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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Implicit Kalman filtering

For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.

Non-NASA Center↗
NASA NTRS2006

General Solution for Theoretical Packet Data Loss Rate

Communications systems which transfer blocks ("frames") of data must use a marker ("frame synchronization pattern") for identifying where a block begins. A technique ("frame synchronization strategy") is used to locate the start of each frame and maintain synchronization as additional blocks are processed. A device which strips out the frame synchronization pattern [FSP] and provides an "end of frame" pulse is called a frame synchronizer. As clock and data errors are introduced into the system, the start-of-block marker becomes displaced and/or corrupted. The capability of the frame synchronizer to stay locked to the pattern under these conditions is a figure of merit for the frame synchronization strategy. It is important to select a strategy which will stay locked nearly all the time at bit error rates where the data is usable. ("Bit error rate" [BER] is the fraction of binary bits which are inverted by passage through a communication system.) The fraction of frames that are discarded because the frame synchronizer is not locked is called "Percent Data Loss" or "Packet Data Loss rate" [PDL]. A general approach for accurately predicting PDL given BER was developed in Theoretical Percent Data Loss Calculation and Measurement Accuracy, T. P. Kelly, LESC-30554, December 1992. Kelly gave a solution in terms of matrix equations, and only addressed "level" channel encoding. This paper goes on to give a closed-form polynomial solution for the most common class of frame synchronizer strategies, and will also address "mark" and "space" (differential) channel encoding, and burst error environments. The paper is divided into four sections and follows a logically ordered presentation, with results developed before they are evaluated. However, most readers will derive the greatest benefit from this paper by treating the results as reference material. The result developed for differential encoding can be extended to other applications (like block codes) where the probability is needed that a block contains only a certain number of errors.

Lansdowne, Chatwin↗
NASA NTRSDate not supplied

Cathode Modeling of Solid-State Batteries

The search for safe, reliable, and compact high-capacity energy storage devices has led to increased interest in all-solid-state battery research. The use of solid electrolytes provides enhanced safety and durability due to their reduced flammability and increased mechanical strength compared to organic liquid electrolytes. Still, the use of solid electrolytes remains challenging. Computational modeling plays a substantial role in addressing these challenges. A particle dynamics electromechanical model for simulating electrochemical processes in a solid-state battery cathode will be presented. The model presents cathode microstructure at the particle level as a mixture of ionically conductive solid electrolyte particles, electrically conductive carbon additives, and cathodic reactant particles. After densification, the particle connectivity is analyzed to reconstruct the complex electric network connecting reactant particles with an anodic and cathodic current collectors through the electrolyte and carbon particles. The Kirchhoff’s matrix equation describing this electric network, is solved to obtain values of various critical parameters, such as the overall conductivity of the cathode for lithium ions and electrons, cathodic reactant material utilization, and the distribution of the electric current and voltages within the cathode. In addition, by representing the reactant particles as electrolyte or galvanic microcells governed by the Butler-Volmer electrochemical equation, the overall performance of battery cells during charge or discharge processes, respectively, can be predicted for a given cathodic powder composition. The presented model, executed on a high-performance computing architecture, essentially provides a valuable guidance in designing and developing future solid-state batteries.

solid-state battery↗
NASA NTRS1987

Solution of the two-dimensional Navier-Stokes equations using sparse matrix solvers

The use of direct sparse matrix solvers in the solution of the Navier-Stokes equations is investigated. The Yale Sparse Matrix Package and its implementation in the solution algorithm is described. The streamfunction-vorticity form of the Navier-Stokes equations are discretized and linearized and the resulting system of equations are solved using this package. Several viscous flow problems are investigated, including flow in a cavity and flow around a NACA0012 airfoil. Massively separated flow around a sine wave airfoil is investigated and high Reynolds number solutions are obtained. A solution of the unsteady flow around a Joukowski airfoil at high angle of attack is presented.

Bender, Erich E.↗
NASA NTRS2017

Parallel Computation of the Jacobian Matrix for Nonlinear Equation Solvers Using MATLAB

Demonstrating speedup for parallel code on a multicore shared memory PC can be challenging in MATLAB due to underlying parallel operations that are often opaque to the user. This can limit potential for improvement of serial code even for the so-called embarrassingly parallel applications. One such application is the computation of the Jacobian matrix inherent to most nonlinear equation solvers. Computation of this matrix represents the primary bottleneck in nonlinear solver speed such that commercial finite element (FE) and multi-body-dynamic (MBD) codes attempt to minimize computations. A timing study using MATLAB's Parallel Computing Toolbox was performed for numerical computation of the Jacobian. Several approaches for implementing parallel code were investigated while only the single program multiple data (spmd) method using composite objects provided positive results. Parallel code speedup is demonstrated but the goal of linear speedup through the addition of processors was not achieved due to PC architecture.

Rose, Geoffrey K.↗
NASA NTRS1949

Response of a Rotating Propeller to Aerodynamic Excitation

The flexural vibration of a rotating propeller blade with clamped shank is analyzed with the object of presenting, in matrix form, equations for the elastic bending moments in forced vibration resulting from aerodynamic forces applied at a fixed multiple of rotational speed. Matrix equations are also derived which define the critical speeds end mode shapes for any excitation order and the relation between critical speed and blade angle. Reference is given to standard works on the numerical solution of matrix equations of the forms derived. The use of a segmented blade as an approximation to a continuous blade provides a simple means for obtaining the matrix solution from the integral equation of equilibrium, so that, in the numerical application of the method presented, the several matrix arrays of the basic physical characteristics of the propeller blade are of simple form, end their simplicity is preserved until, with the solution in sight, numerical manipulations well-known in matrix algebra yield the desired critical speeds and mode shapes frame which the vibration at any operating condition may be synthesized. A close correspondence between the familiar Stodola method and the matrix method is pointed out, indicating that any features of novelty are characteristic not of the analytical procedure but only of the abbreviation, condensation, and efficient organization of the numerical procedure made possible by the use of classical matrix theory.

Arnoldi, Walter E.↗
NASA NTRS1992

Towards the development of micromechanics equations for ceramic matrix composites via fiber substructuring

A generic unit cell model which includes a unique fiber substructuring concept is proposed for the development of micromechanics equations for continuous fiber reinforcement ceramic composites. The unit cell consists of three constituents: fiber, matrix, and an interphase. In the present approach, the unit cell is further subdivided into several slices and the equations of micromechanics are derived for each slice. These are subsequently integrated to obtain ply level properties. A stand alone computer code containing the micromechanics model as a module is currently being developed specifically for the analysis of ceramic matrix composites. Towards this development, equivalent ply property results for a SiC/Ti-15-3 composite with 0.5 fiber volume ratio are presented and compared with those obtained from customary micromechanics models to illustrate the concept. Also, comparisons with limited experimental data for the ceramic matrix composite, SiC/RBSN (Reaction Bonded Silicon Nitride) with a 0.3 fiber volume ratio are given to validate the concepts.

Murthy, P. L. N.↗
NASA NTRS1966

Matrix methods

Partial differential equations and matrix method for obtaining equations of motion in orbit

MOTION EQUATION↗
NASA NTRS1977

Inverse solution of the pseudoscalar transfer equation through nonlinear matrix inversion

Nonlinear matrix inversion operators have been developed which, applied to observed radiances, infer maximal information regarding atmospheric scattering parameters and vertical distribution of radiant sources and sinks. The algorithm has the attractive feature of noise discrimination, attributing instrumental errors to extra-atmospheric sources.

King, J. I. F.↗
NASA NTRS1976

Computation and sensitivity considerations of the Ricatti equation in spacecraft CMG steering laws

The steady-state matrix Ricatti equation is studied with respect to sensitivity and computational burden for a linear regulator controller in spacecraft. The class of systems studied use control moment gyros (CMGs) as the torque driver, assuming that the CMGs are free of gimbal stops. Different solution techniques are evaluated relative to computation time and accuracy to determine which solution method is most acceptable with respect to the prescribed requirements. It is shown that it is not feasible to eliminate off-diagonal Ricatti equation terms in the relevent updata equation due to their high sensitivity, that Potter's algebraic technique requires the least computation time of the methods studied, and that the simple Euler method yields the best results when accuracy and computation time are equally weighted. If an optimal linear regulator formulation is employed, a full Ricatti equation solution of n(n + 1)2 elements of the symmetric positive definite gain matrix which is the solution to the matrix Ricatti equation must be computed at each update cycle.

Colburn, B. K.↗
NASA NTRS1977

Lie theoretic aspects of the Riccati equation

Various features of the application of Lie theory to matrix Riccati equations, of basic importance in control and system theories, are discussed. Particular consideration is given to centralizer foliation, the Cartan decomposition, matrix Riccati equations as Lie systems on Grassmanians, local analysis near a zero point of a vector field, linearization in homogeneous space, the tangent bundle in terms of partitioned matrices, and stability properties of fixed points of Riccati vector fields.

Hermann, R.↗
NASA NTRS1973

Some optimal considerations in attitude control systems

The conventional six-engine reaction control jet relay attitude control law with deadband is shown to be a good linear approximation to a weighted time-fuel optimal control law. Techniques for evaluating the value of the relative weighting between time and fuel for a particular relay control law is studied along with techniques to interrelate other parameters for the two control laws. Vehicle attitude control laws employing control moment gyros are then investigated. Steering laws obtained from the expression for the reaction torque of the gyro configuration are compared to a total optimal attitude control law that is derived from optimal linear regulator theory. This total optimal attitude control law has computational disadvantages in the solving of the matrix Riccati equation. Several computational algorithms for solving the matrix Riccati equation are investigated with respect to accuracy, computational storage requirements, and computational speed.

Boland, J. S., III↗
NASA NTRS1985

A unique set of micromechanics equations for high temperature metal matrix composites

A unique set of micromechanic equations is presented for high temperature metal matrix composites. The set includes expressions to predict mechanical properties, thermal properties and constituent microstresses for the unidirectional fiber reinforced ply. The equations are derived based on a mechanics of materials formulation assuming a square array unit cell model of a single fiber, surrounding matrix and an interphase to account for the chemical reaction which commonly occurs between fiber and matrix. A three-dimensional finite element analysis was used to perform a preliminary validation of the equations. Excellent agreement between properties predicted using the micromechanics equations and properties simulated by the finite element analyses are demonstrated. Implementation of the micromechanics equations as part of an integrated computational capability for nonlinear structural analysis of high temperature multilayered fiber composites is illustrated.

Hopkins, D. A.↗
NASA NTRS1989

A Chebyshev matrix method for spatial modes of the Orr-Sommerfeld equation

The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blausius boundary layer. The problem is linearized by the companion matrix technique for semi-infinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

Danabasoglu, G.↗