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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

On Overview of the Performance and Scientific Results from the Chandra X-Ray Observatory

The Chandra X-Ray Observatory (CXO) was launched on 1999 July 23 by the Columbia Space Shuttle. The first X-rays focused by the telescope were seen on 1999 August 12 after the satellite systems were activated. Beginning with the first observation, it was clear that the telescope was not damaged by the launch environment and was operating as planned. After the early surprise due to the discovery that the telescope concentrated CCD-damaging low-energy protons far more efficiently than had been expected, the observatory is performing optimally and is returning excellent scientific data. Together with other space observatories, especially XMM-Newton, it is obvious that we have entered a new era of discovery in high-energy astrophysics.

Weisskopf, M. C.↗
NASA NTRS2002

Human motion planning based on recursive dynamics and optimal control techniques

This paper presents an efficient optimal control and recursive dynamics-based computer animation system for simulating and controlling the motion of articulated figures. A quasi-Newton nonlinear programming technique (super-linear convergence) is implemented to solve minimum torque-based human motion-planning problems. The explicit analytical gradients needed in the dynamics are derived using a matrix exponential formulation and Lie algebra. Cubic spline functions are used to make the search space for an optimal solution finite. Based on our formulations, our method is well conditioned and robust, in addition to being computationally efficient. To better illustrate the efficiency of our method, we present results of natural looking and physically correct human motions for a variety of human motion tasks involving open and closed loop kinematic chains.

Non-NASA Center↗
NASA NTRS1993

Calculation of optimum airfoils using direct solutions of the Navier-Stokes equations

A method has been developed which calculates the optimum airfoil shape at a specified operating condition. The Reynolds-averaged Navier-Stokes equations with a turbulence model are used as the governing equations for the fluid flow, and are explicitly introduced into the optimization analysis as constraint equations. The locations of all grid points which define the surface of the airfoil are design variables, eliminating the need for shape functions to describe changes in the airfoil geometry. A generalized reduced-gradient method is used to find the optimum airfoil shape. The use of a direct solution technique (Newton's method) to solve the Navier-Stokes equations allows for the efficient solution of the problem. This paper describes the optimization method and presents sample results.

Felker, Fort F.↗
NASA NTRS1992

A non-linearly stable implicit finite element algorithm for hypersonic aerodynamics

A generalized curvilinear coordinate Taylor weak statement implicit finite element algorithm is developed for the two-dimensional and axisymmetric compressible Navier-Stokes equations for ideal and reacting gases. For accurate hypersonic simulation, air is modeled as a mixture of five perfect gases, i.e., molecular and atomic oxygen and nitrogen as well as nitric oxide. The associated pressure is then determined via Newton solution of the classical chemical equilibrium equation system. The directional semidiscretization is achieved using an optimal metric data Galerkin finite element weak statement, on a developed 'companion conservation law system', permitting classical test and trial space definitions. Utilizing an implicit Runge-Kutta scheme, the terminal algorithm is then nonlinearly stable, and second-order accurate in space and time on arbitrary curvilinear coordinates. Subsequently, a matrix tensor product factorization procedure permits an efficient numerical linear algebra handling for large Courant numbers. For ideal- and real-gas hypersonic flows, the algorithm generates essentially nonoscillatory numerical solutions in the presence of strong detached shocks and boundary layer-inviscid flow interactions.

Iannelli, G. S.↗
NASA NTRS1978

Programs for analysis and resizing of complex structures

The paper describes the PARS (Programs for Analysis and Resizing of Structures) system. PARS is a user oriented system of programs for the minimum weight design of structures modeled by finite elements and subject to stress, displacement, flutter and thermal constraints. The system is built around SPAR - an efficient and modular general purpose finite element program, and consists of a series of processors that communicate through the use of a data base. An efficient optimizer based on the Sequence of Unconstrained Minimization Technique (SUMT) with an extended interior penalty function and Newton's method is used. Several problems are presented for demonstration of the system capabilities.

Haftka, R. T.↗
NASA NTRS1974

Optimization of self-acting herringbone journal bearings for maximum stability

The stability of herringbone grooved journal bearings was increased by optimizing the groove depth, width, length, and angle. Optimization was performed on the basis of a small-eccentricity infinite-groove analysis in combination with a previously developed Newton-Raphson procedure for bearings with the smooth member rotating or with the grooved member rotating at low compressibility numbers. A newly-developed vector technique for bearings with the grooved member rotating at high compressibility numbers also was used in the analysis. The design curves obtained are suitable for choosing the optimum bearing for a wide range of operating conditions (compressibility numbers from 0 to 80, length to diameter ratios from 1/4 to 2, and smooth or grooved member rotating). Compared to bearings optimized for maximum load, bearings optimized for maximum stability are shown to provide a drastic increase in bearing-supported mass. Bearings with grooved member rotating are substantially more stable than bearing with smooth member rotating, particularly at high compressibility numbers.

Fleming, D. P.↗
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 NTRS1992

On options for interdisciplinary analysis and design optimization

The interdisciplinary optimization of engineering systems is discussed from the standpoint of the computational alternatives available to the designer. The analysis of such systems typically requires the solution of coupled systems of nonlinear algebraic equations. The solution procedure is necessarily iterative in nature. It is shown that the system can be solved by fixed point iteration, by Newton's method, or by a combination of the two. However, the need for sensitivity analysis may affect the choice of analysis solution method. Similarly, the optimization of the system can be formulated in several ways that are discussed in the paper. It is shown that the effect of the topology of the interaction between disciplines is a key factor in the choice of analysis, sensitivity and optimization methods. Several examples are presented to illustrate the discussion.

Haftka, R. T.↗
NASA NTRS1972

A modified secant method for unconstrained minimization

A gradient-secant algorithm for unconstrained optimization problems is presented. The algorithm uses Armijo gradient method iterations until it reaches a region where the Newton method is more efficient, and then switches over to a secant form of operation. It is concluded that an efficient method for unconstrained minimization has been developed, and that any convergent minimization method can be substituted for the Armijo gradient method.

Polak, E.↗
NASA NTRS1992

A study of equation solvers for linear and non-linear finite element analysis on parallel processing computers

Concurrent computing environments provide the means to achieve very high performance for finite element analysis of systems, provided the algorithms take advantage of multiple processors. The authors have examined several algorithms for both linear and nonlinear finite element analysis. The performance of these algorithms on an Alliant FX/80 parallel supercomputer has been studied. For single load case linear analysis, the optimal solution algorithm is strongly problem dependent. For multiple load cases or nonlinear analysis through a modified Newton-Raphson method, decomposition algorithms are shown to have a decided advantage over element-by-element preconditioned conjugate gradient algorithms.

Watson, Brian C.↗
NASA NTRS1984

The effect of parking orbit constraints on the optimization of ballistic planetary trajectories

The optimization of ballistic planetary trajectories is developed which includes constraints on departure parking orbit inclination and node. This problem is formulated to result in a minimum total Delta V where the entire constrained injection Delta V is included in the optimization. An additional Delta V is also defined to allow for possible optimization of parking orbit inclination when the launch vehicle orbit capability varies as a function of parking orbit inclination. The optimization problem is formulated using primer vector theory to derive partial derivatives of total Delta V with respect to possible free parameters. Minimization of total Delta V is accomplished using a quasi-Newton gradient search routine. The analysis is applied to an Eros rendezvous mission whose transfer trajectories are characterized by high values of launch asymptote declination during particular launch opportunities. Comparisons in performance are made between trajectories where parking orbit constraints are included in the optimization and trajectories where the constraints are not included.

Sauer, C. G., Jr.↗
NASA NTRS1977

Mass-driver reaction engine as Shuttle upper-stage

Optimization has been carried out on the design of a mass-driver intended for upgrading the Shuttle to geosynchronous and lunar-orbit capability. The machine accelerates 2,100 tons/yr of external tankage, in 14-gram segments, to exhaust velocities of 8,000-10,000 m/s. The resulting reaction force raises 1,700 tons/yr. of Shuttle payloads to high orbit, in two round trips. Exhaust velocity and thrust can be optimized for each mission segment. For a mission requiring an exhaust velocity of 8,000 m/sec, thrust is 560 newtons, power is 2.9 megawatts, and efficiency is 75%. Total electrical component mass including power supplies and waste-heat radiators is 89 tons. To insure that reaction mass does not constitute a hazard, segments may be in the form of powder, electrostatically dispersed after acceleration, and/or thrust may be vectored.

Oneill, G. K.↗
NASA NTRS1980

Preliminary design of composite wing-box structures for global damage tolerance

A procedure is presented that incorporates the influence of potential global damage conditions into the design process for minimum-mass wing-box structures. The procedure is based on mathematical-programming optimization techniques. Material-strength, minimum-gage, and panel-buckling constraints are introduced by penalty functions, and Newton's method with approximate second derivatives of the penalty terms is used as the search algorithm to obtain minimum-mass designs. A potential global damage condition is represented by a structural model with the damaged components removed. Example minimum-mass designs are obtained that simultaneously satisfy the constraints of the damaged and undamaged configurations of both graphite-epoxy and aluminum wing-box structural models. These examples are designed with and without the influence of potential damage conditions, and results indicate that for equal mass cases the residual strength of a damaged structure is higher when the influence of potential damage is properly included in the design from the outset. Results of these examples also identify the minimum structural mass increase required to increase residual strength levels.

Starnes, J. H., Jr.↗
NASA NTRS1980

ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.

Fleury, C.↗
NASA NTRS1984

An improved computational approach for multilevel optimum design

A penalty-function algorithm employing Newton's method with approximate second derivatives (Haftka and Starnes, 1980) is developed for two-level hierarchical design optimization problems. The difficulties posed by discontinuous behavior in typical multilevel problems are explained and illustrated for the case of a three-bar truss; the algorithm is formulated; and its advantages are demonstrated in the problem of a portal framework having three beams (described by six cross-section parameters), subjected to two loading conditions, and to be constructed in six different materials for comparison. The final design parameters are listed in a table.

Haftka, R. T.↗
NASA NTRS1979

Optimization of multiple flyby trajectories

A procedure has been developed which minimizes total delta-V (instantaneous velocity change) for a multiple flyby trajectory with constraints on flyby altitude and orientation. The solution is found by varying the locations of maneuver points between each flyby to minimize the delta-Vs at the maneuver points. Each trajectory segment connecting consecutive maneuver points is found by solving an N-body analog to Lambert's problem. Multiconic techniques are used for trajectory propagation and for computation of the state transition matrix. The constrained parameter optimization problem is converted to an unconstrained problem by means of penalty functions and then solved with a quasi-Newton algorithm utilizing analytic first derivatives. This procedure has been successfully applied to Galileo satellite tour trajectories.

Damario, L. A.↗
NASA NTRS2013

Design of a Variational Multiscale Method for Turbulent Compressible Flows

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

Design↗