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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Magnetostrictive direct drive motor

Highly magnetostrictive materials such as Tb.3Dy.7Fe2, commercially known as TERFENOL-D, have been used to date in a variety of devices such as high power actuators and linear motors. The larger magnetostriction available in twinned single crystal TERFENOL-D, approx. 2000 ppm at moderate magnetic field strengths, makes possible a new generation of magnetomechanical devices. NASA researchers are studying the potential of this material as the basis for a direct microstepping rotary motor with torque densities on the order of industrial hydraulics and five times greater than that of the most efficient, high power electric motors. Such a motor would be a micro-radian stepper, capable of precision movements and self-braking in the power-off state. Innovative mechanical engineering techniques are juxtaposed on proper magnetic circuit design to reduce losses in structural flexures, inertias, thermal expansions, eddy currents, and magneto-mechanical coupling, thus optimizing motor performance and efficiency. Mathematical models are presented, including magnetic, structural, and both linear and nonlinear dynamic calculations and simulations. In addition, test results on prototypes are presented.

Naik, Dipak↗
NASA NTRS1991

Joint U.S./Japan Conference on Adaptive Structures, 1st, Maui, HI, Nov. 13-15, 1990, Proceedings

The present volume of adaptive structures discusses the development of control laws for an orbiting tethered antenna/reflector system test scale model, the sizing of active piezoelectric struts for vibration suppression on a space-based interferometer, the control design of a space station mobile transporter with multiple constraints, and optimum configuration control of an intelligent truss structure. Attention is given to the formulation of full state feedback for infinite order structural systems, robustness issues in the design of smart structures, passive piezoelectric vibration damping, shape control experiments with a functional model for large optical reflectors, and a mathematical basis for the design optimization of adaptive trusses in precision control. Topics addressed include approaches to the optimal adaptive geometries of intelligent truss structures, the design of an automated manufacturing system for tubular smart structures, the Sandia structural control experiments, and the zero-gravity dynamics of space structures in parabolic aircraft flight.

Wada, Ben K.↗
NASA NTRS1993

Effect of design selection on response surface performance

The mathematical formulation of the engineering optimization problem is given. Evaluation of the objective function and constraint equations can be very expensive in a computational sense. Thus, it is desirable to use as few evaluations as possible in obtaining its solution. In solving the equation, one approach is to develop approximations to the objective function and/or restraint equations and then to solve the equation using the approximations in place of the original functions. These approximations are referred to as response surfaces. The desirability of using response surfaces depends upon the number of functional evaluations required to build the response surfaces compared to the number required in the direct solution of the equation without approximations. The present study is concerned with evaluating the performance of response surfaces so that a decision can be made as to their effectiveness in optimization applications. In particular, this study focuses on how the quality of approximations is effected by design selection. Polynomial approximations and neural net approximations are considered.

Carpenter, William C.↗
NASA NTRS2021

Debye Dielectric Model Function for Seawater Based on Expanded L-Band Measurement Data Set

New seawater dielectric measurements have recently been made over a broad range of salinities and temperatures at the George Washington University (GW). These measurements have been used to refine the existing dielectric model function of seawater for salinity retrieval. The mathematical structure of the new model function has been investigated to: (a) look for a physical basis for the mathematical form; and (b) to optimize the accuracy of data fitting. The Debye model has been chosen to represent the dielectric constant of seawater as a function of salinity (S), temperature (T) and frequency (f). The retrieved salinity using the Debye model has good agreement with the in-situ data collected by Argo floats. The global differences in retrieved salinity and in-situ data will be presented at the meeting.

ocean salinity↗
DOE OSTI2024

Optimal Design Approaches for Cost-Effective Manufacturing & Deployment of Chemical Process Families with Economies of Numbers

This work builds on our optimization formulation for process family design and extends it to explicitly include the benefits of economies of numbers. Economies of numbers (sometimes referred to as economies of learning) is a well-documented cost saving phenomenon. It characterizes the manufacturing cost savings due to standardization; in particular, it is capturing the correlation between cost reduction and the number of times a particular product has been manufactured. Following an approach similar to that in Gazzaneo et al. (2022), we develop a costing expression that captures material costs and manufacturing costs as a function of the number of unit modules produced. If the platform has a small number of unit module designs, we will be manufacturing a large number of each of these designs and gaining increased benefits from economies of numbers. However, increasing the number of unit module designs in the platform gives each process variant more choices to consider (at the cost of reducing economies of numbers). The optimization formulation in Stinchfield et al. (2023) pre-specified the number of unit module designs to be included in the platform. Here, by including the economies of numbers explicitly, we allow the mathematical programming formulation to determine the optimal number of unit module designs to include in the platform. We demonstrate this approach on multiple case studies, including MEA-based carbon capture and water desalination.

Stinchfield, Georgia↗
NASA NTRS1983

Structural optimization with dynamic behavior constraints

The minimum weight optimum design of damped linearly elastic structural systems subjected to periodic loading with behavior constraints on maximum deflections and side constraints on design variables is addressed. Attention is focused on the two major impediments to an optimal solution: (1) the time parametric nature of the behavior constraints; and (2) the severe nonconvexity of the design space. A solution method based on upper bound approximations for the behavior constraints and an innovative mathematical programming scheme for seeking the optimal frequency subspace is set forth. Numerical results for several test problems illustrate the effectiveness of the method reported.

Mills-Curran, W. C.↗
NASA NTRS1987

Mathematical programming formulations for satellite synthesis

The problem of satellite synthesis can be described as optimally allotting locations and sometimes frequencies and polarizations, to communication satellites so that interference from unwanted satellite signals does not exceed a specified threshold. In this report, mathematical programming models and optimization methods are used to solve satellite synthesis problems. A nonlinear programming formulation which is solved using Zoutendijk's method and a gradient search method is described. Nine mixed integer programming models are considered. Results of computer runs with these nine models and five geographically compatible scenarios are presented and evaluated. A heuristic solution procedure is also used to solve two of the models studied. Heuristic solutions to three large synthesis problems are presented. The results of our analysis show that the heuristic performs very well, both in terms of solution quality and solution time, on the two models to which it was applied. It is concluded that the heuristic procedure is the best of the methods considered for solving satellite synthesis problems.

Bhasin, Puneet↗
NASA NTRS1989

A practical approach for minimum time control of the Spacecraft Control Laboratory Experiment (SCOLE), appendix A

The Space COntrol Laboratory Experiment (SCOLE) is a challenge for control engineering applications. This is a result of the system dynamics, the available measurement information, the actuator capabilities and finally the specified performance requirements set. Results on the use of Model Reference Adaptive Control were reported. In view of the necessity for rapid response, this work deals with an optimal control formulation, with a minimum time requirement and constrained input. A mathematical statement of the problem is presented. The time optimal control formulation is presented and the reasons that make such an approach not promising are discussed. As a result, a pseudo time-optimal control algorithm is discussed. The proposed approach is tested to see if it satisfies the design specifications, and finally a discussion and suggestions for further research are provided.

Kaufman, H.↗
NASA NTRS1994

Quality optimization of thermally sprayed coatings produced by the JP-5000 (HVOF) gun using mathematical modeling

Currently, thermal barrier coatings (TBC) of gas-turbine blades and similar applications have centered around the use of zirconia as a protective coating for high thermal applications. The advantages of zirconia include low thermal conductivity and good thermal shock resistance. Thermally sprayed tungsten carbide hardface coatings are used for a wide range of applications spanning both the aerospace and other industrial markets. Major aircraft engine manufacturers and repair facilities use hardface coatings for original engine manufacture (OEM), as well as in the overhaul of critical engine components. The principle function of these coatings is to resist severe wear environments for such wear mechanisms as abrasion, adhesion, fretting, and erosion. The (JP-5000) thermal spray gun is the most advanced in the High Velocity Oxygen Fuel (HVOF) systems. Recently, it has received considerable attention because of its relative low cost and its production of quality coatings that challenge the very successful but yet very expensive Vacuum Plasma Spraying (VPS) system. The quality of thermal spray coatings is enhanced as porosity, oxidation, residual stress, and surface roughness are reduced or minimized. Higher densification, interfacial bonding strength, hardness and wear resistance of coating are desirable features for quality improvement.

Tawfik, Hazem↗
NASA NTRS1996

Mathematical modeling of the gas and powder flow in the (HVOF) systems to optimize their coatings quality

Thermally sprayed coatings have been extensively used to enhance materials properties and provide surface protection against their working environments in a number of industrial applications. Thermal barrier coatings (TBC) are used to reduce the thermal conductivity of aerospace turbine blades and improve the turbine overall thermal efficiency. TBC allows higher gas operating temperatures and lower blade material temperatures due to the thermal insulation provided by these ceramic coatings. In the automotive industry, coatings are currently applied to a number of moving parts that are subjected to friction and wear inside the engine such as pistons, cylinder liners, valves and crankshafts to enhance their wear resistance and prolong their useful operation and lifetime.

Tawfik, Hazem H.↗
NASA NTRS1980

Evaluation of orbits with incomplete knowledge of the mathematical expectancy and the matrix of covariation of errors

The problem of selecting the optimal algorithm of filtration and the optimal composition of the measurements is examined assuming that the precise values of the mathematical expectancy and the matrix of covariation of errors are unknown. It is demonstrated that the optimal algorithm of filtration may be utilized for making some parameters more precise (for example, the parameters of the gravitational fields) after preliminary determination of the elements of the orbit by a simpler method of processing (for example, the method of least squares).

Bakhshiyan, B. T.↗
NASA NTRS1992

Optimization and analysis of large chemical kinetic mechanisms using the solution mapping method - Combustion of methane

A method of systematic optimization, solution mapping, as applied to a large-scale dynamic model is presented. The basis of the technique is parameterization of model responses in terms of model parameters by simple algebraic expressions. These expressions are obtained by computer experiments arranged in a factorial design. The developed parameterized responses are then used in a joint multiparameter multidata-set optimization. A brief review of the mathematical background of the technique is given. The concept of active parameters is discussed. The technique is applied to determine an optimum set of parameters for a methane combustion mechanism. Five independent responses - comprising ignition delay times, pre-ignition methyl radical concentration profiles, and laminar premixed flame velocities - were optimized with respect to thirteen reaction rate parameters. The numerical predictions of the optimized model are compared to those computed with several recent literature mechanisms. The utility of the solution mapping technique in situations where the optimum is not unique is also demonstrated.

Frenklach, Michael↗
NASA NTRS2000

Optimal Wonderful Life Utility Functions in Multi-Agent Systems

The mathematics of Collective Intelligence (COINs) is concerned with the design of multi-agent systems so as to optimize an overall global utility function when those systems lack centralized communication and control. Typically in COINs each agent runs a distinct Reinforcement Learning (RL) algorithm, so that much of the design problem reduces to how best to initialize/update each agent's private utility function, as far as the ensuing value of the global utility is concerned. Traditional team game solutions to this problem assign to each agent the global utility as its private utility function. In previous work we used the COIN framework to derive the alternative Wonderful Life Utility (WLU), and experimentally established that having the agents use it induces global utility performance up to orders of magnitude superior to that induced by use of the team game utility. The WLU has a free parameter (the clamping parameter) which we simply set to zero in that previous work. Here we derive the optimal value of the clamping parameter, and demonstrate experimentally that using that optimal value can result in significantly improved performance over that of clamping to zero, over and above the improvement beyond traditional approaches.

Wolpert, David H.↗
NASA NTRS1993

Multidisciplinary design optimization - An emerging new engineering discipline

A definition of the multidisciplinary design optimization (MDO) is introduced, and functionality and relationship of the MDO conceptual components are examined. The latter include design-oriented analysis, approximation concepts, mathematical system modeling, design space search, an optimization procedure, and a humane interface.

Sobieszczanski-Sobieski, Jaroslaw↗
NASA NTRS2006

Distributed Constrained Optimization with Semicoordinate Transformations

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by translating the problem into an iterated game, where each agent controls a different variable of the problem, so that the joint probability distribution across the agents moves gives an expected value of the objective function. The dynamics of the agents is designed to minimize a Lagrangian function of that joint distribution. Here we illustrate how the updating of the Lagrange parameters in the Lagrangian is a form of automated annealing, which focuses the joint distribution more and more tightly about the joint moves that optimize the objective function. We then investigate the use of "semicoordinate" variable transformations. These separate the joint state of the agents from the variables of the optimization problem, with the two connected by an onto mapping. We present experiments illustrating the ability of such transformations to facilitate optimization. We focus on the special kind of transformation in which the statistically independent states of the agents induces a mixture distribution over the optimization variables. Computer experiment illustrate this for &sat constraint satisfaction problems and for unconstrained minimization of NK functions.

Macready, William↗
NASA NTRS1990

Shape optimization and CAD

Structural optimization has attracted the attention since the days of Galileo. Olhoff and Taylor have produced an excellent overview of the classical research within this field. However, the interest in structural optimization has increased greatly during the last decade due to the advent of reliable general numerical analysis methods and the computer power necessary to use them efficiently. This has created the possibility of developing general numerical systems for shape optimization. Several authors, eg., Esping; Braibant & Fleury; Bennet & Botkin; Botkin, Yang, and Bennet; and Stanton have published practical and successful applications of general optimization systems. Ding and Homlein have produced extensive overviews of available systems. Furthermore, a number of commercial optimization systems based on well-established finite element codes have been introduced. Systems like ANSYS, IDEAS, OASIS, and NISAOPT are widely known examples. In parallel to this development, the technology of computer aided design (CAD) has gained a large influence on the design process of mechanical engineering. The CAD technology has already lived through a rapid development driven by the drastically growing capabilities of digital computers. However, the systems of today are still considered as being only the first generation of a long row of computer integrated manufacturing (CIM) systems. These systems to come will offer an integrated environment for design, analysis, and fabrication of products of almost any character. Thus, the CAD system could be regarded as simply a database for geometrical information equipped with a number of tools with the purpose of helping the user in the design process. Among these tools are facilities for structural analysis and optimization as well as present standard CAD features like drawing, modeling, and visualization tools. The state of the art of structural optimization is that a large amount of mathematical and mechanical techniques are available for the solution of single problems. By implementing collections of the available techniques into general software systems, operational environments for structural optimization have been created. The forthcoming years must bring solutions to the problem of integrating such systems into more general design environments. The result of this work should be CAD systems for rational design in which structural optimization is one important design tool among many others.

Rasmussen, John↗