Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “convex”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Practical Aspects of Stabilized FEM Discretizations of Nonlinear Conservation Law Systems with Convex Extension

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the Galerkin least-squares (GLS) and the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the POE system. Central to the development of the simplified GLS and DG methods is the Degenerative Scaling Theorem which characterizes right symmetrizes of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobean matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler, Navier-Stokes, and magnetohydrodynamic (MHD) equations. Linear and nonlinear energy stability is proven for the simplified GLS and DG methods. Spatial convergence properties of the simplified GLS and DO methods are numerical evaluated via the computation of Ringleb flow on a sequence of successively refined triangulations. Finally, we consider a posteriori error estimates for the GLS and DG demoralization assuming error functionals related to the integrated lift and drag of a body. Sample calculations in 20 are shown to validate the theory and implementation.

Barth, Timothy↗
NASA NTRS1998

New Convex Grating Types for Concentric Imaging Spectrometers

The properties of convex gratings fabricated by electron-beam lithography are investigated. Three grating types are shown. These gratings allow the optical designer to fully realize the considerable advantages of concentric spectrometer forms.

spectrometers concentric imaging electron beam↗
NASA NTRS2006

A Convex Guidance Algorithm for Formation Reconfiguration

In this paper, a reconfiguration guidance algorithm for formation flying spacecraft is presented. The formation reconfiguration guidance problem is first formulated as a continuous-time minimum-fuel or minimum-energy optimal control problem with collision avoidance and control constraints. The optimal control problem is then discretized to obtain a finite dimensional parameter optimization problem. In this formulation, the collision avoidance constraints are imposed via separating planes between each pair of spacecraft. A heuristic is introduced to choose these separating planes that leads to the convexification of the collision avoidance constraints. Additionally, convex constraints are imposed to guarantee that no collisions occur between discrete time samples. The resulting finite dimensional optimization problem is a second order cone program, for which standard algorithms can compute the global optimum with deterministic convergence and a prescribed level of accuracy. Consequently, the formation reconfiguration algorithm can be implemented onboard a spacecraft for real-time operations.

formation reconfiguration↗
NASA NTRS2000

Imaging spectrometer/camera having convex grating

An imaging spectrometer has fore-optics coupled to a spectral resolving system with an entrance slit extending in a first direction at an imaging location of the fore-optics for receiving the image, a convex diffraction grating for separating the image into a plurality of spectra of predetermined wavelength ranges; a spectrometer array for detecting the spectra; and at least one concave sperical mirror concentric with the diffraction grating for relaying the image from the entrance slit to the diffraction grating and from the diffraction grating to the spectrometer array. In one embodiment, the spectrometer is configured in a lateral mode in which the entrance slit and the spectrometer array are displaced laterally on opposite sides of the diffraction grating in a second direction substantially perpendicular to the first direction. In another embodiment, the spectrometer is combined with a polychromatic imaging camera array disposed adjacent said entrance slit for recording said image.

Reininger, Francis M.↗
NASA NTRS2007

Implementation of a Point Algorithm for Real-Time Convex Optimization

The primal-dual interior-point algorithm implemented in G-OPT is a relatively new and efficient way of solving convex optimization problems. Given a prescribed level of accuracy, the convergence to the optimal solution is guaranteed in a predetermined, finite number of iterations. G-OPT Version 1.0 is a flight software implementation written in C. Onboard application of the software enables autonomous, real-time guidance and control that explicitly incorporates mission constraints such as control authority (e.g. maximum thrust limits), hazard avoidance, and fuel limitations. This software can be used in planetary landing missions (Mars pinpoint landing and lunar landing), as well as in proximity operations around small celestial bodies (moons, asteroids, and comets). It also can be used in any spacecraft mission for thrust allocation in six-degrees-of-freedom control.

Acikmese, Behcet↗
NASA NTRS2010

Streamwise Vortices on the Convex Surfaces of Circular Cylinders and Turbomachinery Blading

In assessing the results please recall that the Mach number regimes and model geometries differ considerably. Selection of the radius of curvature at the 10% chord location is consistent but arbitrary, although it does seem representative for most blades and gives a good fit for the results. Measured spanwise wavelengths of the periodic vortex arrays on blading are predicted well by the Kestin and Wood theory. If this behavior is at all common it could have implications for turbine aerodynamic and blade cooling design. The outcome is to establish that organized streamwise vorticity may occur more frequently on convex surfaces, such as turbine blade suction surfaces, than hitherto appreciated. Investigations and predictions of flow behavior should be extended to encompass that possibility.

Gostelow, Paul↗
NASA NTRS2013

Truss beam having convex-curved rods, shear web panels, and self-aligning adapters

A truss beam comprised of a plurality of joined convex-curved rods with self-aligning adapters (SAA) adhesively attached at each end of the truss beam is disclosed. Shear web panels are attached to adjacent pairs of rods, providing buckling resistance for the truss beam. The rods are disposed adjacent to each other, centered around a common longitudinal axis, and oriented so that adjacent rod ends converge to at least one virtual convergence point on the common longitudinal axis, with the rods' curvature designed to increase prevent buckling for the truss beam. Each SAA has longitudinal bores that provide self-aligning of the rods in the SAA, the self-aligning feature enabling creation of strong adhesive bonds between each SAA and the rods. In certain embodiments of the present invention, pultruded unidirectional carbon fiber rods are coupled with carbon fiber shear web panels and metal SAA(s), resulting in a lightweight, low-cost but strong truss beam that is highly resistant to buckling.

Fernandez, Ian M.↗
NASA NTRS2017

Distributed Fast Motion Planning for Spacecraft Swarms in Cluttered Environments using Spherical Expansions and Sequence of Convex Optimization Problems

This paper presents a novel guidance algorithm for spacecraft swarms in an environment cluttered with many obstacles like a debris field or the asteroid belt. The objective of this algorithm is to reconfigure the swarm to a desired formation in a distributed manner while minimizing fuel and avoiding collisions among themselves and with the obstacles. The agents first use a spherical-expansion-based sampling algorithm to cooperatively explore the workspace and find paths to the desired terminal positions. Using a distributed assignment algorithm, the agents converge on an optimal assignment of the target locations in the desired formation. Then each agent generates a locally optimal trajectory from its current location to its terminal position by solving a sequence of convex optimization problems. As the agent moves along this trajectory, it receives the position of other agents and updates its trajectory to avoid collisions with other agents and the obstacles. Thus the swarm achieves the desired formation in a distributed manner while avoiding collisions. Moreover, this algorithm is computationally efficient, therefore it can be implemented onboard resource-constrained spacecraft. Simulations results show that the proposed distributed algorithm can be used by a spacecraft swarm to reconfigure a desired formation around an asteroid in a collision-free manner.

Bandyopadhyay, Saptarshi↗
NASA NTRS2019

MRAC with Time-Varying Reference Model from Convex Combination

An extension of model reference adaptive control is presented that accommodates use of a time-varying reference model. Specifically, the reference model is taken to be a time-varying convex combination of two linear, time-invariant models. The design is intended to act as a way to smoothly transition between two different reference models without resorting to a scheduled switch. It also provides the ability to use an interpolated reference model when the plant is operating between design points. The time variation of the combination must satisfy some requirements to ensure stability but is otherwise user choice. Subject to these requirements, bounded tracking error behavior is demonstrated via Lyapunov stability analysis for the single-input, single-output, output feedback case. Tracking error convergence is asymptotic when time variation ceases. The proposed design is demonstrated in simulation of a numerical model.

Hashemi, Kelley E.↗
NASA NTRS2024

A Convexification-Based Outer-Approximation Method for Convex and Nonconvex MINLP

The advancement of domain reduction techniques has significantly enhanced the performance of solvers in mathematical programming. This paper delves into the impact of integrating convexification and domain reduction techniques within the Outer-Approximation method. We propose a refined convexification-based Outer-Approximation method alongside a Branch-and-Bound method for both convex and nonconvex Mixed-Integer Nonlinear Programming problems. These methods have been developed and incorporated into the open-source Mixed-Integer Nonlinear Decomposition Toolbox for Pyomo-MindtPy. Comprehensive benchmark tests were conducted, validating the effectiveness and reliability of our proposed algorithms. These tests highlight the improvements achieved by incorporating convexification and domain reduction techniques into the Outer-Approximation and Branch-and-Bound methods.

Optimization↗