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Research Papers

Bayesian Network Classifiers for Set-Based Collaborative Design

[+] Author and Article Information
David W. Shahan

Mechanical Engineering Department,  The University of Texas at Austin, Austin, TX 78712david.shahan@mail.utexas.edu

Carolyn Conner Seepersad

Mechanical Engineering Department,  The University of Texas at Austin, Austin, TX 78712ccseepersad@mail.utexas.edu

Bayesian networks are defined as graphical representations of joint probability distributions, in which there is one node per variable and the edges between the nodes represent the conditional dependences between the variables [26]. Bayesian networks are used to automate the use of Bayes theorem to determine posterior probabilities over a subset of the variables conditioned upon setting the remaining variables to specific values.

J. Mech. Des 134(7), 071001 (Jun 01, 2012) (14 pages) doi:10.1115/1.4006323 History: Received May 26, 2011; Revised March 01, 2012; Published May 31, 2012; Online June 01, 2012

Complex engineering design problems are often decomposed into a set of interdependent, distributed subproblems that are solved by domain-specific experts. These experts must resolve couplings between the subproblems and negotiate satisfactory, system-wide solutions. Set-based approaches help resolve these couplings by systematically mapping satisfactory regions of the design space for each subproblem and then intersecting those maps to identify mutually satisfactory system-wide solutions. In this paper, Bayesian network classifiers are introduced for mapping sets of promising designs, thereby classifying the design space into satisfactory and unsatisfactory regions. The approach is applied to two example problems—a spring design problem and a simplified, multilevel design problem for an unmanned aerial vehicle (UAV). The method is demonstrated to offer several advantages over competing techniques, including the ability to represent arbitrarily shaped and potentially disconnected regions of the design space and the ability to be updated straightforwardly as new information about the satisfactory design space is discovered. Although not demonstrated in this paper, it is also possible to interface the classifier with automated search and optimization techniques and to combine expert knowledge with the results of quantitative simulations when constructing the classifiers.

Copyright © 2012 by American Society of Mechanical Engineers
Topics: Design
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References

Figures

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Figure 1

Mapping the mutually satisfactory design space for coupled subproblems

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Figure 2

Example of Kernel density estimate

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Figure 3

The effect of standard deviation on KDEs

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Figure 4

Example of Parzen window classifier, where the horizontal and vertical axes represent x1 and x2, respectively, from Eq. 9

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Figure 5

The probability decision surface

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Figure 6

Example of KDE from a naïve Bayes classifier

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Figure 7

Fully dependent (left) and fully independent (right) BNs

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Figure 11

Classification error rates for the spring problem

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Figure 12

UAV wing design problem decomposed into system and subsystem design problems

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Figure 13

Subsystems UAV wing design parameters

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Figure 14

Classification of the systems’ design space

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Figure 15

KBN classifier error rates for the systems’ design space

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Figure 16

Interval classifier error rates for the systems’ design space

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Figure 17

Classification of the subsystems’ design space using the systems’ classifier

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Figure 18

Classification error rates for the subsystems’ problem using the systems’ classifier

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Figure 19

Classification of the subsystems’ design space using the systems’ simulation

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Figure 20

Classification error rates for the subsystems’ problem using the systems’ simulation

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Figure 21

Classification of the systems’ design space using a naïve Bayes classifier with loss factors

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Figure 8

Example of naïve Bayes classifier, where the horizontal and vertical axes represent x1 and x2 , respectively, in Eq. 9

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Figure 9

Spring design problem definition [40]

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Figure 10

Classifiers for the spring problem

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