Research Papers

Using Parameterized Pareto Sets to Model Design Concepts

[+] Author and Article Information
Richard J. Malak

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843rmalak@tamu.edu

Christiaan J. J. Paredis

G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332chris.paredis@me.gatech.edu

J. Mech. Des 132(4), 041007 (Apr 19, 2010) (11 pages) doi:10.1115/1.4001345 History: Received April 12, 2008; Revised February 10, 2010; Published April 19, 2010; Online April 19, 2010

The decisions designers make during conceptual design can have a large impact on the success of a project. Conceptual design decisions can be challenging because the imprecise nature of design concepts make them difficult to model. Prior literature exists on using Pareto sets to model design concepts abstractly in the space of decision attributes. However, this approach has limitations when the concept under consideration is a component of a larger system. The need to relate component-level decision attributes to system-level decision objectives can lead to a violation of the assumptions underlying classical Pareto dominance. The main contribution of this article is a new dominance criterion, called parameterized Pareto dominance, which is applicable in such situations. It is a generalization of the classical dominance rule and is found to be sound from a decision-theoretic perspective. A secondary contribution is the articulation of a generalized methodology for constructing concept models based on classical or parameterized Pareto sets using either observational or model-generated data. The modeling procedure, including the new dominance criterion, is demonstrated on observational data about hydraulic cylinders. The question of whether a parameterized Pareto set can be an adequate representation of a component-level design concept is evaluated on a gearbox conceptual design problem for which the component-level decision is subordinate to system-level vehicle design problem.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Illustration of when classical Pareto dominance is (a) and is not (b) applicable

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Figure 2

Dependency relationships between concept-level attributes and system-level attributes for the conceptual design of a gearbox (Sec. 5). Vehicle dynamics are nonmonotonic functions of gear ratio and account for aerodynamic drag, rolling resistance, and engine characteristics.

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Figure 8

Monotonic system-level decision preferences resulting in conflicting preferences at the component-level

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Figure 9

Configuration of off-road vehicle components. Grayed components are already designed; the fixed-ratio gearbox is of interest in this demonstration.

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Figure 11

Fitted tradeoff models for each of the design concepts for gear ratios up to 5

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Figure 10

Layout of the three gearbox concepts: (a) planetary, (b) single-sided reverted, and (c) double-sided reverted

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Figure 3

Visualization of allocation and selection procedure using tradeoff models. The dashed curves are iso-preference curves.

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Figure 4

Illustration of the difference between tradeoff models fit to dominance-filtered implementation data and those fit to all data (filled squares are nondominated points)

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Figure 5

Summary of tradeoff modeling methodology: (a) model generation phase and (b) decision-making phase

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Figure 6

Tradeoff model domain restrictions arising from the data when using these attributes to predict another one

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Figure 7

An example of the difference between classical Pareto dominance and parameterized Pareto dominance



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