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NASA NTRS1991

Rossby waves in a fluctuating zonal mean flow

The effects of the zonal mean wind variability on the energy propagation of a stationary Rossby wave in a barotropic nondivergent atmosphere are studied. It is shown that the random nature of the zonal wind fluctuations do not allow Rossby wave energy to propagate from its energy source. The mechanism for this effect is strongly dependent on the spatial resolution at which the zonal mean flow is assumed to be known. Some speculations are offered on the relation between this mechanism and the systematic error of some low-resolution climate models.

Pandolfo, Lionel↗

NASA NTRS1994

Calibration of the COBE FIRAS instrument

The Far-Infrared Absolute Spectrophotometer (FIRAS) instrument on the Cosmic Background Explorer (COBE) satellite was designed to accurately measure the spectrum of the cosmic microwave background radiation (CMBR) in the frequency range 1-95/cm with an angular resolution of 7 deg. We describe the calibration of this instrument, including the method of obtaining calibration data, reduction of data, the instrument model, fitting the model to the calibration data, and application of the resulting model solution to sky observations. The instrument model fits well for calibration data that resemble sky condition. The method of propagating detector noise through the calibration process to yield a covariance matrix of the calibrated sky data is described. The final uncertainties are variable both in frequency and position, but for a typical calibrated sky 2.6 deg square pixel and 0.7/cm spectral element the random detector noise limit is of order of a few times 10(exp -7) ergs/sq cm/s/sr cm for 2-20/cm, and the difference between the sky and the best-fit cosmic blackbody can be measured with a gain uncertainty of less than 3%.

Fixsen, D. J.↗

NASA NTRS1998

Attitude Estimation Signal Processing: A First Report on Possible Algorithms and Their Utility

In this brief effort, time has been of the essence. The data had to be acquired from APL/Lincoln Labs, stored, and sorted out to obtain the pertinent streams. This has been a significant part of this effort and hardware and software problems have been addressed with the appropriate solutions to accomplish this part of the task. Passed this, some basic and important algorithms are utilized to improve the performance of the attitude estimation systems. These algorithms are an essential part of the signal processing for the attitude estimation problem as they are utilized to reduce the amount of the additive/multiplicative noise that in general may or may not change its structure and probability density function, pdf, in time. These algorithms are not currently utilized in the processing of the data, at least, we are not aware of their use in this attitude estimation problem. Some of these algorithms, like the variable thresholding, are new conjectures, but one would expect that someone somewhere must have utilized this kind of scheme before. The variable thresholding idea is a straightforward scheme to use in case of a slowly varying pdf, or statistical moments of the unwanted random process. The algorithms here are kept simple but yet effective for processing the data and removing the unwanted noise. For the most part, these algorithms can be arranged so that their consecutive and orderly execution would complement the preceding algorithm and improve the overall performance of the signal processing chain.

Riasati, Vahid R.↗

NASA NTRS1993

A predictability study of Lorenz's 28-variable model as a dynamical system

The dynamics of error growth in a two-layer nonlinear quasi-geostrophic model has been studied to gain an understanding of the mathematical theory of atmospheric predictability. The growth of random errors of varying initial magnitudes has been studied, and the relation between this classical approach and the concepts of the nonlinear dynamical systems theory has been explored. The local and global growths of random errors have been expressed partly in terms of the properties of an error ellipsoid and the Liapunov exponents determined by linear error dynamics. The local growth of small errors is initially governed by several modes of the evolving error ellipsoid but soon becomes dominated by the longest axis. The average global growth of small errors is exponential with a growth rate consistent with the largest Liapunov exponent. The duration of the exponential growth phase depends on the initial magnitude of the errors. The subsequent large errors undergo a nonlinear growth with a steadily decreasing growth rate and attain saturation that defines the limit of predictability. The degree of chaos and the largest Liapunov exponent show considerable variation with change in the forcing, which implies that the time variation in the external forcing can introduce variable character to the predictability.

Krishnamurthy, V.↗

NASA NTRS1992

Buckling of stiffened shells with random initial imperfections, thickness and boundary conditions

The paper proposes a method to predict the buckling load of stiffened, composite shells reliably, where besides the randomness of the initial geometric imperfections also a random variation of the wall thickness and the uncertainty of the precise edge conditions is included in the analysis. The introduction of the variability in the thickness from shell to shell, in an ensemble of nominally identical shells, produced by the same manufacturing procedure is motivated by the growing realization of the importance of thickness variations by composite shells. The probabilistic treatment of the boundary conditions is dictated by the fact that 'true', deterministically specified boundary conditions are unlikely to be realizable in practice.

Elishakoff, I.↗

NASA NTRS1992

Statistical characterization of life drivers for a probabilistic design analysis

This paper discusses the issue of statistical characterization of life drivers for a probabilistic design analysis (PDA) approach to support the conventional deterministic structural design methods that are currently used. The probabilistic approach takes into consideration the modeling inadequacies and uncertainties in many design variables such as loads, environments, and material properties. The importance of the distributional assumption is motivated by illustrating an example where the results differ substantially due to the distribution selected. Different types of distributions are discussed and techniques for estimating the parameters are given. Given this information, procedures are outlined for selecting the appropriate distribution based on the particular type of variable (i.e., dimensional, performance) as well as the information that is available (i.e., test data, engineering analysis). Finally, techniques are given for generating random numbers from these selected distributions within the PDA process.

Fox, Eric P.↗

NASA NTRS1990

Analysis of AVHRR, CZCS and historical in situ data off the Oregon Coast

The original scientific objectives of this grant were to: (1) characterize the seasonal cycles and interannual variability for phytoplankton concentrations and sea surface temperature (SST) in the California Current using satellite data; and (2) to explore the spatial and temporal relationship between these variables and surface wind forcing. An additional methodological objective was to develop statistical methods for forming mean fields, which minimize the effects of random data gaps and errors in the irregularly sampled CZCS (Coastal Zone Color Scanner) and AVHRR (Advanced Very High Resolution Radiometer) satellite data. A final task was to evaluate the level of uncertainty in the wind fields used for the statistical analysis. Funding in the first year included part of the cost of an image processing system to enable this and other projects to process and analyze satellite data. This report consists of summaries of the major projects carried out with all or partial support from this grant. The appendices include a list of papers and professional presentations supported by the grant, as well as reprints of the major papers and reports.

Strub, P. Ted↗

NASA NTRS1994

Redshift data and statistical inference

Frequency histograms and the 'power spectrum analysis' (PSA) method, the latter developed by Yu & Peebles (1969), have been widely employed as techniques for establishing the existence of periodicities. We provide a formal analysis of these two classes of methods, including controlled numerical experiments, to better understand their proper use and application. In particular, we note that typical published applications of frequency histograms commonly employ far greater numbers of class intervals or bins than is advisable by statistical theory sometimes giving rise to the appearance of spurious patterns. The PSA method generates a sequence of random numbers from observational data which, it is claimed, is exponentially distributed with unit mean and variance, essentially independent of the distribution of the original data. We show that the derived random processes is nonstationary and produces a small but systematic bias in the usual estimate of the mean and variance. Although the derived variable may be reasonably described by an exponential distribution, the tail of the distribution is far removed from that of an exponential, thereby rendering statistical inference and confidence testing based on the tail of the distribution completely unreliable. Finally, we examine a number of astronomical examples wherein these methods have been used giving rise to widespread acceptance of statistically unconfirmed conclusions.

Newman, William I.↗

NASA NTRS2005

GLOBAL REFERENCE ATMOSPHERIC MODELS FOR AEROASSIST APPLICATIONS

Aeroassist is a broad category of advanced transportation technology encompassing aerocapture, aerobraking, aeroentry, precision landing, hazard detection and avoidance, and aerogravity assist. The eight destinations in the Solar System with sufficient atmosphere to enable aeroassist technology are Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Saturn's moon Titan. Engineering-level atmospheric models for five of these targets - Earth, Mars, Titan, Neptune, and Venus - have been developed at NASA's Marshall Space Flight Center. These models are useful as tools in mission planning and systems analysis studies associated with aeroassist applications. The series of models is collectively named the Global Reference Atmospheric Model or GRAM series. An important capability of all the models in the GRAM series is their ability to simulate quasi-random perturbations for Monte Carlo analysis in developing guidance, navigation and control algorithms, for aerothermal design, and for other applications sensitive to atmospheric variability. Recent example applications are discussed.

Duvall, Aleta↗

NASA NTRS1970

Global search algorithm for optimal control

Random-search algorithm employs local and global properties to solve two-point boundary value problem in Pontryagin maximum principle for either fixed or variable end-time problems. Mixed boundary value problem is transformed to an initial value problem. Mapping between initial and terminal values utilizes hybrid computer.

Brocker, D. H.↗

NASA NTRS1972

Jimsphere wind and turbulence exceedance statistic

Exceedance statistics of winds and gusts observed over Cape Kennedy with Jimsphere balloon sensors are described. Gust profiles containing positive and negative departures, from smoothed profiles, in the wavelength ranges 100-2500, 100-1900, 100-860, and 100-460 meters were computed from 1578 profiles with four 41 weight digital high pass filters. Extreme values of the square root of gust speed are normally distributed. Monthly and annual exceedance probability distributions of normalized rms gust speeds in three altitude bands (2-7, 6-11, and 9-14 km) are log-normal. The rms gust speeds are largest in the 100-2500 wavelength band between 9 and 14 km in late winter and early spring. A study of monthly and annual exceedance probabilities and the number of occurrences per kilometer of level crossings with positive slope indicates significant variability with season, altitude, and filter configuration. A decile sampling scheme is tested and an optimum approach is suggested for drawing a relatively small random sample that represents the characteristic extreme wind speeds and shears of a large parent population of Jimsphere wind profiles.

Adelfang, S. I.↗

NASA NTRS1977

Calibration of a universal indicated turbulence system

Theoretical and experimental work on a Universal Indicated Turbulence Meter is described. A mathematical transfer function from turbulence input to output indication was developed. A random ergodic process and a Gaussian turbulence distribution were assumed. A calibration technique based on this transfer function was developed. The computer contains a variable gain amplifier to make the system output independent of average velocity. The range over which this independence holds was determined. An optimum dynamic response was obtained for the tubulation between the system pitot tube and pressure transducer by making dynamic response measurements for orifices of various lengths and diameters at the source end.

Chapin, W. G.↗

NASA NTRS1990

Ultrasonic correlator versus signal averager as a signal to noise enhancement instrument

Ultrasonic inspection of thick and attenuating materials is hampered by the reduce amplitudes of the propagated waves to a degree that the noise is too high to enable meaningful interpretation of the data. In order to overcome the low signal to noise ratio (S/N), a correlation technique has been developed. In this method, a continuous pseudo-random pattern generated digitally is transmitted and detected by piezoelectric transducers. A correlation is performed in the instrument between the received signal and a variable delayed image of the transmitted one. The result is shown to be proportional to the impulse response of the investigated material, analogous to a signal received from a pulsed system, with an improved S/N ratio. The degree of S/N enhancement depends on the sweep rate. The correlator is described, and it is compared to the method of enhancing S/N ratio by averaging the signals. The similarities and differences between the two are highlighted and the potential advantage of the correlator system is explained.

Kishoni, Doron↗

NASA NTRS1991

Probabilistic lifetime strength of aerospace materials via computational simulation

The results of a second year effort of a research program are presented. The research included development of methodology that provides probabilistic lifetime strength of aerospace materials via computational simulation. A probabilistic phenomenological constitutive relationship, in the form of a randomized multifactor interaction equation, is postulated for strength degradation of structural components of aerospace propulsion systems subjected to a number of effects of primitive variables. These primitive variables often originate in the environment and may include stress from loading, temperature, chemical, or radiation attack. This multifactor interaction constitutive equation is included in the computer program, PROMISS. Also included in the research is the development of methodology to calibrate the constitutive equation using actual experimental materials data together with the multiple linear regression of that data.

Boyce, Lola↗

NASA NTRS1989

Ultrasonic correlator versus signal averager as a signal to noise enhancement instrument

Ultrasonic inspection of thick and attenuating materials is hampered by the reduced amplitudes of the propagated waves to a degree that the noise is too high to enable meaningful interpretation of the data. In order to overcome the low Signal to Noise (S/N) ratio, a correlation technique has been developed. In this method, a continuous pseudo-random pattern generated digitally is transmitted and detected by piezoelectric transducers. A correlation is performed in the instrument between the received signal and a variable delayed image of the transmitted one. The result is shown to be proportional to the impulse response of the investigated material, analogous to a signal received from a pulsed system, with an improved S/N ratio. The degree of S/N enhancement depends on the sweep rate. This paper describes the correlator, and compares it to the method of enhancing S/N ratio by averaging the signals. The similarities and differences between the two are highlighted and the potential advantage of the correlator system is explained.

Kishoni, Doron↗

NASA NTRS1994

An experiment to assess the cost-benefits of code inspections in large scale software development

This experiment (currently in progress) is designed to measure costs and benefits of different code inspection methods. It is being performed with a real development team writing software for a commercial product. The dependent variables for each code unit's inspection are the elapsed time and the number of defects detected. We manipulate the method of inspection by randomly assigning reviewers, varying the number of reviewers and the number of teams, and, when using more than one team, randomly assigning author repair and non-repair of detected defects between code inspections. After collecting and analyzing the first 17 percent of the data, we have discovered several interesting facts about reviewers, about the defects recorded during reviewer preparation and during the inspection collection meeting, and about the repairs that are eventually made. (1) Only 17 percent of the defects that reviewers record in their preparations are true defects that are later repaired. (2) Defects recorded at the inspection meetings fall into three categories: 18 percent false positives requiring no author repair, 57 percent soft maintenance where the author makes changes only for readability or code standard enforcement, and 25 percent true defects requiring repair. (3) The median elapsed calendar time for code inspections is 10 working days - 8 working days before the collection meeting and 2 after. (4) In the collection meetings, 31 percent of the defects discovered by reviewers during preparation are suppressed. (5) Finally, 33 percent of the true defects recorded are discovered at the collection meetings and not during any reviewer's preparation. The results to date suggest that inspections with two sessions (two different teams) of two reviewers per session (2sX2p) are the most effective. These two-session inspections may be performed with author repair or with no author repair between the two sessions. We are finding that the two-session, two-person with repair (2sX2pR) inspections are the most expensive, taking 15 working days of calendar time from the time the code is ready for review until author repair is complete, whereas two-session, two-person with no repair (2sX2pN) inspections take only 10 working days, but find about 10 percent fewer defects.

Porter, A.↗

NASA NTRS2002

Effect of Random Geometric Uncertainty on the Computational Design of a 3-D Flexible Wing

The effect of geometric uncertainty due to statistically independent, random, normally distributed shape parameters is demonstrated in the computational design of a 3-D flexible wing. A first-order second-moment statistical approximation method is used to propagate the assumed input uncertainty through coupled Euler CFD aerodynamic / finite element structural codes for both analysis and sensitivity analysis. First-order sensitivity derivatives obtained by automatic differentiation are used in the input uncertainty propagation. These propagated uncertainties are then used to perform a robust design of a simple 3-D flexible wing at supercritical flow conditions. The effect of the random input uncertainties is shown by comparison with conventional deterministic design results. Sample results are shown for wing planform, airfoil section, and structural sizing variables.

Gumbert, C. R.↗

NASA NTRS1986

M.I.T./Canadian vestibular experiments on the Spacelab-1 mission: 6. Vestibular reactions to lateral acceleration following ten days of weightlessness

Tests of otolith function were performed pre-flight and post-flight on the science crew of the first Spacelab Mission with a rail-mounted linear acceleration sled. Four tests were performed using horizontal lateral (y-axis) acceleration: perception of linear motion, a closed loop nulling task, dynamic ocular torsion, and lateral eye deviations. The motion perception test measured the time to detect the onset and direction of near threshold accelerations. Post-flight measures of threshold and velocity constant obtained during the days immediately following the mission showed no consistent pattern of change among the four crewmen compared to their pre-flight baseline other than an increased variability of response. In the closed loop nulling task, crewmen controlled the motion of the sled and attempted to null a computer-generated random disturbance motion. When performed in the light, no difference in ability was noted between pre-flight and post-flight. In the dark, however, two of the four crewmen exhibited somewhat enhanced performance post-flight. Dynamic ocular torsion was measured in response to sinusoidal lateral acceleration which produces a gravitionertial stimulus equivalent to lateral head tilt without rotational movement of the head. Results available for two crewmen suggest a decreased amplitude of sinusoidal ocular torsion when measured on the day of landing (R+0) and an increasing amplitude when measured during the week following the mission.

short duration↗