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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 217 records · Page 12
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NASA NTRS1976

Structural optimization via a design space hierarchy

Mathematical programming techniques provide a general approach to automated structural design. An iterative method is proposed in which design is treated as a hierarchy of subproblems, one being locally constrained and the other being locally unconstrained. It is assumed that the design space is locally convex in the case of good initial designs and that the objective and constraint functions are continuous, with continuous first derivatives. A general design algorithm is outlined for finding a move direction which will decrease the value of the objective function while maintaining a feasible design. The case of one-dimensional search in a two-variable design space is discussed. Possible applications are discussed. A major feature of the proposed algorithm is its application to problems which are inherently ill-conditioned, such as design of structures for optimum geometry.

Vanderplaats, G. N.↗
NASA NTRS1983

Space Shuttle propulsion parameter estimation using optimal estimation techniques, volume 1

The mathematical developments and their computer program implementation for the Space Shuttle propulsion parameter estimation project are summarized. The estimation approach chosen is the extended Kalman filtering with a modified Bryson-Frazier smoother. Its use here is motivated by the objective of obtaining better estimates than those available from filtering and to eliminate the lag associated with filtering. The estimation technique uses as the dynamical process the six degree equations-of-motion resulting in twelve state vector elements. In addition to these are mass and solid propellant burn depth as the ""system'' state elements. The ""parameter'' state elements can include aerodynamic coefficient, inertia, center-of-gravity, atmospheric wind, etc. deviations from referenced values. Propulsion parameter state elements have been included not as options just discussed but as the main parameter states to be estimated. The mathematical developments were completed for all these parameters. Since the systems dynamics and measurement processes are non-linear functions of the states, the mathematical developments are taken up almost entirely by the linearization of these equations as required by the estimation algorithms.

Source record↗
NASA NTRS1986

Concerning the electrosynthesis of hydrogen peroxide and peroxodisulfates. Section 2: Optimization of electrolysis cells using an electrolyzer for peroxodisulfuric acid as an example

The model is presented of an electrolyzer for peroxodisulfuric acid, and it is analyzed mathematically. Its application for engineering and economic optimization is investigated in detail. The mathematical analysis leads to conclusions concerning the change in position of the optimum with respect to the various target functions due to changes of the individual design-caused and economic parameters.

Schleiff, M.↗
NASA NTRS1982

Fuel optimal maneuvers for spacecraft with fixed thrusters

Several mathematical models, including a minimum integral square criterion problem, were used for the qualitative investigation of fuel optimal maneuvers for spacecraft with fixed thrusters. The solutions consist of intervals of "full thrust" and "coast" indicating that thrusters do not need to be designed as "throttleable" for fuel optimal performance. For the primary model considered, singular solutions occur only if the optimal solution is "pure translation". "Time optimal" singular solutions can be found which consist of intervals of "coast" and "full thrust". The shape of the optimal fuel consumption curve as a function of flight time was found to depend on whether or not the initial state is in the region admitting singular solutions. Comparisons of fuel optimal maneuvers in deep space with those relative to a point in circular orbit indicate that qualitative differences in the solutions can occur. Computation of fuel consumption for certain "pure translation" cases indicates that considerable savings in fuel can result from the fuel optimal maneuvers.

Carter, T. C.↗
NASA NTRS1972

Computerized optimal control system design for reusable and expendable boost vehicles.

An optimization technique has been developed which combines the practical features of hybrid simulation of the dynamic system under study with the systematic approach of modern control theory where a mathematically formulated design criterion is optimized by functional minimization. Standard hybrid computer optimization methods using high-speed repetitive simulations and gradient minimization schemes have been extended to obtain time-varying optimal gain schedules and reduce the sensitivity of the optimized system to parameter and disturbance uncertainties. In this approach the performance index is expressed in meaningful engineering terms that reflect the interactions among all major disciplines, structures, control/actuation system design, aerodynamics and performance. The basic optimization technique is developed and its application to current aerospace control problems including the space shuttle is presented in detail. In the discussion of the application, the controllers resulting from the technique are compared with controllers developed by conventional methods. The paper concludes with a review of the advantages and disadvantages of the technique and plans for future applications.

Connor, C. L.↗
NASA NTRS1980

Structural sizing considerations for large space platforms

Structural optimization studies are made using mathematical programming techniques to examine minimum mass structural proportions of deployable and erectable tetrahedral truss platforms subject to the integrated effects of practical design requirements. Considerations integrated into the optimization process are: 1) lowest natural frequencies of the platform and individual platform components (struts); 2) packaging constraints imposed by the Shuttle cargo bay capacity; 3) initial curvature of the struts; 4) column buckling of the struts due to gravity gradient, orbital transfer, strut length tolerance, or design loads; and 5) practical lower limits for strut diameter and wall thickness. Ultra-low mass designs are shown to be possible with strut proportions much more slender than those conventionally used for earthbound application.

Heard, W. L., Jr.↗
NASA NTRS2001

Improving Simulated Annealing by Replacing Its Variables with Game-Theoretic Utility Maximizers

The game-theory field of Collective INtelligence (COIN) concerns the design of computer-based players engaged in a non-cooperative game so that as those players pursue their self-interests, a pre-specified global goal for the collective computational system is achieved as a side-effect. Previous implementations of COIN algorithms have outperformed conventional techniques by up to several orders of magnitude, on domains ranging from telecommunications control to optimization in congestion problems. Recent mathematical developments have revealed that these previously developed algorithms were based on only two of the three factors determining performance. Consideration of only the third factor would instead lead to conventional optimization techniques like simulated annealing that have little to do with non-cooperative games. In this paper we present an algorithm based on all three terms at once. This algorithm can be viewed as a way to modify simulated annealing by recasting it as a non-cooperative game, with each variable replaced by a player. This recasting allows us to leverage the intelligent behavior of the individual players to substantially improve the exploration step of the simulated annealing. Experiments are presented demonstrating that this recasting significantly improves simulated annealing for a model of an economic process run over an underlying small-worlds topology. Furthermore, these experiments reveal novel small-worlds phenomena, and highlight the shortcomings of conventional mechanism design in bounded rationality domains.

Wolpert, David H.↗
NASA NTRS2001

Improving Simulated Annealing by Recasting it as a Non-Cooperative Game

The game-theoretic field of COllective INtelligence (COIN) concerns the design of computer-based players engaged in a non-cooperative game so that as those players pursue their self-interests, a pre-specified global goal for the collective computational system is achieved "as a side-effect". Previous implementations of COIN algorithms have outperformed conventional techniques by up to several orders of magnitude, on domains ranging from telecommunications control to optimization in congestion problems. Recent mathematical developments have revealed that these previously developed game-theory-motivated algorithms were based on only two of the three factors determining performance. Consideration of only the third factor would instead lead to conventional optimization techniques like simulated annealing that have little to do with non-cooperative games. In this paper we present an algorithm based on all three terms at once. This algorithm can be viewed as a way to modify simulated annealing by recasting it as a non-cooperative game, with each variable replaced by a player. This recasting allows us to leverage the intelligent behavior of the individual players to substantially improve the exploration step of the simulated annealing. Experiments are presented demonstrating that this recasting improves simulated annealing by several orders of magnitude for spin glass relaxation and bin-packing.

Wolpert, David↗
NASA NTRS1990

Accumulated approximation: A new method for structural optimization by iterative improvement

A new method for the solution of non-linear mathematical programming problems in the field of structural optimization is presented. It is an iterative scheme which for each iteration refines the approximation of objective and constraint functions by accumulating the function values of previously visited design points. The method has proven to be competitive for a number of well-known examples of which one is presented here. Furthermore because of the accumulation strategy, the method produces convergence even when the sensitivity analysis is inaccurate.

Rasmussen, John↗
NASA NTRS1979

Air breathing engine/rocket trajectory optimization

This research has focused on improving the mathematical models of the air-breathing propulsion systems, which can be mated with the rocket engine model and incorporated in trajectory optimization codes. Improved engine simulations provided accurate representation of the complex cycles proposed for advanced launch vehicles, thereby increasing the confidence in propellant use and payload calculations. The versatile QNEP (Quick Navy Engine Program) was modified to allow treatment of advanced turboaccelerator cycles using hydrogen or hydrocarbon fuels and operating in the vehicle flow field.

Smith, V. K., III↗
NASA NTRS1981

Optimal air-breathing launch vehicle design

A generalized two-point boundary problem methodology, similar to techniques used in deterministic optimal control studies, is applied to the design and flight analysis of a two-stage air-breathing launch vehicle. Simultaneous consideration is given to configuration and trajectory by treating geometry, dynamic discontinuities, and time-dependent flight variables all as controls to be optimized with respect to a single mathematical performance measure. While minimizing fuel consumption, inequality constraints are applied to dynamic pressure and specific force. The optimal system fuel consumption and staging Mach number are found to vary little with changes in the inequality constraints due to substantial geometry and trajectory adjustments. Staging, from an air-breathing first stage to a rocket-powered second stage, consistently occurs near Mach 3.5. The dynamic pressure bound has its most pronounced effects on vehicle geometry, particularly the air-breathing propulsion inlet area, and on the first-stage altitude profile. The specific force has its greatest influence on the second-stage thrust history.

Hattis, P. D.↗
NASA NTRS1989

Expansion and orthogonalization of measured modes for structure identification

The purpose was to investigate a new simultaneous expansion/orthogonalization method in comparison with two previously published expansion methods and a widely used orthogonalization technique. Each expansion method uses data from an analytical model of the structure to complete the estimate of the mode shape vectors. Berman and Nagy used Guyan expansion in their work with improving analytical models. In this method, modes are expanded one at a time, producing a set not orthogonal with respect to the mass matrix. Baruch and Bar Itzhack's optimal orthogonalization procedure was used to subsequently adjust the expanded modes. A second expansion technique was presented by O'Callahan, Avitabile, and Reimer and separately by Kammer. Again, modes are expanded individually and orthogonalized after expansion with the same optimal technique as above. Finally, a simultaneous expansion/orthogonalization method was developed from the orthogonal Procrustes problem of computational mathematics. In this method modes are optimally expanded as a set and orthogonal with respect to the mass matrix as a result. Two demonstation problems were selected for the comparison of the methods described. The first problem is an 8 degree of freedom spring-mass problem first presented by Kabe. Several conditions were examined for expansion method including the presence of errors in the measured data and in the analysis models. As a second demonstration problem, data from tests of laboratory scale model truss structures was expanded for system identification. Tests with a complete structure produced a correlated analysis model and the stiffness and mass matrices. Tests of various damaged configurations produced measured data for 6 modes at 14 dof locations.

Smith, Suzanne Weaver↗
NASA NTRS2000

The Mathematics of Navigating the Solar System

In navigating spacecraft throughout the solar system, the space navigator relies on three academic disciplines - optimization, estimation, and control - that work on mathematical models of the real world. Thus, the navigator determines the flight path that will consume propellant and other resources in an efficient manner, determines where the craft is and predicts where it will go, and transfers it onto the optimal trajectory that meets operational and mission constraints. Mission requirements, for example, demand that observational measurements be made with sufficient precision that relativity must be modeled in collecting and fitting (the estimation process) the data, and propagating the trajectory. Thousands of parameters are now determined in near real-time to model the gravitational forces acting on a spacecraft in the vicinity of an irregularly shaped body. Completing these tasks requires mathematical models, analyses, and processing techniques. Newton, Gauss, Lambert, Legendre, and others are justly famous for their contributions to the mathematics of these tasks. More recently, graduate students participated in research to update the gravity model of the Saturnian system, including higher order gravity harmonics, tidal effects, and the influence of the rings. This investigation was conducted for the Cassini project to incorporate new trajectory modeling features in the navigation software. The resulting trajectory model will be used in navigating the 4-year tour of the Saturnian satellites. Also, undergraduate students are determining the ephemerides (locations versus time) of asteroids that will be used as reference objects in navigating the New Millennium's Deep Space 1 spacecraft autonomously.

Hintz, Gerald↗
NASA NTRS1984

Structural efficiency studies of corrugated compression panels with curved caps and beaded webs

Curved cross-sectional elements are employed in structural concepts for minimum-mass compression panels. Corrugated panel concepts with curved caps and beaded webs are optimized by using a nonlinear mathematical programming procedure and a rigorous buckling analysis. These panel geometries are shown to have superior structural efficiencies compared with known concepts published in the literature. Fabrication of these efficient corrugation concepts became possible by advances made in the art of superplastically forming of metals. Results of the mass optimization studies of the concepts are presented as structural efficiency charts for axial compression.

Davis, R. C.↗
NASA NTRS1992

Stability and optimal control theory of hereditary systems with applications from oscillating flying vehicles, mechanical systems, and robotics

The author derives an equation determining the dynamics of the deterministic model of a flying vehicle. He next examines a simplified mechanical problem whose optimal feedback control strategy is investigated. From there robotics are incorporated into the mathematical model to develop an equation describing optimal control of the dynamics.

Chukwu, Ethelbert Nwakuche↗
NASA NTRS1991

Helicopter vibration reduction using structural optimization with aeroelastic/multidisciplinary constraints - A survey

This paper presents a survey of the state-of-the-art in the field of structural optimization when applied to vibration reduction of helicopters in forward flight with aeroelastic and multidisciplinary constraints. It emphasizes the application of the modern approach where the optimization is formulated as a mathematical programming problem, the objective function consists of the vibration levels at the hub, and behavior constraints are imposed on the blade frequencies and aeroelastic stability margins, as well as on a number of additional ingredients that can have a significant effect on the overall performance and flight mechanics of the helicopter. It is shown that the integrated multidisciplinary optimization of rotorcraft offers the potential for substantial improvements, which can be achieved by careful preliminary design and analysis without requiring additional hardware such as rotor vibration absorbers of isolation systems.

Friedmann, Peretz P.↗
NASA NTRS1992

Impact of structural optimization with aeroelastic/multidisciplinary constraints on helicopter rotor design

This paper presents a review of the state-of-the-art in the field of structural optimization when applied to vibration reduction of helicopters in forward flight with aeroelastic and multidisciplinary constraints. It emphasizes the application of the modern approach where the optimization is formulated as a mathematical programming problem and the objective function consists of the vibration levels at the hub and behavior constraints are imposed on the blade frequencies, aeroelastic stability margins as well as on a number of additional ingredients which can have a significant effect on the overall performance and flight mechanics of the helicopter. It is shown that the integrated multidisciplinary optimization of rotorcraft offers the potential for substantial improvements which can be achieved by careful preliminary design and analysis without requiring additional hardware such as rotor vibration absorbers or isolation systems.

Friedmann, Peretz P.↗
NASA NTRS1994

Estimating Lives Of Space Shuttle Parts

SSPOC (Space Shuttle Probabilistic Optimization Code) computer program, implements probabilistic mathematical model, accepts defined distributions of parameters controlling life of Space Shuttle main engine. Used to perform tradeoff studies to optimize between service life and acceptable level of risk, with greater accuracy. Also includes probability of removal and failure of parts, along with number of surviving parts for each interval of inspections. Written in FORTRAN 77, and user interface written in PASCAL(R).

Watkins, Tommie, Jr.↗