A Formal Two-Phase Method for Decomposition of Complex Design Problems

[+] Author and Article Information
Li Chen, Zhendong Ding, Simon Li

Design and Manufacturing Integration Laboratory, Department of Mechanical and Industrial Engineering, The University of Toronto, 5 King’s College Road, Toronto, ON, CANADA M5S 3G8

J. Mech. Des 127(2), 184-195 (Mar 25, 2005) (12 pages) doi:10.1115/1.1778186 History: Received September 01, 2003; Revised January 01, 2004; Online March 25, 2005
Copyright © 2005 by ASME
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Resulting matrix after the PPA
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Incidence matrices of the powertrain system design in the extended HCA
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Samples of the decomposition solutions with different numbers of blocks
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Ideal decomposition of an incidence matrix
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Banded diagonal matrix
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Three types of block-angular structured matrix
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Direct conversion of conventional decomposition methods
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Workflow of the two-phase decomposition method
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Functional view of the two-phase decomposition method
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Example of an original incidence matrix
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Flowchart of the extended HCA
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A branch formed according to Column 9 and Column 10
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Column tree and the corresponding tree matrix
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Results for the example matrix after BTC
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Results for the example matrix after BTBA
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Illustration of the BTA algorithm
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Results for the example matrix after BTA
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Partition point in the diagonal matrix
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Matrix after identifying the coordination column and the blocks
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Matrix with two partition points
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Matrix with three misplaced partition points



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