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NASA NTRS1992

Ni-H2 cell separator matrix engineering

This project was initiated to develop alternative separator materials to the previously used asbestos matrices which were removed from the market for health and environmental reasons. The objective of the research was to find a material or combination of materials that had the following characteristics: (1) resistant to the severe conditions encountered in Ni-H2 cells; (2) satisfactory electrical, electrolyte management, and thermal management properties to function properly; (3) environmentally benign; and (4) capable of being manufactured into a separator matrix. During the course of the research it was discovered that separators prepared from wettable polyethylene fibers along and in combination with potassium titanate pigment performed satisfactory in preliminary characterization tests. Further studies lead to the optimization of the separator composition and manufacturing process. Single ply separator sheets were manufactured with 100 percent polyethylene fibers and also with a combination of polyethylene fibers and potassium titanate pigment (PKT) in the ratio of 60 percent PKT and 40 percent fibers. A pilot paper machine was used to produce the experimental separator material by a continuous, wet laid process. Both types of matrices were produced at several different area densities (grams/sq m).

Scott, W. E.↗

NASA NTRS1992

Rational approximations from power series of vector-valued meromorphic functions

Let F(z) be a vector-valued function, F: C yields C(sup N), which is analytic at z = 0 and meromorphic in a neighborhood of z = 0, and let its Maclaurin series be given. In this work we developed vector-valued rational approximation procedures for F(z) by applying vector extrapolation methods to the sequence of partial sums of its Maclaurin series. We analyzed some of the algebraic and analytic properties of the rational approximations thus obtained, and showed that they were akin to Pade approximations. In particular, we proved a Koenig type theorem concerning their poles and a de Montessus type theorem concerning their uniform convergence. We showed how optical approximations to multiple poles and to Laurent expansions about these poles can be constructed. Extensions of the procedures above and the accompanying theoretical results to functions defined in arbitrary linear spaces was also considered. One of the most interesting and immediate applications of the results of this work is to the matrix eigenvalue problem. In a forthcoming paper we exploited the developments of the present work to devise bona fide generalizations of the classical power method that are especially suitable for very large and sparse matrices. These generalizations can be used to approximate simultaneously several of the largest distinct eigenvalues and corresponding eigenvectors and invariant subspaces of arbitrary matrices which may or may not be diagonalizable, and are very closely related with known Krylov subspace methods.

Sidi, Avram↗

NASA NTRS1990

A probabilistic model for the evaluation of fault-tolerant multiprocessor systems using concurrent error detection

A probabilistic model to evaluate fault-tolerant multiprocessor systems has been developed. The matrix-based model and the analysis algorihtms based on it are described. Various probabilities associated with an algorithm-based fault tolerance system are discussed and the fault coverage of a given check is derived analytically and illustrated with examples. The probability matrices that are formed by introducing the spatial probabilities into the matrix model are considered. Based on these matrices, a technique is developed to determine the combined coverage of multiple numbers of checks. Examples of the analysis of systems using the model are given.

Nair, V. S. S.↗

NASA NTRS1992

Application of Taguchi methods to dual mixture ratio propulsion system optimization for SSTO vehicles

The application of advanced technologies to future launch vehicle designs would allow the introduction of a rocket-powered, single-stage-to-orbit (SSTO) launch system early in the next century. For a selected SSTO concept, a dual mixture ratio, staged combustion cycle engine that employs a number of innovative technologies was selected as the baseline propulsion system. A series of parametric trade studies are presented to optimize both a dual mixture ratio engine and a single mixture ratio engine of similar design and technology level. The effect of varying lift-off thrust-to-weight ratio, engine mode transition Mach number, mixture ratios, area ratios, and chamber pressure values on overall vehicle weight is examined. The sensitivity of the advanced SSTO vehicle to variations in each of these parameters is presented, taking into account the interaction of each of the parameters with each other. This parametric optimization and sensitivity study employs a Taguchi design method. The Taguchi method is an efficient approach for determining near-optimum design parameters using orthogonal matrices from design of experiments (DOE) theory. Using orthogonal matrices significantly reduces the number of experimental configurations to be studied. The effectiveness and limitations of the Taguchi method for propulsion/vehicle optimization studies as compared to traditional single-variable parametric trade studies is also discussed.

Stanley, Douglas O.↗

NASA NTRS1992

Robust momentum management and attitude control system for the Space Station

A game theoretic controller is synthesized for momentum management and attitude control of the Space Station in the presence of uncertainties in the moments of inertia. Full state information is assumed since attitude rates are assumed to be very accurately measured. By an input-output decomposition of the uncertainty in the system matrices, the parameter uncertainties in the dynamic system are represented as an unknown gain associated with an internal feedback loop (IFL). The input and output matrices associated with the IFL form directions through which the uncertain parameters affect system response. If the quadratic form of the IFL output augments the cost criterion, then enhanced parameter robustness is anticipated. By considering the input and the input disturbance from the IFL as two noncooperative players, a linear-quadratic differential game is constructed. The solution in the form of a linear controller is used for synthesis. Inclusion of the external disturbance torques results in a dynamic feedback controller which consists of conventional PID (proportional integral derivative) control and cyclic disturbance rejection filters. It is shown that the game theoretic design allows large variations in the inertias in directions of importance.

Rhee, Ihnseok↗

NASA NTRS1992

Element-topology-independent preconditioners for parallel finite element computations

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

Park, K. C.↗

NASA NTRS1991

Sufficient conditions for a local minimum of the Bolza problem with multiple terminal point constraints

Sufficient conditions for a weak relative minimum are derived for a form of the Bolza problem of variational calculus. The derivation ties together first-order and second-order conditions in a unified consistent manner, addresses controllability considerations in some detail, and clarifies some small inconsistencies in earlier work. The resulting second-order conditions of optimality involve the integration of fewer backward-sweep matrix elements than the standard conditions in the literature for problems with an unspecified final time. As a result, the backward-sweep matrices have the same general structure and dimensionality whether the final time is specified or free, with the terminal values of two of three sweep matrices being more complicated in the latter case.

Wood, Lincoln J.↗

NASA NTRS1992

A comparison of the chemistry of pseudotachylyte breccias in the Archean Levack Gneisses of the Sudbury structure, Ontario

The Archean Levack Gneisses of the North Range host millimeter-thick veins and centimeter-thick lenses of pseudotachylyte, as well as substantially larger meter-wide, dykelike bodies of pseudotachylytic 'breccia'. The 'breccia' occurs up to several tens of kilometers away from the Sudbury Igneous Complex and is commonly sited within or near joints and other natural weaknesses such as bedding, dyke contacts, and lithological boundaries. The larger 'breccia' dykes comprise a generally dark matrix containing rounded to subrounded and occasionally angular rock fragments derived predominantly from Levack Gneiss. Selected samples of bulk Sudbury Breccia and Sudbury Breccia matrices were chemically analyzed and compared to existing data on the Levack Gneisses and Sudbury Breccia. The matrices are apparently enriched in Fe and, to a lesser extent, Mg, Ti, and Ca compared to the wallrocks and the majority of clasts. This enrichment can be partly explained by the preferential cataclasis and/or frictional melting of hydrous ferromagnesian wallrock minerals, but also appear to require contamination by more basic exotic lithologies. This suggests that certain components of pseudotachylitic Sudbury Breccia have undergone significant transport during their formation.

Thompson, Lucy M.↗

NASA NTRS1992

Identifiability of linear systems in physical coordinates

Identifiability of linear, time-invariant systems in physical coordinates is discussed. It is shown that identification of the system matrix in physical coordinates can be accomplished by determining a transformation matrix that relates the physical locations of actuators and sensors to the test-data-derived input and output matrices. For systems with symmetric matrices, the solution of a constrained optimization problem is used to characterize all the possible solutions of the transformation matrix. Conditions for the existence of a unique transformation matrix are established easily from the explicit form of the solutions. For systems with limited inputs and outputs, the question about which part of the system can be uniquely identified is also answered. A simple mass-spring system is used to verify the conclusions of this study.

Su, Tzu-Jeng↗

NASA NTRS1991

Basic research on design analysis methods for rotorcraft vibrations

The objective of the present work was to develop a method for identifying physically plausible finite element system models of airframe structures from test data. The assumed models were based on linear elastic behavior with general (nonproportional) damping. Physical plausibility of the identified system matrices was insured by restricting the identification process to designated physical parameters only and not simply to the elements of the system matrices themselves. For example, in a large finite element model the identified parameters might be restricted to the moduli for each of the different materials used in the structure. In the case of damping, a restricted set of damping values might be assigned to finite elements based on the material type and on the fabrication processes used. In this case, different damping values might be associated with riveted, bolted and bonded elements. The method itself is developed first, and several approaches are outlined for computing the identified parameter values. The method is applied first to a simple structure for which the 'measured' response is actually synthesized from an assumed model. Both stiffness and damping parameter values are accurately identified. The true test, however, is the application to a full-scale airframe structure. In this case, a NASTRAN model and actual measured modal parameters formed the basis for the identification of a restricted set of physically plausible stiffness and damping parameters.

Hanagud, S.↗

NASA NTRS1993

Use of system identification techniques for improving airframe finite element models using test data

A method for using system identification techniques to improve airframe finite element models using test data was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in the total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all of the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory.

Hanagud, Sathya V.↗

NASA NTRS1993

Design of multiple-ply laminated composite tapered beams

A study of a special case of symmetric laminated composite cantilever beams is presented. The approach models beams that are tapered both in depth and width and investigates the effect of the ply layup angle and the ply taper on bending and interlaminar shearing stresses. For the determination of stresses and deflections, the beam stiffness matrices are expressed as linear functions of the beam length. Using classical lamination theory (CLT) the stiffness matrices are determined and assembled at strategic locations along the length of the beam. They are then inverted and necessary stiffness parameters are obtained numerically and extracted for determination of design information at each location chosen. Several ply layup configurations are investigated, and design considerations are presented based on the findings. Finally, recommendations for the design of these beams are presented, and a means for anticipating the location of highest stresses is offered.

Rodriguez, P.↗

NASA NTRS1992

Design of dissipative low-authority controllers using an eigensystem assignment technique

A novel method for the design of dissipative, low-authority controllers has been developed. The method uses a sequential approach along with eigensystem assignment to compute rate and position gain matrices that assign a number of closed-loop poles of the system to desired locations. Because the feedback gain matrices are symmetric and nonnegative definite, the closed-loop stability is always guaranteed regardless of the model order or parameter inaccuracies. The resulting (nominal) closed-loop system can have specified damping ratios for m modes, which makes the plant amenable to high-authority controller design, using methods such as LQG/LTR or H-infinity. A numerical example is worked out for a flexible structure in order to demonstrate the proposed technique.

Maghami, P. G.↗

NASA NTRS1993

Vibration localization in mono- and bi-coupled bladed disks - A transfer matrix approach

A transfer matrix approach to the analysis of the dynamics of mistuned bladed disks is presented. The study focuses on mono-coupled systems, in which each blade is coupled to its two neighboring blades, and bi-coupled systems, where each blade is coupled to its four nearest neighbors. Transfer matrices yield the free dynamics, both the characteristic free wave and the normal modes - in closed form for the tuned assemblies. Mistuned assemblies are represented by random transfer matrices and an examination of the effect of mistuning on harmonic wave propagation yields the localization factor - the average rate of spatial wave amplitude decay per blade - in the mono-coupled assembly. Based on a comparison of the wave propagation characteristics of the mono- and bi-coupled assemblies, important conclusions are drawn about the effect of the additional coupling coordinate on the sensitivity to mistuning and the strength of mode localization predicted by a mono-coupled analysis.

Ottarsson, Gisli↗

NASA NTRS1993

Linearization of manipulator dynamics using spatial operators

Linearized dynamics models for manipulators are useful in robot analysis, motion planning, and control applications. Techniques from the spatial operator algebra are used to obtain closed form operator expressions for two types of linearized dynamics models, the linearized inverse and forward dynamics models. Spatially recursive algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and coefficient matrices for the linearized inverse dynamics model are developed first. Subsequently, operator factorization and inversion identities are used to develop corresponding closed-form expressions for the linearized forward dynamics model (LFDM). Once again, these are used to develop algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and the coefficient matrices. The algorithms for the LFDM do not require the explicit computation of the mass matrix nor its numerical inversion and are also of lower complexity than the conventional O(n-cubed) algorithms.

Jain, A.↗

NASA NTRS1993

Boundary formulations for sensitivity analysis without matrix derivatives

A new hybrid approach to continuum structural shape sensitivity analysis employing boundary element analysis (BEA) is presented. The approach uses iterative reanalysis to obviate the need to factor perturbed matrices in the determination of surface displacement and traction sensitivities via a univariate perturbation/finite difference (UPFD) step. The UPFD approach makes it possible to immediately reuse existing subroutines for computation of BEA matrix coefficients in the design sensitivity analysis process. The reanalysis technique computes economical response of univariately perturbed models without factoring perturbed matrices. The approach provides substantial computational economy without the burden of a large-scale reprogramming effort.

Kane, J. H.↗

NASA NTRS1993

Diffraction analysis of frequency selective reflector antennas

In this paper, a unified computational technique is presented which allows the incorporation of the curved frequency-selective surface (FSS) geometry in the computation of the reflector antenna radiation pattern. The scattered fields from an illuminated FSS reflector are formalized using Huygens' principle in such a way that the 'reflecting' and the 'transparent' FSS subreflector cases are treated identically and the thickness of the FSS subreflector remains arbitrary. The analysis utilizes local surface coordinates to describe the reflection/transmission matrices of the FSS subreflector where it is assumed that these matrices are available. In most cases one may use the local tangent plane for approximating the plane of the FSS in the local coordinate surface of the reflector. The paper demonstrates how the local curved coordinate system can be introduced in the diffraction modeling of FSS reflectors and its importance in accurately predicting the side-lobe and crosspolarization levels. Results of numerical simulations are presented for several FSS subreflector configurations.

Rahmat-Samii, Yahya↗

NASA NTRS1993

A consistent model reduction of measured modal parameters for reduced-order active control

The problem of synthesizing reduced-order linear models of vibrating structures for the design of fixed-order dynamic feedback control is investigated. The present technique builds on a recently developed procedure for constructing an objective set of mass and stiffness matrices from measured modal parameters that are akin to the Craig-Bampton synthesized ones obtained from finite element models. The constructed mass and stiffness matrices are determined directly from the identification of experimental data, however, rather than through correlation or reconciliation of a finite element model. A model truncation criterion is then applied to the identified minimum-order mass and stiffness model to satisfy certain observability/controllability requirements for the reduced model. Numerical examples illustrate the effectiveness of the proposed technique for synthesizing reduced-order controllers from system realizations of experimental data. The dynamic performance of the resulting closed-loop models is assessed using the known full-order structural dynamics and compared with existing model reduction techniques.

Alvin, K. F.↗