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RESEARCH PAPERS

On Selecting Single-Level Formulations for Complex System Design Optimization

[+] Author and Article Information
James T. Allison

Department of Mechanical Engineering,  University of Michigan, 2250 G. G. Brown Bldg., Ann Arbor, MI 48109optimize@umich.edu

Michael Kokkolaras

Department of Mechanical Engineering,  University of Michigan, 2250 G. G. Brown Bldg., Ann Arbor, MI 48109mk@umich.edu

Panos Y. Papalambros

Department of Mechanical Engineering,  University of Michigan, 2250 G. G. Brown Bldg., Ann Arbor, MI 48109pyp@umich.edu

J. Mech. Des 129(9), 898-906 (Sep 27, 2006) (9 pages) doi:10.1115/1.2747632 History: Received April 24, 2006; Revised September 27, 2006

Design of complex products with several interacting subsystems or disciplinary analyses poses substantive challenges to both analysis and optimization, necessitating specialized solution techniques. A product or system may qualify as complex due to large scale or due to strong interactions. Single-level strategies for complex system optimization centralize decision-making authority, while multilevel strategies distribute the decision-making process. This article studies important differences between two popular single-level formulations: multidisciplinary feasible (MDF) and individual disciplinary feasible (IDF). Results presented aim at aiding practitioners in selecting between formulations. Specifically, while IDF incurs some computational overhead, it may find optima hidden to MDF and is more efficient computationally for strongly coupled problems; further, MDF is sensitive to variations in coupling strength, while IDF is not. Conditions that lead to failure of MDF are described. Two new reproducible design examples are introduced to illustrate these findings and to provide test problems for other investigations.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

The system analysis block with nonhierarchic relationships between subsystems

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Figure 2

MDF architecture

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Figure 3

IDF architecture

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Figure 4

Two-element coupled system

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Figure 5

System with multiple fixed points

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Figure 6

IDF optimization space visualization

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Figure 7

Vane airflow sensor schematic (after (22))

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Figure 8

Simplified representation of a vane airflow sensor

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Figure 9

Coupling relationship in airflow sensor analysis

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Figure 10

Comparison of MDF and IDF solution time as a function of coupling strength

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Figure 11

Comparison of MDF and IDF function evaluations as a function of coupling strength

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Figure 12

GE J-79 turbojet engine turbine blades (24)

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Figure 13

Turbine blade model schematic

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Figure 14

Turbine blade coupling and functional relationships

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Figure 15

Comparison of MDF and IDF solution time as a function of coupling strength

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