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Results for “Mathematical 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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Flexible Approximation Model Approach for Bi-Level Integrated System Synthesis

Bi-Level Integrated System Synthesis (BLISS) is an approach that allows design problems to be naturally decomposed into a set of subsystem optimizations and a single system optimization. In the BLISS approach, approximate mathematical models are used to transfer information from the subsystem optimizations to the system optimization. Accurate approximation models are therefore critical to the success of the BLISS procedure. In this paper, new capabilities that are being developed to generate accurate approximation models for BLISS procedure will be described. The benefits of using flexible approximation models such as Kriging will be demonstrated in terms of convergence characteristics and computational cost. An approach of dealing with cases where subsystem optimization cannot find a feasible design will be investigated by using the new flexible approximation models for the violated local constraints.

Sobieszczanski-Sobieski, Jaroslaw↗
NASA NTRS1971

Application of Monte Carlo techniques to optimization of high-energy beam transport in a stochastic environment

An algorithm employing a modified sequential random perturbation, or creeping random search, was applied to the problem of optimizing the parameters of a high-energy beam transport system. The stochastic solution of the mathematical model for first-order magnetic-field expansion allows the inclusion of state-variable constraints, and the inclusion of parameter constraints allowed by the method of algorithm application eliminates the possibility of infeasible solutions. The mathematical model and the algorithm were programmed for a real-time simulation facility; thus, two important features are provided to the beam designer: (1) a strong degree of man-machine communication (even to the extent of bypassing the algorithm and applying analog-matching techniques), and (2) extensive graphics for displaying information concerning both algorithm operation and transport-system behavior. Chromatic aberration was also included in the mathematical model and in the optimization process. Results presented show this method as yielding better solutions (in terms of resolutions) to the particular problem than those of a standard analog program as well as demonstrating flexibility, in terms of elements, constraints, and chromatic aberration, allowed by user interaction with both the algorithm and the stochastic model. Example of slit usage and a limited comparison of predicted results and actual results obtained with a 600 MeV cyclotron are given.

Parrish, R. V.↗
NASA NTRS1993

Genetic learning in rule-based and neural systems

The design of neural networks and fuzzy systems can involve complex, nonlinear, and ill-conditioned optimization problems. Often, traditional optimization schemes are inadequate or inapplicable for such tasks. Genetic Algorithms (GA's) are a class of optimization procedures whose mechanics are based on those of natural genetics. Mathematical arguments show how GAs bring substantial computational leverage to search problems, without requiring the mathematical characteristics often necessary for traditional optimization schemes (e.g., modality, continuity, availability of derivative information, etc.). GA's have proven effective in a variety of search tasks that arise in neural networks and fuzzy systems. This presentation begins by introducing the mechanism and theoretical underpinnings of GA's. GA's are then related to a class of rule-based machine learning systems called learning classifier systems (LCS's). An LCS implements a low-level production-system that uses a GA as its primary rule discovery mechanism. This presentation illustrates how, despite its rule-based framework, an LCS can be thought of as a competitive neural network. Neural network simulator code for an LCS is presented. In this context, the GA is doing more than optimizing and objective function. It is searching for an ecology of hidden nodes with limited connectivity. The GA attempts to evolve this ecology such that effective neural network performance results. The GA is particularly well adapted to this task, given its naturally-inspired basis. The LCS/neural network analogy extends itself to other, more traditional neural networks. Conclusions to the presentation discuss the implications of using GA's in ecological search problems that arise in neural and fuzzy systems.

Smith, Robert E.↗
NASA NTRS1974

NBODY - a multipurpose trajectory optimization computer program

Documentation of the NBODY trajectory optimization program is presented in the form of a mathematical development plus a user's manual. Optimal multistage-launch ascent trajectories may be determined by variational thrust steering during the upper phase. Optimal low-thrust interplanetary spacecraft trajectories may also be calculated with solar power or constant power, all-propulsion or embedded coast arcs, fixed or optimal thrust angles, and a variety of terminal end conditions. A hybrid iteration scheme solves the boundary-value problem, while either transversality conditions or a univariate search scheme optimize vehicle or trajectory parameters.

Strack, W. C.↗
NASA NTRS1977

An optimality criterion for sizing members of heated structures with temperature constraints

A thermal optimality criterion is presented for sizing members of heated structures with multiple temperature constraints. The optimality criterion is similar to an existing optimality criterion for design of mechanically loaded structures with displacement constraints. Effectiveness of the thermal optimality criterion is assessed by applying it to one- and two-dimensional thermal problems where temperatures can be controlled by varying the material distribution in the structure. Results obtained from the optimality criterion agree within 2 percent with results from a closed-form solution and with results from a mathematical programming technique. The thermal optimality criterion augments existing optimality criteria for strength and stiffness related constraints and offers the possibility of extension of optimality techniques to sizing structures with combined thermal and mechanical loading.

Rao, G. V.↗
NASA NTRS1993

On l(1): Optimal decentralized performance

In this paper, the Manousiouthakis parametrization of all decentralized stabilizing controllers is employed in mathematically formulating the l(sup 1) optimal decentralized controller synthesis problem. The resulting optimization problem is infinite dimensional and therefore not directly amenable to computations. It is shown that finite dimensional optimization problems that have value arbitrarily close to the infinite dimensional one can be constructed. Based on this result, an algorithm that solves the l(sup 1) decentralized performance problems is presented. A global optimization approach to the solution of the infinite dimensional approximating problems is also discussed.

Sourlas, Dennis↗
NASA NTRS1966

Preview control behavior and optimal control norms

Model based on optimal control theory for characterizing human operator in preview control task to provide reference frame for studying performance value and learning in manual control

HUMAN PERFORMANCE↗
NASA NTRS1979

Codes for a priority queue on a parallel data bus

Some codes for arbitration of priorities among subsystem computers or peripheral device controllers connected to a parallel data bus are described. At arbitration time, several subsystems present wire-OR, parallel code words to the bus, and the central computer can identify the subsystem of highest priority and determine which of two or more transmission services the subsystem requires. A mathematical discussion of the optimality of the codes with regard to the number of subsystems that may participate in the scheme for a given number of wires is presented along with the number of services that each subsystem may request.

Wallis, D. E.↗
NASA NTRS1989

Nonlinear control of a supermaneuverable aircraft

This paper describes a technique which may be used to design the flight control system for a highly maneuverable aircraft. The control system was provided to stabilize the dynamics of the aircraft model and allow it to fly simulated, poststall 'supermaneuvers'. Although the aircraft dynamics are highly nonlinear under these conditions, the gain-scheduled, flight control system was designed using basically linear techniques. A manuever generator was implemented to pilot the mathematical model through prescribed optimal trajectories. The control system design performed well while executing maneuvers involving small angular rates where the governing dynamics could be considered linear. However, the performance deteriorated once the model was subjected to high angular rates at high angle of attack.

Snell, S. Antony↗
NASA NTRS1992

The Enabler: A reevaluation of design concepts and construction of a scaled model

The basic objective of the student's work this quarter was to make an in depth examination of the design concepts used on the lunar vehicle 'The Enabler'. Several changes were made to the vehicle including a redesigned wheel, a more compact boom and a reduced articulation angle. The vehicle's final dimensions were determined through an optimization process by defining mathematical equations for several of the vehicle's defined objectives. These included the ability to scale a one meter object, traverse a one meter crevice, and maintain a wheel-to-wheel clearance of three inches while at maximum articulation. The final dimensions of the vehicle were used to construct an approximate 1/4 scale model of the chassis and wheels. The boom, however, was constructed on a 1/5 scale (from the original design). This was due to the redesign of the boom and the limitations of the constructing material and PVC fittings.

Bess, David↗
NASA NTRS1998

Three Program Architecture for Design Optimization

In this presentation, I would like to review historical perspective on the program architecture used to build design optimization capabilities based on mathematical programming and other numerical search techniques. It is rather straightforward to classify the program architecture in three categories as shown above. However, the relative importance of each of the three approaches has not been static, instead dynamically changing as the capabilities of available computational resource increases. For example, we considered that the direct coupling architecture would never be used for practical problems, but availability of such computer systems as multi-processor. In this presentation, I would like to review the roles of three architecture from historical as well as current and future perspective. There may also be some possibility for emergence of hybrid architecture. I hope to provide some seeds for active discussion where we are heading to in the very dynamic environment for high speed computing and communication.

Miura, Hirokazu↗
NASA NTRS2019

Trajectory Design of the Lucy Mission to Explore the Diversity of the Jupiter Trojans

Lucy, NASA’s next Discovery-class mission, will explore the diversity of the Jupiter Trojan asteroids. The Jupiter Trojans are thought to be remnants of the early solar system that were scattered inward when the gas giants migrated to their current positions as described in the Nice model. There are two stable subpopulations, or “swarms,” captured at the Sun-Jupiter L4 and L5 regions. These objects are the most accessible samples of what the outer solar system may have originally looked like. Lucy will launch in 2021 and will visit five Trojans, including one binary system. This paper discusses the target selection process, including a description of “alternate Lucys” that were ultimately passed over in favor of the final design. The mathematics of the trajectory optimization are also discussed.

Lucy↗
NASA NTRS2021

Learning spatial response functions from large multi-sensor AIRS and MODIS datasets

We use large datasets from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS) to derive AIRS spatial response functions and study their potential variations over the mission. The new reconstructed spatial response functions can be used to reduce errors in the radiances in non-uniform scenes and improve products generated using both AIRS and MODIS data. AIRS spatial response functions are distinct for each of its 2378 channels and each of its 90 scan angles. We develop the mathematical model and the optimization framework for deriving spatial response functions for two AIRS channels with low water vapor absorption and various scan angles. We quantify uncertainties in the derived reconstructions and study how they differ from pre-flight spatial response functions. We show that our approach generates reconstructions that agree with the data more accurately compared to pre-flight spatial responses. We derive spatial response functions using data collected during successive dates in order to ascertain the repeatability of the reconstructed spatial response functions. We also compare the derived spatial response functions based on data collected in the beginning, the middle, and at the current state of the mission in order to study changes in reconstructions over time.

Vese, Luminita↗
NASA NTRS2001

Robust Airfoil Optimization to Achieve Consistent Drag Reduction Over a Mach Range

We prove mathematically that in order to avoid point-optimization at the sampled design points for multipoint airfoil optimization, the number of design points must be greater than the number of free-design variables. To overcome point-optimization at the sampled design points, a robust airfoil optimization method (called the profile optimization method) is developed and analyzed. This optimization method aims at a consistent drag reduction over a given Mach range and has three advantages: (a) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (b) there is no random airfoil shape distortion for any iterate it generates, and (c) it allows a designer to make a trade-off between a truly optimized airfoil and the amount of computing time consumed. For illustration purposes, we use the profile optimization method to solve a lift-constrained drag minimization problem for 2-D airfoil in Euler flow with 20 free-design variables. A comparison with other airfoil optimization methods is also included.

Li, Wu↗