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Research Papers

Design Optimization Problem Reformulation Using Singular Value Decomposition

[+] Author and Article Information
Somwrita Sarkar

Faculty of Architecture, Design and Planning, University of Sydney, Australiassar3264@mail.usyd.edu.au

Andy Dong

Faculty of Architecture, Design and Planning, University of Sydney, Australiaandy@arch.usyd.edu.au

John S. Gero

Krasnow Institute for Advanced Study,George Mason Universityjohn@johngero.com

J. Mech. Des 131(8), 081006 (Jul 20, 2009) (10 pages) doi:10.1115/1.3179148 History: Received September 24, 2008; Revised May 21, 2009; Published July 20, 2009

This paper presents a design optimization problem reformulation method based on singular value decomposition, dimensionality reduction, and unsupervised clustering. The method calculates linear approximations of associative patterns of symbol co-occurrences in a design problem representation to induce implicit coupling strengths between variables and constraints. Unsupervised clustering of these approximations is used to heuristically identify useful reformulations. In contrast to knowledge-rich Artificial Intelligence methods, this method derives from a knowledge-lean, unsupervised pattern recognition perspective. We explain the method on an analytically formulated decomposition problem, and apply it to various analytic and nonanalytic problem forms to demonstrate design decomposition and design “case” identification. A single method is used to demonstrate multiple design reformulation tasks. The results show that the method can be used to infer multiple well-formed reformulations starting from a single problem representation in a knowledge-lean manner.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) Example problem, and (b) occurrence matrix A

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Figure 2

SVD analysis of A

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Figure 3

Truncated SVD with retained k=2 for A

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Figure 4

Increasing k changes variable-function relationships

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Figure 5

Variable-function relationships in k=2 approximation

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Figure 6

Cosines between x1 and functions

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Figure 7

Problem decomposition by K-means algorithm

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Figure 8

The HCD problem statement

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Figure 9

(a) k=2 approximation for HCD problem, (b) high positive cosines (k=2) between functions gives the links between functions in (a), and (c) multi-objective hydraulic cylinder problem graph

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Figure 10

(a) FDT problem and (b) solution, and (c) DSM problem and (d) solution

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Figure 11

Decomposition results for FDT problem

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Figure 12

Decomposition results for DSM problem

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Figure 13

(a) The ACS problem, (b) design variables and states; (c) and (d) occurrence matrices

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Figure 14

Correct, extra, and missed cases for k=2,3,4

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Figure 15

(a) Precision and (b) recall measurements

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