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Results for “Discrete Optimization”

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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

On the Development of an Efficient Parallel Hybrid Solver with Application to Acoustically Treated Aero-Engine Nacelles

A finite element solution to the convected Helmholtz equation in a nonuniform flow is used to model the noise field within 3-D acoustically treated aero-engine nacelles. Options to select linear or cubic Hermite polynomial basis functions and isoparametric elements are included. However, the key feature of the method is a domain decomposition procedure that is based upon the inter-mixing of an iterative and a direct solve strategy for solving the discrete finite element equations. This procedure is optimized to take full advantage of sparsity and exploit the increased memory and parallel processing capability of modern computer architectures. Example computations are presented for the Langley Flow Impedance Test facility and a rectangular mapping of a full scale, generic aero-engine nacelle. The accuracy and parallel performance of this new solver are tested on both model problems using a supercomputer that contains hundreds of central processing units. Results show that the method gives extremely accurate attenuation predictions, achieves super-linear speedup over hundreds of CPUs, and solves upward of 25 million complex equations in a quarter of an hour.

Watson, Willie R.↗
NASA NTRS2006

Small Body GN&C Research Report: A G-Guidance Enhancement to Increase Mission Functionality

G-Guidance is a robust G&C (guidance and control) algorithm developed under the small-body GN&C task. The G-Guidance scheme utilizes a model predictive control approach, along with a convexification of the governing dynamics, control constraints, and trajectory/state constraints. This report details an enhancement to the FY2005 G-Guidance algorithm; the addition of a fire-second approach helps to nullify velocity errors and hit desired final velocities much more precisely than the original Fire-first scheme developed in FY2005. The enhancement preserves the primary benefit of the algorithm, which is to ensure required thruster silent times during trajectory maneuvers. The fire-second scheme increases the versatility of the algorithm for missions employing G-Guidance. For instance, a landing sequence could employ the fire-second scheme to ensure a null final velocity at landing, whereas an ascent sequence could utilize a fire-first scheme to ensure there is no drift of the spacecraft toward the ground at the beginning of the maneuver. Examples are provided within to demonstrate a fire-first versus fire-second guidance scheme. As in the existing G-Guidance algorithm, the examples and schemes incorporate gravity models and thruster firing times into discrete dynamics that are solved as a optimal control problem to minimize fuel consumption or thruster energy expenditure.

velocity errors↗
NASA NTRS2005

Small Body GN&C Research Report: A Guidance and Control Technique for Small-Body Proximity Operations with Guaranteed Guidance Resolvability and Required Thruster Silent Time

The guidance and control (G&C) algorithms for enabling small-body proximity operations are developed by using a model predictive control approach along with a convexification of the governing dynamics, control constraints, and trajectory/state constraints. The open-loop guidance is solved ahead of time or in a resolvable, real-time manner through the use of PWG (Pseudo Way-point Generation), a technique developed in this research. The PWG scheme ensures required thruster silent times during trajectory maneuvers. The feedback control is implemented to track the PWG trajectories in a manner that guarantees the resolvability for the open-loop problem, enabling the ability to update the G&C in a model-predictive manner. The schemes incorporate gravity models and thruster ring times into discrete dynamics that are solved as a optimal control problem to minimize fuel consumption or thruster energy expenditure. The optimal control problem is cast as an LMI (Linear Matrix Inequality) and then solved through Semi-Definite Programming techniques in a computationally efficient manner that provides convergence and constraint guarantees.

guidance and control (G&C)↗
NASA NTRS2015

Turbo-Brayton Power Converter

Future NASA space missions will require advanced thermal-to-electric power converters that are reliable, efficient, and lightweight. Creare, LLC, is developing a turbo-Brayton power converter that offers high efficiency and specific power. The converter employs gas bearings to provide maintenance free, long-life operation. Discrete components can be packaged to fit optimally with other subsystems, and the converter's continuous gas flow can communicate directly with remote heat sources and heat rejection surfaces without the need for ancillary heat-transfer components and intermediate flow loops. Creare has completed detailed analyses, trade studies, fabrication trials, and preliminary designs for the components and converter assembly. The company is fabricating and testing a breadboard converter.

Breedlove, Jeffrey↗
NASA NTRS1976

Optimal one-section and two-section circular sound-absorbing duct liners for plane-wave and monopole sources without flow

A discrete frequency study is made of the influence of source characteristics on the optimal properties of acoustically lined uniform and two section ducts. Two simplified sources, a plane wave and a monopole, are considered in some detail and over a greater frequency range than has been previously studied. Source and termination impedance effects are given limited examination. An example of a turbomachinery source and three associated source variants is also presented. Optimal liner designs based on modal theory approach the Cremer criterion at low frequencies and the geometric acoustics limit at high frequencies. Over an intermediate frequency range, optimal two section liners produced higher transmission losses than did the uniform configurations. Source distribution effects were found to have a significant effect on optimal liner design, but source and termination impedance effects appear to be relatively unimportant.

Lester, H. C.↗
NASA NTRS1990

Optimal rejection of bounded persistent disturbances in periodic systems

The problem of optimal rejection of bounded persistent disturbances is solved in the case of linear discrete-time period systems. The solution consists of solving an equivalent time-invariant standard l1 optimization problem subject to an additional constraint. This constraint ensures the causality of the resulting periodic controller. By the duality theory, the problem is shown to be equivalent to a linear programming problem, which is no harder than the standard l1 problem.

Dahleh, Munther A.↗
NASA NTRS1992

Optimal and robust controllers for periodic and multirate systems

The problem of optimal rejection of bounded persistent disturbances is solved in the case of linear discrete-time periodic systems. The solution consists of solving an equivalent time-invariant standard l1 optimization problem subject to an additional constraint. This constraint assures the causality of the resulting periodic controller. By the duality theory, the problem is shown to be equivalent to a linear programming problem, which is no harder than the standard l1 problem. Also, it is shown that the method of solution presented applies exactly to the problem of disturbance rejection in the case of multirate sampled data systems. Finally, the results are applied to the problem of robust stabilization of periodic and multirate systems.

Dahleh, Munther A.↗
DOE OSTI2026

Active learning of a crystal plasticity flow rule from discrete dislocation dynamics simulations

Continuum-scale material deformation models, such as crystal plasticity (CP), can significantly enhance their predictive accuracy by incorporating input from lower-scale (i.e. mesoscale) models. The procedure to generate and extract the relevant information is however typically complex and ad hoc, involving decision and intervention by domain experts, leading to long development times. In this study, we develop a principled approach for calibration of continuum-scale models using lower scale information by representing a CP flow rule as a Gaussian process model. This representation allows for efficient parameter space exploration, guided by the uncertainty embedded in the model through a process known as Bayesian optimization (BO). We demonstrate a semi-autonomous BO loop which instantiates discrete dislocation dynamics simulations whose initial conditions are automatically chosen to optimize the uncertainty of a model CP flow rule. Our self-guided computational pipeline efficiently generated a dataset and corresponding model whose error, uncertainty, and physical feature sensitivities were validated with comparison to an independent dataset four times larger, demonstrating a valuable and efficient active learning implementation readily transferable to similar material systems.

36 MATERIALS SCIENCE↗
NASA NTRS1976

On optimal soft-decision demodulation

A necessary condition is derived for optimal J-ary coherent demodulation of M-ary (M greater than 2) signals. Optimality is defined as maximality of the symmetric cutoff rate of the resulting discrete memoryless channel. Using a counterexample, it is shown that the condition derived is generally not sufficient for optimality. This condition is employed as the basis for an iterative optimization method to find the optimal demodulator decision regions from an initial 'good guess'. In general, these regions are found to be bounded by hyperplanes in likelihood space; the corresponding regions in signal space are found to have hyperplane asymptotes for the important case of additive white Gaussian noise. Some examples are presented, showing that the regions in signal space bounded by these asymptotic hyperplanes define demodulator decision regions that are virtually optimal.

Lee, L.-N.↗
NASA NTRS1988

Multirate digital control system design

Methods for multirate digital control system design are discussed. A simple method for sampling rate selection based on control bandwidths is proposed. Methods for generating a discrete-time state model of a sampled-data plant and a discrete-time equivalent to an analog cost function for a sampled-data plant are described. The succesive loop closures and linear quadratic Gaussian synthesis methods are reviewed, and a constrained optimization synthesis method is introduced. The proposed sampling rate selection, discretization, and synthesis methods are applied to two example design problems. Multirate and single-rate compensators synthesized by the different methods are compared, based on closed-loop responses, with compensators having the same real-time computation load.

Berg, Martin C.↗
NASA NTRS2002

Quadratic Optimization in the Problems of Active Control of Sound

We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

Loncaric, J.↗
NASA NTRS2012

Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology

This paper presents a novel approach to design of the supersonic aircraft outer mold line (OML) by optimizing the A-weighted loudness of sonic boom signature predicted on the ground. The optimization process uses the sensitivity information obtained by coupling the discrete adjoint formulations for the augmented Burgers Equation and Computational Fluid Dynamics (CFD) equations. This coupled formulation links the loudness of the ground boom signature to the aircraft geometry thus allowing efficient shape optimization for the purpose of minimizing the impact of loudness. The accuracy of the adjoint-based sensitivities is verified against sensitivities obtained using an independent complex-variable approach. The adjoint based optimization methodology is applied to a configuration previously optimized using alternative state of the art optimization methods and produces additional loudness reduction. The results of the optimizations are reported and discussed.

Rallabhandi, Siriam K.↗
NASA NTRS1994

Perceptual Optimization of DCT Color Quantization Matrices

Many image compression schemes employ a block Discrete Cosine Transform (DCT) and uniform quantization. Acceptable rate/distortion performance depends upon proper design of the quantization matrix. In previous work, we showed how to use a model of the visibility of DCT basis functions to design quantization matrices for arbitrary display resolutions and color spaces. Subsequently, we showed how to optimize greyscale quantization matrices for individual images, for optimal rate/perceptual distortion performance. Here we describe extensions of this optimization algorithm to color images.

Watson, Andrew B.↗
NASA NTRS2004

Application of a Momentum Source Model to the RAH-66 Comanche FANTAIL

A Momentum Source Model has been revised and implemented in the flow solver OVERFLOW-D. In this approach, the fan forces are evaluated from two-dimensional airfoil tables as a function of local Mach number and angle-of-attack and applied as source terms in the discretized Navier-Stokes equations. The model revisions include a new model for forces in the tip region and axial distribution of the source terms. The model revisions improve the results significantly. The Momentum Source Model agrees well with a discrete blade model for all computed collective pitch angles. The two models agree well with experimental data for thrust vs. torque. The Momentum Source Model is a good complement to Discrete Blade Models for ducted fan computations. The lower computational and labor costs make parametric studies, optimization studies and interactional aerodynamics studies feasible for cases beyond what is practical with a Discrete Blade Model today.

Nygaard, Tor A.↗
NASA NTRS1973

A mesh gradient technique for numerical optimization

A class of successive-improvement optimization methods in which directions of descent are defined in the state space along each trial trajectory are considered. The given problem is first decomposed into two discrete levels by imposing mesh points. Level 1 consists of running optimal subarcs between each successive pair of mesh points. For normal systems, these optimal two-point boundary value problems can be solved by following a routine prescription if the mesh spacing is sufficiently close. A spacing criterion is given. Under appropriate conditions, the criterion value depends only on the coordinates of the mesh points, and its gradient with respect to those coordinates may be defined by interpreting the adjoint variables as partial derivatives of the criterion value function. In level 2, the gradient data is used to generate improvement steps or search directions in the state space which satisfy the boundary values and constraints of the given problem.

Willis, E. A., Jr.↗
NASA NTRS1987

Single step optimization of manipulator maneuvers with variable structure control

One step ahead optimization has been recently proposed for spacecraft attitude maneuvers as well as for robot manipulator maneuvers. Such a technique yields a discrete time control algorithm implementable as a sequence of state-dependent, quadratic programming problems for acceleration optimization. Its sensitivity to model accuracy, for the required inversion of the system dynamics, is shown in this paper to be alleviated by a fast variable structure control correction, acting between the sampling intervals of the slow one step ahead discrete time acceleration command generation algorithm. The slow and fast looping concept chosen follows that recently proposed for optimal aiming strategies with variable structure control. Accelerations required by the VSC correction are reserved during the slow one step ahead command generation so that the ability to overshoot the sliding surface is guaranteed.

Chen, N.↗
NASA NTRS1973

Open-loop-feedback-optimal adaptive stochastic control of linear systems

This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.

Ku, R.↗