarctica: mathematical models of the thermal regime

Microbial activity in the Antarctic cryptoendolithic habitat is regulated primarily by temperature. Previous field studies have provided some information on the thermal regime in this habitat, but this type of information is limited by the remoteness of the site and the harsh climatic conditions. Therefore, a mathematical model of the endolithic thermal regime was constructed to augment the field data. This model enabled the parameters affecting the horizontal and altitudinal distribution of the community to be examined. The model predicts that colonization should be possible on surfaces with zenith angle less than 15 degrees. At greater zenith angles, colonization should be restricted to surfaces with azimuth angles less than 135 degrees or greater than 225 degrees. The upper elevational limit of the community should be less than 2,500 m. The thermal regime probably does not influence the zonation of the community within a rock.

Non-NASA Center↗

NASA NTRS2021

Screening and Qualification of BME Feedthrough Capacitors for a Space Project

Surface mount technology feedthrough ceramic capacitors are gaining popularity in Hi-Rel systems due to small size and great filtering characteristics. In this work, BME feedthrough capacitors compliant with AEC-Q200 requirements have been evaluated, screened and qualified for a space project. Evaluation included analysis of the effect of post-soldering thermal shocks, temperature dependencies of leakage currents, distribution of breakdown voltages, assessments of high-current capability, and thermal resistance of the parts. The parts have been screened and qualified at conditions close to the military requirements for ceramic capacitors. No failures were detected during screening including burning-in, but two samples failed during monitored 2000 hour life testing at 125C and two times rated voltage. Failure analysis revealed manufacturing defects that required additional analysis of screening and qualification test conditions. Highly accelerated life testing (HALT) has been carried out to assess reliability acceleration factors and the probability of failure at the use conditions. An approach to selection of adequate burning-in and life test conditions is discussed.

Alexander Teverovsky↗

NASA NTRS2021

Screening and Qualification of BME Feedthrough Capacitors for a Space Project

Alexander Teverovsky↗

NASA NTRS1994

Crystallization history of the 1984 Mauna Loa lava flow

During a 3-week eruption in 1984, Mauna Loa produced vent lavas that increased in crystallinity from less than 1 to 30%, and 27-km-long flows that increased in crystallinity as they moved downstream. We examined the crystallization history of these lavas using crystal size distribution (CSD) analysis to study the rates of crystallization, viscosity increase, and latent heating. Typical average growth and nucleation rates were 5 x 10(exp -9) cm/s and 5/cu cm/s for microphenocrysts (20- to 500-micron size crystals nucleated in the rift zone) and 5 x 10(exp -8) cm/s and 5 x 10(exp 4)/cu cm/s for microlites (1- to 20-micron size crystals nucleated in the channel). These crystallization rates are high compared with those found in other CSD studies of igneous rocks, probably due to highly nonequilibrium conditions brought on by rapid degassing in the rift zone and cooling in the lava channel. Growth and nucleation rates decreased with time at the vent and with distance downstream. The maximum downstream total crystallinity measured is 39% (25% microlites, 14% microphenocrysts) in a quenched sample 14 km from the vent. Growth and nucleation rates cannot be calculated for postemplacement samples, but they place upper limits of 53-58% on the amount of crystallization in the channel 9-20 km from the vent. Crystallization could have been mostly responsible for the 10(exp 5)-fold downstream increase in apparent viscosity, although degassing and increasing incorporation of solid lava fragments also contributed. Another effect of crystallization on the lava flow was the sizeable latent heating (0.01 J/g/s over the first half of the flow length, if the crystallinity of downstream quench samples is representative of the hot fluid core), which may have been counteracted by entrainment of cooler material. Measurements of crystallization are shown to be crucial in the study of lava flow emplacement dynamics.

Crisp, Joe↗

NASA NTRS1994

Statistical analysis of mesoscale rainfall: Dependence of a random cascade generator on large-scale forcing

Under the theory of independent and identically distributed random cascades, the probability distribution of the cascade generator determines the spatial and the ensemble properties of spatial rainfall. Three sets of radar-derived rainfall data in space and time are analyzed to estimate the probability distribution of the generator. A detailed comparison between instantaneous scans of spatial rainfall and simulated cascades using the scaling properties of the marginal moments is carried out. This comparison highlights important similarities and differences between the data and the random cascade theory. Differences are quantified and measured for the three datasets. Evidence is presented to show that the scaling properties of the rainfall can be captured to the first order by a random cascade with a single parameter. The dependence of this parameter on forcing by the large-scale meteorological conditions, as measured by the large-scale spatial average rain rate, is investigated for these three datasets. The data show that this dependence can be captured by a one-to-one function. Since the large-scale average rain rate can be diagnosed from the large-scale dynamics, this relationship demonstrates an important linkage between the large-scale atmospheric dynamics and the statistical cascade theory of mesoscale rainfall. Potential application of this research to parameterization of runoff from the land surface and regional flood frequency analysis is briefly discussed, and open problems for further research are presented.

Over, Thomas, M.↗

NASA NTRS2018

Dynamic Adjustment of Simulation Parameters for Efficient Vehicle Prognostics

Model-based diagnostics and prognostics rely on state estimation and uncertainty management algorithms to produce useful information for system operators and maintainers. This information enables more informed operational decisions, condition-based maintenance, and overall mission safety assurance. Typically, uncertainty is associated with vehicle state-of-health estimation and prediction results because of modeling errors, internal or external sources of noise, and sensor inaccuracy. Probabilistic uncertainty management methods including Sequential Monte Carlo simulation are commonly used to reason about state-of-health estimates and predictions in the presence of these sources of uncertainty. However, such algorithms can be computationally expensive as they require a very large number of samples to obtain a sufficiently accurate quantification of the end of life probability distribution. As a result, highly mobile autonomous systems that leverage the prognostic results for mission-level replanning are often constrained in their processing capability because of these computationally expensive simulation approaches. Therefore, in this paper, we investigate algorithmic methods for dynamically adjusting simulation time step as well as number of samples to achieve highly efficient prognostic results while maintaining results accuracy. Results obtained from simulated flight experiments of an electric unmanned aerial vehicle are presented to verify the efficacy of such algorithms.

Prognostics↗

NASA NTRS1977

Random and systematic measurement errors in acoustic impedance as determined by the transmission line method

The effect of random and systematic errors associated with the measurement of normal incidence acoustic impedance in a zero-mean-flow environment was investigated by the transmission line method. The influence of random measurement errors in the reflection coefficients and pressure minima positions was investigated by computing fractional standard deviations of the normalized impedance. Both the standard techniques of random process theory and a simplified technique were used. Over a wavelength range of 68 to 10 cm random measurement errors in the reflection coefficients and pressure minima positions could be described adequately by normal probability distributions with standard deviations of 0.001 and 0.0098 cm, respectively. An error propagation technique based on the observed concentration of the probability density functions was found to give essentially the same results but with a computation time of about 1 percent of that required for the standard technique. The results suggest that careful experimental design reduces the effect of random measurement errors to insignificant levels for moderate ranges of test specimen impedance component magnitudes. Most of the observed random scatter can be attributed to lack of control by the mounting arrangement over mechanical boundary conditions of the test sample.

Parrott, T. L.↗

NASA NTRS1983

Limits on the prediction of helicopter rotor noise using thickness and loading sources: Validation of helicopter noise prediction techniques

The techniques of helicopter rotor noise prediction attempt to describe precisely the details of the noise field and remove the empiricisms and restrictions inherent in previous methods. These techniques require detailed inputs of the rotor geometry, operating conditions, and blade surface pressure distribution. The Farassat noise prediction techniques was studied, and high speed helicopter noise prediction using more detailed representations of the thickness and loading noise sources was investigated. These predictions were based on the measured blade surface pressures on an AH-1G rotor and compared to the measured sound field. Although refinements in the representation of the thickness and loading noise sources improve the calculation, there are still discrepancies between the measured and predicted sound field. Analysis of the blade surface pressure data indicates shocks on the blades, which are probably responsible for these discrepancies.

Succi, G. P.↗

NASA NTRS1985

Failure detection and accommodation in structural dynamics systems using analytic redundancy

The concept of analytic redundancy is extended to identify nonzero constant output failures in large spacecraft active control sensors and actuators, using a set of distributed sensors which do not nominally produce equivalent signals but are related through the structural dynamics of the system. The suboptimal technique uses a Sequential Probability Ratio Test on the residual sequence of a Kalman filter based on a modal structure model, to determine failure of a component based on an assumed failure hypothesis. The specific failure is identified and then the Kalman filter gains are reconfigured for the identified remaining working sensor set. Experimental data using an apparatus whose dynamics are representative of a large spacecraft show the nominal filter performance under failed and unfailed conditions.

Williams, J. P.↗

NASA NTRS2003

Presumed PDF Modeling of Early Flame Propagation in Moderate to Intense Turbulence Environments

The present paper describes the results obtained from a one-dimensional time dependent numerical technique that simulates early flame propagation in a moderate to intense turbulent environment. Attention is focused on the development of a spark-ignited, premixed, lean methane/air mixture with the unsteady spherical flame propagating in homogeneous and isotropic turbulence. A Monte-Carlo particle tracking method, based upon the method of fractional steps, is utilized to simulate the phenomena represented by a probability density function (PDF) transport equation. Gaussian distributions of fluctuating velocity and fuel concentration are prescribed. Attention is focused on three primary parameters that influence the initial flame kernel growth: the detailed ignition system characteristics, the mixture composition, and the nature of the flow field. The computational results of moderate and intense isotropic turbulence suggests that flames within the distributed reaction zone are not as vulnerable, as traditionally believed, to the adverse effects of increased turbulence intensity. It is also shown that the magnitude of the flame front thickness significantly impacts the turbulent consumption flame speed. Flame conditions studied have fuel equivalence ratio s in the range phi = 0.6 to 0.9 at standard temperature and pressure.

Carmen, Christina↗