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This is Volume 3, Programs and Projects 1969-1978, of a multi-volume series providing a 20-year compilation of summary statistical and other data descriptive of NASA's programs in aeronautics and manned and unmanned spaceflight. This series is an important component of NASA published historical reference works, used by NASA personnel, managers, external researchers, and other government agencies.
Prediction of helicopter main rotor noise due to ingestion of atmospheric turbulence was analyzed. The analysis combines several different models that describe the fluid mechanics of the turbulence and the ingestion process. Two models, atmospheric turbulence, and mean flow and turbulence contraction were covered. The third model, covered in a separate report, describes the rotor acoustic mode. The method incorporates the atmospheric turbulence model and a rapid distortion turbulence contraction description to determine the statistics of the anisotropic turbulence at the rotor plane. The analytical basis for a module was provided which was incorporated in NASA's ROTONET helicopter noise prediction program. The mean flow and turbulence statistics associated with the atmospheric boundary layer were modeled including effects of atmospheric stability length, wind speed, and altitude. The turbulence distortion process is modeled as a deformation of vortex filaments (which represent the turbulence field) by a mean flow field due to the rotor inflow.
A statistical consideration of the energy, the linear momentum, and the angular momentum of the photons that make up a thermal radiation field was presented. A general nonequilibrium statistical thermodynamics approach toward a macroscopic description of thermal radiation transport was developed and then applied to the restricted equilibrium statistical thermostatics derivation of the energy, linear momentum, and intrinsic angular momentum equations for an isotropic photon gas. A brief treatment of a nonisotropic photon gas, as an example of the results produced by the nonequilibrium statistical thermodynamics approach, was given. The relativistic variation of temperature and the invariance of entropy were illustrated.
This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.
The mathematical description and implementation of the statistical estimation procedure known as the Houston integrated spatial/spectral estimator (HISSE) is discussed. HISSE is based on a normal mixture model and is designed to take advantage of spectral and spatial information of LANDSAT data pixels, utilizing the initial classification and clustering information provided by the AMOEBA algorithm. The HISSE calculates parametric estimates of class proportions which reduce the error inherent in estimates derived from typical classify and count procedures common to nonparametric clustering algorithms. It also singles out spatial groupings of pixels which are most suitable for labeling classes. These calculations are designed to aid the analyst/interpreter in labeling patches with a crop class label. Finally, HISSE's initial performance on an actual LANDSAT agricultural ground truth data set is reported.
Cloudiness simulations with the UCLA/Goddard general circulation model were analyzed by comparison of simulated and radiation statistics with corresponding observations. A description of the model formulation is given by Suarez et al. (1983), and some results are discussed by Randall et al. (1985). The global mean cloudiness is near 50%, in agreement with observations. However, comparison with the satellite observations of Susskind et al. (1983) shows that the model produces too many low level clouds at high latitudes and too few high clouds in the tropics. The simulated outgoing longwave radiation at the top of the atmosphere is too low in middle and high latitudes, and much too high in regions of deep convection. The most serious deficiency of the current model's cloudiness simulation is its gross underprediction of the cirrus cloudiness associated with deep convection.
Persistent anomalies with recurrent spatial patterns play an important role in the atmosphere's low-frequency variability. A connection between statistical and dynamical methods of description and prediction of persistent anomalies is established by computing and analyzing the empirical orthogonal functions (EOFs) in a simple deterministic model, on the one hand, and in Southern Hemisphere geopotential heights, on the other. The dynamical model is governed by the fully nonlinear, equivalent-barotropic vorticity equation on the sphere, with simplified forcing, dissipation and topography. The Southern Hemisphere data consist in gridded daily maps of 500 mb heights from June 1972 to July 1983. Two types of persistent anomalies appear in this time series, both having a strong wavenumber-three component; they differ by the value of the constant phase of this wave and by the strength of the wavenumber-one component. The first two EOFs bear a striking resemblance to these two patterns. It is concluded that the dynamical interpretation of EOFs is their pointing from the time mean to the most populated regions of the system's phase space. Pursuing this interpretation, a Markov-chain formulation of transitions from one persistent anomaly regime to another is introduced, and the implications for long-range forecasting are discussed.
An approach to data compression is discussed in which the effect achieved by compression is evaluated by the closeness of the approach to the minimum possible volume. An attempt is made to systematize the known results on data compression. The review contains: description of methods of data compression based on statistical coding and information theory; application of methods of interpolation and extrapolation; a specific compression method (related to description of the histogram of a sample); some criteria of effectiveness and methods of service information representation; and discussion of models suggested for theoretical analysis.
Clear vision and accurate localization of objects in the environment are prerequisites for reliable performance of motor tasks. Space flight confronts the crewmember with a stimulus rearrangement that requires adaptation to function effectively with the new requirements of altered spatial orientation and motor coordination. Adaptation and motor learning driven by the effects of cerebellar disorders may share some of the same demands that face our astronauts. One measure of spatial localization shared by the astronauts and those suffering from cerebellar disorders that is easily quantified, and for which a neurobiological substrate has been identified, is the control of the angle of gaze (the "line of sight"). The disturbances of gaze control that have been documented to occur in astronauts and cosmonauts, both in-flight and postflight, can be directly related to changes in the extrinsic gravitational environment and intrinsic proprioceptive mechanisms thus, lending themselves to description by simple non-linear statistical models. Because of the necessity of developing robust normal response populations and normative populations against which abnormal responses can be evaluated, the basic models can be formulated using normal, non-astronaut test subjects and subsequently extended using centrifugation techniques to alter the gravitational and proprioceptive environment of these subjects. Further tests and extensions of the models can be made by studying abnormalities of gaze control in patients with cerebellar disease. A series of investigations were conducted in which a total of 62 subjects were tested to: (1) Define eccentric gaze-holding parameters in a normative population, and (2) explore the effects of linear acceleration on gaze-holding parameters. For these studies gaze-holding was evaluated with the subjects seated upright (the normative values), rolled 45 degrees to both the left and right, or pitched back 30 and 90 degrees. In a separate study the further effects of acceleration on gaze stability was examined during centrifugation (+2 G (sub x) and +2 G (sub z) using a total of 23 subjects. In all of our investigations eccentric gaze-holding was established by having the subjects acquire an eccentric target (+/-30 degrees horizontal, +/- 15 degrees vertical) that was flashed for 750 msec in an otherwise dark room. Subjects were instructed to hold gaze on the remembered position of the flashed target for 20 sec. Immediately following the 20 sec period, subjects were cued to return to the remembered center position and to hold gaze there for an additional 20 sec. Following this 20 sec period the center target was briefly flashed and the subject made any corrective eye movement back to the true center position. Conventionally, the ability to hold eccentric gaze is estimated by fitting the natural log of centripetal eye drifts by linear regression and calculating the time constant (G) of these slow phases of "gaze-evoked nystagmus". However, because our normative subjects sometimes showed essentially no drift (tau (sub c) = m), statistical estimation and inference on the effect of target direction was performed on values of the decay constant theta = 1/(tau (sub c)) which we found was well modeled by a gamma distribution. Subjects showed substantial variance of their eye drifts, which were centrifugal in approximately 20 % of cases, and > 40% for down gaze. Using the ensuing estimated gamma distributions, we were able to conclude that rightward and leftward gaze holding were not significantly different, but that upward gaze holding was significantly worse than downward (p<0.05). We also concluded that vertical gaze holding was significantly worse than horizontal (p<0.05). In the case of left and right roll, we found that both had a similar improvement to horizontal gaze holding (p<0.05), but didn't have a significant effect on vertical gaze holding. For pitch tilts, both tilt angles significantly decreased gaze-holding ility in all directions (p<0.05). Finally, we found that hyper-g centrifugation significantly decreased gaze holding ability in the vertical plane. The main findings of this study are as follows: (1) vertical gaze-holding is less stable than horizontal, (2) gaze-holding to upward targets is less stable than to downward targets, (3) tilt affects gaze holding, and (4) hyper-g affects gaze holding. This difference between horizontal and vertical gaze-holding may be ascribed to separate components of the velocity-to-position neural integrator for eye movements, and to differences in orbital mechanics. The differences between upward and downward gaze-holding may be ascribed to an inherent vertical imbalance in the vestibular system. Because whole body tilt and hyper-g affects gaze-holding, it is implied that the otolith organs have direct connections to the neural integrator and further studies of astronaut gaze-holding are warranted. Our statistical method for representing the range of normal eccentric gaze stability can be readily applied to normals who maybe exposed to environments which may modify the central integrator and require monitoring, and to evaluate patients with gaze-evoked nystagmus by comparing to the above established normative criteria.
Many tasks in fluids engineering require knowledge of the turbulence in jets. There is a strong, although fragmented, literature base for low order statistics, such as jet spread and other meanvelocity field characteristics. Some sources, particularly for low speed cold jets, also provide turbulence intensities that are required for validating Reynolds-averaged Navier-Stokes (RANS) Computational Fluid Dynamics (CFD) codes. There are far fewer sources for jet spectra and for space-time correlations of turbulent velocity required for aeroacoustics applications, although there have been many singular publications with various unique statistics, such as Proper Orthogonal Decomposition, designed to uncover an underlying low-order dynamical description of turbulent jet flow. As the complexity of the statistic increases, the number of flows for which the data has been categorized and assembled decreases, making it difficult to systematically validate prediction codes that require high-level statistics over a broad range of jet flow conditions. For several years, researchers at NASA have worked on developing and validating jet noise prediction codes. One such class of codes, loosely called CFD-based or statistical methods, uses RANS CFD to predict jet mean and turbulent intensities in velocity and temperature. These flow quantities serve as the input to the acoustic source models and flow-sound interaction calculations that yield predictions of far-field jet noise. To develop this capability, a catalog of turbulent jet flows has been created with statistics ranging from mean velocity to space-time correlations of Reynolds stresses. The present document aims to document this catalog and to assess the accuracies of the data, e.g. establish uncertainties for the data. This paper covers the following five tasks: Document acquisition and processing procedures used to create the particle image velocimetry (PIV) datasets. Compare PIV data with hotwire and laser Doppler velocimetry (LDV) data published in the open literature. Compare different datasets acquired at roughly the same flow conditions to establish uncertainties. Create a consensus dataset for a range of hot jet flows, including uncertainty bands. Analyze this consensus dataset for self-consistency and compare jet characteristics to those of the open literature. One final objective fulfilled by this work was the demonstration of a universal scaling for the jet flow fields, at least within the region of interest to aeroacoustics. The potential core length and the spread rate of the half-velocity radius were used to collapse of the mean and turbulent velocity fields over the first 20 jet diameters in a highly satisfying manner.
Tests were conducted at NASA Lewis Research Center to characterize the proof-of-concept matrix switches built under NASA contract by Ford Aerospace and Aeronautics Corporation at Palo Alto, California, and the General Electric Company at Valley Forge, Pennsylvania. The contract requirements and goals are tabulated along with the results of the NASA tests. Characteristics examined are bandwidth, insertion loss, ripple, switching speed, isolation, standing wave ratio (input and output), deviation from linear phase, noise figure, reconfiguration rates, spurious responses, gain compression, and third order intermodulation distortion. A brief description of the testing method and a statistical analysis of the test results for each of the switches are provided.
The evaluation of multilayer ceramic capacitors (MLCCs) with base-metal electrodes (BMEs) for potential NASA space project applications requires an in-depth understanding of their reliability. The reliability of an MLCC is defined as the ability of the dielectric material to retain its insulating properties under stated environmental and operational conditions for a specified period of time t. In this presentation, a general mathematic expression of a reliability model for a BME MLCC is developed and discussed. The reliability model consists of three parts: (1) a statistical distribution that describes the individual variation of properties in a test group of samples (Weibull, log normal, normal, etc.), (2) an acceleration function that describes how a capacitors reliability responds to external stresses such as applied voltage and temperature (All units in the test group should follow the same acceleration function if they share the same failure mode, independent of individual units), and (3) the effect and contribution of the structural and constructional characteristics of a multilayer capacitor device, such as the number of dielectric layers N, dielectric thickness d, average grain size r, and capacitor chip size S. In general, a two-parameter Weibull statistical distribution model is used in the description of a BME capacitors reliability as a function of time. The acceleration function that relates a capacitors reliability to external stresses is dependent on the failure mode. Two failure modes have been identified in BME MLCCs: catastrophic and slow degradation. A catastrophic failure is characterized by a time-accelerating increase in leakage current that is mainly due to existing processing defects (voids, cracks, delamination, etc.), or the extrinsic defects. A slow degradation failure is characterized by a near-linear increase in leakage current against the stress time; this is caused by the electromigration of oxygen vacancies (intrinsic defects). The two identified failure modes follow different acceleration functions. Catastrophic failures follow the traditional power-law relationship to the applied voltage. Slow degradation failures fit well to an exponential law relationship to the applied electrical field. Finally, the impact of capacitor structure on the reliability of BME capacitors is discussed with respect to the number of dielectric layers in an MLCC unit, the number of BaTiO3 grains per dielectric layer, and the chip size of the capacitor device.
This manual describes the operation and theory of the PC-CARES (Personal Computer-Ceramic Analysis and Reliability Evaluation of Structures) computer program for the IBM PC and compatibles running PC-DOS/MS-DOR OR IBM/MS-OS/2 (version 1.1 or higher) operating systems. The primary purpose of this code is to estimate Weibull material strength parameters, the Batdorf crack density coefficient, and other related statistical quantities. Included in the manual is the description of the calculation of shape and scale parameters of the two-parameter Weibull distribution using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. The methods for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull line, as well as the techniques for calculating the Batdorf flaw-density constants are also described.
Analyzing data sets collected in experiments or by observations is a Core scientific activity. Typically, experimentd and observational data are &aught with uncertainty, and the analysis is based on a statistical model of the conjectured underlying processes, The large data volumes collected by modern instruments make computer support indispensible for this. Consequently, scientists spend significant amounts of their time with the development and refinement of the data analysis programs. AutoBayes [GF+02, FS03] is a fully automatic synthesis system for generating statistical data analysis programs. Externally, it looks like a compiler: it takes an abstract problem specification and translates it into executable code. Its input is a concise description of a data analysis problem in the form of a statistical model as shown in Figure 1; its output is optimized and fully documented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Internally, however, it is quite different: AutoBayes derives a customized algorithm implementing the given model using a schema-based process, and then further refines and optimizes the algorithm into code. A schema is a parameterized code template with associated semantic constraints which define and restrict the template s applicability. The schema parameters are instantiated in a problem-specific way during synthesis as AutoBayes checks the constraints against the original model or, recursively, against emerging sub-problems. AutoBayes schema library contains problem decomposition operators (which are justified by theorems in a formal logic in the domain of Bayesian networks) as well as machine learning algorithms (e.g., EM, k-Means) and nu- meric optimization methods (e.g., Nelder-Mead simplex, conjugate gradient). AutoBayes augments this schema-based approach by symbolic computation to derive closed-form solutions whenever possible. This is a major advantage over other statistical data analysis systems which use numerical approximations even in cases where closed-form solutions exist. AutoBayes is implemented in Prolog and comprises approximately 75.000 lines of code. In this paper, we take one typical scientific data analysis problem-analyzing planetary nebulae images taken by the Hubble Space Telescope-and show how AutoBayes can be used to automate the implementation of the necessary anal- ysis programs. We initially follow the analysis described by Knuth and Hajian [KHO2] and use AutoBayes to derive code for the published models. We show the details of the code derivation process, including the symbolic computations and automatic integration of library procedures, and compare the results of the automatically generated and manually implemented code. We then go beyond the original analysis and use AutoBayes to derive code for a simple image segmentation procedure based on a mixture model which can be used to automate a manual preproceesing step. Finally, we combine the original approach with the simple segmentation which yields a more detailed analysis. This also demonstrates that AutoBayes makes it easy to combine different aspects of data analysis.
Program synthesis is the systematic, automatic construction of efficient executable code from high-level declarative specifications. AutoBayes is a fully automatic program synthesis system for the statistical data analysis domain; in particular, it solves parameter estimation problems. It has seen many successful applications at NASA and is currently being used, for example, to analyze simulation results for Orion. The input to AutoBayes is a concise description of a data analysis problem composed of a parameterized statistical model and a goal that is a probability term involving parameters and input data. The output is optimized and fully documented C/C++ code computing the values for those parameters that maximize the probability term. AutoBayes can solve many subproblems symbolically rather than having to rely on numeric approximation algorithms, thus yielding effective, efficient, and compact code. Statistical analysis is faster and more reliable, because effort can be focused on model development and validation rather than manual development of solution algorithms and code.
Research on coronal mass ejections (CMF) took a variety of forms, both observational and theoretical. On the observational side there were: case studies of individual events, in which it was attempted to provide the most complete descriptions possible, using correlative observations in diverse wavelengths; statistical studies of the properties CMEs and their associated activity; observations which may tell us about the initiation of mass ejections; interplanetary observations of associated shocks and energetic particles even observations of CMEs traversing interplanetary space; and the beautiful synoptic charts which show to what degree mass ejections affect the background corona and how rapidly (if at all) the corona recovers its pre-disturbance form. These efforts are described in capsule form with an emphasis on presenting pictures, graphs, and tables so that the reader can form a personal appreciation of the work and its results.
Nonlinear optimization algorithm helps in finding best-fit curve. Nonlinear Curve Fitting Program, NLINEAR, interactive curve-fitting routine based on description of quadratic expansion of X(sup 2) statistic. Utilizes nonlinear optimization algorithm calculating best statistically weighted values of parameters of fitting function and X(sup 2) minimized. Provides user with such statistical information as goodness of fit and estimated values of parameters producing highest degree of correlation between experimental data and mathematical model. Written in FORTRAN 77.
Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. Recently, such systems have been increasingly employing photon-counting photodetector technology, which changes the statistics of the observed photocurrent. This requires time-of-arrival estimators to be developed and their performances characterized. The statistics of the output of an ideal photodetector, which are well modeled as a Poisson point process, were considered. An analytical model was developed for the mean-square error of the maximum likelihood (ML) estimator, demonstrating two phenomena that cause deviations from the minimum achievable error at low signal power. An approximation was derived to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time. Comparing the analytic model performance predictions to those obtained via simulations, it was verified that the model accurately predicts the ML performance over all regimes considered. There is little prior art that attempts to understand the fundamental limitations to time-of-arrival estimation from Poisson statistics. This work establishes both a simple mathematical description of the error behavior, and the associated physical processes that yield this behavior. Previous work on mean-square error characterization for ML estimators has predominantly focused on additive Gaussian noise. This work demonstrates that the discrete nature of the Poisson noise process leads to a distinctly different error behavior.