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NASA NTRS1988

MHOST: An efficient finite element program for inelastic analysis of solids and structures

An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.

Nakazawa, S.↗

NASA NTRS1990

Fast secant methods for the iterative solution of large nonsymmetric linear systems

A family of secant methods based on general rank-1 updates was revisited in view of the construction of iterative solvers for large non-Hermitian linear systems. As it turns out, both Broyden's good and bad update techniques play a special role, but should be associated with two different line search principles. For Broyden's bad update technique, a minimum residual principle is natural, thus making it theoretically comparable with a series of well known algorithms like GMRES. Broyden's good update technique, however, is shown to be naturally linked with a minimum next correction principle, which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized partial differential equations of convection diffusion type in 2-D with integral layers give a first impression of the possible power of the derived good Broyden variant.

Deuflhard, Peter↗

NASA NTRS2010

Reactive Collision Avoidance Algorithm

The reactive collision avoidance (RCA) algorithm allows a spacecraft to find a fuel-optimal trajectory for avoiding an arbitrary number of colliding spacecraft in real time while accounting for acceleration limits. In addition to spacecraft, the technology can be used for vehicles that can accelerate in any direction, such as helicopters and submersibles. In contrast to existing, passive algorithms that simultaneously design trajectories for a cluster of vehicles working to achieve a common goal, RCA is implemented onboard spacecraft only when an imminent collision is detected, and then plans a collision avoidance maneuver for only that host vehicle, thus preventing a collision in an off-nominal situation for which passive algorithms cannot. An example scenario for such a situation might be when a spacecraft in the cluster is approaching another one, but enters safe mode and begins to drift. Functionally, the RCA detects colliding spacecraft, plans an evasion trajectory by solving the Evasion Trajectory Problem (ETP), and then recovers after the collision is avoided. A direct optimization approach was used to develop the algorithm so it can run in real time. In this innovation, a parameterized class of avoidance trajectories is specified, and then the optimal trajectory is found by searching over the parameters. The class of trajectories is selected as bang-off-bang as motivated by optimal control theory. That is, an avoiding spacecraft first applies full acceleration in a constant direction, then coasts, and finally applies full acceleration to stop. The parameter optimization problem can be solved offline and stored as a look-up table of values. Using a look-up table allows the algorithm to run in real time. Given a colliding spacecraft, the properties of the collision geometry serve as indices of the look-up table that gives the optimal trajectory. For multiple colliding spacecraft, the set of trajectories that avoid all spacecraft is rapidly searched on-line. The optimal avoidance trajectory is implemented as a receding-horizon model predictive control law. Therefore, at each time step, the optimal avoidance trajectory is found and the first time step of its acceleration is applied. At the next time step of the control computer, the problem is re-solved and the new first time step is again applied. This continual updating allows the RCA algorithm to adapt to a colliding spacecraft that is making erratic course changes.

Scharf, Daniel↗

NASA NTRS1999

Collaborative Study of Analysis of High Resolution Infrared Atmospheric Spectra Between NASA Langley Research Center and the University of Denver

The Langley-D.U. collaboration on the analysis of high resolution infrared atmospheric spectra covered a number of important studies of trace gases identification and quantification from field spectra, and spectral line parameters analysis. The collaborative work included: Quantification and monitoring of trace gases from ground-based spectra available from various locations and seasons and from balloon flights. Studies toward identification and quantification of isotopic species, mostly oxygen and Sulfur isotopes. Search for new species on the available spectra. Update of spectroscopic line parameters, by combining laboratory and atmospheric spectra with theoretical spectroscopy methods. Study of trends of atmosphere trace constituents. Algorithms developments, retrievals intercomparisons and automatization of the analysis of NDSC spectra, for both column amounts and vertical profiles.

Goldman, Aaron↗

NASA NTRS1995

Optimization of Time-Dependent Particle Tracing Using Tetrahedral Decomposition

An efficient algorithm is presented for computing particle paths, streak lines and time lines in time-dependent flows with moving curvilinear grids. The integration, velocity interpolation and step-size control are all performed in physical space which avoids the need to transform the velocity field into computational space. This leads to higher accuracy because there are no Jacobian matrix approximations or expensive matrix inversions. Integration accuracy is maintained using an adaptive step-size control scheme which is regulated by the path line curvature. The problem of cell-searching, point location and interpolation in physical space is simplified by decomposing hexahedral cells into tetrahedral cells. This enables the point location to be done analytically and substantially faster than with a Newton-Raphson iterative method. Results presented show this algorithm is up to six times faster than particle tracers which operate on hexahedral cells yet produces almost identical particle trajectories.

Kenwright, David↗

NASA NTRS1993

A spectroscopic search for colliding stellar winds in O-type close binary systems. IV - Iota Orionis

We present H-alpha and He I 6678 A line profiles for the eccentric orbit binary Iota Ori. We have applied a tomography algorithm which uses the established orbital velocity curves and intensity ratio to reconstruct the spectral line profiles for each star. The He I profiles appear as pure photospheric lines, and H-alpha shows variable emission in the line core throughout the orbit (which is typical of O giants) and in the blue wing near periastron passage. We show that the blue wing emission is consistent with an origin between the stars which probably results from a dramatic focusing of the primary's stellar wind at periastron. We also present IUE archival spectra of the UV wind lines N V 1240 A and C IV 1550 A.

Gies, Douglas R.↗

NASA NTRS1995

Optimization methods, flux conserving methods for steady state Navier-Stokes equation

Navier-Stokes equation as discretized by new flux conserving method proposed by Chang and Scott results in the system: vector F(vector x) = 0, where F is a vector valued function. The Optimization method we use is based on Quasi-Newton methods: given a nonlinear function vector F(vector x) = 0, we solve, Delta(vector x) = -BF(vector x), where Delta(vector x) is the correction term and B is the inverse Jacobian of F(x). Then, iteratively, vector(x(sub (i+1))) = vector(x (sub i)) + alpha.Delta(vector x(sub i)), where alpha is a line search correction term determined by a line search routine. We use the BFCG's update the Jacobian matrix B(sub k) at each iteration. It is well known that B(sub k) approaches B(*) at the solution X(*). This algorithm has several advantages over the Newton-Raphson method. For example, we do not need to calculate the Jacobian matrix at each iteration which is computationally very expensive.

Adeyeye, John↗

NASA NTRS2000

A Search for Supernova in Star-Burst Galaxies

The rate at which massive supernovae occur in galaxies can be related directly to the rate of formation of massive stars this rate in turn can be computed from measurements and theoretical models of stellar mss distributions. Other measurements such as chemical composition and the dynamical structure of galaxies can also be used to infer the rate of massive supernovae. Various lines of reasoning using these measurements and theories of star formation have predicted a supernova rate which might be as much as ten times the rate of supernovae that had been observed using optical telescopes. The unseen supernovae were thought to be undetected due to a variety of circumstances, with the primary problem being extinction imposed by dust along the line of observation. This research used new infrared observations of the Infrared Space Observatory (ISO) space craft to explore active galaxies with a technique unhindered by dust extinction. New image processing algorithms for ISO point source analysis and cosmic ray deglitching were developed in order to search through a fairly complete set of the ISO data.

Rank, David M.↗

NASA NTRS1980

The Seasat low rate data processing system

The development of the algorithms for data processing and distribution, the circuitry, and the performance of the Seasat low rate data processing system are reviewed. The system controls data from the radar altimeter, scatterometer, microwave radiometer, and the visible and IR radiometer for independent transmission of each instrument's readings. The downlink operates at 25 kb/sec, and a yearlong program of geophysical evaluation proceeded shortly after launch, allowing on-line engineering evaluation and alteration of the control algorithms in the system. Some data is preformatted for immediate distribution and storage in archival quality. A catalog and abstracts are provided to users allowing a RAM search from remote terminals for historical conditions. Procedures for verifying and altering the algorithms are detailed.

Brown, J. W.↗

NASA NTRS1995

A microcontroller-based three degree-of-freedom manipulator testbed

A wheeled exploratory vehicle is under construction at the Mars Mission Research Center at North Carolina State University. In order to serve as more than an inspection tool, this vehicle requires the ability to interact with its surroundings. A crane-type manipulator, as well as the necessary control hardware and software, has been developed for use as a sample gathering tool on this vehicle. The system is controlled by a network of four Motorola M68HC11 microcontrollers. Control hardware and software were developed in a modular fashion so that the system can be used to test future control algorithms and hardware. Actuators include three stepper motors and one solenoid. Sensors include three optical encoders and one cable tensiometer. The vehicle supervisor computer provides the manipulator system with the approximate coordinates of the target object. This system maps the workspace surrounding the given location by lowering the claw, along a set of evenly spaced vertical lines, until contact occurs. Based on this measured height information and prior knowledge of the target object size, the system determines if the object exists in the searched area. The system can find and retrieve a 1.25 in. diameter by 1.25 in. tall cylinder placed within the 47.5 sq in search area in less than 12 minutes. This manipulator hardware may be used for future control algorithm verification and serves as a prototype for other manipulator hardware.

Brown, Robert Michael, Jr.↗

NASA NTRS1990

A positional estimation technique for an autonomous land vehicle in an unstructured environment

This paper presents a solution to the positional estimation problem of an autonomous land vehicle navigating in an unstructured mountainous terrain. A Digital Elevation Map (DEM) of the area in which the robot is to navigate is assumed to be given. It is also assumed that the robot is equipped with a camera that can be panned and tilted, and a device to measure the elevation of the robot above the ground surface. No recognizable landmarks are assumed to be present in the environment in which the robot is to navigate. The solution presented makes use of the DEM information, and structures the problem as a heuristic search in the DEM for the possible robot location. The shape and position of the horizon line in the image plane and the known camera geometry of the perspective projection are used as parameters to search the DEM. Various heuristics drawn from the geometric constraints are used to prune the search space significantly. The algorithm is made robust to errors in the imaging process by accounting for the worst care errors. The approach is tested using DEM data of areas in Colorado and Texas. The method is suitable for use in outdoor mobile robots and planetary rovers.

Talluri, Raj↗

NASA NTRS2001

Visualization of CFD Results in Immersive Virtual Environments

An object-oriented event-driven immersive virtual environment (VE) is described for the visualization of computational fluid dynamics (CFD) results. The VE incorporates the following types of primitive software objects: interface objects, support objects, geometric entities, and finite elements. The fluid domain is discretized using either a multi-block structured grid or an unstructured finite element mesh. The VE allows natural 'fly-through' visualization of the model, the CFD grid, and the model's surroundings. In order to help visualize the flow and its effects on the model, the VE incorporates the following objects: stream objects (lines, surface-restricted lines. ribbons. and volumes); colored surfaces; elevation surfaces; surface arrows; global and local iso-surfaces; vortex cores; and separation/attachment surfaces and lines. Most of these objects can be used for dynamically probing the flow. Particles and arrow animations can be displayed on top of stream objects. Primitive response quantities as well as derived quantities can be used. A recursive tree search algorithm is used for real-time point and value search in the CFD grid.

Wasfy, Tamer M.↗

NASA NTRS1991

A parallel trajectory optimization tool for aerospace plane guidance

A parallel trajectory optimization algorithm is being developed. One possible mission is to provide real-time, on-line guidance for the National Aerospace Plane. The algorithm solves a discrete-time problem via the augmented Lagrangian nonlinear programming algorithm. The algorithm exploits the dynamic programming structure of the problem to achieve parallelism in calculating cost functions, gradients, constraints, Jacobians, Hessian approximations, search directions, and merit functions. Special additions to the augmented Lagrangian algorithm achieve robust convergence, achieve (almost) superlinear local convergence, and deal with constraint curvature efficiency. The algorithm can handle control and state inequality constraints such as angle-of-attack and dynamic pressure constraints. Portions of the algorithm have been tested. The nonlinear programming core algorithm performs well on a variety of static test problems and on an orbit transfer problem. The parallel search direction algorithm can reduce wall clock time by a factor of 10 for this part of the computation task.

Psiaki, Mark L.↗

NASA NTRS2004

Hexagonal Pixels and Indexing Scheme for Binary Images

A scheme for resampling binaryimage data from a rectangular grid to a regular hexagonal grid and an associated tree-structured pixel-indexing scheme keyed to the level of resolution have been devised. This scheme could be utilized in conjunction with appropriate image-data-processing algorithms to enable automated retrieval and/or recognition of images. For some purposes, this scheme is superior to a prior scheme that relies on rectangular pixels: one example of such a purpose is recognition of fingerprints, which can be approximated more closely by use of line segments along hexagonal axes than by line segments along rectangular axes. This scheme could also be combined with algorithms for query-image-based retrieval of images via the Internet. A binary image on a rectangular grid is generated by raster scanning or by sampling on a stationary grid of rectangular pixels. In either case, each pixel (each cell in the rectangular grid) is denoted as either bright or dark, depending on whether the light level in the pixel is above or below a prescribed threshold. The binary data on such an image are stored in a matrix form that lends itself readily to searches of line segments aligned with either or both of the perpendicular coordinate axes. The first step in resampling onto a regular hexagonal grid is to make the resolution of the hexagonal grid fine enough to capture all the binaryimage detail from the rectangular grid. In practice, this amounts to choosing a hexagonal-cell width equal to or less than a third of the rectangular- cell width. Once the data have been resampled onto the hexagonal grid, the image can readily be checked for line segments aligned with the hexagonal coordinate axes, which typically lie at angles of 30deg, 90deg, and 150deg with respect to say, the horizontal rectangular coordinate axis. Optionally, one can then rotate the rectangular image by 90deg, then again sample onto the hexagonal grid and check for line segments at angles of 0deg, 60deg, and 120deg to the original horizontal coordinate axis. The net result is that one has checked for line segments at angular intervals of 30deg. For even finer angular resolution, one could, for example, then rotate the rectangular-grid image +/-45deg before sampling to perform checking for line segments at angular intervals of 15deg.

Johnson, Gordon G.↗

NASA NTRS2018

Silhouette-Informed Trajectory Generation Through a Wire Maze for Small UAS

Current rapidly-exploring random tree (RRT) algorithms rely on proximity query packages that often include collision checkers, tolerance verification, and distance computation algorithms for the generation of safe paths. In this paper, we broaden the information available to the path-planning algorithm by incorporating silhouette information of nearby obstacles in conflict. A silhouette-informed tree (SIT) is generated through the flight-safe region of a wire maze for a single unmanned aerial system (UAS). The silhouette is used to extract local geometric information of nearby obstacles and provide path alternatives around these obstacles. Thus, focusing the search for the generation of new tree branches near these obstacles, and decreasing the number of samples required to explore the narrow corridors within the wire maze. The SIT is then processed to extract a path that connects the initial location of the UAS with the goal, reduce the number of line segments in this path if possible, and smooth the resulting path using Pythagorean Hodograph Bezier curves. To ensure that the smoothed path remains in the flight-safe region of the configuration space, a tolerance verification algorithm for Bezier curves and convex polytopes in three dimensions is proposed. Lastly, temporal specifications are imposed on the smoothed path in the shape of an arbitrary speed profile.

Puig-Navarro, Javier↗

NASA NTRS2002

Collaborative Study for Analysis of High Resolution Infrared Atmospheric Spectra Between NASA Langley Research Center and the University of Denver

The Langley-D.U. collaboration on the analysis of high resolultion infrared atmospheric spectra covered a number of important studies of trace gases identification and quantification from field spectra, and spectral line parameters analysis. The collaborative work included: 1) Quantification and monitoring of trace gases from ground-based spectra available from various locations and seasons and from balloon flights; 2) Identification and preliminary quantification of several isotopic species, including oxygen and Sulfur isotopes; 3) Search for new species on the available spectra, including the use of selective coadding of ground-based spectra for high signal to noise; 4) Update of spectroscopic line parameters, by combining laboratory and atmospheric spectra with theoretical spectroscopy methods; 5) Study of trends and correlations of atmosphere trace constituents; and 6) Algorithms developments, retrievals intercomparisons and automatization of the analysis of NDSC spectra, for both column amounts and vertical profiles.

Goldman, A.↗

NASA NTRSDate not supplied

Uncovering Hazards Using a Multi-Objective Optimization to Explore the Faulty State-Space

Considering resilience when designing complex engineered systems is crucial to ensure the system is safe under unexpected hazardous scenarios. Traditional risk-based approaches, such as Failure Modes and Effects Analysis (FMEA) are useful for designing the system to mitigate hazardous scenarios that can be identified by the designer, but often require experience or prior knowledge of system failures to generate. More recently, researchers have developed simulation tools that enable the designer to model large sets of hazardous scenarios (driven by both internal faults and external factors) through simulation. While these tools enable a wider scope of fault modes to be evaluated (e.g., by injecting combined set of fault modes or injecting modes at different times), the resulting assessments (like FMEA) still require knowledge of the specific modes to be evaluated. However, failure to analyze a wide variety of fault scenarios can lead to an incomplete picture of the system resilience, especially to "surprise events'' which may be difficult for the designer to identify and predict beforehand. To overcome this challenge, previous work developed a fault sampling approach for resilience simulations which would procedurally-generate a wide variety of potential faults by systematically perturbing the health states of the system. While the resulting fault modes generated covered a much larger space hazards than would be otherwise considered (and identified many unique failure trajectories which would not have otherwise been identified), it also significantly increased the computational cost of the analysis and resulted in the simulation and analysis of a large set of essentially duplicate scenarios. Additionally, as the number of dimensions in the faulty state-space increases, the full elaboration of possible modes becomes computationally infeasible, justifying the use of a more targeted search. To resolve this limitation, this work proposes the use of a multiobjective optimization algorithm to search the health state space for potential fault modes that are both (1) hazardous and (2) unique. To solve this type of problem, this work proposes the use of a cooperative co-evolutionary algorithm. To demonstrate this approach, it will be applied to a model of an autonomous rover which uses line markings to navigate, focusing on potential hazards in the drive system which could cause the rover to crash. To determine the merit of the approach, it will further be compared with the previously-presented range elaboration approach and a random mode generation approach on the basis of computational efficiency and found modes.

Resilience↗

NASA NTRS1993

Real-time trajectory optimization on parallel processors

A parallel algorithm has been developed for rapidly solving trajectory optimization problems. The goal of the work has been to develop an algorithm that is suitable to do real-time, on-line optimal guidance through repeated solution of a trajectory optimization problem. The algorithm has been developed on an INTEL iPSC/860 message passing parallel processor. It uses a zero-order-hold discretization of a continuous-time problem and solves the resulting nonlinear programming problem using a custom-designed augmented Lagrangian nonlinear programming algorithm. The algorithm achieves parallelism of function, derivative, and search direction calculations through the principle of domain decomposition applied along the time axis. It has been encoded and tested on 3 example problems, the Goddard problem, the acceleration-limited, planar minimum-time to the origin problem, and a National Aerospace Plane minimum-fuel ascent guidance problem. Execution times as fast as 118 sec of wall clock time have been achieved for a 128-stage Goddard problem solved on 32 processors. A 32-stage minimum-time problem has been solved in 151 sec on 32 processors. A 32-stage National Aerospace Plane problem required 2 hours when solved on 32 processors. A speed-up factor of 7.2 has been achieved by using 32-nodes instead of 1-node to solve a 64-stage Goddard problem.

Psiaki, Mark L.↗