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At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Effects of structural offset, axial shortening, and gravitational torque on the slewing of a flexible spacecraft

The large-angle maneuvering of a Shuttle-beam-reflector spacecraft in the plane of a circular earth orbit is examined by considering the effects of the structural offset connection, the axial shortening, and the gravitational torque on the slewing motion. The offset effect is analyzed by changing the attachment point of the reflector to the beam. As the attachment point is moved away from the mass center of the reflector, the responses of the nonlinear system deviate from those of the linearized system. The axial geometric shortening effect induced by the deformation of the beam contributes to the system equations through second order terms in the modal amplitudes and rates. The gravitational torque effect is relatively small.

Li, Feiyue↗
NASA NTRS1992

Recognition of partially occluded threat objects using the annealed Hopefield network

Recognition of partially occluded objects has been an important issue to airport security because occlusion causes significant problems in identifying and locating objects during baggage inspection. The neural network approach is suitable for the problems in the sense that the inherent parallelism of neural networks pursues many hypotheses in parallel resulting in high computation rates. Moreover, they provide a greater degree of robustness or fault tolerance than conventional computers. The annealed Hopfield network which is derived from the mean field annealing (MFA) has been developed to find global solutions of a nonlinear system. In the study, it has been proven that the system temperature of MFA is equivalent to the gain of the sigmoid function of a Hopfield network. In our early work, we developed the hybrid Hopfield network (HHN) for fast and reliable matching. However, HHN doesn't guarantee global solutions and yields false matching under heavily occluded conditions because HHN is dependent on initial states by its nature. In this paper, we present the annealed Hopfield network (AHN) for occluded object matching problems. In AHN, the mean field theory is applied to the hybird Hopfield network in order to improve computational complexity of the annealed Hopfield network and provide reliable matching under heavily occluded conditions. AHN is slower than HHN. However, AHN provides near global solutions without initial restrictions and provides less false matching than HHN. In conclusion, a new algorithm based upon a neural network approach was developed to demonstrate the feasibility of the automated inspection of threat objects from x-ray images. The robustness of the algorithm is proved by identifying occluded target objects with large tolerance of their features.

Kim, Jung H.↗
NASA NTRS1993

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

Scott, James R.↗
NASA NTRS1992

Comparison between the performance of two classes of fuzzy controllers

This paper presents an application comparison between two classes of fuzzy controllers: the Clearness Transformation Fuzzy Controller (CTFC) and the CRI-based Fuzzy Controller. The comparison is performed by studying the application of the controllers to simulation examples of nonlinear systems. The CTFC is a new approach for the organization of fuzzy controllers based on a cognitive model of parameter driven control, the notion of fuzzy patterns to represent fuzzy knowledge and the Clearness Transformation Rule of Inference (CTRI) for approximate reasoning. The approach facilitates the implementation of the basic modules of the controller: the fuzzifier, defuzzifier, and the control protocol in a rule-based architecture. The CTRI scheme for approximate reasoning does not require the formation of fuzzy relation matrices yielding improved performance in comparison with the traditional organization of fuzzy controllers.

Janabi, T. H.↗
NASA NTRS1992

Error-based adaptive non-linear control and regions of feasibility

The nonlinear adaptive algorithm of Kanellakopoulos et al. (1991) was modified to produce an error-based algorithm. This permits global stabilizability for a large subset of pure-feedback nonlinear systems. The algorithm was demonstrated on the single-input stabilization problem, but extends easily to the multiple input tracking problems.

Teel, Andrew R.↗
NASA NTRS1993

Pinching solutions of slender cylindrical jets

Simplified equations for slender jets are derived for a circular jet of one fluid flowing into an ambient second fluid, the flow being confined in a circular tank. Inviscid flows are studied which include both surface tension effects and Kelvin-Helmholtz instability. For slender jets a coupled nonlinear system of equations is found for the jet shape and the axial velocity jump across it. The equations can break down after a finite time and similarity solutions are constructed, and studied analytically and numerically. The break-ups found pertain to the jet pinching after a finite time, without violation of the slender jet ansatz. The system is conservative and admissible singular solutions are those which conserve the total energy, mass, and momentum. Such solutions are constructed analytically and numerically, and in the case of vortex sheets with no surface tension certain solutions are given in closed form.

Papageorgiou, Demetrios T.↗
NASA NTRS1993

Delay analysis of combinations of pass transistors and classical logic gates

Combinations of pass transistors and logic gates driving nonlinear capacitive loads are analyzed for the presence of characteristics that will permit easier and more accurate digital logic simulation. Accurate time delay models are developed by studying the nature of the response of simplified circuit models to variations of input waveform rise and fall times and output loading. The nonlinear effects of the CMOS logic devices are minimized to permit easier interpretation of the influence of nonlinear capacitive loads. The performance of a CMOS inverter with a complex nonlinear load consisting of a pass transistor that separates a range of capacitances is compared to the same inverter circuit with a linear capacitive load to develop an understanding of the unique requirements of modeling a nonlinear system. Several methods of modeling the delay of CMOS circuits are reviewed, and a multi-parameter linear model is described. General guidelines for designing CMOS circuits with complex load circuits are developed, emphasizing that the circuit output rise delays and fall delays must be separately analyzed.

Gibson, Jonathan S.↗
NASA NTRS1993

The block adaptive multigrid method applied to the solution of the Euler equations

In the present study, a scheme capable of solving very fast and robust complex nonlinear systems of equations is presented. The Block Adaptive Multigrid (BAM) solution method offers multigrid acceleration and adaptive grid refinement based on the prediction of the solution error. The proposed solution method was used with an implicit upwind Euler solver for the solution of complex transonic flows around airfoils. Very fast results were obtained (18-fold acceleration of the solution) using one fourth of the volumes of a global grid with the same solution accuracy for two test cases.

Pantelelis, Nikos↗
NASA NTRS1992

The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomials coefficients using trees

This note is concerned with the explicit symbolic computation of expressions involving differential operators and their actions on functions. The derivation of specialized numerical algorithms, the explicit symbolic computation of integrals of motion, and the explicit computation of normal forms for nonlinear systems all require such computations. More precisely, if R = k(x(sub 1),...,x(sub N)), where k = R or C, F denotes a differential operator with coefficients from R, and g member of R, we describe data structures and algorithms for efficiently computing g. The basic idea is to impose a multiplicative structure on the vector space with basis the set of finite rooted trees and whose nodes are labeled with the coefficients of the differential operators. Cancellations of two trees with r + 1 nodes translates into cancellation of O(N(exp r)) expressions involving the coefficient functions and their derivatives.

Crouch, P. E.↗
NASA NTRS1994

Maneuvering and control of flexible space robots

This paper is concerned with a flexible space robot capable of maneuvering payloads. The robot is assumed to consist of two hinge-connected flexible arms and a rigid end-effector holding a payload; the robot is mounted on a rigid platform floating in space. The equations of motion are nonlinear and of high order. Based on the assumption that the maneuvering motions are one order of magnitude larger than the elastic vibrations, a perturbation approach permits design of controls for the two types of motion separately. The rigid-body maneuvering is carried out open loop, but the elastic motions are controlled closed loop, by means of discrete-time linear quadratic regulator theory with prescribed degree of stability. A numerical example demonstrates the approach. In the example, the controls derived by the perturbation approach are applied to the original nonlinear system and errors are found to be relatively small.

Meirovitch, Leonard↗
NASA NTRS1992

Simulation of particle mixing by turbulent convective flows on the connection machine

Mixing of particles by chaotic flow fields was simulated on the Connection Machine. Each cell was assigned to the processor, and the coordinates of particles residing on the cell were kept in the local memory of the processor. This approach implies the exchange between the local memories, when a particle moves from one cell to another. Approximately 10 exp 5 particles were injected into a time-dependent flow field obtained by solving the nonlinear system of partial differential equations describing turbulent thermal convection. The flow field was calculated on a CRAY, and data were transferred to a CM-200 through a high-speed HIPPI channel.

Malevsky, A. V.↗
NASA NTRS1994

Multilevel algorithms for nonlinear optimization

Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of the derivative computations for MDO. The algorithms are an extension to the nonlinear programming problem of the successful class of local Brown-Brent algorithms for nonlinear equations. Our extensions allow the user to partition constraints into arbitrary blocks to fit the application, and they separately process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization strategy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations. Multilevel algorithms for solving nonlinear systems of equations are a special case of the multilevel optimization methods. In this case, they can be viewed as a trust-region globalization of the Brown-Brent class.

Alexandrov, Natalia↗
NASA NTRS1993

Observability during planetary approach navigation

The objective of the research is to develop an analytic technique to predict the relative navigation capability of different Earth-based radio navigation measurements. In particular, the problem is to determine the relative ability of geocentric range and Doppler measurements to detect the effects of the target planet gravitational attraction on the spacecraft during the planetary approach and near-encounter mission phases. A complete solution to the two-dimensional problem has been developed. Relatively simple analytic formulas are obtained for range and Doppler measurements which describe the observability content of the measurement data along the approach trajectories. An observability measure is defined which is based on the observability matrix for nonlinear systems. The results show good agreement between the analytic observability analysis and the computational batch processing method.

Bishop, Robert H.↗
NASA NTRS1995

Implicit method for the computation of unsteady flows on unstructured grids

An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Inviscid and viscous unsteady flows are computed to validate the procedure. The issue of the mass matrix which arises with vertex-centered finite volume schemes is addressed. The present formulation allows the mass matrix to be inverted indirectly. A mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies. As an example of flow over bodies in relative motion, flow over a multi-element airfoil system undergoing deployment is computed.

Venkatakrishnan, V.↗
NASA NTRS1996

Multigrid Acceleration of Time-Accurate DNS of Compressible Turbulent Flow

An efficient scheme for the direct numerical simulation of 3D transitional and developed turbulent flow is presented. Explicit and implicit time integration schemes for the compressible Navier-Stokes equations are compared. The nonlinear system resulting from the implicit time discretization is solved with an iterative method and accelerated by the application of a multigrid technique. Since we use central spatial discretizations and no artificial dissipation is added to the equations, the smoothing method is less effective than in the more traditional use of multigrid in steady-state calculations. Therefore, a special prolongation method is needed in order to obtain an effective multigrid method. This simulation scheme was studied in detail for compressible flow over a flat plate. In the laminar regime and in the first stages of turbulent flow the implicit method provides a speed-up of a factor 2 relative to the explicit method on a relatively coarse grid. At increased resolution this speed-up is enhanced correspondingly.

Broeze, Jan↗
NASA NTRS1993

On the Prediction of the Number of Solitons Excited by an Arbitrary Potential: An Observation from Inverse Scattering

A heuristic estimate for the soliton production rate by a pulse is verified for the Korteweg - de Vries equation using inverse scattering. An observation from this result, which is shown to hold for some other nonlinear equations and for the case of the 'forced' nonlinear Schroedinger equation, is that production is determined by quantities that are invariant under rescaling of the original nonlinear equations. We speculate that this result may be useful to the development of an inverse scattering theory for 'forced' nonlinear systems.

Hansen, P. J.↗
NASA NTRS1997

Using High-Order Methods on Lower-Order Geometries

The desire to obtain acoustic information from the numerical solution of a nonlinear system of equations is a demanding proposition for a computational algorithm. High-order accuracy is required for the propagation of high-frequency, low-amplitude waves. The accuracy of an algorithm can be compromised by low-order errors that naturally occur in the solution of a particular problem. Such errors arise from two sources: the presence of discontinuities in the flow field or because the geometry on which the problem is defined is not everywhere smooth to the order of the scheme. The performance of high-order accurate essentially non-oscillatory (ENO) schemes on piecewise smooth solutions is well documented. Herein, the performance of these methods on smooth solutions defined on piecewise smooth geometries is investigated. The propagation of sound in a quasi-one-dimensional nozzle is considered as a test case. Some of the issues involved in the extension to two spatial dimensions are discussed.

Casper, Jay↗
NASA NTRS1997

Adaptive Performance Seeking Control Using Fuzzy Model Reference Learning Control and Positive Gradient Control

Performance Seeking Control attempts to find the operating condition that will generate optimal performance and control the plant at that operating condition. In this paper a nonlinear multivariable Adaptive Performance Seeking Control (APSC) methodology will be developed and it will be demonstrated on a nonlinear system. The APSC is comprised of the Positive Gradient Control (PGC) and the Fuzzy Model Reference Learning Control (FMRLC). The PGC computes the positive gradients of the desired performance function with respect to the control inputs in order to drive the plant set points to the operating point that will produce optimal performance. The PGC approach will be derived in this paper. The feedback control of the plant is performed by the FMRLC. For the FMRLC, the conventional fuzzy model reference learning control methodology is utilized, with guidelines generated here for the effective tuning of the FMRLC controller.

Kopasakis, George↗