The NASA Langley MDO method evaluation study seeks to arrive at a set of guidelines for using promising MDO methods by accumulating and analyzing computational data for such methods. The data are collected by conducting a series of reproducible experiments. In the first phase of the study, three MDO methods were implemented in the iSIGHT z framework and used to solve a set of ten relatively simple problems. In this paper, we comment on the general considerations for conducting method evaluation studies and report some initial results obtained to date. In particular, although the results are not conclusive because of the small initial test set, preliminary numbers suggest that the performance of the methods tends to be consistent with their predicted theoretical properties. Key Words: Multidisciplinary Design Optimization, Method Evaluation AMS Subject Classification: 65K05, 49M37 Introduction Multidisciplinary Design Optimization (MDO) problems are optimization problems that desc...

We discuss criteria by which one can classify, analyze, and evaluate approaches to solving multidisciplinary design optimization (MDO) problems. Central to our discussion is the often overlooked distinction between questions of formulating MDO problems and solving the resulting computational problem. We illustrate our general remarks by comparing several approaches to MDO that have been proposed. INTRODUCTION There are likely as many definitions of multidisciplinary design optimization (MDO) as there are areas and phases of design. For our discussion, we shall take MDO to mean the systematic approach to optimization of complex, coupled engineering systems, where "multidisciplinary " refers to the different aspects that must be included in a design problem. For instance, the design of aircraft involves, among other disciplines, aerodynamics, structural analysis, propulsion, and control. See Sobieszczanski-Sobieski and Haftka (1997), Alexandrov and Hussaini (1997) for overviews of the ...

Collaborative optimization is a new design architecture specifically created for large-scale distributed-analysis applications. In this approach, a problem is decomposed into a user-defined number of subspace optimization problems that are driven towards interdisciplinary compatibility and the appropriate solution by a system-level coordination process. This decentralized design strategy allows domain-specific issues to be accommodated by disciplinary analysts, while requiring interdisciplinary decisions to be reached by consensus. The present investigation focuses on application of the collaborative optimization architecture to the multidisciplinary design of a single-stage-to-orbit launch vehicle. Vehicle design, trajectory, and cost issues are directly modeled. Posed to suit the collaborative architecture, the design problem is characterized by 95 design variables and 16 constraints. Numerous collaborative solutions are obtained. Comparison of these solutions demonstrates the influe...

Historical evolution of engineering disciplines and the complexity of the MDO problem suggest that disciplinary autonomy is a desirable goal in formulating and solving MDO problems. We examine the notion of disciplinary autonomy and discuss the analytical properties of three approaches to formulating and solving MDO problems that achieve varying degrees of autonomy by distributing the problem along disciplinary lines. Two of the approaches---Optimization by Linear Decomposition and Collaborative Optimization---are based on bilevel optimization and reflect what we call a structural perspective. The third approach, Distributed Analysis Optimization, is a single-level approach that arises from what we call an algorithmic perspective. The main conclusion of the paper is that disciplinary autonomy may come at a price: in the bilevel approaches, the system-level constraints introduced to relax the interdisciplinary coupling and enable disciplinary autonomy can cause analytical and computatio...

This work is concerned with an approach to formulating the multidisciplinary optimization (MDO) problem that reflects an algorithmic perspective on MDO problem solution. The algorithmic perspective focuses on formulating the problem in light of the abilities and inabilities of optimization algorithms, so that the resulting nonlinear programming problem can be solved reliably and efficiently by conventional optimization techniques. We propose a modular approach to formulating MDO problems that takes advantage of the problem structure, maximizes the autonomy of implementation, and allows for multiple easily interchangeable problem statements to be used depending on the available resources and the characteristics of the application problem. Key Words: Autonomy, complex system design, distributed analysis optimization, multidisciplinary analysis, multidisciplinary optimization, nonlinear programming, sensitivities, system synthesis Introduction The underlying theme of this and related p...

A procedure for generating a customized weight function for wing bending material weight of a High Speed Civil Transport (HSCT) is described. The weight function is based on HSCT configuration parameters. A response surface methodology is used to fit a quadratic polynomial to data gathered from a large number of structural optimizations. To reduce the time of performing a large number of structural optimizations, coarse-grained parallelization with a master-slave processor assignment on an Intel Paragon computer is used. The results of the structural optimization are noisy. Noise reduction in the structural optimization results is discussed. It is shown that the response surface filters out this noise. A statistical design of experiments technique is used to minimize the number of required structural optimizations and to maintain accuracy. Simple analysis techniques are used to find regions of the design space where reasonable HSCT designs could occur, thus customizing the weight function to the design requirements of the HSCT, while the response surface itself is created employing detailed analysis methods. Analysis of variance is used to reduce the number of polynomial terms in the response surface model function. Linear and constant corrections based on a small number of high fidelity results are employed to improve the accuracy of the response surface model. Configuration optimization of the HSCT employing a customized weight function is compared to the configuration optimization of the HSCT with a general weight function.

A model of a linear aerospike rocket nozzle that consists of coupled aerodynamic and structural analyses has been developed. A nonlinear computational fluid dynamics code is used to calculate the aerodynamic thrust, and a three-dimensional finite-element model is used to determine the structural response and weight. The model will be used to demonstrate multidisciplinary design optimization (MDO) capabilities for relevant engine concepts, assess performance of various MDO approaches, and provide a guide for future application development. In this study, the MDO problem is formulated using the multidisciplinary feasible (MDF) strategy. The results for the MDF formulation are presented with comparisons against separate aerodynamic and structural optimized designs. Significant improvements are demonstrated by using a multidisciplinary approach in comparison with the single-discipline design strategy. A multidisciplinary analytic model of a linear aerospike rocket nozzle has been developed; this model includes predictions of nozzle thrust, nozzle weight, and effectivevehicle

These notes describe some recent ideas for distributed design and their application to large-scale aerospace systems. In this type of multidisciplinary optimization, design tasks are decomposed into domain-specific subproblems, and coordinated to achieve an optimal system. Focusing on collaborative optimization, one form of design decomposition, the notes detail the methods, summarize recent results, and suggest new variants of these approaches that improve performance. 2.

This paper explores the use of decomposition-based methods for aircraft family design. The traditional approach in multidisciplinary design optimization is to decompose a problem along disciplinary lines. For aircraft family design problems, a more natural approach is decomposition by individual aircraft. This decomposition facilitates the concurrent development of several aircraft variants, providing substantial autonomy to individual aircraft development programs. Two decomposition-based methods are applied to the aircraft family problem: collaborative optimization and analytical target cascading. This paper marks the beginning of a collaborative effort to clarify the distinctions between these two methods, and to identify how these differences impact the relative performance and applicability of these methods. Initial product family results illustrate how decomposition-based methods can be applied to the aircraft family problem. I.

ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a disser-tation for the degree of Doctor of Philosophy.