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NASA NTRS1992

On slowly varying systems - l-infinity to l-infinity performance and implications to robust adaptive control

The authors present a result on the l-infinity to l-infinity performance of slowly time varying systems. In particular, it is shown that the performance of such systems cannot be much worse than that of the frozen-time systems which are time invariant. This result is used to characterize a class of indirect adaptive controllers that can stabilize a time-invariant system subjected to both parametric and l-infinity to l-infinity bounded unstructured uncertainty. Pertaining to this class of controllers, a particular indirect adaptive scheme is proposed that provides the greatest upper bound on the size of the unstructured uncertainty for which stability is ensured.

Voulgaris, Petros G.↗
NASA NTRS1992

Optical pattern recognition III; Proceedings of the Meeting, Orlando, FL, Apr. 21, 22, 1992

Consideration is given to transitioning of optical processing into systems (TOPS), optical correlator hardware, phase-only optical correlation filters, optical distortion-invariant correlation filters, and optical neural networks. Particular attention is given to a test target for optical correlators, a TOPS electronic warfare channelizer program, a portable video-rate optical correlator, a joint transform correlator employing electron trapping materials, a novelty filtered optical correlator using a photorefractive crystal, a comparison of correlation performance of smart ternary phase-amplitude filters with gray-scale and binary input scenes, real-time distortion-tolerant composite filters for automatic target identification, landscaping the correlation surface, fast designing of a circular harmonic filter using simulated annealing, feature-based correlation filters for distortion invariance, automatic target recognition using a feature-based optical neural network, and a holographic inner-product processor for pattern recognition.

Casasent, David P.↗
NASA NTRS1993

Coarse-coded higher-order neural networks for PSRI object recognition

A higher-order neural network (HONN) can be designed to be invariant to changes in scale, translation, and inplane rotation. Invariances are built directly into the architecture of a HONN and do not need to be learned. Consequently, fewer training passes and a smaller training set are required to learn to distinguish between objects. The size of the input field is limited, however, because of the memory required for the large number of interconnections in a fully connected HONN. By coarse coding the input image, the input field size can be increased to allow the larger input scenes required for practical object recognition problems. We describe a coarse coding technique and present simulation results illustrating its usefulness and its limitations. Our simulations show that a third-order neural network can be trained to distinguish between two objects in a 4096 x 4096 pixel input field independent of transformations in translation, in-plane rotation, and scale in less than ten passes through the training set. Furthermore, we empirically determine the limits of the coarse coding technique in the object recognition domain.

Spirkovska, Lilly↗
NASA NTRS1993

Three-dimensional object recognition using similar triangles and decision trees

A system, TRIDEC, that is capable of distinguishing between a set of objects despite changes in the objects' positions in the input field, their size, or their rotational orientation in 3D space is described. TRIDEC combines very simple yet effective features with the classification capabilities of inductive decision tree methods. The feature vector is a list of all similar triangles defined by connecting all combinations of three pixels in a coarse coded 127 x 127 pixel input field. The classification is accomplished by building a decision tree using the information provided from a limited number of translated, scaled, and rotated samples. Simulation results are presented which show that TRIDEC achieves 94 percent recognition accuracy in the 2D invariant object recognition domain and 98 percent recognition accuracy in the 3D invariant object recognition domain after training on only a small sample of transformed views of the objects.

Spirkovska, Lilly↗
NASA NTRS1994

Optical-Correlator Neural Network Based On Neocognitron

Multichannel optical correlator implements shift-invariant, high-discrimination pattern-recognizing neural network based on paradigm of neocognitron. Selected as basic building block of this neural network because invariance under shifts is inherent advantage of Fourier optics included in optical correlators in general. Neocognitron is conceptual electronic neural-network model for recognition of visual patterns. Multilayer processing achieved by iteratively feeding back output of feature correlator to input spatial light modulator and updating Fourier filters. Neural network trained by use of characteristic features extracted from target images. Multichannel implementation enables parallel processing of large number of selected features.

Chao, Tien-Hsin↗
NASA NTRS1992

A study of the fine scale motions of incompressible time-developing mixing layers

This work is an extension of a project conducted at the previous CTR summer program and was reported by Chen et al. (1990). In that program, the geometry and topology of the dissipating motions in a variety of shear flows was examined. All data was produced by direct numerical simulations (DNS). The partial derivatives of the velocity field were determined at every grid point in the flow and various invariants and related quantities were computed from the velocity gradient tensor. Motions characterized by high rates of kinetic energy dissipation and high enstrophy were of particular interest. Scatter diagrams of the invariants were mapped out and interesting and unexpected patterns were seen. Each type of shear layer produced its own characteristic scatter plot. In the present project, attention is focused on the incompressible plane mixing layer, and the scatter diagrams are replaced with more useful joint probability density contours. Comparison of the topology of the dissipating motions of flows at different Reynolds numbers are made. Also, plane mixing layers at the same Reynolds number but with different initial conditions are compared.

Soria, J.↗
NASA NTRS1994

Performance evaluation of digital phase-locked loops for advanced deep space transponders

The performances of the digital phase-locked loops (DPLL's) for the advanced deep-space transponders (ADT's) are investigated. DPLL's considered in this article are derived from the analog phase-locked loop, which is currently employed by the NASA standard deep space transponder, using S-domain to Z-domain mapping techniques. Three mappings are used to develop digital approximations of the standard deep space analog phase-locked loop, namely the bilinear transformation (BT), impulse invariant transformation (IIT), and step invariant transformation (SIT) techniques. The performance in terms of the closed loop phase and magnitude responses, carrier tracking jitter, and response of the loop to the phase offset (the difference between in incoming phase and reference phase) is evaluated for each digital approximation. Theoretical results of the carrier tracking jitter for command-on and command-off cases are then validated by computer simulation. Both theoretical and computer simulation results show that at high sampling frequency, the DPLL's approximated by all three transformations have the same tracking jitter. However, at low sampling frequency, the digital approximation using BT outperforms the others. The minimum sampling frequency for adequate tracking performance is determined for each digital approximation of the analog loop. In addition, computer simulation shows that the DPLL developed by BT provides faster response to the phase offset than IIT and SIT.

Nguyen, T. M.↗
NASA NTRS1994

A new approach to the photon localization problem

Since wavelets form a representation of the Poincare group, it is possible to construct a localized superposition of light waves with different frequencies in a Lorentz-covariant manner. This localized wavelet satisfies a Lorentz-invariant uncertainty relation, and also the Lorentz-invariant Parseval's relation. A quantitative analysis is given for the difference between photons and localized waves. It is then shown that this localized entity corresponds to a relativistic photon with a sharply defined momentum in the non-localization limit. Waves are not particles. It is confirmed that the wave-particle duality is subject to the uncertainty principle.

Han, D.↗
NASA NTRS1994

The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

Yeon, Kyu Hwang↗
NASA NTRS1994

Growth-phase thinning of the near-Earth current sheet during the CDAW 6 substorm

The thinning of the near-Earth current sheet during the growth phase of the Coordinated Data Analysis Workshop (CDAW) 6 magnetospheric substorm is studied. The expansion onset of the substorm occurred at 1054 UT, March 22, 1979. During the growth phase, two spacecraft, International Sun Earth Explorer (ISEE) 1 and ISEE 2, were within the current sheet approximately 13 R(sub E) from the Earth and obtained simultaneous high-resolution magnetic data at two points in the current sheet. Plasma data were also provided by the ISEE spacecraft and solar wind data by IMP 8. To facilitate the analysis, the GSM magnetic field data are transformed to a 'neutral sheet coordinate system' in which the new x axis is parallel to the average magnetic field above and below the neutral sheet and the new y axis lies in the GSM equatorial plane. A model based on the assumption that the current sheet is a time-invariant structure fails to predict neutral sheet crossing times. Consequently, the Harris sheet model, which allows one to remove the restriction of time invariancy, is used instead. It is found that during the growth phase, a model parameter corresponding to the thickness of the current sheet decreased exponentially from about 5 R(sub E) to 1 R(sub E) with a time constant of about 14 min. In addition, the ISEE 1 and ISEE 2 neutral sheet crossings after expansion onset indicate that the neutral sheet was moving upward at 7 km/s relative to the spacecraft. Since both crossings occurred in approximately 80 s, the current sheet thickness is estimated to be about 500 km. These results demonstrate that the near-Earth current sheet undergoes dramatic thinning during the substorm growth phase and expansion onset.

Sanny, Jeff↗
NASA NTRS1994

Ionospheric footprint of magnetosheathlike particle precipitation observed by an incoherent scatter radar

We have examined Sondrestrom incoherent scatter radar observations of ionospheric plasma density and temperature distributions and measurements of F region ion drifts that were made during a prenoon pass of the Defense Meteorological Satellite Program (DMSP)-F7 satellite through the radar field of view. The spacecraft traversed a region of intense electron precipitation with a characteristic energy below approximately 200 eV. Particles with such low characteristic energies are believed to be directly or indirectly of magnetosheath origin. The precipitation region had a width about 2 deg invariant latitude and covered the low-latitude boundary layer (LLBL), the cusp, and the equatorward section of the plasma mantle (PM). The corotating radar observed a patch of enhanced electron density and elevated electron temperature in the F2 region between about 10.5 and 12 magnetic local time in the same invariant latitude range where DMSP-F7 detected the soft-electron flux. The ion drift pattern, also obtained by radar, shows that it is unlikely that the plasma patch was produced by solar radiation and advected into the radar field of view. We suggest that the radar observed modifications of the ionospheric plasma distribution, which resulted from direct entry of magnetosheath electrons into the magnetosphere and down to ionospheric altitudes. Model calculations of the ionospheric response to the observed electron precipitation support our interpretation. The spectral characteristics of the electron flux in the LLBL, cusp, and equatorward section of the PM were in this case too similar to allow to distinguish between them by using incoherent scatter radar measurements only.

Watermann, Jurgen↗
NASA NTRS1994

The cosmological dependence of cluster density profiles

We use N-body simulations to study the shape of mean cluster density and velocity profiles in the nonlinear regime formed via gravitational instability. The dependence of the final structure on both cosmology and initial density field is examined, using a grid of cosmologies and scale-free initial power spectra P(k) varies as k(exp n). Einstein-de Sitter, open (Omega(sub 0) = 0.2 and 0.1) and flat, low density (Omega(sub 0) = 0.2 lambda(sub 0) = 0.8) models are examined, with initial spectral indices n = -2, -1 and 0. For each model, we stack clusters in an appropriately scaled manner to define an average density profile in the nonlinear regime. The profiles are well fit by a power law rho(r) varies as r(exp -alpha) for radii whereat the local density contrast is between 100 and 3000. This covers 99% of the cluster volume. We find a clear trend toward steeper slopes (larger alphas) with both increasing n and decreasing Omega(sub 0). The Omega(sub 0) dependence is partially masked by the n dependence; there is degeneracy in the values of alpha between the Einstein-de Sitter and flat, low-density cosmologies. However, the profile slopes in the open models are consistently higher than the Omega = 1 values for the range of n examined. Cluster density profiles are thus potentially useful cosmological diagnostics. We find no evidence for a constant density core in any of the models, although the density profiles do tend to flatten at small radii. Much of the flattening is due to the force softening required by the simulations. An attempt is made to recover the unsoftened profiles assuming angular momentum invariance. The recovered profiles in Einstein-de Sitter cosmologies are consistent with a pure power law up to the highest density contrasts (10(exp 6)) accessible with our resolution. The low-density models show significant deviation from a power law above density contrasts approximately 10(exp 5). We interpret this curvature as reflecting the non-scale-invariant nature of the background cosmology in these models. These results are at the limit of our resolution and so should be tested in the future using simulations with larger numbers of particles. Such simulations will also provide insight on the broader problem of understanding, in a statistical sense, the full phase space structure of collapsed, cosmological halos.

Crone, Mary M.↗
NASA NTRS1994

The dynamic cusp at low altitudes: A case study utilizing Viking, DMSP-F7 and Sondrestrom incoherent scatter radar observations

Coincident multi-instrument magnetospheric and ionospheric observations have made it possible to determine the position of the ionospheric footprint of the magnetospheric cusp and to monitor its evolution over time. The data used include charged particle and magnetic field measurements from the Earth-orbiting Viking and DMSP-F7 satellites, electric field measurements from Viking, interplanetary magnetic field and plasma data from IMP-8, and Sondrestrom incoherent scatter radar observations of the ionospheric plasma density, temperature, and convection. Viking detected cusp precipitation poleward of 75.5 deg invariant latitude. The ionospheric response to the observed electron precipitation was simulated using an auroral model. It predicts enhanced plasma density and elevated electron temperature in the upper E- and F- regions. Sondrestrom radar observations are in agreement with the predictions. The radar detected a cusp signature on each of five consecutive antenna elevation scans covering 1.2h local time. The cusp appeared to be about 2 deg invariant latitude wide, and its ionospheric footprint shifted equatorward by nearly 2 deg during this time, possibly influenced by an overall decrease in the interplanetary magnetic field (IMF) B(sub z) component. The radar plasma drift data and the Viking magnetic and electric field data suggest that the cusp was associated with a continuous, rather than a patchy, merging between the IMF and the geomagnetic field.

Watermann, J.↗
NASA NTRS1993

Solar flux forecasting using mutual information with an optimal delay

Solar flux F(sub 10.7) directly affects the atmospheric density, thereby changing the lifetime and prediction of satellite orbits. For this reason, accurate forecasting of F(sub 10.7) is crucial for orbit determination of spacecraft. Our attempts to model and forecast F(sub 10.7) uncovered highly entangled dynamics. We concluded that the general lack of predictability in solar activity arises from its nonlinear nature. Nonlinear dynamics allow us to predict F(sub 10.7) more accurately than is possible using stochastic methods for time scales shorter than a characteristic horizon, and with about the same accuracy as using stochastic techniques when the forecasted data exceed this horizon. The forecast horizon is a function of two dynamical invariants: the attractor dimension and the Lyapunov exponent. In recent years, estimation of the attractor dimension reconstructed from a time series has become an important tool in data analysis. In calculating the invariants of the system, the first necessary step is the reconstruction of the attractor for the system from the time-delayed values of the time series. The choice of the time delay is critical for this reconstruction. For an infinite amount of noise-free data, the time delay can, in principle, be chosen almost arbitrarily. However, the quality of the phase portraits produced using the time-delay technique is determined by the value chosen for the delay time. Fraser and Swinney have shown that a good choice for this time delay is the one suggested by Shaw, which uses the first local minimum of the mutual information rather than the autocorrelation function to determine the time delay. This paper presents a refinement of this criterion and applies the refined technique to solar flux data to produce a forecast of the solar activity.

Ashrafi, S.↗
NASA NTRS1992

Conservative-coordinate transformations for atmospheric measurements

This lecture describes a technique by which atmospheric measurements of trace species with medium to long lifetimes can be 'coincidentally' compared and validated even though measurements are taken at different locations and different times In other words, the method, under suitable counditions, can remove a large amount of the natural meteorological variability. The technique involves the use of quasi-Lagrangian or conservative coordinates - air parcel tags which are invariant or nearly invariant under the motion of the parcel. The technique is called 'reconstruction', since measurements taken at one location can be reconstructed at different locations. In order to do this, the data are transformed into the conservative coordinates and accumulated. Within the conservative reference frame, much of the meteorological variability is removed. Once enough data are obtained within the system, the observations can be tranformed back into physical space at any location and compared with other measurements. The method by which the trace species data are obtained makes no difference; satellite, balloon, rocket, aircraft and ground-based data all become equivalent and can be intercompared. The conservative-coordinate system not only allows for intercomparison of data, but shows how data can be taken in such a way as to maximize the physical scope of the information. In other words, the method automatically suggests when conditions might be suitable to obtain information with different environmental situations. It also allows for the forecast of constituent fields using only the meteorological forecasts and limited observational data.

Schoeberl, M. R.↗
NASA NTRS1993

A survey of propfan noise propagation at cruise

Acoustic measurements collected during the Propfan Test Assessment (PTA) program in 1989 had demonstrated that cruising Propfans have undesirably high far-field noise level. This study attempts to investigate the source of these noise disturbances generated by a single-rotating propeller with supersonic tip speed. Various atmospheric and propagation effects responsible for shaping the far-field acoustics will be examined. A methodology for analyzing Propfan propagation noise is proposed based on the theory of geometrical acoustics. This approach allows acoustic rays to be traced into the far-field via Snell's law. Amplitude variation along the rays are evaluated by applying the Blokhintzev energy invariant principle. Additional terms are appended to the energy invariant principle to account for propagation and atmospheric effects. A FORTRAN program is written to analyze the rays emitted from a helicoidal source path traced by supersonic helical speed blade tip. Earlier papers by Myers and Farassat have demonstrated the presence of Mach envelopes that lead to formation of caustics. Linear geometric acoustics is used to ascertain the existence of these nonlinear caustics in the far-field. The importance of caustics to Propfan noise generation is then studied.

Sim, Ben WEL-C.↗
NASA NTRS1995

The Mode 1 mechanical crack tip stress field in hyperelastic and incompressible materials

The finite deformation field of a plane strain Mode 1 crack in a hyperelastic and incompressible material was examined under the assumptions of small scale nonlinearity. Finite element analyses were performed for two different material laws, a Neo-Hookean material and a third order invariant of a Rivlin material. The numerical results for both materials were compared to the appropriate theoretical asymptotic solution. A local cavitation locus surrounding the crack tip was identified for the Neo-Hookean material. For the third order invariant Rivlin material, maximum values of the dominant stress component were found close to the surface of the crack, above and below the deformed crack tip.

Quigley, Claudia J.↗
NASA NTRS1996

Study of the velocity gradient tensor in turbulent flow

The behavior of the velocity gradient tensor, A(ij)=delta u(i)/delta x(j), was studied using three turbulent flows obtained from direct numerical simulation The flows studies were: an inviscid calculation of the interaction between two vortex tubes, a homogeneous isotropic flow, and a temporally evolving planar wake. Self-similar behavior for each flow was obtained when A(ij) was normalized with the mean strain rate. The case of the interaction between two vortex tubes revealed a finite sized coherent structure with topological characteristics predictable by a restricted Euler model. This structure was found to evolve with the peak vorticity as the flow approached singularity. Invariants of A(ij) within this structure followed a straight line relationship of the form: gamma(sup 3)+gammaQ+R=0, where Q and R are the second and third invariants of A(ij), and the eigenvalue gamma is nearly constant over the volume of this structure. Data within this structure have local strain topology of unstable-node/saddle/saddle. The characteristics of the velocity gradient tensor and the anisotropic part of a related acceleration gradient tensor H(ij) were also studied for a homogeneous isotropic flow and a temporally evolving planar wake. It was found that the intermediate principal eigenvalue of the rate-of-strain tensor of H(ij) tended to be negative, with local strain topology of the type stable-node/saddle/saddle. There was also a preferential eigenvalue direction. The magnitude of H(ij) in the wake flow was found to be very small when data were conditioned at high local dissipation regions. This result was not observed in the relatively low Reynolds number simulation of homogeneous isotropic flow. A restricted Euler model of the evolution of A(ij) was found to reproduce many of the topological features identified in the simulations.

Cheng, Wei-Ping↗