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At least 667 records · Page 37

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NASA NTRS1980

Global optimality of extremals: An example

The question of the existence and location of Darboux points is crucial for minimally sufficient conditions for global optimality and for computation of optimal trajectories. A numerical investigation is presented of the Darboux points and their relationship with conjugate points for a problem of minimum fuel, constant velocity, and horizontal aircraft turns to capture a line. This simple second order optimal control problem shows that ignoring the possible existence of Darboux points may play havoc with the computation of optimal trajectories.

Kreindler, E.↗

NASA NTRS1980

Use of constrained optimization in the conceptual design of a medium-range subsonic transport

Constrained parameter optimization was used to perform the optimal conceptual design of a medium range transport configuration. The impact of choosing a given performance index was studied, and the required income for a 15 percent return on investment was proposed as a figure of merit. A number of design constants and constraint functions were systematically varied to document the sensitivities of the optimal design to a variety of economic and technological assumptions. A comparison was made for each of the parameter variations between the baseline configuration and the optimally redesigned configuration.

Sliwa, S. M.↗

NASA NTRS1981

FRANOPP: Framework for analysis and optimization problems user's guide

Framework for analysis and optimization problems (FRANOPP) is a software aid for the study and solution of design (optimization) problems which provides the driving program and plotting capability for a user generated programming system. In addition to FRANOPP, the programming system also contains the optimization code CONMIN, and two user supplied codes, one for analysis and one for output. With FRANOPP the user is provided with five options for studying a design problem. Three of the options utilize the plot capability and present an indepth study of the design problem. The study can be focused on a history of the optimization process or on the interaction of variables within the design problem.

Riley, K. M.↗

NASA NTRS1981

Numerical optimization of circulation control airfoils

A numerical procedure for optimizing circulation control airfoils, which consists of the coupling of an optimization scheme with a viscous potential flow analysis for blowing jet, is presented. The desired airfoil is defined by a combination of three baseline shapes (cambered ellipse, and cambered ellipse with drooped and spiralled trailing edges). The coefficients of these shapes are used as design variables in the optimization process. Under the constraints of lift augmentation and lift-to-drag ratios, the optimal airfoils are found to lie between those of cambered ellipse and the drooped trailing edge, towards the latter as the angle of attack increases. Results agree qualitatively with available experimental data.

Tai, T. C.↗

NASA NTRS1982

The use of optimization techniques to design controlled diffusion compressor blading

A method for automating compressor blade design using numerical optimization, and applied to the design of a controlled diffusion stator blade row is presented. A general purpose optimization procedure is employed, based on conjugate directions for locally unconstrained problems and on feasible directions for locally constrained problems. Coupled to the optimizer is an analysis package consisting of three analysis programs which calculate blade geometry, inviscid flow, and blade surface boundary layers. The optimizing concepts and selection of design objective and constraints are described. The procedure for automating the design of a two dimensional blade section is discussed, and design results are presented.

Sanger, N. L.↗

NASA NTRS1982

Circumferentially segmented duct lines optimized for axisymmetric and standing wave sources

Optimum and off-optimum properties of circumferentially segmented duct liners are compared with those of uniform liners to identify any potential benefits of circumferentially segmented liners. High- and low-order spinning-mode sources are considered in the study. The solution for the segmented liner is obtained by a multimodal expansion of the segmented-liner eigenmodes in terms of a series of hardwall duct models. The coefficients in the hard-wall series are obtained by using Galerkin's method. Results show that for some frequencies and duct lengths, circumferentially segmented liners scatter energy equally between a higher and lower order circumferential wave number. Studies for higher order spinning-mode sources show that an optimized segmented liner with a hard-wall/soft-wal admittance variation representing an optimum configuration gives better performance than an optimized uniform liner. Overall, the greatest benefit of the segmented liner over the uniform liner occurs under off-optimum conditions. The optimized segmented liner gives more effective broadband performance than the optimized uniform liner.

Watson, W. R.↗

NASA NTRS1982

On Kaplun's optimal co-ordinates

Optimal co-ordinates were introduced by Kaplun (1954) as a result of his study on the role of co-ordinate systems in boundary-layer theory. In this paper the basic ideas of optimal co-ordinates are examined and many restrictions of Kaplun's optimal co-ordinates are removed. His rule for constructing optimal co-ordinates is found to apply unaltered to axisymmetric flows, to flows with oncoming streams containing vorticity, to free boundary layers such as jets, to free-convection flows and to compressible flows. It is also extended to unsteady boundary layers, and to three-dimensional boundary layers using a pair of stream functions.

Legner, H. H.↗

NASA NTRS1983

Structural optimization by multilevel decomposition

A method is described for decomposing an optimization problem into a set of subproblems and a coordination problem which preserves coupling between the subproblems. The method is introduced as a special case of multilevel, multidisciplinary system optimization and its algorithm is fully described for two level optimization for structures assembled of finite elements of arbitrary type. Numerical results are given for an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition. It is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers, using different computers to work concurrently on the same large problem.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1983

Improved method for transonic airfoil design-by-optimization

An improved method for use of optimization techniques in transonic airfoil design is demonstrated. FLO6QNM incorporates a modified quasi-Newton optimization package, and is shown to be more reliable and efficient than the method developed previously at NASA-Ames, which used the COPES/CONMIN optimization program. The design codes are compared on a series of test cases with known solutions, and the effects of problem scaling, proximity of initial point to solution, and objective function precision are studied. In contrast to the older method, well-converged solutions are shown to be attainable in the context of engineering design using computational fluid dynamics tools, a new result. The improvements are due to better performance by the optimization routine and to the use of problem-adaptive finite difference step sizes for gradient evaluation.

Kennelly, R. A., Jr.↗

NASA NTRS1983

Improved method for transonic airfoil design-by-optimization

An improved method for use of optimization techniques in transonic airfoil design is demonstrated. FLO6QNM incorporates a modified quasi-Newton optimization package, and is shown to be more reliable and efficient than the method developed previously at NASA-Ames, which used the COPES/CONMIN optimization problem. The design codes are compared on a series of test cases with known solutions, and the effects of problem scaling, proximity of initial point to solution, and objective function precision are studied. In contrast to the older method, well-converged solutions are shown to be attainable in the context of engineering design using computational fluid dynamics tools, a new result. The improvements are due to better performance by the optimization routine and to the use of problem-adaptive finite difference step sizes for gradient evaluation.

Kennelly, R. A., Jr.↗

NASA NTRS1983

Optimal design of a passive vibration absorber for a truss beam

The selection of the design parameters of passive vibration absorbers attached to a long cantilevered beam is studied. This study was motivated by the need for conducting parametric analysis of dynamics and control for Space-Shuttle-attached long beams. An optimization scheme using a quadratic cost function is introduced yielding the optimal sizing of the tip vibration absorber. Analytical solutions for an optimal absorber are presented for the case of one beam vibrational mode coupled with the absorber dynamics, and results are extended to cover the multiple mode case. An algorithm is developed to make an initial estimate of optimal tuning parameters which minimize the quadratic error cost function. Examples are given to illustrate the design concept.

Juang, J.-N.↗

NASA NTRS1983

Optimization and closed loop guidance of drag modulated aeroassisted orbital transfer

An analysis of optimal and near optimal atmospheric flight trajectories for drag modulated aeroassisted orbital transfer is presented. An explicit and adaptive closed loop guidance approach for this mode of orbit transfer is also presented with performance near the optimal nominal trajectories. The orbital transfer of interest is for return from high earth orbit to low earth orbit. Most of what is discussed in this paper concerns the aeroassisted or atmospheric segment which lowers the apogee of the high earth orbit to the apogee of the low earth orbit. Minimization of the total impulsive delta-V at this low earth orbit apogee is the optimization criterion. Control about this impulse due to a number of potential error sources in atmospheric braking is the requirement imposed on closed loop guidance.

Kechichian, J. A.↗

NASA NTRS1985

Optimization of Controlled Structures

A formulation is presented for the coupled optimal design of a structural system and its control by defining a composite objective function as a linear combination of two components: a structural objective and a control objective. For the case when the structural objective is a function of the structural design variables only, and when the control objective is represented by the quadratic functional of the response and control energy, one can analytically express the optimal control in terms of any set of admissible structural design variables. The expression for the optimal control is used recursively in an iterative Newton-Raphson search scheme, the goal of which is to determine a corresponding optimal set of structural design variables that minimize the composite objective function. A numerical example is given to illustrate the computational procedure.

Salama, M.↗

NASA NTRS1984

Approximate solutions to minimax optimal control problems for aeroassisted orbital transfer

The maneuver considered in the present investigation involves the coplanar transfer of a spacecraft from a high earth orbit (HEO) to a low earth orbit (LEO). HEO can be a geosynchronous earth orbit (GEO). The basic concept utilized involves the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. The considered type of flight is also called synergetic space flight. With respect to the atmospheric part of the maneuver, trajectory control is achieved by means of lift modulation. The Bolza problem of optimal control is stated, and the first-order optimality conditions for this problem are given. The one-arc approach, the two-arc approach, and the three-subarc approach are discussed. Attention is given to the Chebyshev problem of optimal control, details concerning aeroassisted orbital transfer (AOT), AOT optimization problems, and numerical experiments.

Miele, A.↗

NASA NTRS1984

Optimal low-thrust, three-burn orbit transfers with large plane changes

Optimal low-thrust, three-burn solutions have been obtained for orbit transfers between a 28.5-degree inclined low earth orbit and a series of 63.4-degree inclined circular orbits as well as a series of 63.4-degree inclined elliptical orbits with twelve hour periods. Solutions have also been obtained for orbit transfers between 97-degree inclined orbits and a 57-degree inclined low earth orbit. Thrust to weight ratios as low as 0.02 were considered. A hybrid nonlinear programming method was used to obtain the solutions. Analysis of the optimal steering during various burns reveals a natural division of the steering strategies into two categories based on whether a burn results in a change predominantly in semi-major axis or orbit plane. The similarity of these optimal steering strategies to previously obtained simple near-optimal steering strategies is discussed.

Zondervan, K. P.↗

NASA NTRS1985

Structural shape optimization - A survey

This paper is a survey of structural shape optimization with an emphasis on techniques dealing with shape optimization of the boundaries of two and three dimensional bodies. Attention is focused on the special problems of structural shape optimization which are due to a finite element model which must change during the optimization process. These problems include the requirement for sophisticated automated mesh generation techniques and careful choice of design variables. They also include special problems in obtaining sufficiently accurate sensitivity derivatives.

Haftka, R. T.↗

NASA NTRS1985

Finite element engine blade structural optimization

The Structural Tailoring of Engine Blades (STAEBL) computer program was developed to perform engine fan blade numerical optimizations. These blade optimizations seek a minimum weight or cost design that satisfies realistic blade design constraints, by tuning one to twenty design variables. The STAEBL system has been generalized to include both fan and compressor blade numerical optimizations. The system analyses have been significantly improved through the inclusion of an efficient plate finite element analysis for blade stress and frequency determinations. Additionally, a finite element based approximate severe foreign object damage (FOD) analysis has been included. The new FOD analysis gives very accurate estimates of the full nonlinear bird ingestion solution. Optimizations of fan and compressor blades have been performed using the system, showing significant cost and weight reductions, while comparing very favorably with refined design validation procedures.

Brown, K. W.↗

NASA NTRS1985

Onboard near-optimal climb-dash energy management

This paper studies optimal and near-optimal trajectories of high-performance aircraft in symmetric flight. Onboard, real-time, near-optimal guidance is considered for the climb-dash mission, using some of the boundary-layer structure and hierarchical ideas from singular perturbations. In the case of symmetric flight, this resembles neighborhood-optimal guidance using energy-to-go as the running variable. However, extension to three-dimensional flight is proposed, using families of nominal paths with heading-to-go as the additional running variable. Some computational results are presented for the symmetric case.

Weston, A.↗