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At least 685 records · Page 38
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NASA NTRS1986

Simulator for multilevel optimization research

A computer program designed to simulate and improve multilevel optimization techniques is described. By using simple analytic functions to represent complex engineering analyses, the simulator can generate and test a large variety of multilevel decomposition strategies in a relatively short time. This type of research is an essential step toward routine optimization of large aerospace systems. The paper discusses the types of optimization problems handled by the simulator and gives input and output listings and plots for a sample problem. It also describes multilevel implementation techniques which have value beyond the present computer program. Thus, this document serves as a user's manual for the simulator and as a guide for building future multilevel optimization applications.

Padula, S. L.↗
NASA NTRS1986

Senstitivty analysis and optimization of nodal point placement for vibration reduction

A method is developed for sensitivity analysis and optimization of nodal point locations in connection with vibration reduction. A straightforward derivation of the expression for the derivative of nodal locations is given, and the role of the derivative in assessing design trends is demonstrated. An optimization process is developed which uses added lumped masses on the structure as design variables to move the node to a preselected location - for example, where low response amplitude is required or to a point which makes the mode shape nearly orthogonal to the force distribution, thereby minimizing the generalized force. The optimization formulation leads to values for added masses that adjust a nodal location while minimizing the total amount of added mass required to do so. As an example, the node of the second mode of a cantilever box beam is relocated to coincide with the centroid of a prescribed force distribution, thereby reducing the generalized force substantially without adding excessive mass. A comparison with an optimization formulation that directly minimizes the generalized force indicates that nodal placement gives essentially a minimum generalized force when the node is appropriately placed.

Pritchard, J. I.↗
NASA NTRS1986

Discrete-time Markovian-jump linear quadratic optimal control

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.

Chizeck, H. J.↗
NASA NTRS1986

Numerical difficulties associated with using equality constraints to achieve multi-level decomposition in structural optimization

There has been recent interest in multidisciplinary multilevel optimization applied to large engineering systems. The usual approach is to divide the system into a hierarchy of subsystems with ever increasing detail in the analysis focus. Equality constraints are usually placed on various design quantities at every successive level to ensure consistency between levels. In many previous applications these equality constraints were eliminated by reducing the number of design variables. In complex systems this may not be possible and these equality constraints may have to be retained in the optimization process. In this paper the impact of such a retention is examined for a simple portal frame problem. It is shown that the equality constraints introduce numerical difficulties, and that the numerical solution becomes very sensitive to optimization parameters for a wide range of optimization algorithms.

Thareja, R.↗
NASA NTRS1986

Optimal landing of a helicopter in autorotation

The landing of a helicopter in autorotation is formulated as a nonlinear optimal control problem. A unique feature in the present formulation is the addition of path inequality constraints on both the control and the state vectors. The control variable inequality constraint is a reflection of the limitation on the rotor thrust coefficient. The state-variable inequality constraint is an upper bound on the vertical sink-rate of the helicopter during descent. Optimal trajectories are calculated for entry conditions well within the height-velocity (H-V) restriction curve, with the helicopter initially in hover or in forward flight. The optimal solutions exhibited control techniques similar to those used by helicopter pilots in actual autorotational landings. The study indicates that, subject to pilot acceptability, a substantial reduction could be made in the H-V restriction zone using optimal control techniques.

Lee, A. Y.↗
NASA NTRS1984

Structural Optimization in automotive design

Although mathematical structural optimization has been an active research area for twenty years, there has been relatively little penetration into the design process. Experience indicates that often this is due to the traditional layout-analysis design process. In many cases, optimization efforts have been outgrowths of analysis groups which are themselves appendages to the traditional design process. As a result, optimization is often introduced into the design process too late to have a significant effect because many potential design variables have already been fixed. A series of examples are given to indicate how structural optimization has been effectively integrated into the design process.

Bennett, J. A.↗
NASA NTRS1984

Multidisciplinary optimization applied to a transport aircraft

Decomposition of a large optimization problem into several smaller subproblems has been proposed as an approach to making large-scale optimization problems tractable. To date, the characteristics of this approach have been tested on problems of limited complexity. The objective of the effort is to demonstrate the application of this multilevel optimization method on a large-scale design study using analytical models comparable to those currently being used in the aircraft industry. The purpose of the design study which is underway to provide this demonstration is to generate a wing design for a transport aircraft which will perform a specified mission with minimum block fuel. A definition of the problem; a discussion of the multilevel composition which is used for an aircraft wing; descriptions of analysis and optimization procedures used at each level; and numerical results obtained to date are included. Computational times required to perform various steps in the process are also given. Finally, a summary of the current status and plans for continuation of this development effort are given.

Giles, G. L.↗
NASA NTRS1984

Overview: Applications of numerical optimization methods to helicopter design problems

There are a number of helicopter design problems that are well suited to applications of numerical design optimization techniques. Adequate implementation of this technology will provide high pay-offs. There are a number of numerical optimization programs available, and there are many excellent response/performance analysis programs developed or being developed. But integration of these programs in a form that is usable in the design phase should be recognized as important. It is also necessary to attract the attention of engineers engaged in the development of analysis capabilities and to make them aware that analysis capabilities are much more powerful if integrated into design oriented codes. Frequently, the shortcoming of analysis capabilities are revealed by coupling them with an optimization code. Most of the published work has addressed problems in preliminary system design, rotor system/blade design or airframe design. Very few published results were found in acoustics, aerodynamics and control system design. Currently major efforts are focused on vibration reduction, and aerodynamics/acoustics applications appear to be growing fast. The development of a computer program system to integrate the multiple disciplines required in helicopter design with numerical optimization technique is needed. Activities in Britain, Germany and Poland are identified, but no published results from France, Italy, the USSR or Japan were found.

Miura, H.↗
NASA NTRS1984

A rotor optimization using regression analysis

The design and development of helicopter rotors is subject to the many design variables and their interactions that effect rotor operation. Until recently, selection of rotor design variables to achieve specified rotor operational qualities has been a costly, time consuming, repetitive task. For the past several years, Kaman Aerospace Corporation has successfully applied multiple linear regression analysis, coupled with optimization and sensitivity procedures, in the analytical design of rotor systems. It is concluded that approximating equations can be developed rapidly for a multiplicity of objective and constraint functions and optimizations can be performed in a rapid and cost effective manner; the number and/or range of design variables can be increased by expanding the data base and developing approximating functions to reflect the expanded design space; the order of the approximating equations can be expanded easily to improve correlation between analyzer results and the approximating equations; gradients of the approximating equations can be calculated easily and these gradients are smooth functions reducing the risk of numerical problems in the optimization; the use of approximating functions allows the problem to be started easily and rapidly from various initial designs to enhance the probability of finding a global optimum; and the approximating equations are independent of the analysis or optimization codes used.

Giansante, N.↗
NASA NTRS1984

Dual structural-control optimization of large space structures

A new approach is proposed for solving dual structural-control optimization problems for high-order flexible space structures where reduced-order structural models are employed. For a given initial structural dessign, a quadratic control cost is minimized subject to a constant-mass constraint. The sensitivity of the optimal control cost with respect to the stuctural design variables is then determined and used to obtain successive structural redesigns using a contrained gradient optimization algorithm. This process is repeated until the constrained control cost sensitivity becomes negligible. A numerical example is presented which demonstrates that this new approach effectively addresses the problem of dual optimization for potentially very high-order structures.

Messac, A.↗
NASA NTRS1984

Structural optimization with constraints on transients response

An exceptionally elegant method for structural optimization with constraints on the static response presented by Shield and Prager is discussed. Their derivation of the optimality condition was facilitated by a reformulation of the structural elasticity equations in terms of what was then a new variational principle, the principle of stationary mutual potential energy. Their optimality condition relates the design variable to an appropriately defined mutual strain energy. An alternative but related approach, based upon the principle of stationary mutual complementary energy, presented by N. C. Haung, is also discussed. The simplicity of these principles lies in the facts that the energy functionals are stationary at the solution to the field equations and that their stationary value is proportional to the quantity to be optimized.

Reiss, R.↗
NASA NTRS1984

Problems in large-scale structural optimization

A general design optimization model for large complex systems is defined. Major features of the model that challenge various optimization algorithms are discussed. Requirements of a model optimization algorithm are identified. Objectives of the study of various algorithms are defined and a basis for conducting such a study is developed. Primal as well as transformation methods are analytically studied and a unified viewpoint of various methods is presented. Several numerical examples are solved using different methods to study their performance. Conclusions drawn from the study are presented and discussed. Areas of future research in nonlinear programming as well as structural optimization are identified and discussed.

Arora, J. S.↗
NASA NTRS1984

Fundamental differences between optimization code test problems in engineering applications

The purpose here is to suggest that there is at least one fundamental difference between the problems used for testing optimization codes and the problems that engineers often need to solve; in particular, the level of precision that can be practically achieved in the numerical evaluation of the objective function, derivatives, and constraints. This difference affects the performance of optimization codes, as illustrated by two examples. Two classes of optimization problem were defined. Class One functions and constraints can be evaluated to a high precision that depends primarily on the word length of the computer. Class Two functions and/or constraints can only be evaluated to a moderate or a low level of precision for economic or modeling reasons, regardless of the computer word length. Optimization codes have not been adequately tested on Class Two problems. There are very few Class Two test problems in the literature, while there are literally hundreds of Class One test problems. The relative performance of two codes may be markedly different for Class One and Class Two problems. Less sophisticated direct search type codes may be less likely to be confused or to waste many function evaluations on Class Two problems. The analysis accuracy and minimization performance are related in a complex way that probably varies from code to code. On a problem where the analysis precision was varied over a range, the simple Hooke and Jeeves code was more efficient at low precision while the Powell code was more efficient at high precision.

Eason, E. D.↗
NASA NTRS1987

Sensitivity and optimization of composite structures using MSC/NASTRAN

Design sensitivity analysis for composites will soon be available in MSC/NASTRAN. The design variables for composites can be lamina thicknesses, orientation angles, material properties or a combination of all three. With the increasing use of composites in aerospace and automotive industries, this general capability can be used in its own right for carrying out sensitivity analysis of complicated real-life structures. As part of a research effort, the sensitivity analysis was coupled with a general purpose optimizer. This preliminary version of the optimizer is capable of dealing with minimum weight structural design with a rather general design variable linking capability at the element level or system level. Only sizing type of design variables (i.e., lamina thicknesses) can be handled by the optimizer. Test cases were run and validated by comparison with independent finite element packages. The linking of design sensitivity capability for composites in MSC/NASTRAN with an optimizer would give designers a powerful automated tool to carry out practical opitmization design of real-life complicated composite structures.

Nagendra, Gopal K.↗
NASA NTRS1987

Sensitivity derivatives and optimization of nodal point locations for vibration reduction

A method is developed for sensitivity analysis and optimization of nodal point locations in connection with vibration reduction. A straightforward derivation of the expression for the derivative of nodal locations is given, and the role of the derivative in assessing design trends is demonstrated. An optimization process is developed which uses added lumped masses on the structure as design variables to move the node to a preselected location; for example, where low response amplitude is required or to a point which makes the mode shape nearly orthogonal to the force distribution, thereby minimizing the generalized force. The optimization formulation leads to values for added masses that adjust a nodal location while minimizing the total amount of added mass required to do so. As an example, the node of the second mode of a cantilever box beam is relocated to coincide with the centroid of a prescribed force distribution, thereby reducing the generalized force substantially without adding excessive mass. A comparison with an optimization formulation that directly minimizes the generalized force indicates that nodal placement gives essentially a minimum generalized force when the node is appropriately placed.

Pritchard, Jocelyn I.↗
NASA NTRS1987

Distributed computer system enhances productivity for SRB joint optimization

Initial calculations of a redesign of the solid rocket booster joint that failed during the shuttle tragedy showed that the design had a weight penalty associated with it. Optimization techniques were to be applied to determine if there was any way to reduce the weight while keeping the joint opening closed and limiting the stresses. To allow engineers to examine as many alternatives as possible, a system was developed consisting of existing software that coupled structural analysis with optimization which would execute on a network of computer workstations. To increase turnaround, this system took advantage of the parallelism offered by the finite difference technique of computing gradients to allow several workstations to contribute to the solution of the problem simultaneously. The resulting system reduced the amount of time to complete one optimization cycle from two hours to one-half hour with a potential of reducing it to 15 minutes. The current distributed system, which contains numerous extensions, requires one hour turnaround per optimization cycle. This would take four hours for the sequential system.

Rogers, James L., Jr.↗
NASA NTRS1987

Optimal signal-to-noise in digital phase lock amplifiers

An expression for the optimal signal-to-noise ratio for linear phase lock amplifiers is derived. In its digital form the optimal method can be implemented by real-time signal processing techniques. The case of detector-noise-limited systems is analyzed in detail; it is found that the optimal technique can be used to eliminate effectively the detector's time constant from the set of parameters determining the overall efficiency. This has important implications for optical detection system design. Also reported is an experimental verification of the optimal method, thus establishing its practicality.

Doering, Charles R.↗
NASA NTRS1987

A method for nonlinear optimization with discrete design variables

A numerical method is presented for the solution of nonlinear discrete optimization problems. The applicability of discrete optimization to engineering design is discussed, and several standard structural optimization problems are solved using discrete design variables. The method uses approximation techniques to create subproblems suitable for linear mixed-integer programming methods. The method employs existing software for continuous optimization and integer programming.

Olsen, Gregory R.↗