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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Recursive partitioned inversion of large (1500 x 1500) symmetric matrices

A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models.

Putney, B. H.↗
NASA NTRS1989

Development of kinematic equations and determination of workspace of a 6 DOF end-effector with closed-kinematic chain mechanism

This report presents results from the research grant entitled Active Control of Robot Manipulators, funded by the Goddard Space Flight Center, under Grant NAG5-780, for the period July 1, 1988 to January 1, 1989. An analysis is presented of a 6 degree-of-freedom robot end-effector built to study telerobotic assembly of NASA hardware in space. Since the end-effector is required to perform high precision motion in a limited workspace, closed-kinematic mechanisms are chosen for its design. A closed-form solution is obtained for the inverse kinematic problem and an iterative procedure employing Newton-Raphson method is proposed to solve the forward kinematic problem. A study of the end-effector workspace results in a general procedure for the workspace determination based on link constraints. Computer simulation results are presented.

Nguyen, Charles C.↗
NASA NTRS1991

Numerical recovery of material parameters in Euler-Bernoulli beam models

A fully Sinc-Galerkin method for recovering the spatially varying stiffness parameter in fourth-order time-dependence problems with fixed and cantilever boundary conditions is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains. This yields an approximation solution which converges exponentially and is valid on the infinite time interval. When the forward methods are applied to parameter recovery problems, the resulting inverse problems are ill-posed. Tikhonov regularization is applied and the resulting minimization problems are solved via a quasi-Newton/trust region algorithm. The L-curve method is used to determine an appropriate value of the regularization parameter. Numerical results which highlight the method are given for problems with both fixed and cantilever boundary conditions.

Smith, R. C.↗
NASA NTRS1964

Inverse estimation

Inverse estimation technique for problems in experimental design

PROBLEM SOLVING↗
NASA NTRS1984

A solution of Mx(double dot) + Cx(dot) + Kx = 0 applicable to the design of active dampers

A solution is presented for the equations of motion for the damped linear oscillator, Mx(double dot) + Cx(dot) + Kx = 0. The algorithm solves a transformed set of equations in terms of the modal variables of the undamped system and, at the same time, solves the adjoint equation of the transformed problem. The adjoint solution is normalized to give the inverse of the solution matrix of the transformed problem. The normalized inverse is useful in design for direct computation of sensitivity derivatives of damping ratios with respect to damping rates. The algorithm is programmed to reduce storage requirements by a factor of three-fourths compared to standard complex eigenvalue subroutines. A numerical example is included.

Thurston, G. A.↗
NASA NTRS1985

Venus gravity west of Beta Regio

Doppler tracking data from the Pioneer Venus Orbiter (PVO) have been used to estimate the anomalous gravity field in the region of Venus west of Beta Regio. The analysis invokes a Kalman filter-smoother to solve the nonlinear spacecraft state estimation problem and a linear Bayesian estimator to perform the geophysical inversion. The topographic map for this region, derived from the PVO radar, has been filtered to have the same distortions and degree of smoothing as the gravity map. The undulations of the gravity are about 0.2 times as large as expected from the topography, on the assumption that the latter is uncompensated. A comparison of the gravity and topography by means of the spectral admittance is consistent with Airy compensation at a depth of 50 km, if the surface material has a density of 2.6 g/cu cm. However, this is not a unique interpretation.

Goldberg, Z. M.↗
NASA NTRS1972

Limb radiance inversion: Iterative convergence for a nonlinear kernal

The features of the limb inversion problem that differentiate it from the nadir problem are described; the most important of these are the sharply peaked weighting functions and the nonlinear kernel that arises because the atmosphere is required to be in hydrostatic balance. The problem may be split into two parts: given the pressure at one level and the measured radiances, can the temperatures be retrieved? And how can the pressure be obtained at one level? The second problem is shown to depend on the first, which is solved iteratively. The convergence properties and final accuracies are presented. Inversion to obtain trace constituents is briefly discussed.

Gille, J. C.↗
DOE OSTI2025

On the motion of compact objects in relativistic viscous fluids

We present a world-line effective field theory of compact objects moving relativistically through a viscous fluid. The theory is valid when velocity gradients are small compared to the inverse size of the object. Working within the EFT eliminates the need to solve a boundary value problem by turning all interactions between the fluid and the object into a source term in the action. We use the EFT to derive the relativistic equations of motion for a compact object immersed in a viscous fluid in a curved background, when the relative velocity of the object and the fluid is small compared to the speed of light.

astrophysical black holes↗
DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗
DOE OSTI2025

Closed-Form Approximation of the Total Variation Proximal Operator

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved using proximal methods, but the way in which they are applied is constrained by the absence of a closed-form expression for the proximal operator of the TV function. A closed-form approximation of the TV proximal operator has previously been proposed, but its accuracy was not theoretically explored in detail. Here, we address this gap by making several new theoretical contributions, proving that the approximation leads to a proximal operator of some convex function, it is equivalent to a gradient descent step on a smoothed version of TV, and that its error can be fully characterized and controlled with its scaling parameter. We experimentally validate our theoretical results on image denoising and sparse-view computed tomography (CT) image reconstruction.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Recursive dynamics of topological trees of rigid bodies via Kalman filtering and Bryson-Frazier smoothing

The inverse and forward dynamics problems for a set of rigid bodies connected by hinges to form a topological tree are solved by using recursive techniques from linear filtering and smoothing theory. An inward filtering sequence computes a set of constraint moments and forces. This is followed by an outward sequence to determine a corresponding set of angular and linear accelerations. An inward sequence begins at the tips of all of the terminal bodies of the tree and proceeds inwardly through all of the branches until it reaches the root. Similarly, an outward sequence begins at the root and propagates to all of the tree branches until it reaches the tips of the terminal bodies. The paper also provides an approach to evaluate recursively the composite multibody system inertia matrix and its inverse.

Rodriguez, G.↗
NASA NTRS1982

A general algorithm for solving the algebraic Riccati equation

The generalized eigenvalue problem provides a suitable framework for reliable solutions of many system theoretic, control, and estimation problems. A general algorithm for solving the matrix algebraic Riccati equation (ARE) which utilizes a pencil structure is described here. This algorithm avoids unnecessary inversion of cost or transition matrices, making it a numerically sound way to solve for the gains and/or ARE with singular quadratic costs, for cases satisfying detectability and stabilizability conditions. Examples are solution with discrete dead-beat control, noiseless measurements in Kalman filters and time-delays in discrete-time systems, which cause difficulties in the Hamiltonian standard eigenvalue problem formulation. The ARE algorithm implementatiton and numerical examples are shown.

Walker, R. A.↗
NASA NTRS1976

Numerical solutions of the triple-deck equations for laminar trailing-edge stall

The problem of determining the effect of laminar boundary layers on the lift of thin wings in subsonic flow at high Reynolds numbers is considered. The boundary value problem is formulated in the framework of the triple-deck theory of Brown and Stewartson. The resulting fourth-order boundary value was solved by an iterative finite-difference technique. An inverse iteration procedure provides proper treatment of the trailing-edge singularity, and asymptotic far-field expansions and coordinate stretchings are used to deal with the problem of the slow algebraic decay of the solution.

Chow, R.↗
NASA NTRS1989

Shape control of high degree-of-freedom variable geometry trusses

Common static trusses are constrained to permit no relative motion between truss elements. A Variable Geometry Truss (VGT), however, is a truss which contains some number of variable length links. The extensible links allow the truss to change shape in a precise, controllable manner. These changes can also be used to control the vibrational response of a truss structure or to perform robotic tasks. Many geometric configurations, both planar and spatial, are possible candidates for VGT manipulators. Here, only two geometries are discussed; the three degree-of-freedom (DOF) spatial octahedral/octahedral truss and the three DOF planar tetrahedral truss. These truss geometries are used as the fundamental element in a repeating chain of trusses. This results in a highly dexterous manipulator with perhaps 30 to 60 degrees of freedom that retains the favorable stiffness properties of a conventional truss. From a fixed base, this type of manipulator could perform shape or vibration control while extending and snaking through complex passageways or moving around obstacles to perform robotic tasks. The approach taken here is to first concentrate on fully understanding the forward and inverse kinematics of the fundamental elements and then utilizing the insight thus gained to solve the more complex problem of the kinematic chains.

Salerno, R. J.↗
NASA NTRS2000

Validation of a "Kane's Dynamics" Model for the Active Rack Isolation System

Many microgravity space-science experiments require vibratory acceleration levels unachievable without active isolation. The Boeing Corporation's Active Rack Isolation System (ARIS) employs a novel combination of magnetic actuation and mechanical linkages, to address these isolation requirements on the International Space Station (ISS). ARIS provides isolation at the rack (international Standard Payload Rack, or ISPR) level. Effective model-based vibration isolation requires (1) an isolation device, (2) an adequate dynamic (i.e., mathematical) model of that isolator, and (3) a suitable, corresponding controller, ARIS provides the ISS response to the first requirement. In November 1999, the authors presented a response to the second ("A 'Kane's Dynamics' model for the Active Rack Isolation System", Hampton and Beech) intended to facilitate an optimal-controls approach to the third. This paper documents the validation of that high-fidelity dynamic model of ARIS. As before, this model contains the full actuator dynamics, however, the umbilical models are not included in this presentation. The validation of this dynamics model was achieved by utilizing two Commercial Off the Shelf (COTS) software tools: Deneb's ENVISION, and Online Dynamics' AUTOLEV. ENVISION is a robotics software package developed for the automotive industry that employs 3-dimensional (3-D) Computer Aided Design (CAD) models to facilitate both forward and inverse kinematics analyses. AUTOLEV is a DOS based interpreter that is designed in general to solve vector based mathematical problems and specifically to solve Dynamics problems using Kane's method.

Beech, Geoffrey S.↗
NASA NTRS2004

A "Kane's Dynamics" Model for the Active Rack Isolation System Part Two: Nonlinear Model Development, Verification, and Simplification

Many microgravity space-science experiments require vibratory acceleration levels that are unachievable without active isolation. The Boeing Corporation's active rack isolation system (ARIS) employs a novel combination of magnetic actuation and mechanical linkages to address these isolation requirements on the International Space Station. Effective model-based vibration isolation requires: (1) An isolation device, (2) an adequate dynamic; i.e., mathematical, model of that isolator, and (3) a suitable, corresponding controller. This Technical Memorandum documents the validation of that high-fidelity dynamic model of ARIS. The verification of this dynamics model was achieved by utilizing two commercial off-the-shelf (COTS) software tools: Deneb's ENVISION(registered trademark), and Online Dynamics Autolev(trademark). ENVISION is a robotics software package developed for the automotive industry that employs three-dimensional computer-aided design models to facilitate both forward and inverse kinematics analyses. Autolev is a DOS-based interpreter designed, in general, to solve vector-based mathematical problems and specifically to solve dynamics problems using Kane's method. The simplification of this model was achieved using the small-angle theorem for the joint angle of the ARIS actuators. This simplification has a profound effect on the overall complexity of the closed-form solution while yielding a closed-form solution easily employed using COTS control hardware.

Beech, G. S.↗
NASA NTRS1993

Mathmatical modeling for diffractive optics

We consider a 'diffractive optic' to be a biperiodic surface separating two half-spaces, each having constant constitutive parameters; within a unit cell of the periodic surface and across the transition zone between the two half-spaces, the constitutive parameters can be a continuous, complex-valued function. Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the 'direct' problem and for the 'inverse' problem. In problems of the 'direct' class, the diffractive optic is specified, and the full set of Maxwell's equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. An example of a metallic grating at a Wood anomaly is presented as a case where other approaches are known to have convergence problems. In problems of the 'inverse' class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. Two approaches are described: phase reconstruction in the far-field approximation; and relaxed optimal design based on the Helmholtz equation. Practical examples are discussed for each approach to the inverse problem, including array generators in the far-field case and antireflective structures for the relaxed optimal design.

Dobson, David↗
NASA NTRS1974

Solving multiple scattering problems in planetary atmospheres

Multiple scattering problems, radiative transfer problems in planetary atmospheres within extended visible portion of the spectrum, are examined. The direct and inverse problems and the extinction coefficient are defined, along with other scattering characteristics. Albedos in semi-infinite and finite atmospheres are considered, as well as surface illumination, energy deposition, and polarization. The Eddington approximation figures prominently in the calculations. Precise numerical methods and analytical solutions are included.

Irvine, W. M.↗