Probabilistic Analytical Target Cascading: A Moment Matching Formulation for Multilevel Optimization Under Uncertainty

[+] Author and Article Information
Huibin Liu

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208-3111

Wei Chen1

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208-3111weichen@northwestern.edu

Michael Kokkolaras, Panos Y. Papalambros

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125

Harrison M. Kim

Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801hmkim@uiuc.edu

A minimum deviation optimization problem is an optimization problem that strives to minimize deviations of actual system responses from assigned target values.

Design consistency means that the values of coupling responses and linking variables are matched among elements.


Corresponding author.

J. Mech. Des 128(4), 991-1000 (Oct 26, 2005) (10 pages) doi:10.1115/1.2205870 History: Received June 29, 2005; Revised October 26, 2005

Analytical target cascading (ATC) is a methodology for hierarchical multilevel system design optimization. In previous work, the deterministic ATC formulation was extended to account for random variables represented by expected values to be matched among subproblems and thus ensure design consistency. In this work, the probabilistic formulation is augmented to allow the introduction and matching of additional probabilistic characteristics. A particular probabilistic analytical target cascading (PATC) formulation is proposed that matches the first two moments of interrelated responses and linking variables. Several implementation issues are addressed, including representation of probabilistic design targets, matching responses and linking variables under uncertainty, and coordination strategies. Analytical and simulation-based optimal design examples are used to illustrate the new formulation. The accuracy of the proposed PATC formulation is demonstrated by comparing PATC results to those obtained using a probabilistic all-in-one formulation.

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

System decomposition approaches

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Figure 2

Information flow for particular PATC formulation

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Figure 3

Information flow in the bi-level hierarchical decomposition of geometric programming problem

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Figure 4

Comparison of actual CDFs of responses of O11 and O12

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Figure 5

Verification of distributions of power loss in two scenarios



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