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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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Optimization of payload mass placement in a dual keel space station

In order to keep a Space Station in a stable low-Earth orbit, angular momentum storage and translational attitude control systems will have to be used. In order to minimize the size of these attitude control systems, the induced gravity gradient torque effects will have to be minimized. This can be done by minimizing the cross-products of inertia of the Station through the management of payload placement with the Station geometry. A derived and automated methodology is presented which utilizes mathematical nonlinear programming techniques. An optimal arrangement of a set of five payloads on a Dual Keel Space Station was found that minimized the cross products of inertia and thus the required controllability resources.

Ferebee, Melvin J., Jr.↗
NASA NTRS1979

Acoustic duct liner optimization using finite elements

Determination of a mathematical model which may be used for obtaining optimum acoustic liners in aeroengine ducts was the goal of this study. Starting with a baseline finite element model which consumed too much computer time to permit optimum liner evaluation for realistic ducts and source frequencies, a survey was conducted of candidate methods for reducing computational effort. A highly effective boundary exclusive decomposition method was developed which enables L-U decomposition of a major partition of the global matrix to be performed once only. Timing experiments using the technique in duct liner optimization show a reduction of between one and two orders of magnitude in the central processor unit (CPU) time of the baseline model.

Abrahamson, A. L.↗
NASA NTRS2000

Development of a Composite Tailoring Procedure for Airplane Wings

The quest for finding optimum solutions to engineering problems has existed for a long time. In modern times, the development of optimization as a branch of applied mathematics is regarded to have originated in the works of Newton, Bernoulli and Euler. Venkayya has presented a historical perspective on optimization in [1]. The term 'optimization' is defined by Ashley [2] as a procedure "...which attempts to choose the variables in a design process so as formally to achieve the best value of some performance index while not violating any of the associated conditions or constraints". Ashley presented an extensive review of practical applications of optimization in the aeronautical field till about 1980 [2]. It was noted that there existed an enormous amount of published literature in the field of optimization, but its practical applications in industry were very limited. Over the past 15 years, though, optimization has been widely applied to address practical problems in aerospace design [3-5]. The design of high performance aerospace systems is a complex task. It involves the integration of several disciplines such as aerodynamics, structural analysis, dynamics, and aeroelasticity. The problem involves multiple objectives and constraints pertaining to the design criteria associated with each of these disciplines. Many important trade-offs exist between the parameters involved which are used to define the different disciplines. Therefore, the development of multidisciplinary design optimization (MDO) techniques, in which different disciplines and design parameters are coupled into a closed loop numerical procedure, seems appropriate to address such a complex problem. The importance of MDO in successful design of aerospace systems has been long recognized. Recent developments in this field have been surveyed by Sobieszczanski-Sobieski and Haftka [6].

Chattopadhyay, Aditi↗
DOE OSTI2025

MethodOpt: a Shiny-based graphical user interface for multivariate optimization of sampling and analytical instrumentation

Method optimization is an important step in producing useful data in various experimental settings involving the use of sampling and analytical instrumentation, such as gas-chromatography mass-spectrometry or other analytical techniques. However, traditional optimization techniques often lack the sophistication of more modern optimization techniques developed in areas of applied mathematics. A graphical user interface has been developed that implements a multivariate, multi-objective optimization technique for spectra-generating sampling and analytical instrumentation, which saves substantial time and resources compared to the more traditional approaches to method development.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1973

Analysis and optimization of cyclic methods in orbit computation

The mathematical analysis and computation of the K=3, order 4; K=4, order 6; and K=5, order 7 cyclic methods and the K=5, order 6 Cowell method and some results of optimizing the 3 backpoint cyclic multistep methods for solving ordinary differential equations are presented. Cyclic methods have the advantage over traditional methods of having higher order for a given number of backpoints while at the same time having more free parameters. After considering several error sources the primary source for the cyclic methods has been isolated. The free parameters for three backpoint methods were used to minimize the effects of some of these error sources. They now yield more accuracy with the same computing time as Cowell's method on selected problems. This work is being extended to the five backpoint methods. The analysis and optimization are more difficult here since the matrices are larger and the dimension of the optimizing space is larger. Indications are that the primary error source can be reduced. This will still leave several parameters free to minimize other sources.

Pierce, S.↗
NASA NTRS1993

Uncertainty reasoning in expert systems

Intelligent control is a very successful way to transform the expert's knowledge of the type 'if the velocity is big and the distance from the object is small, hit the brakes and decelerate as fast as possible' into an actual control. To apply this transformation, one must choose appropriate methods for reasoning with uncertainty, i.e., one must: (1) choose the representation for words like 'small', 'big'; (2) choose operations corresponding to 'and' and 'or'; (3) choose a method that transforms the resulting uncertain control recommendations into a precise control strategy. The wrong choice can drastically affect the quality of the resulting control, so the problem of choosing the right procedure is very important. From a mathematical viewpoint these choice problems correspond to non-linear optimization and are therefore extremely difficult. In this project, a new mathematical formalism (based on group theory) is developed that allows us to solve the problem of optimal choice and thus: (1) explain why the existing choices are really the best (in some situations); (2) explain a rather mysterious fact that fuzzy control (i.e., control based on the experts' knowledge) is often better than the control by these same experts; and (3) give choice recommendations for the cases when traditional choices do not work.

Kreinovich, Vladik↗
NASA NTRS1974

Stress tests on cylinders and aluminum panels

An optimization study of composite stiffened cylinders is discussed. The mathematical model for the buckling has been coupled successfully with the optimization program AESOP. The buckling analysis is based on the use of the smeared theory for the buckling of stiffened orthotropic cylindrical shells. The loading, radius, and length of the cylinder are assumed to be known parameters. An optimum solution gives the value of cross-sectional dimensions and laminate orientations. The different types of buckling modes are identified. Mathematical models are developed to show the relationships of the parameters.

Sobel, L. H.↗
NASA NTRS1982

An optimal control approach to the design of moving flight simulators

An abstract flight simulator design problem is formulated in the form of an optimal control problem, which is solved for the linear-quadratic-Gaussian special case using a mathematical model of the vestibular organs. The optimization criterion used is the mean-square difference between the physiological outputs of the vestibular organs of the pilot in the aircraft and the pilot in the simulator. The dynamical equations are linearized, and the output signal is modeled as a random process with rational power spectral density. The method described yields the optimal structure of the simulator's motion generator, or 'washout filter'. A two-degree-of-freedom flight simulator design, including single output simulations, is presented.

Sivan, R.↗
DOE OSTI2026

Intrusive Uncertainty Quantification and Optimal Experiment Design in the Open-Source Pyomo Ecosystem

This contribution describes ParmEst and Pyomo.DoE, two pillars of the open-source Python-based Pyomo ecosystem for computational optimization with (partial differential) algebraic equation mathematical models. Specifically, ParmEst facilitates intrusive frequentist parameter estimation (PE) and uncertainty quantification (UQ) through built-in features, such as covariance matrix estimation, bootstrapping, and likelihood ratio tests. Complementary, Pyomo.DoE enables optimal experiment design by maximizing various metrics of the Fisher information matrix, such as A-optimality (trace), D-optimality (determinant), E-optimality (minimum eigenvalue), and ME-optimality (condition number). ParmEst and Pyomo.DoE can solve high-dimensional optimization problems by leveraging the model structure and exact derivative information. Finally, we will discuss future opportunities to integrate PE and UQ capabilities with optimization under uncertainty, including robust optimization with non-convex models via PyROS.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2004

OTIS 3.2 Software Released

Trajectory, mission, and vehicle engineers concern themselves with finding the best way for an object to get from one place to another. These engineers rely upon special software to assist them in this. For a number of years, many engineers have used the OTIS program for this assistance. With OTIS, an engineer can fully optimize trajectories for airplanes, launch vehicles like the space shuttle, interplanetary spacecraft, and orbital transfer vehicles. OTIS provides four modes of operation, with each mode providing successively stronger optimization capability. The most powerful mode uses a mathematical method called implicit integration to solve what engineers and mathematicians call the optimal control problem. OTIS 3.2, which was developed at the NASA Glenn Research Center, is the latest release of this industry workhorse and features new capabilities for parameter optimization and mission design. OTIS stands for Optimal Control by Implicit Simulation, and it is implicit integration that makes OTIS so powerful at solving trajectory optimization problems. Why is this so important? The optimization process not only determines how to get from point A to point B, but it can also determine how to do this with the least amount of propellant, with the lightest starting weight, or in the fastest time possible while avoiding certain obstacles along the way. There are numerous conditions that engineers can use to define optimal, or best. OTIS provides a framework for defining the starting and ending points of the trajectory (point A and point B), the constraints on the trajectory (requirements like "avoid these regions where obstacles occur"), and what is being optimized (e.g., minimize propellant). The implicit integration method can find solutions to very complicated problems when there is not a lot of information available about what the optimal trajectory might be. The method was first developed for solving two-point boundary value problems and was adapted for use in OTIS. Implicit integration usually allows OTIS to find solutions to problems much faster than programs that use explicit integration and parametric methods. Consequently, OTIS is best suited to solving very complicated and highly constrained problems.

Riehl, John P.↗
NASA NTRS1969

Optimal stochastic control.

Optimal stochastic control, discussing dynamic mathematical models described by differential equations

Wonham, W. M.↗
NASA NTRS1976

Design of structures for optimum geometry

A general method is proposed for geometric optimization of finite element structures on the assumption that a reasonable initial geometry is specified. The number of finite elements, number of joints, and the element-joint relationships are specified and are not changed during the optimization process. The structure may be statically indeterminate and may support multiple loading conditions. Design variables include geometric and member sizing parameters. Design objectives may be minimum weight or cost, and constraints include strength and stiffness limitations. The optimization procedure is a general mathematical programming approach. An iterative design algorithm is outlined, and the method is specialized for truss structures. Design examples are given.

Vanderplaats, G. N.↗
NASA NTRS1978

Development of methodology for optimum design of structures at elevated temperatures

This paper surveys a number of activities aimed at applying optimum design techniques to structures where high temperatures are important design considerations. An improved variant of fully-stressed design (FSD), denoted thermal fully-stressed design (TFSD), is described which converges significantly faster than FSD for problems where thermal stresses are comparable in magnitude to mechanical stresses. Second, an optimality criterion is described for sizing structures subjected to temperature constraints. Simultaneous requirements on strength and temperatures are handled by two different techniques: (1) a state-of-the-art mathematical programming method and (2) the optimality criterion technique for temperature constraints combined with FSD for strength constraints. A method is described to optimize the insulation and ply thicknesses of an insulated composite panel with a time-varying temperature applied to the outer surface of the insulation and a general set of in-plane loads applied to the panel.

Adelman, H. M.↗
NASA NTRS1979

Multivariate approximation methods and applications to geophysics and geodesy

The first report in a series is presented which is intended to be written by the author with the purpose of treating a class of approximation methods of functions in one and several variables and ways of applying them to geophysics and geodesy. The first report is divided in three parts and is devoted to the presentation of the mathematical theory and formulas. Various optimal ways of representing functions in one and several variables and the associated error when information is had about the function such as satellite data of different kinds are discussed. The framework chosen is Hilbert spaces. Experiments were performed on satellite altimeter data and on satellite to satellite tracking data.

Munteanu, M. J.↗
NASA NTRS1990

Multilevel decomposition approach to the preliminary sizing of a transport aircraft wing

A multilevel/multidisciplinary optimization scheme for sizing an aircraft wing structure is described. A methodology using nonlinear programming in application to a very large engineering problem is presented. This capability is due to the decomposition approach. Over 1300 design variables are considered for this nonlinear optimization task. In addition, a mathematical link is established coupling the detail of structural sizing to the overall system performance objective, such as fuel consumption. The scheme is implemented as a three level system analyzing aircraft mission performance at the top level, the total aircraft structure as the middle level, and individual stiffened wing skin cover panels at the bottom level. Numerical show effectiveness of the method and its good convergence characteristics.

Wrenn, Gregory A.↗