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NASA NTRS2019

Multilevel Monte Carlo Estimation of Unbiased Expectation via Sample Reuse and the Low Variance Estimation of Asymptotic Rates

A new variant of the multilevel Monte Carlo estimator [5, 3, 9, 12] is presented for the estimation of expectation statistics that utilizes sample reuse in specified levels, explicitly removes approximation error bias associated with numerically computed output quantities of interest that have an asymptotic limit behavior, and permits a low variance estimate of the asymptotic rate of convergence to that limit. In addition, it is shown that this new multilevel Monte Carlo variant can yield a computational cost savings. A review of Monte Carlo and multilevel Monte Carlo estimators is presented that includes analysis of expected value, expected mean squared error, and the calculation of optimized multilevel sample size parameters. The multilevel Monte Carlo estimator produces estimates of expectation for numerically approximated output quantities of interest that are biased by approximation error. When the quantity of interest can be modeled as the asymptotic limit of numerically approximated output quantities of interest, it is theoretically possible to remove this approximation error bias in the multilevel Monte Carlo estimator. In actual implementations, however, this procedure is unreliable due to statistical variability and inaccuracy in estimating the needed asymptotic limit. Analysis and numerical experiment show that the proposed variant of the multilevel Monte Carlo method greatly reduces (in some cases eliminates) the statistical variability in this limit estimation.

Barth, Timothy↗
NASA NTRS1976

Laminar supersonic flow over a backstep - A numerical solution at higher Reynolds numbers

The Allen-Cheng solution of the flow over a backward facing step is extended to Reynolds numbers up to 16,000 and to inflow boundary-layer height ratios as low as 0.1 by moving the downstream boundary into the recompression region and by smoothing the resulting errors. The boundary conditions in the supersonic outer flow and the downstream boundary conditions in the wake are determined by an extrapolation procedure. Computational results are compared with relevant experimental data. Fair agreement is found between the calculated base pressures and the experimental values, whereas agreement between heat transfer rates appears to be qualitative only.

Kronzon, Y.↗
NASA NTRS1978

Urine monitoring system failure analysis and operational verification test report

Failure analysis and testing of a prototype urine monitoring system (UMS) are reported. System performance was characterized by a regression formula developed from volume measurement test data. When the volume measurement test data. When the volume measurement data was imputted to the formula, the standard error of the estimate calculated using the regression formula was found to be within 1.524% of the mean of the mass of the input. System repeatability was found to be somewhat dependent upon the residual volume of the system and the evaporation of fluid from the separator. The evaporation rate was determined to be approximately 1cc/minute. The residual volume in the UMS was determined by measuring the concentration of LiCl in the flush water. Observed results indicated residual levels in the range of 9-10ml, however, results obtained during the flushing efficiency test indicated a residual level of approximately 20ml. It is recommended that the phase separator pumpout time be extended or the design modified to minimize the residual level.

Glanfield, E. J.↗
NASA NTRS1994

A real-time prediction of UTC

The reference time scale for all scientific and technologic applications on the Earth, the Universal Coordinated Time (UTC), must be as stable, reliable, and accurate as possible. With this in view the BIPM and before it the BIH, have always calculated and then disseminated UTC with a delay of about 80 days. There are three fundamental reasons for doing this: (1) It takes some weeks for data, gathered from some 200 clocks spread world-wide, to be collected and for errors to be eliminated; (2) changes in clock rates can only be measured with high precision well after the fact; and (3) the measurement noise originating in time links, in particular using Loran-C, is smoothed out only when averaging over an extended period. Until mid-1992, the ultimate stability of UTC was reached at averaging times of about 100 days and corresponded to an Allan deviation sigma(sub y)(tau) of about 1,5x10(exp -14) then compared to the best primary clock in the world, the PTB CS2. For several years now, a predicted UTC has been computed by the USNO through an extrapolation of the values as published in deferred time by the BIPM. This is made available through the USNO Series 4, through the USNO Automated Data Service, and through GPS signals. Due to the instability of UTC, the poor predictability of the available clocks, and the intentional SA degradation of GPS signals, the real-time access to this extrapolated UTC has represented the true deferred-time UTC only to within several hundreds of nanoseconds.

Thomas, Claudine↗
NASA NTRS1987

Measuring Viscosities of Gases at Atmospheric Pressure

Variant of general capillary method for measuring viscosities of unknown gases based on use of thermal mass-flowmeter section for direct measurement of pressure drops. In technique, flowmeter serves dual role, providing data for determining volume flow rates and serving as well-characterized capillary-tube section for measurement of differential pressures across it. New method simple, sensitive, and adaptable for absolute or relative viscosity measurements of low-pressure gases. Suited for very complex hydrocarbon mixtures where limitations of classical theory and compositional errors make theoretical calculations less reliable.

Singh, Jag J.↗
NASA NTRS1997

Temperature Dependence of the O + HO2 Rate Coefficient

A pulsed laser photolysis technique has been employed to investigate the kinetics of the radical-radical reaction O((sup 3)P) + HO2 OH + O2 over the temperature range 266-391 K in 80 Torr of N2 diluent gas. O((sup 3)P) was produced by 248.5-nm KrF laser photolysis of O3 followed by rapid quenching of O(1D) to O((sup 3)P) while HO2 was produced by simultaneous photolysis of H2O2 to create OH radicals which, in turn, reacted with H2O2 to yield HO2. The O((sup 3)P) temporal profile was monitored by using time-resolved resonance fluorescence spectroscopy. The HO2 concentration was calculated based on experimentally measured parameters. The following Arrhenius expression describes our experimental results: k(sub 1)(T) equals (2.91 +/- 0.70) x 10(exp -11) exp[(228 +/- 75)/T] where the errors are 2 sigma and represent precision only. The absolute uncertainty in k, at any temperature within the range 266-391 K is estimated to be +/- 22 percent. Our results are in excellent agreement with a discharge flow study of the temperature dependence of k(sub 1) in 1 Torr of He diluent reported by Keyser, and significantly reduce the uncertainty in the rate of this important stratospheric reaction at subambient temperatures.

Nicovich, J. M.↗
NASA NTRS1995

Rotational Energy Transfer and Collisional Induced Raman Linewidths in N2 Gas: Energy Transfer Rates - 1

Rotationally inelastic transitions of N2 have been studied in the coupled state (CS) and infinite-order-sudden (IOS) approximations, using the N2-N2 rigidrotor potential of van der Avoird et al. For benchmarking purposes, close coupling (CC) calculations have also been carried out over a limited energy range. The CC and CS cross sections have been obtained both with and without identical molecule exchange symmetry, whereas exchange was neglected in the IOS calculations. The CS results track the CC cross sections rather well; between 113 - 219 cm(exp -1) the average deviation is 14%. Comparison between the CS and IOS cross sections at the high energy end of the CS calculation, 500 - 680 cm(exp -1), shows that IOS is sensitive to the amount of inelasticity and the results for large DELTA J transitions are subject to larger errors. It is found that the state-to-state cross sections with even and odd exchange symmetry agree to better than 2% and are well represented as a sum of direct and exchange cross sections for distinguishable molecules, an indication of the applicability of a classical treatment for this system. This result, however, does not apply to partial cross sections for given total J, but arises from a near cancellation in summing over partial waves. In order to use rigid-rotor results for the calculation of effective rotational excitation rates of N2 in the v=1 vibrational level colliding with bath N2 molecules in the v=0 level, it is assumed that exchange scattering between molecules in different vibrational levels is negligible and direct scattering is independent of Y. Good agreement with room temperature experimental data is obtained. The effective rates determined using the IOS and energy corrected sudden (ECS) approximations are also in reasonable agreement with experiment, with the ECS results being somewhat better. The problem with a degeneracy factor in earlier cross section expressions for collisions between identical molecules is pointed out and corrected.

Huo, Winifred M.↗
NASA NTRS1986

Electron-nitrogen molecular collisions in high-temperature nonequilibrium air

Ab initio calculation of vibrational excitation and deexcitation cross sections of N2 by low energy resonant electron impact have been carried out. The calculation includes initial target state in v = 0-12 and final target state in v = 0-17. The calculated cross sections are found to agree with available experimental data to within reported experimental error. Effect of target rotation has been investigated. Comparison of vibrational excitation cross sections at J = 0, 50, and 150 shows that the major effect of target rotation is to lower the resonance energy. Vibrational excitation and deexcitation rate coefficients are tabulated for electron temperatures of 1100-55,000 K. The present tabulation supercedes an earlier compilation by the Naval Research Laboratory that was derived from experimental data with a factor-of-two error. The tabulated rate coefficients are suited for flowfield modeling of aeroassisted orbital transfer vehicles.

Huo, W. M.↗
NASA NTRS2010

Effects of Increasing Drag on Conjunction Assessment

Conjunction Assessment Risk Analysis relies heavily on the computation of the Probability of Collision (Pc) and the understanding of the sensitivity of this calculation to the position errors as defined by the covariance. In Low Earth Orbit (LEO), covariance is predominantly driven by perturbations due to atmospheric drag. This paper describes the effects of increasing atmospheric drag through Solar Cycle 24 on Pc calculations. The process of determining these effects is found through analyzing solar flux predictions on Energy Dissipation Rate (EDR), historical relationship between EDR and covariance, and the sensitivity of Pc to covariance. It is discovered that while all LEO satellites will be affected by the increase in solar activity, the relative effect is more significant in the LEO regime around 700 kilometers in altitude compared to 400 kilometers. Furthermore, it is shown that higher Pc values can be expected at larger close approach miss distances. Understanding these counter-intuitive results is important to setting Owner/Operator expectations concerning conjunctions as solar maximum approaches.

Frigm, Ryan Clayton↗
NASA NTRS1977

In-flight gyro drift rate calibration on the Viking Orbiters

The drift rates of the attitude control gyros onboard the Viking Orbiters were calibrated several times during flight. The calibration was performed by engaging the gyro control of attitude for a six-hour period, recording the Viking Orbiter coordinates of the sun and the roll reference star as a function of time, and processing these data by a computer program. The computer program calculated drift rates for each data increment, and then smoothed the calculated rate versus the time function for all the data on the basis of a Gauss-Markov gyro-drift model. The effects of data noise were minimized by using a relatively long time constant in the Gauss-Markov model and by empirically determining a set of corrections for celestial inertial scale factor error differences. In this way the rms error of the data fit was lessened.

Breckenridge, W. G.↗
NASA NTRS1979

Flyby- and rendezvous-type comet missions from the standpoint of large-particle dust experiments

The measurement by cometary flyby and rendezvous missions of the dust particles emitted from a cometary nucleus and believed to be the major source of the interplanetary dust is considered. The impact rate per unit area of particles in a given size range on a spacecraft dust sensor is calculated in terms of the distance between comet and probe and the particle emission rate and velocity. It is concluded that large-particle (greater than 100-micron) dust analysis experiments cannot be conducted on flyby missions to short-period comets since the required miss distance is orders of magnitude smaller than the targeting error, while for a rendezvous mission much greater miss distances are possible due to the longer period of cometary contact. The problem of designing dust sensors to operate at the subkilometer per second intercept velocities of a rendezvous mission is also noted.

Sekanina, Z.↗
NASA NTRS1985

Photolysis rates based on Schumann-Runge band approximations and irradiance measurements

The photolysis rate (J3) for CF2Cl2(F-12) in the stratosphere has been computed for three altitudes using measured solar fluxes from a balloon borne spectrometer. The rate is compared with that obtained by computing the attenuated flux using effective cross sections appropriate for the Schumann-Runge bands (J1) (Allen and Frederick, 1982). The result shows that the error in the F-12 photolysis rate caused by using the Allen and Frederick approximation is about 10 percent (J1 less than J3) for altitudes between 32 and 38 km with solar zenith angles less than about 62 degrees. For species other than O2, this implies that the discrepancy in photolysis rates associated with the Schumann-Runge band approximations are not likely to be important. Within the Schumann-Runge band region the computed errors for F-12 photolysis are about 10.5 percent at 38.13 km and increase with decreasing altitude. If this error applies to O2 photolysis, there may be the possibility of an incorrect calculation of net odd oxygen production in photochemical models.

Herman, J. R.↗
NASA NTRS1993

Determining electron temperature and density in a hydrogen microwave plasma

A three-temperature thermo-chemical model is developed for analyzing the chemical composition and energy states of a hydrogen microwave plasma used for studying diamond deposition. The chemical and energy exchange rate coefficients are determined from cross section data, assuming Maxwellian velocity distributions for electrons. The model is reduced to a zero-dimensional problem to solve for the electron temperature and ion mole fraction, using measured vibrational and rotational temperatures. The calculations indicate that the electron temperature may be determined to within a few percent error even though the uncertainty in dissociation fraction is many times larger.

Scott, Carl D.↗
NASA NTRS2003

Effect of Viscosity on the Crystallization of Undercooled Liquids

There have been numerous studies of glasses indicating that low-gravity processing enhances glass formation. NASA PI s are investigating the effect of low-g processing on the nucleation and crystal growth rates. Dr. Ethridge is investigating a potential mechanism for glass crystallization involving shear thinning of liquids in 1-g. For shear thinning liquids, low-g (low convection) processing will enhance glass formation. The study of the viscosity of glass forming substances at low shear rates is important to understand these new crystallization mechanisms. The temperature dependence of the viscosity of undercooled liquids is also very important for NASA s containerless processing studies. In general, the viscosity of undercooled liquids is not known, yet knowledge of viscosity is required for crystallization calculations. Many researchers have used the Turnbull equation in error. Subsequent nucleation and crystallization calculations can be in error by many orders of magnitude. This demonstrates the requirement for better methods for interpolating and extrapolating the viscosity of undercooled liquids. This is also true for undercooled water. Since amorphous water ice is the predominant form of water in the universe, astrophysicists have modeled the crystallization of amorphous water ice with viscosity relations that may be in error by five orders-of-magnitude.

Source record↗
NASA NTRS2012

NGSLR's Measurement of the Retro-Reflector Array Response of Various LEO to GNSS Satellites

"NASA's Next Generation Satellite Laser Ranging System (NGSLR) has successfully demonstrated daylight and nighttime tracking this year to s atellites from LEO to GNSS orbits, using a 7-8 arcsecond beam divergence, a 43% QE Hamamatsu MCP-PMT with single photon detection, a narrow field of view (11 arcseconds), and a 1 mJ per pulse 2kHz repetition rate laser. We have compared the actual return rates we are getting against the theoretical link calculations, using the known system confi guration parameters, an estimate of the sky transmission using locall y measured visibility, and signal processing to extract the signal from the background noise. We can achieve good agreement between theory and measurement in most passes by using an estimated pOinting error. We will s~.()w the results of this comparison along with our conclusio ns."

McGarry, Jan↗
NASA NTRS1991

Bandwidth requirements for direct detection optical communication receivers with PPM signaling

The performance of a direct detection optical communication receiver for pulse position modulation (PPM) signal formats which contains an avalanche photodiode photodetector is calculated as a function of the parameters which characterize a raised cosine filter used in the receiver. It is shown that the performance penalty of this receiver relative to that of an optimal receiver which contains an integrator and assumes a perfectly rectangular PPM pulse shape is less than 1 dB at a receiver bit error rate of 10 exp -6. The advantage of the raised cosine filter is that the electrical bandwidth required is no more than one-half that of the integrator, that is, 1/tau as opposed to 2/tau where tau is the PPM time slot duration.

Davidson, Frederic M.↗
NASA NTRS2005

Performance Analysis on Fault Tolerant Control System

In a fault tolerant control (FTC) system, a parameter varying FTC law is reconfigured based on fault parameters estimated by fault detection and isolation (FDI) modules. FDI modules require some time to detect fault occurrences in aero-vehicle dynamics. In this paper, an FTC analysis framework is provided to calculate the upper bound of an induced-L(sub 2) norm of an FTC system with existence of false identification and detection time delay. The upper bound is written as a function of a fault detection time and exponential decay rates and has been used to determine which FTC law produces less performance degradation (tracking error) due to false identification. The analysis framework is applied for an FTC system of a HiMAT (Highly Maneuverable Aircraft Technology) vehicle. Index Terms fault tolerant control system, linear parameter varying system, HiMAT vehicle.

Shin, Jong-Yeob↗
NASA NTRS2014

Combined Uncertainty and A-Posteriori Error Bound Estimates for CFD Calculations: Theory and Implementation

Simulation codes often utilize finite-dimensional approximation resulting in numerical error. Some examples include, numerical methods utilizing grids and finite-dimensional basis functions, particle methods using a finite number of particles. These same simulation codes also often contain sources of uncertainty, for example, uncertain parameters and fields associated with the imposition of initial and boundary data,uncertain physical model parameters such as chemical reaction rates, mixture model parameters, material property parameters, etc.

CFD↗