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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

An Optimization study on a hybrid computer

The maximum principle is applied to minimum-time optimal-control problems, and an optimization algorithm is presented which can be implemented on a hybrid computer. The state and adjoint equations are set up on ASTRAC 2, a high-speed analog computer capable of 1000 differential equation solutions per second. The optimization algorithm is implemented on a PDP-9, an 18-bit, digital computer. The optimization scheme has global and local search phases and uses a vector optimization criterion. Second and third-order bang-bang control systems are studied as examples.

Gonzalez, R. S.↗
NASA NTRS1992

Asymptotic integration algorithms for first-order ODEs with application to viscoplasticity

When constructing an algorithm for the numerical integration of a differential equation, one must first convert the known ordinary differential equation (ODE), which is defined at a point, into an ordinary difference equation (O(delta)E), which is defined over an interval. Asymptotic, generalized, midpoint, and trapezoidal, O(delta)E algorithms are derived for a nonlinear first order ODE written in the form of a linear ODE. The asymptotic forward (typically underdamped) and backward (typically overdamped) integrators bound these midpoint and trapezoidal integrators, which tend to cancel out unwanted numerical damping by averaging, in some sense, the forward and backward integrations. Viscoplasticity presents itself as a system of nonlinear, coupled first-ordered ODE's that are mathematically stiff, and therefore, difficult to numerically integrate. They are an excellent application for the asymptotic integrators. Considering a general viscoplastic structure, it is demonstrated that one can either integrate the viscoplastic stresses or their associated eigenstrains.

Freed, Alan D.↗
NASA NTRS2011

Assessment of an Automated Touchdown Detection Algorithm for the Orion Crew Module

Orion Crew Module (CM) touchdown detection is critical to activating the post-landing sequence that safe?s the Reaction Control Jets (RCS), ensures that the vehicle remains upright, and establishes communication with recovery forces. In order to accommodate safe landing of an unmanned vehicle or incapacitated crew, an onboard automated detection system is required. An Orion-specific touchdown detection algorithm was developed and evaluated to differentiate landing events from in-flight events. The proposed method will be used to initiate post-landing cutting of the parachute riser lines, to prevent CM rollover, and to terminate RCS jet firing prior to submersion. The RCS jets continue to fire until touchdown to maintain proper CM orientation with respect to the flight path and to limit impact loads, but have potentially hazardous consequences if submerged while firing. The time available after impact to cut risers and initiate the CM Up-righting System (CMUS) is measured in minutes, whereas the time from touchdown to RCS jet submersion is a function of descent velocity, sea state conditions, and is often less than one second. Evaluation of the detection algorithms was performed for in-flight events (e.g. descent under chutes) using hi-fidelity rigid body analyses in the Decelerator Systems Simulation (DSS), whereas water impacts were simulated using a rigid finite element model of the Orion CM in LS-DYNA. Two touchdown detection algorithms were evaluated with various thresholds: Acceleration magnitude spike detection, and Accumulated velocity changed (over a given time window) spike detection. Data for both detection methods is acquired from an onboard Inertial Measurement Unit (IMU) sensor. The detection algorithms were tested with analytically generated in-flight and landing IMU data simulations. The acceleration spike detection proved to be faster while maintaining desired safety margin. Time to RCS jet submersion was predicted analytically across a series of simulated Orion landing conditions. This paper details the touchdown detection method chosen and the analysis used to support the decision.

Gay, Robert S.↗
NASA NTRS1992

Automatic differentiation of advanced CFD codes for multidisciplinary design

Automated multidisciplinary design of aircraft and other flight vehicles requires the optimization of complex performance objectives with respect to a number of design parameters and constraints. The effect of these independent design variables on the system performance criteria can be quantified in terms of sensitivity derivatives which must be calculated and propagated by the individual discipline simulation codes. Typical advanced CFD analysis codes do not provide such derivatives as part of a flow solution; these derivatives are very expensive to obtain by divided (finite) differences from perturbed solutions. It is shown that sensitivity derivatives can be obtained accurately and efficiently using the ADIFOR source translator for automatic differentiation. In particular, it is demonstrated that the 3-D, thin-layer Navier-Stokes, multigrid flow solver called TLNS3D is amenable to automatic differentiation in the forward mode even with its implicit iterative solution algorithm and complex turbulence modeling. It is significant that by using computational differentiation, consistent discrete nongeometric sensitivity derivatives have been obtained from an aerodynamic 3-D CFD code in a relatively short time, e.g., O(man-week) not O(man-year).

Bischof, C.↗
NASA NTRS2002

Field-Programmable Gate Array Computer in Structural Analysis: An Initial Exploration

This paper reports on an initial assessment of using a Field-Programmable Gate Array (FPGA) computational device as a new tool for solving structural mechanics problems. A FPGA is an assemblage of binary gates arranged in logical blocks that are interconnected via software in a manner dependent on the algorithm being implemented and can be reprogrammed thousands of times per second. In effect, this creates a computer specialized for the problem that automatically exploits all the potential for parallel computing intrinsic in an algorithm. This inherent parallelism is the most important feature of the FPGA computational environment. It is therefore important that if a problem offers a choice of different solution algorithms, an algorithm of a higher degree of inherent parallelism should be selected. It is found that in structural analysis, an 'analog computer' style of programming, which solves problems by direct simulation of the terms in the governing differential equations, yields a more favorable solution algorithm than current solution methods. This style of programming is facilitated by a 'drag-and-drop' graphic programming language that is supplied with the particular type of FPGA computer reported in this paper. Simple examples in structural dynamics and statics illustrate the solution approach used. The FPGA system also allows linear scalability in computing capability. As the problem grows, the number of FPGA chips can be increased with no loss of computing efficiency due to data flow or algorithmic latency that occurs when a single problem is distributed among many conventional processors that operate in parallel. This initial assessment finds the FPGA hardware and software to be in their infancy in regard to the user conveniences; however, they have enormous potential for shrinking the elapsed time of structural analysis solutions if programmed with algorithms that exhibit inherent parallelism and linear scalability. This potential warrants further development of FPGA-tailored algorithms for structural analysis.

Singleterry, Robert C., Jr.↗
NASA NTRS1979

Utility of a finite element solution algorithm for initial-value problems

The Galerkin criterion within a finite element Weighted Residuals formulation is employed to establish an implicit solution algorithm for an initial-value partial differential equation. Numerical solutions of a transient parabolic and a hyperbolic equation, obtained using linear, quadratic and two cubic finite element basis functions, are employed to quantize accuracy and confirm and refine theoretical convergence rate estimates. The linear basis algorithm for the hyperbolic equation displays excellent accuracy on a coarse computational grid and a high-order convergence rate with discretization refinement. Good accuracy and a strong convergence rate in surface flux are determined for a nonhomogeneous Neumann boundary constraint applied to a parabolic equation. The results amply demonstrate the impact of the nondiagonal finite element initial-value matrix structure on solution accuracy and/or convergence rate.

Baker, A. J.↗
NASA NTRS1981

Accuracy and convergence of a finite element algorithm for turbulent boundary layer flow

The Galerkin-Weighted Residuals formulation is employed to derive an implicit finite element solution algorithm for the nonlinear parabolic partial differential equation system governing turbulent boundary layer flow. Solution accuracy and convergence with discretization refinement are quantized in several error norms using linear and quadratic basis functions. Richardson extrapolation is used to isolate integration truncation error in all norms, and Newton iteration is employed for all equation solutions performed in double-precision. The mathematical theory supporting accuracy and convergence concepts for linear elliptic equations appears extensible to the nonlinear equations characteristic of turbulent boundary layer flow.

Soliman, M. O.↗
NASA NTRS1984

Theoretical and experimental analysis of laser altimeters for barometric measurements over the ocean

The statistical characteristics and the waveforms of ocean-reflected laser pulses are studied. The received signal is found to be corrupted by shot noise and time-resolved speckle. The statistics of time-resolved speckle and its effects on the timing accuracy of the receiver are studied in the general context of laser altimetry. For estimating the differential propagation time, various receiver timing algorithms are proposed and their performances evaluated. The results indicate that, with the parameters of a realistic altimeter, a pressure measurement accuracy of a few millibars is feasible. The data obtained from the first airborne two-color laser altimeter experiment are processed and analyzed. The results are used to verify the pressure measurement concept.

Tsai, B. M.↗
NASA NTRS1988

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

Yung, Chain Nan↗
NASA NTRS1989

Visual perception and grasping for the extravehicular activity robot

The development of an approach to the visual perception of object surface information using laser range data in support of robotic grasping is discussed. This is a very important problem area in that a robot such as the EVAR must be able to formulate a grasping strategy on the basis of its knowledge of the surface structure of the object. A description of the problem domain is given as well as a formulation of an algorithm which derives an object surface description adequate to support robotic grasping. The algorithm is based upon concepts of differential geometry namely, Gaussian and mean curvature.

Starks, Scott A.↗
NASA NTRS1988

Symbolic generation of constitutive equations

The use of the symbolic manipulation program MACSYMA for the automatic generation of constitutive equations describing the thermomechanical behavior of complex materials such as metal-matrix composites is demonstrated. Problem-specific algorithms are developed; e.g., for partial differentiation by the chain rule, automatic generation of tree structures, special tensor analysis, and the simplification of expressions. The resulting subprogram package, SDICE, is shown to be fully applicable to both isotropic and anisotropic materials; its potential usefulness as a basis for FEM analyses is indicated.

Tan, H. Q.↗
NASA NTRS1989

Auroral excitation of the N2 2P(0,0) and VK(0,9) bands

The low-energy secondary electron flux caused by auroral electron precipitation is examined using data from the Atmosphere Explorer C satellite. An energetic electron transport algorithm is used to compute the differential electron flux produced by measured primaries. Emissions of N2 in the 2P(0,0) band at 337 nm and the VK(0,9) band at 335 nm predicted by the model are compared with photometric observation of their combined volume emission rate altitude profile made by the visible airglow experiment. Reasonable correspondence between model and measurement is obtained. Ratios of emissions at 337 nm and 630 nm to the N2(+) 1N(0,0) band at 428 nm are also studied. It is concluded that the 337/428 nm ratio responds to changes in the characteristic energy of primary auroral electrons only insofar as part of the 337 nm brightness is due to N2 VK(0,9) emission. The 630/428 nm ratio, which is strongly dependent on characteristic energy, also varies significantly with changes in atomic oxygen density.

Solomon, Stanley C.↗
NASA NTRS1992

Systematic Disturbance Of Optimal Rotational Trajectory

Algorithm introduces systematic disturbance into otherwise optimal rotation of body from prescribed initial to prescribed final orientation. Disturbance introduced as deviation of actual axis of rotation from optimal one, like wobble of top. Algorithm effects rotational transformations and solves differential equations necessary to compute disturbed trajectory. Devised for use with motion-control program and three-dimensional computer-graphical display to study ability of observers to distinguish between optimal and suboptimal rotational trajectories.

Grunwald, Arthur J.↗
NASA NTRS1994

Semigroup approximation and robust stabilization of distributed parameter systems

Theoretical results that enable rigorous statements of convergence and exponential stability of Galerkin approximations of LQR controls for infinite dimensional, or distributed parameter, systems have proliferated over the past ten years. In addition, extensive progress has been made over the same time period in the derivation of robust control design strategies for finite dimensional systems. However, the study of the convergence of robust finite dimensional controllers to robust controllers for infinite dimensional systems remains an active area of research. We consider a class of soft-constrained differential games evolving in a Hilbert space. Under certain conditions, a saddle point control can be given in feedback form in terms of a solution to a Riccati equation. By considering a related LQR problem, we can show a convergence result for finite dimensional approximations of this differential game. This yields a computational algorithm for the feedback gain that can be derived from similar strategies employed in infinite dimensional LQR control design problems. The approach described in this paper also inherits the additional properties of stability robustness common to game theoretic methods in finite dimensional analysis. These theoretical convergence and stability results are verified in several numerical experiments.

Kurdila, A. J.↗
NASA NTRS1995

FORTRAN program for analyzing ground-based radar data: Usage and derivations, version 6.2

A postflight FORTRAN program called 'radar' reads and analyzes ground-based radar data. The output includes position, velocity, and acceleration parameters. Air data parameters are also provided if atmospheric characteristics are input. This program can read data from any radar in three formats. Geocentric Cartesian position can also be used as input, which may be from an inertial navigation or Global Positioning System. Options include spike removal, data filtering, and atmospheric refraction corrections. Atmospheric refraction can be corrected using the quick White Sands method or the gradient refraction method, which allows accurate analysis of very low elevation angle and long-range data. Refraction properties are extrapolated from surface conditions, or a measured profile may be input. Velocity is determined by differentiating position. Accelerations are determined by differentiating velocity. This paper describes the algorithms used, gives the operational details, and discusses the limitations and errors of the program. Appendices A through E contain the derivations for these algorithms. These derivations include an improvement in speed to the exact solution for geodetic altitude, an improved algorithm over earlier versions for determining scale height, a truncation algorithm for speeding up the gradient refraction method, and a refinement of the coefficients used in the White Sands method for Edwards AFB, California. Appendix G contains the nomenclature.

Haering, Edward A., Jr.↗