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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

A multi-point force appropriation method based upon a singular value decomposition approach

Force appropriation methods aim to provide an estimate for the force pattern required to excite a 'pure' normal mode in a vibration test where multiple exciters are available. In this paper, a new method based upon a Singular Value Decompositon approach is presented. The appropriated force vector which minimizes the in-plane response components while maximizing the required quadrature components is found, subject to a fixed force norm. The method can accommodate more transducers than exciters and also more exciters than effective degrees of freedom. The method is demonstrated upon a six degree of freedom theoretical model and it is shown that an estimate for the effective degrees of freedom can be obtained.

Juang, Jer-Nan↗
NASA NTRS1990

Reduced and simplified chemical kinetics for air dissociation using Computational Singular Perturbation

The Computational Singular Perturbation CSP methods is employed (1) in the modeling of a homogeneous isothermal reacting system and (2) in the numerical simulation of the chemical reactions in a hypersonic flowfield. Reduced and simplified mechanisms are constructed. The solutions obtained on the basis of these approximate mechanisms are shown to be in very good agreement with the exact solution based on the full mechanism. Physically meaningful approximations are derived. It is demonstrated that the deduction of these approximations from CSP is independent of the complexity of the problem and requires no intuition or experience in chemical kinetics.

Goussis, D. A.↗
NASA NTRS1989

Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series

Two dimensions of a dynamical system given by experimental time series are distinguished. Statistical dimension gives a theoretical upper bound for the minimal number of degrees of freedom required to describe the attractor up to the accuracy of the data, taking into account sampling and noise problems. The dynamical dimension is the intrinsic dimension of the attractor and does not depend on the quality of the data. Singular Spectrum Analysis (SSA) provides estimates of the statistical dimension. SSA also describes the main physical phenomena reflected by the data. It gives adaptive spectral filters associated with the dominant oscillations of the system and clarifies the noise characteristics of the data. SSA is applied to four paleoclimatic records. The principal climatic oscillations and the regime changes in their amplitude are detected. About 10 degrees of freedom are statistically significant in the data. Large noise and insufficient sample length do not allow reliable estimates of the dynamical dimension.

Vautard, R.↗
NASA NTRS1990

Optimal control of singularly perturbed nonlinear systems with state-variable inequality constraints

The established necessary conditions for optimality in nonlinear control problems that involve state-variable inequality constraints are applied to a class of singularly perturbed systems. The distinguishing feature of this class of two-time-scale systems is a transformation of the state-variable inequality constraint, present in the full order problem, to a constraint involving states and controls in the reduced problem. It is shown that, when a state constraint is active in the reduced problem, the boundary layer problem can be of finite time in the stretched time variable. Thus, the usual requirement for asymptotic stability of the boundary layer system is not applicable, and cannot be used to construct approximate boundary layer solutions. Several alternative solution methods are explored and illustrated with simple examples.

Calise, A. J.↗
NASA NTRS1989

Inversion of imaging spectrometry data using singular value decomposition

The use of imaging spectrometers, which acquire data that are both spectrally contiguous images and spatially contiguous spectra, for quantitative remote sensing of the earth is addressed. Such data sets cannot be analyzed fully using either existing spectroscopic or image techniques. Singular value decomposition (SVD) is used here for spectral unmixing and determination of the spatial scales of mixing. It is shown that when it is used to invert the mixing endmember library, SVD allows more insight into library characteristics and more control of the inversion process than other commonly used matrix inversion techniques.

Boardman, Joe W.↗
NASA NTRS1990

Heating of the corona by magnetic singularities

Theoretical models of current-sheet formation and magnetic heating in the solar corona are examined analytically. The role of photospheric connectivity in determining the topology of the coronal magnetic field and its equilibrium properties is explored; nonequilibrium models of current-sheet formation (assuming an initially well connected field) are described; and particular attention is given to models with discontinuous connectivity, where magnetic singularities arise from smooth footpoint motions. It is shown that current sheets arise from connectivities in which the photospheric flux structure is complex, with three or more polarity regions and a magnetic null point within the corona.

Antiochos, Spiro K.↗
NASA NTRS1991

Can a man-made universe be achieved by quantum tunneling without an initial singularity?

Essentially all modern particle theories suggest the possible existence of a false vacuum state; a metastable state with an energy density that cannot be lowered except by means of a very slow phase transition. Inflationary cosmology makes use of such a state to drive the expansion of the big bang, allowing the entire observed universe to evolve from a very small initial mass. A sphere of false vacuum in the present universe, if larger than a certain critical mass, could inflate to form a new universe which would rapidly detach from its parent. A false vacuum bubble of this size, however, cannot be produced classically unless an initial singularity is present from the outset. The possibility is explored that a bubble of subcritical size, which classically would evolve to a maximum size and collapse, might instead tunnel through a barrier to produce a new universe. The tunneling rate using semiclassical quantum gravity is estimated, and some interesting ambiguities in the formulas are discovered.

Guth, Alan H.↗
NASA NTRS1992

Vibration attenuation of the NASA Langley evolutionary structure experiment using H(sub infinity) and structured singular value (micron) robust multivariable control techniques

The use is studied of active control to attenuate structural vibrations of the NASA Langley Phase Zero Evolutionary Structure due to external disturbance excitations. H sub infinity and structured singular value (mu) based control techniques are used to analyze and synthesize control laws for the NASA Langley Controls Structures Interaction (CSI) Evolutionary Model (CEM). The CEM structure experiment provides an excellent test bed to address control design issues for large space structures. Specifically, control design for structures with numerous lightly damped, coupled flexible modes, collocated and noncollocated sensors and actuators and stringent performance specifications. The performance objectives are to attenuate the vibration of the structure due to external disturbances, and minimize the actuator control force. The control design problem formulation for the CEM Structure uses a mathematical model developed with finite element techniques. A reduced order state space model for the control design is formulated from the finite element model. It is noted that there are significant variations between the design model and the experimentally derived transfer function data.

Balas, Gary J.↗
NASA NTRS1990

Singularity-robustness and task-prioritization in configuration control of redundant robots

The authors present a singularity-robust task-prioritized reformulation of the configuration control for redundant robot manipulators. This reformation suppresses large joint velocities to induce minimal errors in the task performance by modifying the task trajectories. Furthermore, the same framework provides a means for assignment of priorities between the basic task of end-effector motion and the user-defined additional task for utilizing redundancy. This allows automatic relaxation of the additional task constraints in favor of the desired end-effector motion when both cannot be achieved exactly.

Seraji, H.↗
NASA NTRS1993

Configuration-Control Scheme Copes With Singularities

Improved configuration-control scheme for robotic manipulator having redundant degrees of freedom suppresses large joint velocities near singularities, at expense of small trajectory errors. Provides means to enforce order of priority of tasks assigned to robot. Basic concept of configuration control of redundant robot described in "Increasing The Dexterity Of Redundant Robots" (NPO-17801).

Seraji, Homayoun↗
NASA NTRS1993

Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.

Vaughan, William W.↗
NASA NTRS1993

The complex structured singular value

A tutorial introduction to the complex structured singular value (mu) is presented, with an emphasis on the mathematical aspects of mu. The mu-based methods discussed here have been useful for analyzing the performance and robustness properties of linear feedback systems. Several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared, and a simple synthesis problem is studied. Uncertain systems are represented using linear fractional transformations which naturally unify the frequency-domain and state space methods.

Packard, A.↗
NASA NTRS1993

Reconstruction of low-dimensional magnetospheric dynamics by singular spectrum analysis

Singular spectrum analysis was used to study global magnetospheric dynamics using time series auroral electrojet (AE) data. The calculated correlation dimension of approximately 2.5 confirms the low dimensionality of earlier results. This technique indicated that global magnetospheric dynamics can be described by three variables whose dynamical features were obtained from the AE data.

Sharma, A. S.↗
NASA NTRS1994

A note on singularities of the 3-D Euler equation

In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.

Tanveer, S.↗
NASA NTRS1994

Finite-surface method for the Maxwell equations with corner singularities

The finite-surface method for the two-dimensional Maxwell equations in generalized coordinates is extended to treat perfect conductor boundaries with sharp corners. Known singular forms of the grid and the electromagnetic fields in the neighborhood of each corner are used to obtain accurate approximations to the surface and line integrals appearing in the method. Numerical results are presented for a harmonic plane wave incident on a finite flat plate. Comparisons with exact solutions show good agreement.

Vinokur, Marcel↗
NASA NTRS1995

Electronic structure and the van Hove singularity scenario in high-T(sub c)H(g)Ba2CuO(4+delta) superconductors

The electronic structure and the hole concentrations in the high Tc superconductor HgBa2CuO(4+delta) (delta = O, 1) has been investigated by employing a first principles full potential self-consistent LMTO method with the local density functional theory. The scalar relativistic effects have been considered. The hole concentrations of the Cu-d and O-p(x,y) orbitals are seen to be larger for the HgBaCuO5 system than those of the HgBaCuO4 solid. However, the van Hove singularity (vHs) induced Cu-d and O-p peak which is seen to lie comparatively away and above the Fermi level in the delta = 1 system shifts towards the Fermi level in the delta = 0 system. Thus, the superconducting behavior appears to originate from the occurrence of the vHs peak at the Fermi level. The Fermi surface nesting area in the delta = 0 compound is seen to be larger than in the delta = 1 compound. The calculation reveals that the increase in pressure on the crystal enhances the hole concentrations but without showing any optimum value, On the other hand, the vHs peak approaches to-wards the Fermi level with pressure and crosses the Fermi surface near V/Vo approximately equals 0.625 (V and Vo are the crystal volumes at high and normal pressures, respectively). Our calculated value of the bulk modulus equal to 0.626 Mbar predicts the occurrence of this crossover at about 24 GPa which is in complete agreement with the experimental value. At this pressure the compound has maximum nesting area and self-doped behavior.

Agrawal, Bal K.↗
NASA NTRS1996

On the Stochastic Quantization Method: Characteristics and Applications to Singular Systems

Introducing the generalized Langevin equation, we extend the stochastic quantization method so as to deal with singular dynamical systems beyond the ordinary territory of quantum mechanics. We also show how the uncertainty relation is built up to the quantum mechanical limit with respect to fictitious time, irrespective of its initial value, within the framework of the usual stochastic quantization method.

Kanenaga, Masahiko↗