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Research Papers

Methodical Extensions for Decomposition of Matrix-Based Design Problems

[+] Author and Article Information
Simon Li

Concordia Institute for Information Systems Engineering, Concordia University, 1455 de Maisonneuve Boulevard West, EV7.648, Montreal, QC, H3G 1M8, Canadalisimon@ciise.concordia.ca

J. Mech. Des 132(6), 061003 (May 20, 2010) (11 pages) doi:10.1115/1.4001534 History: Received August 21, 2009; Revised March 04, 2010; Published May 20, 2010; Online May 20, 2010

The two-phase method is a matrix-based approach for system decomposition, in which a system is represented by a rectangular matrix to capture dependency relationships of two sets of system elements. While the two-phase method has its own advantages in problem decomposition, this paper focuses on two methodical extensions to improve the method’s capability. The first extension is termed nonbinary dependency analysis, which can handle nonbinary dependency information, in addition to just binary information, of the model. This extension is based on the formal analysis of a resemblance coefficient to quantify the couplings among the model’s elements. The second extension is termed heuristic partitioning analysis, which allows the method to search for a reasonably good decomposition solution with less computing effort. This extension can be viewed as an alternative to the original partitioning approach that uses an enumerative approach to search for an optimal solution. At the end, the relief valve redesign example is applied to illustrate and justify the newly developed method components.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Workflow of the two-phase method

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Figure 2

Case setup for the justification of the min/max coefficient

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Figure 3

A sample diagonal matrix and partition lines

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Figure 4

Comparison of two decomposition solutions

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Figure 5

Coupling-partition plots of the sample rectangular matrix

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Figure 6

Partitioning of the sample rectangular matrix

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Figure 7

Re-arranged RCMs

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Figure 8

Nonbinary matrix of the relief valve example

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Figure 9

Coupling-partition plots for the relief valve system

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Figure 10

Decomposition solution of the relief valve system using the nonbinary matrix

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Figure 11

Decomposition solution of the relief valve system using the binary matrix

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