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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
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 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 NTRS2000

Acoustic Absorption Characteristics of an Orifice With a Mean Bias Flow

The objective of the study reported here was to acquire acoustic and flow data for numerical validation of impedance models that simulate bias flow through perforates. The impedance model is being developed by researchers at High Technology Corporation. This report documents normal incidence impedance measurements a singular circular orifice with mean flow passing through it. All measurements are made within a 1.12 inch (28.5 mm) diameter impedance tube. The mean flow is introduced upstream of the orifice (with the flow and incident sound wave travelling in the same direction) with an anechoic termination downstream of the orifice. Velocity profiles are obtained upstream of the orifice to characterize the inflow boundary conditions. Velocity in the center of the orifice is also obtained. All velocity measurements are made with a hot wire anemometer and subsequent checked with mass flow measurements made concurrently. All impedance measurements are made using the Two-Microphone Method. Although we have left the analysis of the data to the developers of the impedance models that simulate bias flow through perforate, our initial examination indicates that our results follow the trends consistent with published theory on impedance of perforates with a steady bias flow.

Ahuja, K. K.↗
NASA NTRS1991

Three-dimensional kinematic reconnection of plasmoids

The kinematic reconnection model of Lau and Finn (1990) is applied in a theoretical investigation of three-dimensional plasmoid morphology, as seen in the solar corona and earth magnetotail. The derivation of the governing equations is outlined; long, short, and periodic plasmoid models are developed; and the evolution of the stable and unstable manifolds in these models is presented graphically. It is inferred that sheet currents and tangential discontinuities can form on surfaces topologically identical to those where Delta(phi) about equal to Delta(z) singularities occur in the kinematic reconnection model, and can be broadened in a similar way by nonideal effects. Two such surfaces exist in long plasmoids, and also in short plasmoids in the presence of finite resistivity; the intertwined surfaces characteristic of the periodic plasmoid form a fractal set but merge in the presence of finite resistivity, producing structures similar to those proposed by the sheet-current theory of Parker (1983).

Lau, Yun-Tung↗
NASA NTRS1980

Equilibrium response of flight control systems

The steady-state behavior of an aircraft in response to control and disturbance inputs has a major impact on its performance and flying qualities, and it is, to a large extent, not readily predicted by the aircraft's stability and transient behavior. Singular as well as nonsingular response can result as a consequence of the command vector's definition, i.e., equilibrium in the command vector can imply disequilibrium in the state. The flight control structure can be modified to account for this characteristic, and it is shown that systems with identical eigenvalues and eigenvectors but dissimilar command vectors have markedly different responses.

Stengel, R. F.↗
NASA NTRS1981

Optimal maneuvers at supersonic speeds in a vertical plane

This paper presents several optimal maneuvers of supersonic aircraft in a vertical plane. The general dimensionless equations of motion are derived and the computation of the optimal trajectories are carried out using the aerodynamics and engine characteristics of a light-weight fighter called the supercruiser. Because of the normalizing of the control variables, namely, the load factor and the thrust-to-weight ratio, the results applied to any supersonic aircraft. The optimality of the singular thrust control and the optimal junction of different subarcs are discussed. The proposed method of computing the optimal trajectory is very efficient and makes explicit the selection of the optimal control. The technique should be useful for performance assessment of supersonic aircraft with potential for implementation of onboard flight control system.

Vinh, N. X.↗
NASA NTRS1991

Robust control of systems with real parameter uncertainty and unmodelled dynamics

During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value.

Chang, Bor-Chin↗
NASA NTRS1973

An improved method for the aerodynamic analysis of wing-body-tail configurations in subsonic and supersonic flow. Part 1: Theory and application

A new method has been developed for calculating the pressure distribution and aerodynamic characteristics of wing-body-tail combinations in subsonic and supersonic potential flow. A computer program has been developed to perform the numerical calculations. The configuration surface is subdivided into a large number of panels, each of which contains an aerodynamic singularity distribution. A constant source distribution is used on the body panels, and a vortex distribution having a linear variation in the streamwise direction is used on the wing and tail panels. The normal components of velocity induced at specified control points by each singularity distribution are calculated and make up the coefficients of a system of linear equations relating the strengths of the singularities to the magnitude of the normal velocities. The singularity strengths which satisfy the boundary condition of tangential flow at the control points for a given Mach number and angle of attack are determined by solving this system of equations using an interactive procedure. Once the singularity strengths are known, the pressure coefficients are calculated, and the forces and moments acting on the configuration determined by numerical integration.

Woodward, F. A.↗
NASA NTRS1988

A methodology for the synthesis of robust feedback systems

A new methodology is developed for the synthesis of linear, time-variant (LTI) controllers for multivariable LTI systems. The resulting closed-loop system is nominally stable and exhibits a known level of performance. In addition, robustness of the feedback system is guaranteed, i.e., stability and performance are retained in the presence of multiple unstructured uncertainty blocks located at various points in the feedback loop. The design technique is referred to as the Causality Recovery Methodology (CRM). The CRM relies on the Youla parameterization of all stabilizing compensators to ensure nominal stability of the feedback system. A frequency-domain inequality in terms of the structured singular value mu defines the robustness specification. The optimal compensator, with respect to the mu condition, is shown to be noncausal in general. The aim of the CRM is to find a stable, causal transfer function matrix that approximates the robustness characteristics of the optimal solution. The CRM, via a series of infinite-dimensional convex programs, produces a closed-loop system whose performance robustness is at least as good as that of any initial design. The algorithm is approximated by a finite dimensional process for the purposes of implementation. Two numerical examples confirm the potential viability of the CRM concept; however, the robustness improvement comes at the expense of increased computational burden and compensator complexity.

Milich, David Albert↗
NASA NTRS1987

Singular perturbations and time scales (SPaTS) in discrete control systems-An overview

Recent developments in the theory of singular perturbations and time scales (SPaTS) in discrete control systems are reviewed. Sources of discrete models and the effect of the discretizing interval on the model are examined. The analysis of two-time scale systems is presented to bring out typical characteristic features of SPaTS. In the control of the two-time scale systems, the important issue of multirate sampling is addressed.

Naidu, D. S.↗
NASA NTRS1988

Eigenstructure assignment for the control of highly augmented aircraft

Eigenstructure assignment is utilized to design flight control laws for aircraft with many control effectors. It is shown that a previous eigenstructure design for the flight propulsion control coupling (FPCC) aircraft lateral dynamics with three control surfaces exhibits a lack of stability robustness because the control distribution matrix is nearly rank-deficient. A method is mapped back, reducing the control space to two dimensions by using the singular value decomposition. After the design is complete, the controller is mapped back to the original three-dimensional control space. This design approach yields a controller with both smaller gains and improved multivariable stability margins at the aircraft inputs. An interesting characteristics of the control mapping, as applied to the given example, is that the most effective inputs have the larger gains while the less effective inputs have smaller gains.

Sobel, Kenneth M.↗
NASA NTRS1991

Helicopter flight-control design using an H(2) method

Rate-command and attitude-command flight-control designs for a UH-60 helicopter in hover are presented and were synthesized using an H(2) method. Using weight functions, this method allows the direct shaping of the singular values of the sensitivity, complementary sensitivity, and control input transfer-function matrices to give acceptable feedback properties. The designs were implemented on the Vertical Motion Simulator, and four low-speed hover tasks were used to evaluate the control system characteristics. The pilot comments from the accel-decel, bob-up, hovering turn, and side-step tasks indicated good decoupling and quick response characteristics. However, an underlying roll PIO tendency was found to exist away from the hover condition, which was caused by a flap regressing mode with insufficient damping.

Takahashi, Marc D.↗
NASA NTRS1988

A simple, analytic 3-dimensional downburst model based on boundary layer stagnation flow

A simple downburst model is developed for use in batch and real-time piloted simulation studies of guidance strategies for terminal area transport aircraft operations in wind shear conditions. The model represents an axisymmetric stagnation point flow, based on velocity profiles from the Terminal Area Simulation System (TASS) model developed by Proctor and satisfies the mass continuity equation in cylindrical coordinates. Altitude dependence, including boundary layer effects near the ground, closely matches real-world measurements, as do the increase, peak, and decay of outflow and downflow with increasing distance from the downburst center. Equations for horizontal and vertical winds were derived, and found to be infinitely differentiable, with no singular points existent in the flow field. In addition, a simple relationship exists among the ratio of maximum horizontal to vertical velocities, the downdraft radius, depth of outflow, and altitude of maximum outflow. In use, a microburst can be modeled by specifying four characteristic parameters, velocity components in the x, y and z directions, and the corresponding nine partial derivatives are obtained easily from the velocity equations.

Oseguera, Rosa M.↗
NASA NTRS1989

Finite element modeling of frictionally restrained composite interfaces

The use of special interface finite elements to model frictional restraint in composite interfaces is described. These elements simulate Coulomb friction at the interface, and are incorporated into a standard finite element analysis of a two-dimensional isolated fiber pullout test. Various interfacial characteristics, such as the distribution of stresses at the interface, the extent of slip and delamination, load diffusion from fiber to matrix, and the amount of fiber extraction or depression are studied for different friction coefficients. The results are compared to those obtained analytically using a singular integral equation approach, and those obtained by assuming a constant interface shear strength. The usefulness of these elements in micromechanical modeling of fiber-reinforced composite materials is highlighted.

Ballarini, Roberto↗
NASA NTRS2010

Establishing Consensus Turbulence Statistics for Hot Subsonic Jets

Many tasks in fluids engineering require knowledge of the turbulence in jets. There is a strong, although fragmented, literature base for low order statistics, such as jet spread and other meanvelocity field characteristics. Some sources, particularly for low speed cold jets, also provide turbulence intensities that are required for validating Reynolds-averaged Navier-Stokes (RANS) Computational Fluid Dynamics (CFD) codes. There are far fewer sources for jet spectra and for space-time correlations of turbulent velocity required for aeroacoustics applications, although there have been many singular publications with various unique statistics, such as Proper Orthogonal Decomposition, designed to uncover an underlying low-order dynamical description of turbulent jet flow. As the complexity of the statistic increases, the number of flows for which the data has been categorized and assembled decreases, making it difficult to systematically validate prediction codes that require high-level statistics over a broad range of jet flow conditions. For several years, researchers at NASA have worked on developing and validating jet noise prediction codes. One such class of codes, loosely called CFD-based or statistical methods, uses RANS CFD to predict jet mean and turbulent intensities in velocity and temperature. These flow quantities serve as the input to the acoustic source models and flow-sound interaction calculations that yield predictions of far-field jet noise. To develop this capability, a catalog of turbulent jet flows has been created with statistics ranging from mean velocity to space-time correlations of Reynolds stresses. The present document aims to document this catalog and to assess the accuracies of the data, e.g. establish uncertainties for the data. This paper covers the following five tasks: Document acquisition and processing procedures used to create the particle image velocimetry (PIV) datasets. Compare PIV data with hotwire and laser Doppler velocimetry (LDV) data published in the open literature. Compare different datasets acquired at roughly the same flow conditions to establish uncertainties. Create a consensus dataset for a range of hot jet flows, including uncertainty bands. Analyze this consensus dataset for self-consistency and compare jet characteristics to those of the open literature. One final objective fulfilled by this work was the demonstration of a universal scaling for the jet flow fields, at least within the region of interest to aeroacoustics. The potential core length and the spread rate of the half-velocity radius were used to collapse of the mean and turbulent velocity fields over the first 20 jet diameters in a highly satisfying manner.

Bridges, James↗
NASA NTRS1984

Modeling material failure with a vectorized routine

The computational aspects of modelling material failure in structural wood members are presented with particular reference to vector processing aspects. Wood members are considered to be highly orthotropic, inhomogeneous, and discontinuous due to the complex microstructure of wood material and the presence of natural growth characteristics such as knots, cracks and cross grain in wood members. The simulation of strength behavior of wood members is accomplished through the use of a special purpose finite element/fracture mechanics routine, program STARW (Strength Analysis Routine for Wood). Program STARW employs quadratic finite elements combined with singular crack tip elements in a finite element mesh. Vector processing techniques are employed in mesh generation, stiffness matrix formation, simultaneous equation solution, and material failure calculations. The paper addresses these techniques along with the time and effort requirements needed to convert existing finite element code to a vectorized version. Comparisons in execution time between vectorized and nonvectorized routines are provided.

Cramer, S. M.↗
NASA NTRS1972

The collision singularity in a perturbed n-body problem.

Collision of all bodies in a perturbed n-body problem is analyzed by an extension of the author's results for a perturbed two-body problem (1969). A procedure is set forth to prove that the absolute value of energy in a perturbed n-body system remains bounded until the moment of collision. It is shown that the characteristics of motion in both perturbed problems are basically the same.

Sperling, H. J.↗
NASA NTRS1981

Edge delamination in angle-ply composite laminates, part 5

A theoretical method was developed for describing the edge delamination stress intensity characteristics in angle-ply composite laminates. The method is based on the theory of anisotropic elasticity. The edge delamination problem is formulated using Lekhnitskii's complex-variable stress potentials and an especially developed eigenfunction expansion method. The method predicts exact orders of the three-dimensional stress singularity in a delamination crack tip region. With the aid of boundary collocation, the method predicts the complete stress and displacement fields in a finite-dimensional, delaminated composite. Fracture mechanics parameters such as the mixed-mode stress intensity factors and associated energy release rates for edge delamination can be calculated explicity. Solutions are obtained for edge delaminated (theta/-theta theta/-theta) angle-ply composites under uniform axial extension. Effects of delamination lengths, fiber orientations, lamination and geometric variables are studied.

Wang, S. S.↗