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At least 883 records · Page 49
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NASA NTRS1986

Preconditioning for first-order spectral discretization

Efficient solution of the equations from spectral discretizations is essential if the high-order accuracy of these methods is to be realized. Direct solution of these equations is rarely feasible, thus iterative techniques are required. A preconditioning scheme for first-order Chebyshev collocation operators is proposed herein, in which the central finite difference mesh is finer than the collocation mesh. Details of the proper techniques for transferring information between the meshes are given here, and the scheme is analyzed by examination of the eigenvalue spectra of the preconditioned operators. The effect of artificial viscosity required in the inversion of the finite difference operator is examined. A second preconditioning scheme, involving a high-order upwind finite difference operator of the van Leer type is also analyzed to provide a comparison with the present scheme. Finally, the performance of the present scheme is verified by application to several test problems.

Streett, C. L.↗
NASA NTRS1984

Wave approach to brightness temperature from a bounded layer of random discrete scatterers

By using the fluctuation-dissipation theorem, the strong fluctuation theory is applied to the calculation of brightness temperatures from a bounded layer of random discrete scatterers with the zeroth- and first-order approximations. Various functional dependences on wavelength, polarization, observation angle, medium depth, scatterer constituents, and other physical parameters are discussed. Theoretical results are favorably matched with experimental data for passive remote sensing of snowpacks.

Jin, Y.-Q.↗
NASA NTRS1986

Discrete-time Markovian-jump linear quadratic optimal control

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.

Chizeck, H. J.↗
NASA NTRS1985

Existence and stability, and discrete BB and rank conditions, for general mixed-hybrid finite elements in elasticity

In this paper, all possible forms of mixed-hybrid finite element methods that are based on multi-field variational principles are examined as to the conditions for existence, stability, and uniqueness of their solutions. The reasons as to why certain 'simplified hybrid-mixed methods' in general, and the so-called 'simplified hybrid-displacement method' in particular (based on the so-called simplified variational principles), become unstable, are discussed. A comprehensive discussion of the 'discrete' BB-conditions, and the rank conditions, of the matrices arising in mixed-hybrid methods, is given. Some recent studies aimed at the assurance of such rank conditions, and the related problem of the avoidance of spurious kinematic modes, are presented.

Xue, W.-M.↗
NASA NTRS1986

Sensitivity analysis of discrete structural systems

Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

Adelman, H. M.↗
NASA NTRS1986

Dynamics of a discrete auroral arc

Porcupine Flight 4 data were used to determine the field-aligned currents associated with a southward moving discrete auroral arc in the postmidnight sector. Three different methods were used for determining the field-aligned current which should give identical results if the arcs are quasi-stationary and no parallel electric field exists between the payload and the dynamo region of the ionosphere. As long as the rocket is above the arc, the three methods agree. The integral of precipitating electron flux, the local magnetic field perturbations, and the divergence of the horizontal Pedersen current all indicate an upward current of 5 + or - 3 microamperes/sq m. Immediately north of the arc a strong downward current of about 10-20 microamperes/sq m is detected. The magnitude, however, is not well known because the rocket's velocity relative to the arc cannot be clearly established. Further north of the southward moving arc, the two methods that can be applied (magnetic field perturbations and divergence of the horizontal Pedersen current) yield contradictory results not only about the magnitude of the current but also about the direction of the current. It is suggested that this discrepancy is due to time-dependent electric field.

Bruening, K.↗
NASA NTRS1986

Time scale analysis of a closed-loop discrete optimal control system

A two-time scale discrete control system is considered. The closed-loop optimal linear quadratic (LQ) regulator for the system requires the solution of a full-order algebraic matrix Riccati equation. Alternatively, the original system is decomposed into reduced-order slow and fast subsystems. The closed-loop optimal control of the subsystems requires the solution of two algebraic matrix Riccati equations of order lower than that required for the full-order system. A composite, closed-loop suboptimal control is created from the sum of the slow and fast feedback optimal controls. Numerical results obtained for an aircraft model show a very close agreement between the exact (optimal) solutions and computationally simpler composite (suboptimal) solutions. The main advantage of the method is the considerable reduction in the overall computational requirements for the closed-loop optimal control of digital flight systems.

Naidu, D. S.↗
NASA NTRS1986

Prediction of helicopter rotor discrete frequency noise: A computer program incorporating realistic blade motions and advanced acoustic formulation

A computer program has been developed at the Langley Research Center to predict the discrete frequency noise of conventional and advanced helicopter rotors. The program, called WOPWOP, uses the most advanced subsonic formulation of Farassat that is less sensitive to errors and is valid for nearly all helicopter rotor geometries and flight conditions. A brief derivation of the acoustic formulation is presented along with a discussion of the numerical implementation of the formulation. The computer program uses realistic helicopter blade motion and aerodynamic loadings, input by the user, for noise calculation in the time domain. A detailed definition of all the input variables, default values, and output data is included. A comparison with experimental data shows good agreement between prediction and experiment; however, accurate aerodynamic loading is needed.

Brentner, K. S.↗
NASA NTRS1986

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Gibson, J. S.↗
NASA NTRS1986

Discrete mechanism damping effects in the solar array flight experiment

Accelerometer data were collected during on-orbit structural dynamic testing of the Solar Array Flight Experiment aboard the Space Shuttle, and were analyzed at Lockheed Missile and Space Co. to determine the amount of damping present in the structure. The results of this analysis indicated that the damping present in the fundamental in-plane mode of the structure substantially exceeded that of the fundamental out-of-plane mode. In an effort to determine the source of the higher in-plane damping, a test was performed involving a small device known as a constant-force spring motor or constant-torque mechanism. Results from this test indicate that this discrete device is at least partially responsible for the increased in-plane modal damping of the Solar Array Flight Experiment structure.

Pinson, E. D.↗
NASA NTRS1987

Diffraction efficiency of photothermoplastic layers for the recording of discrete holograms

An experimental and theoretical study of the dependence of eta of a digital phase Fourier hologram of a point object on the amount of deformation delta and the discrete-structure parameters representing the hologram is detailed. An expression is given for eta. Experiments were performed on photothermoplastic layers based on polyvinyl carbazole and trinitrofluorenone charge transfer complexes. The maximum eta, 2%, is found at delta = 0.56 micron.

Koreshev, S. N.↗
NASA NTRS1986

Inherent robustness of discrete-time adaptive control systems

Global stability robustness with respect to unmodeled dynamics, arbitrary bounded internal noise, as well as external disturbance is shown to exist for a class of discrete-time adaptive control systems when the regressor vectors of these systems are persistently exciting. Although fast adaptation is definitely undesirable, so far as attaining the greatest amount of global stability robustness is concerned, slow adaptation is shown to be not necessarily beneficial. The entire analysis in this paper holds for systems with slowly varying return difference matrices; the plants in these systems need not be slowly varying.

Ma, C. C. H.↗
NASA NTRS1987

Galerkin/Runge-Kutta discretizations for semilinear parabolic equations

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for semilinear parabolic initial boundary value problems. Unlike any classical counterpart, this class offers arbitrarily high, optimal order convergence. In support of this claim, error estimates are proved, and computational results are presented. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗
NASA NTRS1987

Improving stability margins in discrete-time LQG controllers

Some of the problems are discussed which are encountered in the design of discrete-time stochastic controllers for problems that may adequately be described by the Linear Quadratic Gaussian (LQG) assumptions; namely, the problems of obtaining acceptable relative stability, robustness, and disturbance rejection properties. A dynamic compensator is proposed to replace the optimal full state feedback regulator gains at steady state, provided that all states are measurable. The compensator increases the stability margins at the plant input, which may possibly be inadequate in practical applications. Though the optimal regulator has desirable properties the observer based controller as implemented with a Kalman filter, in a noisy environment, has inadequate stability margins. The proposed compensator is designed to match the return difference matrix at the plant input to that of the optimal regulator while maintaining the optimality of the state estimates as directed by the measurement noise characteristics.

Oranc, B. Tarik↗
NASA NTRS1987

Anomalous transport in discrete arcs and simulation of double layers in a model auroral circuit

The evolution and long-time stability of a double layer (DL) in a discrete auroral arc requires that the parallel current in the arc, which may be considered uniform at the source, be diverted within the arc to charge the flanks of the U-shaped double layer potential structure. A simple model is presented in which this current redistribution is effected by anomalous transport based on electrostatic lower hybrid waves driven by the flank structure itself. This process provides the limiting constraint on the double layer potential. The flank charging may be represented as that of a nonlinear transmission line. A simplified model circuit, in which the transmission line is represented by a nonlinear impedance in parallel with a variable resistor, is incorporated in a one-dimensional simulation model to give the current density at the DL boundaries. Results are presented for the scaling of the DL potential as a function of the width of the arc and the saturation efficiency of the lower hybrid instability mechanism.

Smith, Robert A.↗
NASA NTRS1987

Parallel discrete event simulation: A shared memory approach

With traditional event list techniques, evaluating a detailed discrete event simulation model can often require hours or even days of computation time. Parallel simulation mimics the interacting servers and queues of a real system by assigning each simulated entity to a processor. By eliminating the event list and maintaining only sufficient synchronization to insure causality, parallel simulation can potentially provide speedups that are linear in the number of processors. A set of shared memory experiments is presented using the Chandy-Misra distributed simulation algorithm to simulate networks of queues. Parameters include queueing network topology and routing probabilities, number of processors, and assignment of network nodes to processors. These experiments show that Chandy-Misra distributed simulation is a questionable alternative to sequential simulation of most queueing network models.

Reed, Daniel A.↗
NASA NTRS1987

Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗
NASA NTRS1986

Effects of anomalous transport on the potentials of discrete auroral arcs

The evolution of U-shaped double layers in discrete auroral arcs occurs much faster than the global current in the arc flux tube can be redistributed. For asymptotic stability of the arc on MHD time scales, this implies that local transport mechanisms are required to charge the nearly field-aligned flanks of the equipotential structure over an extended region along the magnetic field. The diversion of the uniform upstream current provides a constraint which limits the double-layer potential.

Smith, R. A.↗