Multilevel Methods for Optimal Design
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nonlinear optimization↗
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New evidence favoring multilevel decomposition and optimization
The issue of the utility of multilevel decomposition and optimization remains controversial. To date, only the structural optimization community has actively developed and promoted multilevel optimization techniques. However, even this community acknowledges that multilevel optimization is ideally suited for a rather limited set of problems. It is warned that decomposition typically requires eliminating local variables by using global variables and that this in turn causes ill-conditioning of the multilevel optimization by adding equality constraints. The purpose is to suggest a new multilevel optimization technique. This technique uses behavior variables, in addition to design variables and constraints, to decompose the problem. The new technique removes the need for equality constraints, simplifies the decomposition of the design problem, simplifies the programming task, and improves the convergence speed of multilevel optimization compared to conventional optimization.
Padula, Sharon L.↗
An integrated optimum design approach for high speed prop rotors
The objective is to develop an optimization procedure for high-speed and civil tilt-rotors by coupling all of the necessary disciplines within a closed-loop optimization procedure. Both simplified and comprehensive analysis codes are used for the aerodynamic analyses. The structural properties are calculated using in-house developed algorithms for both isotropic and composite box beam sections. There are four major objectives of this study. (1) Aerodynamic optimization: The effects of blade aerodynamic characteristics on cruise and hover performance of prop-rotor aircraft are investigated using the classical blade element momentum approach with corrections for the high lift capability of rotors/propellers. (2) Coupled aerodynamic/structures optimization: A multilevel hybrid optimization technique is developed for the design of prop-rotor aircraft. The design problem is decomposed into a level for improved aerodynamics with continuous design variables and a level with discrete variables to investigate composite tailoring. The aerodynamic analysis is based on that developed in objective 1 and the structural analysis is performed using an in-house code which models a composite box beam. The results are compared to both a reference rotor and the optimum rotor found in the purely aerodynamic formulation. (3) Multipoint optimization: The multilevel optimization procedure of objective 2 is extended to a multipoint design problem. Hover, cruise, and take-off are the three flight conditions simultaneously maximized. (4) Coupled rotor/wing optimization: Using the comprehensive rotary wing code CAMRAD, an optimization procedure is developed for the coupled rotor/wing performance in high speed tilt-rotor aircraft. The developed procedure contains design variables which define the rotor and wing planforms.
Chattopadhyay, Aditi↗
Algorithms for bilevel optimization
General multilevel nonlinear optimization problems arise in design of complex systems and can be used as a means of regularization for multi-criteria optimization problems. Here, for clarity in displaying our ideas, we restrict ourselves to general bi-level optimization problems, and we present two solution approaches. Both approaches use a trust-region globalization strategy, and they can be easily extended to handle the general multilevel problem. We make no convexity assumptions, but we do assume that the problem has a nondegenerate feasible set. We consider necessary optimality conditions for the bi-level problem formulations and discuss results that can be extended to obtain multilevel optimization formulations with constraints at each level.
Alexandrov, Natalia↗
Development and application of optimum sensitivity analysis of structures
The research focused on developing an algorithm applying optimum sensitivity analysis for multilevel optimization. The research efforts have been devoted to assisting NASA Langley's Interdisciplinary Research Office (IRO) in the development of a mature methodology for a multilevel approach to the design of complex (large and multidisciplinary) engineering systems. An effort was undertaken to identify promising multilevel optimization algorithms. In the current reporting period, the computer program generating baseline single level solutions was completed and tested out.
Barthelemy, J. F. M.↗
Multilevel control optimization using subsystem relative performance index sensitivity
A method is presented for the design of optimal feedback controllers for large multivariable systems with subsystem sensitivity constraints. The weighted sum of subsystem and/or operational mode relative performance index sensitivities is defined as the overall performance index. The method is developed for linear systems with quadratic performance criteria and either full or partial state feedback. An example concerning the design of a stability augmentation system for a VTOL aircraft in the transition mode demonstrates the effectiveness of the design method.
Leininger, G. G.↗
Structural optimization by multilevel decomposition
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Sobieszczanski-Sobieski, J.↗
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.↗
A multilevel control system for the large space telescope
A multilevel scheme was proposed for control of Large Space Telescope (LST) modeled by a three-axis-six-order nonlinear equation. Local controllers were used on the subsystem level to stabilize motions corresponding to the three axes. Global controllers were applied to reduce (and sometimes nullify) the interactions among the subsystems. A multilevel optimization method was developed whereby local quadratic optimizations were performed on the subsystem level, and global control was again used to reduce (nullify) the effect of interactions. The multilevel stabilization and optimization methods are presented as general tools for design and then used in the design of the LST Control System. The methods are entirely computerized, so that they can accommodate higher order LST models with both conceptual and numerical advantages over standard straightforward design techniques.
D D Siljak↗
Optimal control of distributed parameter systems using multilevel techniques
Optimal control of distributed parameter systems using multilevel techniques
APPROXIMATION METHOD↗
Optimization of aircraft configurations in a multidisciplinary environment
A decomposition and multidisciplinary optimization methodology for aircraft design is presented, based on multilevel optimization and use of global sensitivity equations to account for interdisciplinary effects. A brief study of a hypersonic cruise vehicle is developed to illustrate methodology. The vehicle is sized for minimum take-off gross weight considering aerodynamics, structures, and mission performance.
Logan, Trent R.↗
Improved calculation of optimum design sensitivity
Optimum design parameter sensitivity analysis has become an important topic in recent years. The principal reasons for obtaining optimum design sensitivity information with respect to various problem parameters are (l) to predict revised optimum designs, associated with specified perturbations of the problem parameters, without re-optimizing the problem and, (2) to provide sensitivity information in multilevel optimization strategies. Methods for calculating these derivatives were proposed by several authors. The most important drawback in estimating parameter sensitivities by the current methods is that they do not allow for changes in the active constraint set. Changes in the active constraint set produce discontinuities in the optimum design sensitivities, and therefore, a correct formulation has to be cast in terms of directional derivatives. Optimum design parameter sensitivity analysis is addressed in terms of directional derivatives so as to include possible discontinuities and it also presents a method for estimating optimum design sensitivities using finite differences.
Sepulveda, Abdon E.↗
Optimization of nonlinear aeroelastic tailoring criteria
A static flexible fighter aircraft wing configuration is presently addressed by a multilevel optimization technique, based on both a full-potential concept and a rapid structural optimization program, which can be applied to such aircraft-design problems as maneuver load control, aileron reversal, and lift effectiveness. It is found that nonlinearities are important in the design of an aircraft whose flight envelope encompasses the transonic regime, and that the present structural suboptimization produces a significantly lighter wing by reducing ply thicknesses.
Abdi, F.↗
Interdisciplinary optimum design
Problems related to interdisciplinary interactions in the design of a complex engineering systems are examined with reference to aerospace applications. The interdisciplinary optimization problems examined include those dealing with controls and structures, materials and structures, control and stability, structure and aerodynamics, and structure and thermodynamics. The discussion is illustrated by the following specific applications: integrated aerodynamic/structural optimization of glider wing; optimization of an antenna parabolic dish structure for minimum weight and prescribed emitted signal gain; and a multilevel optimization study of a transport aircraft.
Sobieszczanski-Sobieski, Jaroslaw↗
The Third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization
The third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization was held on 24-26 Sept. 1990. Sessions were on the following topics: dynamics and controls; multilevel optimization; sensitivity analysis; aerodynamic design software systems; optimization theory; analysis and design; shape optimization; vehicle components; structural optimization; aeroelasticity; artificial intelligence; multidisciplinary optimization; and composites.
V.B. Venkayya↗
Efficient single-level solution of hierarchical problems in structural optimization
A demonstration is made of the use of single-level hierarchical solution techniques for engineering design, which, unlike the formulation stage-applied multilevel techniques, are applied at the solution stage. A single-level decomposition technique is developed which reduces computational costs and memory requirements without incurring the disadvantages of multilevel optimization. Savings of 75 percent are obtained in a case involving 500 design variables and 2408 constraints.
Thareja, Rajiv R.↗
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.↗
Rapid design of aerospace vehicle
This document presents in viewgraph form techniques for the optimal design of aerospace vehicles which take into account vehicle shape, aerodynamic performance, and weight minimization. Methods include multilevel optimization with linear decomposition, multi-constraint optimization, global sensitivity matrix, and calculation of sensitivity derivatives using both first and second order derivatives. The effects of including flexibility in the optimization is discussed.
Abdi, Frank↗