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At least 1,513 records · Page 84

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NASA NTRS1996

Accurate Time/Frequency Transfer Method Using Bi-Directional WDM Transmission

An accurate time transfer method is proposed using b-directional wavelength division multiplexing (WDM) signal transmission along a single optical fiber. This method will be used in digital telecommunication networks and yield a time synchronization accuracy of better than 1 ns for long transmission lines over several tens of kilometers. The method can accurately measure the difference in delay between two wavelength signals caused by the chromatic dispersion of the fiber in conventional simple bi-directional dual-wavelength frequency transfer methods. We describe the characteristics of this difference in delay and then show that the accuracy of the delay measurements can be obtained below 0.1 ns by transmitting 156 Mb/s times reference signals of 1.31 micrometer and 1.55 micrometers along a 50 km fiber using the proposed method. The sub-nanosecond delay measurement using the simple bi-directional dual-wavelength transmission along a 100 km fiber with a wavelength spacing of 1 nm in the 1.55 micrometer range is also shown.

Imaoka, Atsushi↗

NASA NTRS1995

Two-Flux and Green's Function Method for Transient Radiative Transfer in a Semi-Transparent Layer

A method using a Green's function is developed for computing transient temperatures in a semitransparent layer by using the two-flux method coupled with the transient energy equation. Each boundary of the layer is exposed to a hot or cold radiative environment, and is heated or cooled by convection. The layer refractive index is larger than one, and the effect of internal reflections is included with the boundaries assumed diffuse. The analysis accounts for internal emission, absorption, heat conduction, and isotropic scattering. Spectrally dependent radiative properties are included, and transient results are given to illustrate two-band spectral behavior with optically thin and thick bands. Transient results using the present Green's function method are verified for a gray layer by comparison with a finite difference solution of the exact radiative transfer equations; excellent agreement is obtained. The present method requires only moderate computing times and incorporates isotropic scattering without additional complexity. Typical temperature distributions are given to illustrate application of the method by examining the effect of strong radiative heating on one side of a layer with convective cooling on the other side, and the interaction of strong convective heating with radiative cooling from the layer interior.

Siegel, Robert↗

NASA NTRS1996

Single Transducer Ultrasonic Imaging Method that Eliminates the Effect of Plate Thickness Variation in the Image

This article describes a single transducer ultrasonic imaging method that eliminates the effect of plate thickness variation in the image. The method thus isolates ultrasonic variations due to material microstructure. The use of this method can result in significant cost savings because the ultrasonic image can be interpreted correctly without the need for machining to achieve precise thickness uniformity during nondestructive evaluations of material development. The method is based on measurement of ultrasonic velocity. Images obtained using the thickness-independent methodology are compared with conventional velocity and c-scan echo peak amplitude images for monolithic ceramic (silicon nitride), metal matrix composite and polymer matrix composite materials. It was found that the thickness-independent ultrasonic images reveal and quantify correctly areas of global microstructural (pore and fiber volume fraction) variation due to the elimination of thickness effects. The thickness-independent ultrasonic imaging method described in this article is currently being commercialized under a cooperative agreement between NASA Lewis Research Center and Sonix, Inc.

Roth, Don J.↗

NASA NTRS1996

Commercial Implementation of Ultrasonic Velocity Imaging Methods via Cooperative Agreement Between NASA Lewis Research Center and Sonix, Inc.

This article describes the commercial implementation of ultrasonic velocity imaging methods developed and refined at NASA Lewis Research Center on the Sonix c-scan inspection system. Two velocity imaging methods were implemented: thickness-based and non-thickness-based reflector plate methods. The article demonstrates capabilities of the commercial implementation and gives the detailed operating procedures required for Sonix customers to achieve optimum velocity imaging results. This commercial implementation of velocity imaging provides a 100x speed increase in scanning and processing over the lab-based methods developed at LeRC. The significance of this cooperative effort is that the aerospace and other materials development-intensive industries which use extensive ultrasonic inspection for process control and failure analysis will now have an alternative, highly accurate imaging method commercially available.

Roth, Don J.↗

NASA NTRS1996

Standard Test Methods for Textile Composites

Standard testing methods for composite laminates reinforced with continuous networks of braided, woven, or stitched fibers have been evaluated. The microstructure of these textile' composite materials differs significantly from that of tape laminates. Consequently, specimen dimensions and loading methods developed for tape type composites may not be applicable to textile composites. To this end, a series of evaluations were made comparing testing practices currently used in the composite industry. Information was gathered from a variety of sources and analyzed to establish a series of recommended test methods for textile composites. The current practices established for laminated composite materials by ASTM and the MIL-HDBK-17 Committee were considered. This document provides recommended test methods for determining both in-plane and out-of-plane properties. Specifically, test methods are suggested for: unnotched tension and compression; open and filled hole tension; open hole compression; bolt bearing; and interlaminar tension. A detailed description of the material architectures evaluated is also provided, as is a recommended instrumentation practice.

Masters, John E.↗

NASA NTRS1996

Comparison of New Methods for Assessing Community Response to High Energy Impulsive Sounds

The latest CHABA Working Group to have reviewed published information about the effects of high energy impulsive sounds (such as sonic booms) on communities has recommended abandonment of the dosage-response relationship identified by its predecessor in favor of two alternate prediction method. Both of the new assessment methods continue to rely on C-weighted measurements of impulsive sounds One of the two assessment methods retains the standard assumptions of the 'equal energy hypothesis' (the notion that annoyance is governed simply by the product of level, duration, and number noise events), and further assumes that the rate of growth of the prevalence of annoyance is proportional to the rate of growth of loudness with level. The other assessment method, however, assumes a level dependent (non-equal energy) summation of the C-weighted sound exposure levels of individual impulsive events. Since predictions of the second method are distribution-dependent, they are not readily represents graphically in the form of a single dosage-response function. The effects on annoyance predictions of variance in distributions of CSEL values of impulsive sounds are explored in this presentation.

Fidell, Sanford↗

NASA NTRS1995

The Schwinger Variational Method

Variational methods have proven invaluable in theoretical physics and chemistry, both for bound state problems and for the study of collision phenomena. The application of the Schwinger variational (SV) method to e-molecule collisions and molecular photoionization has been reviewed previously. The present chapter discusses the implementation of the SV method as applied to e-molecule collisions. Since this is not a review of cross section data, cross sections are presented only to server as illustrative examples. In the SV method, the correct boundary condition is automatically incorporated through the use of Green's function. Thus SV calculations can employ basis functions with arbitrary boundary conditions. The iterative Schwinger method has been used extensively to study molecular photoionization. For e-molecule collisions, it is used at the static exchange level to study elastic scattering and coupled with the distorted wave approximation to study electronically inelastic scattering.

Huo, Winifred M.↗

NASA NTRS1996

Multigrid and Krylov Subspace Methods for the Discrete Stokes Equations

Discretization of the Stokes equations produces a symmetric indefinite system of linear equations. For stable discretizations, a variety of numerical methods have been proposed that have rates of convergence independent of the mesh size used in the discretization. In this paper, we compare the performance of four such methods: variants of the Uzawa, preconditioned conjugate gradient, preconditioned conjugate residual, and multigrid methods, for solving several two-dimensional model problems. The results indicate that where it is applicable, multigrid with smoothing based on incomplete factorization is more efficient than the other methods, but typically by no more than a factor of two. The conjugate residual method has the advantage of being both independent of iteration parameters and widely applicable.

Elman, Howard C.↗

NASA NTRS1997

Mechanical System Reliability and Cost Integration Using a Sequential Linear Approximation Method

The development of new products is dependent on product designs that incorporate high levels of reliability along with a design that meets predetermined levels of system cost. Additional constraints on the product include explicit and implicit performance requirements. Existing reliability and cost prediction methods result in no direct linkage between variables affecting these two dominant product attributes. A methodology to integrate reliability and cost estimates using a sequential linear approximation method is proposed. The sequential linear approximation method utilizes probability of failure sensitivities determined from probabilistic reliability methods as well a manufacturing cost sensitivities. The application of the sequential linear approximation method to a mechanical system is demonstrated.

Kowal, Michael T.↗

NASA NTRS1997

Continued Development of the Discontinuous Galerkin Method for Computational Aeroacoustic Applications

The formulation and the implementation of boundary conditions within the context of the quadrature-free form of the discontinuous Galerkin method are presented for several types of boundary conditions for the Euler equations. An important feature of the discontinuous Galerkin method is that the interior point algorithm is well behaved in the neighborhood of the boundary and requires no modifications. This feature leads to a simple and accurate treatment for wall boundary conditions and simple inflow and outflow boundary conditions. Curved walls are accurately treated with only minor changes to the implementation described in earlier work. The 'perfectly matched layer' approach to nonreflecting boundary conditions is easily applied to the discontinuous Galerkin. The compactness of the discontinuous Galerkin method makes it better suited for buffer-zone-type methods than high-order finite-difference methods. Results are presented for wall, characteristic inflow and outflow, and nonreflecting boundary conditions.

Atkins, H. L.↗

NASA NTRS1997

Modeling of Structural-Acoustic Interaction Using Coupled FE/BE Method and Control of Interior Acoustic Pressure Using Piezoelectric Actuators

A coupled finite element (FE) and boundary element (BE) approach is presented to model full coupled structural/acoustic/piezoelectric systems. The dual reciprocity boundary element method is used so that the natural frequencies and mode shapes of the coupled system can be obtained, and to extend this approach to time dependent problems. The boundary element method is applied to interior acoustic domains, and the results are very accurate when compared with limited exact solutions. Structural-acoustic problems are then analyzed with the coupled finite element/boundary element method, where the finite element method models the structural domain and the boundary element method models the acoustic domain. Results for a system consisting of an isotropic panel and a cubic cavity are in good agreement with exact solutions and experiment data. The response of a composite panel backed cavity is then obtained. The results show that the mass and stiffness of piezoelectric layers have to be considered. The coupled finite element and boundary element equations are transformed into modal coordinates, which is more convenient for transient excitation. Several transient problems are solved based on this formulation. Two control designs, a linear quadratic regulator (LQR) and a feedforward controller, are applied to reduce the acoustic pressure inside the cavity based on the equations in modal coordinates. The results indicate that both controllers can reduce the interior acoustic pressure and the plate deflection.

Mei, Chuh↗

NASA NTRS1997

Improvements in Block-Krylov Ritz Vectors and the Boundary Flexibility Method of Component Synthesis

A method of dynamic substructuring is presented which utilizes a set of static Ritz vectors as a replacement for normal eigenvectors in component mode synthesis. This set of Ritz vectors is generated in a recurrence relationship, proposed by Wilson, which has the form of a block-Krylov subspace. The initial seed to the recurrence algorithm is based upon the boundary flexibility vectors of the component. Improvements have been made in the formulation of the initial seed to the Krylov sequence, through the use of block-filtering. A method to shift the Krylov sequence to create Ritz vectors that will represent the dynamic behavior of the component at target frequencies, the target frequency being determined by the applied forcing functions, has been developed. A method to terminate the Krylov sequence has also been developed. Various orthonormalization schemes have been developed and evaluated, including the Cholesky/QR method. Several auxiliary theorems and proofs which illustrate issues in component mode synthesis and loss of orthogonality in the Krylov sequence have also been presented. The resulting methodology is applicable to both fixed and free- interface boundary components, and results in a general component model appropriate for any type of dynamic analysis. The accuracy is found to be comparable to that of component synthesis based upon normal modes, using fewer generalized coordinates. In addition, the block-Krylov recurrence algorithm is a series of static solutions and so requires significantly less computation than solving the normal eigenspace problem. The requirement for less vectors to form the component, coupled with the lower computational expense of calculating these Ritz vectors, combine to create a method more efficient than traditional component mode synthesis.

Carney, Kelly Scott↗

NASA NTRS1997

Multilevel methods for elliptic problems on unstructured grids

Multilevel methods on unstructured grids for elliptic problems are reviewed. The advantages of these techniques are the flexible approximation of the boundaries of complicated physical domains and the ability to adapt the grid to the resolution of fine scaled structures. Multilevel methods, which include multigrid methods and domain decomposition methods, depend on the correct splitting of appropriate finite element spaces. The standard splittings used in the structured grid case cannot be directly extended to unstructured grids due to their requirement for a hierarchical grid structure. Issues related to the application of multilevel methods to unstructured grids are discussed, including how the coarse spaces and transfer operators are defined and how different types of boundary conditions are treated. An obvious way to generate a coarse mesh is to regrid the physical domain several times. Several alternatives are proposed and discussed: node nested coarse spaces, agglomerated coarse spaces and algebraically generated coarse spaces.

Chan, Tony F.↗

NASA NTRS1997

The Path Resistance Method for Bounding the Smallest Nontrivial Eigenvalue of a Laplacian

We introduce the path resistance method for lower bounds on the smallest nontrivial eigenvalue of the Laplacian matrix of a graph. The method is based on viewing the graph in terms of electrical circuits; it uses clique embeddings to produce lower bounds on lambda(sub 2) and star embeddings to produce lower bounds on the smallest Rayleigh quotient when there is a zero Dirichlet boundary condition. The method assigns priorities to the paths in the embedding; we show that, for an unweighted tree T, using uniform priorities for a clique embedding produces a lower bound on lambda(sub 2) that is off by at most an 0(log diameter(T)) factor. We show that the best bounds this method can produce for clique embeddings are the same as for a related method that uses clique embeddings and edge lengths to produce bounds.

Guattery, Stephen↗

NASA NTRS1995

Modified Interior Distance Functions (Theory and Methods)

In this paper we introduced and developed the theory of Modified Interior Distance Functions (MIDF's). The MIDF is a Classical Lagrangian (CL) for a constrained optimization problem which is equivalent to the initial one and can be obtained from the latter by monotone transformation both the objective function and constraints. In contrast to the Interior Distance Functions (IDF's), which played a fundamental role in Interior Point Methods (IPM's), the MIDF's are defined on an extended feasible set and along with center, have two extra tools, which control the computational process: the barrier parameter and the vector of Lagrange multipliers. The extra tools allow to attach to the MEDF's very important properties of Augmented Lagrangeans. One can consider the MIDFs as Interior Augmented Lagrangeans. It makes MIDF's similar in spirit to Modified Barrier Functions (MBF's), although there is a fundamental difference between them both in theory and methods. Based on MIDF's theory, Modified Center Methods (MCM's) have been developed and analyzed. The MCM's find an unconstrained minimizer in primal space and update the Lagrange multipliers, while both the center and the barrier parameter can be fixed or updated at each step. The MCM's convergence was investigated, and their rate of convergence was estimated. The extension of the feasible set and the special role of the Lagrange multipliers allow to develop MCM's, which produce, in case of nondegenerate constrained optimization, a primal and dual sequences that converge to the primal-dual solutions with linear rate, even when both the center and the barrier parameter are fixed. Moreover, every Lagrange multipliers update shrinks the distance to the primal dual solution by a factor 0 less than gamma less than 1 which can be made as small as one wants by choosing a fixed interior point as a 'center' and a fixed but large enough barrier parameter. The numericai realization of MCM leads to the Newton MCM (NMCM). The approximation for the primal minimizer one finds by Newton Method followed by the Lagrange multipliers update. Due to the MCM convergence, when both the center and the barrier parameter are fixed, the condition of the MDF Hessism and the neighborhood of the primal ninimizer where Newton method is 'well' defined remains stable. It contributes to both the complexity and the numerical stability of the NMCM.

Polyak, Roman A.↗

NASA NTRS1995

The Use of Kirchhoff's Method in Jet Aeroacoustics

Supersonic jet aeroacoustics will be studied using computational techniques. In the study, a Kirchhoff method is used to predict flow generated noise in the mid- and far-fields. This type of method shows promise because it is based on surface integrals and not the volume integrals found in traditional acoustic prediction methods. The Kirchhoff method is dependent on accurate prediction of flow variables in the near-field. Here, computational fluid dynamics (CFD) programs are used for these predictions. Specifically, an existing large eddy simulation (LES) code will be modified for aeroacoustic applications. Issues involved in the implementation of the Kirchhoff method as well as the coupling with the CFD code will be discussed. Important physical noise parameters will be identified and investigated in the study.

Lyrintzis, Anastasios S.↗

NASA NTRS1994

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Nash, Stephen G.↗

NASA NTRS1997

Experiences Using Lightweight Formal Methods for Requirements Modeling

This paper describes three case studies in the lightweight application of formal methods to requirements modeling for spacecraft fault protection systems. The case studies differ from previously reported applications of formal methods in that formal methods were applied very early in the requirements engineering process, to validate the evolving requirements. The results were fed back into the projects, to improve the informal specifications. For each case study, we describe what methods were applied, how they were applied, how much effort was involved, and what the findings were. In all three cases, formal methods enhanced the existing verification and validation processes, by testing key properties of the evolving requirements, and helping to identify weaknesses. We conclude that the benefits gained from early modeling of unstable requirements more than outweigh the effort needed to maintain multiple representations.

Easterbrook, Steve↗