Design Optimization of Hierarchically Decomposed Multilevel Systems Under Uncertainty

[+] Author and Article Information
Michael Kokkolaras

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

Zissimos P. Mourelatos

Department of Mechanical Engineering, Oakland University, Rochester, MImourelat@oakland.edu

Panos Y. Papalambros

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

J. Mech. Des 128(2), 503-508 (May 02, 2005) (6 pages) doi:10.1115/1.2168470 History: Received July 07, 2004; Revised May 02, 2005

This paper presents a methodology for design optimization of hierarchically decomposed systems under uncertainty. We propose an extended, probabilistic version of the deterministic analytical target cascading (ATC) formulation by treating uncertain quantities as random variables and posing probabilistic design constraints. A bottom-to-top coordination strategy is used for the ATC process. Given that first-order approximations may introduce unacceptably large errors, we use a technique based on the advanced mean value method to estimate uncertainty propagation through the multilevel hierarchy of elements that comprise the decomposed system. A simple yet illustrative hierarchical bilevel engine design problem is used to demonstrate the proposed methodology. The results confirm the applicability of the proposed probabilistic ATC formulation and the accuracy of the uncertainty propagation technique.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Example of hierarchically decomposed multilevel system

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Figure 2

ATC information flow at element j of level i

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Figure 3

Hierarchical bilevel system

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Figure 4

Power loss due to friction (subsystem's response): (a) PDF obtained using the AMV-based technique and (b) frequency diagram obtained using Monte Carlo simulation



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