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NASA NTRS1991

On the embedding-dimension analysis of AE and AL time series

Several authors have employed the embedding-dimension method to analyze time series of geomagnetic indices, with differing results for the value of the correlation dimension nu. It is argued that these differences may arise from corresponding differences in the length and construction of the various data sets used. Practical application of the method to sets of discretized data requires use of a delay time scale set by the autocorrelation time of the data set. It is found that a particular data set containing 35 days of AE exhibits an autocorrelation time tau(c) longer by an order of magnitude than that of a short-duration (less than 5 days) set, raising the possibility that extant analyses of long-duration sets may have employed delay times shorter than tau(c). In addition, the power spectrum of AE reveals modulation at a period of 24 hr. A numerical experiment on the logistic map shows that such modulation introduces an extra degree of freedom in the data, resulting in an augmented correlation dimension.

Shan, Lin-Hua↗

NASA NTRS1991

Robustness analysis of multirate and periodically time varying systems

A new method for analyzing the stability and robustness of multirate and periodically time varying systems is presented. It is shown that a multirate or periodically time varying system can be transformed into an equivalent time invariant system. For a SISO system, traditional gain and phase margins can be found by direct application of the Nyquist criterion to this equivalent time invariant system. For a MIMO system, structured and unstructured singular values can be used to determine the system's robustness. The limitations and implications of utilizing this equivalent time invariant system for calculating gain and phase margins, and for estimating robustness via singular value analysis are discussed.

Berg, Martin C.↗

NASA NTRS1992

Real-Time Connected-Element Radio Interferometry

In connected-element-interferometry (CEI), differences between times of arrival of signals at two antennas measured more accurately than in very-long-baseline interferometry (VLBI). Analog and digital fiber-optic links along relatively short baseline enable transmission of precise timing signals and real-time digital processing to determine phase delays between signals received at stations A and B. Baseline typically of order of tens of kilometers. Techniques adaptable to radio laboratories and navigation systems requiring distribution of precise time signals and accurate measurements of time.

Edwards, Charles D., Jr.↗

NASA NTRS1992

Central difference TVD and TVB schemes for time dependent and steady state problems

We use central differences to solve the time dependent Euler equations. The schemes are all advanced using a Runge-Kutta formula in time. Near shocks, a second difference is added as an artificial viscosity. This reduces the scheme to a first order upwind scheme at shocks. The switch that is used guarantees that the scheme is locally total variation diminishing (TVD). For steady state problems it is usually advantageous to relax this condition. Then small oscillations do not activate the switches and the convergence to a steady state is improved. To sharpen the shocks, different coefficients are needed for different equations and so a matrix valued dissipation is introduced and compared with the scalar viscosity. The connection between this artificial viscosity and flux limiters is shown. Any flux limiter can be used as the basis of a shock detector for an artificial viscosity. We compare the use of the van Leer, van Albada, mimmod, superbee, and the 'average' flux limiters for this central difference scheme. For time dependent problems, we need to use a small enough time step so that the CFL was less than one even though the scheme was linearly stable for larger time steps. Using a total variation bounded (TVB) Runge-Kutta scheme yields minor improvements in the accuracy.

Jorgenson, P.↗

NASA NTRS1991

A two-dimensional time domain near zone to far zone transformation

In a previous paper, a time domain transformation useful for extrapolating 3-D near zone finite difference time domain (FDTD) results to the far zone was presented. In this paper, the corresponding 2-D transform is outlined. While the 3-D transformation produced a physically observable far zone time domain field, this is not convenient to do directly in 2-D, since a convolution would be required. However, a representative 2-D far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required it can be obtained by inverse Fourier transform of the final frequency domain result.

Luebbers, Raymond J.↗

NASA NTRS1991

A two-dimensional time domain near zone to far zone transformation

A time domain transformation useful for extrapolating three dimensional near zone finite difference time domain (FDTD) results to the far zone was presented. Here, the corresponding two dimensional transform is outlined. While the three dimensional transformation produced a physically observable far zone time domain field, this is not convenient to do directly in two dimensions, since a convolution would be required. However, a representative two dimensional far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required, it can be obtained by inverse Fourier transform of the final frequency domain result.

Luebbers, Raymond J.↗

NASA NTRS1991

Methodology for object-oriented real-time systems analysis and design: Software engineering

Successful application of software engineering methodologies requires an integrated analysis and design life-cycle in which the various phases flow smoothly 'seamlessly' from analysis through design to implementation. Furthermore, different analysis methodologies often lead to different structuring of the system so that the transition from analysis to design may be awkward depending on the design methodology to be used. This is especially important when object-oriented programming is to be used for implementation when the original specification and perhaps high-level design is non-object oriented. Two approaches to real-time systems analysis which can lead to an object-oriented design are contrasted: (1) modeling the system using structured analysis with real-time extensions which emphasizes data and control flows followed by the abstraction of objects where the operations or methods of the objects correspond to processes in the data flow diagrams and then design in terms of these objects; and (2) modeling the system from the beginning as a set of naturally occurring concurrent entities (objects) each having its own time-behavior defined by a set of states and state-transition rules and seamlessly transforming the analysis models into high-level design models. A new concept of a 'real-time systems-analysis object' is introduced and becomes the basic building block of a series of seamlessly-connected models which progress from the object-oriented real-time systems analysis and design system analysis logical models through the physical architectural models and the high-level design stages. The methodology is appropriate to the overall specification including hardware and software modules. In software modules, the systems analysis objects are transformed into software objects.

Schoeffler, James D.↗

NASA NTRS1992

Long-term particle flux variability indicated by comparison of Interplanetary Dust Experiment (IDE) timed impacts for LDEF's first year in orbit with impact data for the entire 5.75-year orbital lifetime

The electronic sensors of the Interplanetary Dust Experiment (IDE) recorded precise impact times and approximate directions for submicron to approximately 100-micron size particles on all six primary sides of the spacecraft for the first 346 days of the Long Duration Exposure Facility (LDEF) orbital mission. Previously-reported analyses of the timed impact data have established their spatio-temporal features, including the demonstration that a preponderance of the particles in this regime are orbital debris and that a large fraction of the debris particles are encountered as megameter-size clouds, some of which persist for long times. Short-term fluxes within such clouds can rise several orders of magnitude above the long-term average. These finding are consistent with the results of the first catastrophic hypervelocity laboratory impacts on a real satellite, recently reported in the press. Analysis continues on the geometric and evolutionary characteristics of these clouds, as well as on the isolation and characterization of the natural micrometeoroid component in the IDE data, but the unexpectedly large short-term variations in debris flux raises the question of how representative an indication of the multi-year average flux is given by the nearly one year of timed data. It has, therefore, always been one of the goals of IDE to conduct an optical survey of the craters on the IDE detectors, to obtain full-mission fluxes for comparisons with the timed data. This work is underway, and the results presently in hand are significant. Optical scanning of the ram and wake (East and West) panels is complete, and it is clear that the first year was in some respects not representative of the subsequent years. The 5.75-year average flux on East panel was 90 percent of the value predicted by the average flux recorded during the first year, while it was only 34 percent on West panel. This suggests that western hemisphere spacecraft launches are a major contributor to the long-term flux and that their contribution is primarily in the smaller end of the size distribution. This conclusion follows from the fact that a closely-spaced series of launch failures (Titan, Delta, Ariane, and Challenger) caused a virtual hiatus in launch activity during a large part of the later years of the LDEF mission. We hope to provide a quantification of the particle size distribution function in this case.

Mulholland, J. Derral↗

NASA NTRS1992

Real-time processing of radar return on a parallel computer

NASA is working with the FAA to demonstrate the feasibility of pulse Doppler radar as a candidate airborne sensor to detect low altitude windshears. The need to provide the pilot with timely information about possible hazards has motivated a demand for real-time processing of a radar return. Investigated here is parallel processing as a means of accommodating the high data rates required. A PC based parallel computer, called the transputer, is used to investigate issues in real time concurrent processing of radar signals. A transputer network is made up of an array of single instruction stream processors that can be networked in a variety of ways. They are easily reconfigured and software development is largely independent of the particular network topology. The performance of the transputer is evaluated in light of the computational requirements. A number of algorithms have been implemented on the transputers in OCCAM, a language specially designed for parallel processing. These include signal processing algorithms such as the Fast Fourier Transform (FFT), pulse-pair, and autoregressive modelling, as well as routing software to support concurrency. The most computationally intensive task is estimating the spectrum. Two approaches have been taken on this problem, the first and most conventional of which is to use the FFT. By using table look-ups for the basis function and other optimizing techniques, an algorithm has been developed that is sufficient for real time. The other approach is to model the signal as an autoregressive process and estimate the spectrum based on the model coefficients. This technique is attractive because it does not suffer from the spectral leakage problem inherent in the FFT. Benchmark tests indicate that autoregressive modeling is feasible in real time.

Aalfs, David D.↗

NASA NTRS1992

Test of an orbiting hydrogen maser clock system using laser time transfer

We describe a joint Smithsonian Astrophysical Laboratory/National Aeronautics and Space Administration (SAO/NASA) program for flight testing a atomic hydrogen maser clock system designed for long-term operation in space. The clock system will be carried by a shuttle-launched EURECA spacecraft. Comparisons with earth clocks to measure the clock's long-term frequency stability (tau = 10(exp 4) seconds) will be made using laser time transfer from existing NASA laser tracking stations. We describe the design of the maser clock and its control systems, and the laser timing technique. We describe the precision of station time synchronization and the limitations in the comparison between the earth and space time scales owing to gravitational and relativistic effects. We will explore the implications of determining the spacecraft's location by an on-board Global Position System (GPS) receiver, and of using microwave techniques for time and frequency transfer.

Vessot, Robert F. C.↗

NASA NTRS1991

Time-dependent aerodynamic analysis of ducted and unducted propfans at angle of attack

A three-dimensional unsteady aerodynamic analysis is described for predicting the time-dependent flow about ducted and unducted propfans operating at angle of attack. Although the freestream is assumed to be uniform, the flow relative to the rotating blades varies with circumferential position, resulting in an inherent unsteadiness due to the nonaxial inflow. The time-dependent Euler equations are solved utilizing a Runge-Kutta time-stepping scheme. The analysis is based on a finite-volume discretization employing a multiple-block grid network. To permit the use of large calculation time steps, an implicit residual smoothing scheme previously tested for unsteady flow calculations in two dimensions is extended to three spatial dimensions. For unducted propfans, a single H-type grid block is used for each blade passage to determine the time-periodic flowfield. For ducted propfans (ultra-high bypass fans) a body-centered C-type grid is wrapped about the cowl to improve the accuracy of the analysis in the high gradient flow region near the cowl leading edge. Numerical results are compared with available data for both ducted and unducted propfans operating at angle of attack.

Hall, Edward J.↗

NASA NTRS1992

Central difference TVD and TVB schemes for time dependent and steady state problems

Jorgenson, P.↗

NASA NTRS1992

A new explicit variable time-integration self-starting methodology for computational structural dynamics

A new explicit variable time-integration methodology and architecture which possesses self-starting attributes, eliminates the need to involve acceleration computations, and which has improved accuracy characteristics in comparison to the traditional central-difference-type formulations customarily advocated is described for applicability to computational structural dynamics. To sharpen the focus of the present study, an explicit variable time-integration architecture which is relatively simple, yet effective, is described. Unlike variable explicit time-integration formulations adopted in the past, the present self-starting variable time-integration architecture and implementation aspects facilitate a simplified representation and a straightforward and effective approach for combining finite element meshes requiring different time steps in a single analysis. Numerical test cases are provided which demonstrate the applicability of the proposed formulations.

Tamma, Kumar K.↗

NASA NTRS1990

The effect of molecular relaxation processes in air on the rise time of sonic booms

A theory is developed to explain the effect of molecular relaxation processes on the rise time of sonic booms. To determine the rise time of sonic booms, both O2 and N2 relaxation processes must be included. The N2 relaxation process delays the shock pressure reaching the maximum pressure, and the O2 relaxation process causes a shock profile to have a gentle slope. The N2 relaxation controls the lower part of overpressure; the O2 relaxation controls the higher part. The constant rise time curves show that the rise times increase as the overpressures and humidity decrease. The present approach gives longer rise times than those acquired by Bass et al. for given shock overpressures.

Kang, Jongmin↗

NASA NTRS1990

Real-time quality assurance testing using photonic techniques: Application to iodine water system

A feasibility study of the use of inspection systems incorporating photonic sensors and multivariate analyses to provide an instrumentation system that in real-time assures quality and that the system in control has been conducted. A system is in control when the near future of the product quality is predictable. Off-line chemical analyses can be used for a chemical process when slow kinetics allows time to take a sample to the laboratory and the system provides a recovery mechanism that returns the system to statistical control without intervention of the operator. The objective for this study has been the implementation of do-it-right-the-first-time and just-in-time philosophies. The Environment Control and Life Support Systems (ECLSS) water reclamation system that adds iodine for biocidal control is an ideal candidate for the study and implementation of do-it-right-the-first-time technologies.

Arendale, W. F.↗

NASA NTRS1993

Training high performance skills using above real-time training

The Above Real-Time Training (ARTT) concept is a unique approach to training high performance skills. ARTT refers to a training paradigm that places the operator in a simulated environment that functions at faster than normal time. Such a training paradigm represents a departure from the intuitive, but not often supported, feeling that the best practice is determined by the training environment with the highest fidelity. This approach is hypothesized to provide greater 'transfer value' per simulation trial, by incorporating training techniques and instructional features into the simulator. These techniques allow individuals to acquire these critical skills faster and with greater retention. ARTT also allows an individual trained in 'fast time' to operate at what appears to be a more confident state, when the same task is performed in a real-time environment. Two related experiments are discussed. The findings appear to be consistent with previous findings that show positive effects of task variation during training. Moreover, ARTT has merit in improving or maintaining transfer with sharp reductions in training time. There are indications that the effectiveness of ARTT varies as a function of task content and possibly task difficulty. Other implications for ARTT are discussed along with future research directions.

Guckenberger, Dutch↗

NASA NTRS1992

Two neural network algorithms for designing optimal terminal controllers with open final time

Multilayer neural networks, trained by the backpropagation through time algorithm (BPTT), have been used successfully as state-feedback controllers for nonlinear terminal control problems. Current BPTT techniques, however, are not able to deal systematically with open final-time situations such as minimum-time problems. Two approaches which extend BPTT to open final-time problems are presented. In the first, a neural network learns a mapping from initial-state to time-to-go. In the second, the optimal number of steps for each trial run is found using a line-search. Both methods are derived using Lagrange multiplier techniques. This theoretical framework is used to demonstrate that the derived algorithms are direct extensions of forward/backward sweep methods used in N-stage optimal control. The two algorithms are tested on a Zermelo problem and the resulting trajectories compare favorably to optimal control results.

Plumer, Edward S.↗

NASA NTRS1993

Long-term microparticle flux variability indicated by comparison of Interplanetary Dust Experiment (IDE) timed impacts for LDEF's first year in orbit with impact data for the entire 5.77-year orbital lifetime

The electronic sensors of the Interplanetary Dust Experiment (IDE) recorded precise impact times and approximate directions for submicron to approximately 100 micron size particles on all six primary sides of the spacecraft for the first 346 days of the LDEF orbital mission. Previously-reported analyses of the timed impact data have established their spatio-temporal features, including the demonstration that a preponderance of the particles in this regime are orbital debris and that a large fraction of the debris particles are encountered in megameter-size clouds. Short-term fluxes within such clouds can rise several orders of magnitude above the long-term average. These unexpectedly large short-term variations in debris flux raise the question of how representative an indication of the multi-year average flux is given by the nearly one year of timed data. One of the goals of the IDE was to conduct an optical survey of impact sites on detectors that remained active during the entire LDEF mission, to obtain full-mission fluxes. We present here the comparisons and contrasts among the new IDE optical survey impact data, the IDE first-year timed impact data, and impact data from other LDEF micrometeoroid and debris experiments. The following observations are reported: (1) the 5.77 year long-term integrated microparticle impact fluxes recorded by IDE detectors matched the integrated impact fluxes measured by other LDEF investigators for the same period; (2) IDE integrated microparticle impact fluxes varied by factors from 0.5 to 8.3 for LDEF days 1-346, 347-2106 and 1-2106 (5.77 years) on rows 3 (trailing edge, or West), 6 (South side), 12 (North side), and the Earth and Space ends; and (3) IDE integrated microparticle impact fluxes varied less than 3 percent for LDEF days 1-346, 347-2106 and 1-2106 (5.77 years) on row 9 (leading edge, or East). These results give further evidence of the accuracy and internal consistency of the recorded IDE impact data. This leads to the further conclusion that the utility of long-term ratios for impacts on various sides of a stabilized satellite in low Earth orbit (LEO) is extremely limited. These observations and their consequences highlight the need for continuous, real time monitoring of the dynamic microparticle environment in LEO.

Simon, Charles G.↗