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NASA NTRS1976

The uncertainty threshold principle - Fundamental limitations of optimal decision making under dynamic uncertainty

The fundamental limitations of the optimal control of dynamic systems with random parameters are analyzed by studying a scalar linear-quadratic optimal control example. It is demonstrated that optimum long-range decision making is possible only if the dynamic uncertainty (quantified by the means and covariances of the random parameters) is below a certain threshold. If this threshold is exceeded, there do not exist optimum decision rules. This phenomenon is called the 'uncertainty threshold principle'. The implications of this phenomenon to the field of modelling, identification, and adaptive control are discussed.

Athans, M.↗

NASA NTRS1977

Digital control of high performance aircraft using adaptive estimation techniques

In this paper, an adaptive signal processing algorithm is joined with gain-scheduling for controlling the dynamics of high performance aircraft. A technique is presented for a reduced-order model (the longitudinal dynamics) of a high performance STOL aircraft. The actual controller views the nonlinear behavior of the aircraft as equivalent to a randomly switching sequence of linear models taken from a preliminary piecewise-linear fit of the system nonlinearities. The adaptive nature of the estimator is necessary to select the proper sequence of linear models along the flight trajectory. Nonlinear behavior is approximated by effective switching of the linear models at random times, with durations reflecting aircraft motion in response to pilot commands.

Van Landingham, H. F.↗

NASA NTRS1977

Optimum coherent imaging of a limited field of view in the presence of angular and aperture noise

The question of image distribution reconstruction for coherent illumination of an object located in the aperture far zone is considered from first principles without postulating any particular optical spread function. The object function is mathematically modeled as a complex random function of angular coordinates, and it is assumed that the object distribution of interest is angularly limited to a certain a priori assigned field of view (FOV). A linear reconstruction procedure that is uniformly optimal in the FOV is established by using the methods of statistical estimation. Two special cases are examined: imaging a limited sector of a wide-angle random scene and objects in the FOV immersed in a wide-angle background of angular noise. It is noted that the domain of application of the reconstruction method is restricted to microwave frequencies.

Borgiotti, G. V.↗

NASA NTRS1977

On estimating gravity anomalies - A comparison of least squares collocation with conventional least squares techniques

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described.

Argentiero, P.↗

NASA NTRS1976

Macroscopic study of time unsteady noise of an aircraft engine during static tests

Static tests of aircraft engines can exhibit greater than 10 dB random unsteadiness of tone noise levels because flow disturbances that prevail near test site facilities are ingested. Presumably such changes are related to installation and test site features. This paper presents some properties of unsteady noise observed at a NASA-Lewis facility during tests of a Lycoming YF-102 turbofan engine. Time and spatial variations in tone noise obtained from closely spaced far-field and inlet duct microphones are displayed. Long (0.5 sec) to extremely short (0.001 sec) intermittent tone bursts are observed. Unsteadiness of the tone, its harmonics, and the broadband noise show little similarity. In the far-field, identity of tone bursts is retained over a directivity angle of less than 10 deg. In the inlet duct, tone bursts appear to propagate axially but exhibit little circumferential similarity. They show only slight relationship to tone bursts observed in the far field. The results imply an intermittent generation of random mixtures of propagating duct modes.

Clark, B. J.↗

NASA NTRS1976

Noise and vibration ride comfort criteria

A program is underway at Langley Research Center to develop a comprehensive ride quality model based upon the various physical and psychological factors that most affect passenger ride comfort. Two of the most important factors, namely, vibration and noise were studied to (1) determine whether composite or separate noise and vibration criteria are needed for the prediction of ride quality, (2) determine a noise correction for the previously-defined vibration criteria of the ride quality model, (3) assess whether these noise corrections depend on the nature of the vibration stimuli, i.e., deterministic as opposed to random, and (4) specify noise-vibration criteria for this combined environment. The stimuli for the study consisted of octave bands of noise centered at 500 or 2000 Hz and vertical vibrations composed of either 5 Hz sinusoidal vibration or random vibrations centered at 5 Hz and with a 5 Hz bandwidth. The noise stimuli were presented at levels ranging from ambient to 95 dB(A) and the vibrations at levels ranging from 0.02 to 0.13 g-rms.

Dempsey, T. K.↗

NASA NTRS1977

Effect of flight on jet noise from supersonic underexpanded flows

Experiments on underexpanded cold jet flows from a convergent nozzle under simulated flight conditions have shown that a large periodic spinning motion of the jet can occur with greatly enhanced broadband noise production. Shadowgraph pictures indicate that this oscillatory jet motion accompanies the generation of random weak shock waves at the source. These waves appear to be generated at the point downstream of the nozzle exit where the shock cells in the jet begin to disappear. The weak shock waves propagate upstream and have been identified to be the cause of enhanced broadband jet noise production in flight. In addition, the results show that the boundary layer flow conditions over the outside of the primary nozzle (simulating engine cowl flow in flight) have a key role in the production of these random weak shock waves.

Sarohia, V.↗

NASA NTRS1978

Statistical model for asperity-contact time fraction in elastohydrodynamic lubrication

Relations for the asperity contact time fraction during elastohydrodynamic (EHD) lubrication of a typical ball bearing are presented. The analysis is based on a two-dimensional random surface model, and actual profile traces of the bearing surfaces were used as statistical sample records. The results of the analysis show that transition from 90 percent contact to 1 percent contact occurs within a dimensionless film thickness range of approximately 4 to 5. This thickness ratio is several times larger than reported in the literature where one-dimensional random surface models were used.

Sidik, S. M.↗

NASA NTRS1978

A study of forecast growth with a barotropic model of the atmosphere

A barotropic model of the atmosphere was used to test various sources of forecast error. These errors are classified as truncation error, physical error, or initial error. It was shown that growth patterns due to each category differ significantly. Initial errors were shown not to grow in a barotropic model contrary to reports of other studies which indicate that they basically do grow. Also, random initial errors were shown to decrease due to the filtering effect of the model itself. Results seem to indicate that instabilities are required for error growth, be they barotropic or baroclinic, and that random errors are not representative of true initial conditions.

Halberstam, I. M.↗

NASA NTRS1978

Scintillation observations near the sun

Results on the electron density spectrum, the random velocity and the mean velocity of the solar wind in the region from 5 to 100 solar radii are presented. Results are based on intensity scintillations of incoherent radio sources at different locations and different radio frequencies. The shape of the electron density irregularity spectrum is shown to be well modeled by a power law in wavenumber with a slope that abruptly steepens at higher wavenumbers. This two slope power law model is shown to have a break (defined as the wavenumber of the change of slope) that increases with decreasing distance from the Sun. The fractional random velocity is shown to be insignificant at distances of greater than 40 solar radii, but shows a steady increase with decreasing solar distance inside of 40 solar radii.

Coles, W. A.↗

NASA NTRS1978

A distribution model for the aerial application of granular agricultural particles

A model is developed to predict the shape of the distribution of granular agricultural particles applied by aircraft. The particle is assumed to have a random size and shape and the model includes the effect of air resistance, distributor geometry and aircraft wake. General requirements for the maintenance of similarity of the distribution for scale model tests are derived and are addressed to the problem of a nongeneral drag law. It is shown that if the mean and variance of the particle diameter and density are scaled according to the scaling laws governing the system, the shape of the distribution will be preserved. Distributions are calculated numerically and show the effect of a random initial lateral position, particle size and drag coefficient. A listing of the computer code is included.

Fernandes, S. T.↗

NASA NTRS1978

Coded aperture imaging with uniformly redundant arrays

The paper discusses uniformly redundant arrays (URA) as applied to coded aperture imaging. The URA system offers the high-transmission characteristics of random arrays as well as a flat sidelobe advantage. The high-transmission yields the imaging of very low-intensity sources and the flat sidelobes provide the suppression of inherent noise which obscures low-contrast sources. Simulations have shown that the URA with shot and background noise produces a better reconstructed object than random arrays without shot or background noise. The URA also offers an arrangement which involves a mosaic of basic URA patterns forming a circular correlation of the object on the picture plane. Thus the information needed to reconstruct the object is contained in an area equal to that of the basic aperture pattern. This smaller required detector is important in applications including X-ray astronomy.

Fenimore, E. E.↗

NASA NTRS1978

An initial state perturbation experiment with the GISS model

Monthly mean global forecasts for January 1975 have been computed with the Goddard Institute for Space Studies model from four slightly different sets of initial conditions - a 'control' state and three random perturbations thereof - to simulate the effects of initial state uncertainty on forecast quality. Differences among the forecasts are examined in terms of energetics, synoptic patterns and forecast statistics. The 'noise level' of the model predictions is depicted on global maps of standard deviations of sea level pressures, 500 mb heights and 850 mb temperatures for the set of four forecasts. Initial small-scale random errors do not appear to result in any major degradation of the large-scale monthly mean forecast beyond that generated by the model itself, nor do they appear to represent the major source of large-scale forecast error.

Spar, J.↗

NASA NTRS1978

Computer simulation of the velocity diffusion of cosmic rays

Monte Carlo simulation experiments have been performed in order to study the velocity diffusion of charged particles in a static turbulent magnetic field. By following orbits of particles moving in a large ensemble of random magnetic field realizations with suitably chosen statistical properties, a pitch-angle diffusion coefficient is derived. Results are presented for a variety of particle rigidities and rms random field strengths and compared with the predictions of standard quasi-linear theory and the nonlinear partially averaged field theory.

Kaiser, T. B.↗

NASA NTRS1978

The correlation function for density perturbations in an expanding universe. III The three-point and predictions of the four-point and higher order correlation functions

Higher-order correlation functions for the large-scale distribution of galaxies in space are investigated. It is demonstrated that the three-point correlation function observed by Peebles and Groth (1975) is not consistent with a distribution of perturbations that at present are randomly distributed in space. The two-point correlation function is shown to be independent of how the perturbations are distributed spatially, and a model of clustered perturbations is developed which incorporates a nonuniform perturbation distribution and which explains the three-point correlation function. A model with hierarchical perturbations incorporating the same nonuniform distribution is also constructed; it is found that this model also explains the three-point correlation function, but predicts different results for the four-point and higher-order correlation functions than does the model with clustered perturbations. It is suggested that the model of hierarchical perturbations might be explained by the single assumption of having density fluctuations or discrete objects all of the same mass randomly placed at some initial epoch.

Mcclelland, J.↗

NASA NTRS1978

Remote sensing of sea state by analysis of backscattered microwave phase fluctuations

The relative phase of a normally incident microwave signal scattered off the sea surface is a random function of space and time. The statistics of these random phase fluctuations contain information about the wave-height statistics. This study demonstrates that the wave-height spectra can be deduced directly in terms of the spectra of the phase fluctuations without recourse to inversion techniques even when surface roughness exceeds many wavelengths of the incident signal. In the particular case of a nadir-directed satellite-mounted microwave source operating in the backscatter mode, the wave-height and phase spatial spectra are proportional with a constant proportionality of (2k0) squared, where k0 is the wavenumber of the scattered signal.

Clifford, S. F.↗

NASA NTRS1979

Real-time video-image analysis

Digitizer and storage system allow rapid random access to video data by computer. RAPID (random-access picture digitizer) uses two commercially-available, charge-injection, solid-state TV cameras as sensors. It can continuously update its memory with each frame of video signal, or it can hold given frame in memory. In either mode, it generates composite video output signal representing digitized image in memory.

Eskenazi, R.↗

NASA NTRS1978

A study of digital holographic filters generation. Phase 2: Digital data communication system, volume 1

An empirical study of the performance of the Viterbi decoders in bursty channels was carried out and an improved algebraic decoder for nonsystematic codes was developed. The hybrid algorithm was simulated for the (2,1), k = 7 code on a computer using 20 channels having various error statistics, ranging from pure random error to pure bursty channels. The hybrid system outperformed both the algebraic and the Viterbi decoders in every case, except the 1% random error channel where the Viterbi decoder had one bit less decoding error.

Ingels, F. M.↗