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Special section: Strategies for Design Under Uncertainty

An Information-Theoretic Metric of System Complexity With Application to Engineering System Design

[+] Author and Article Information
Douglas Allaire1

 Aerospace Computational Design Laboratory, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139dallaire@mit.edu

Qinxian He, John Deyst, Karen Willcox

 Aerospace Computational Design Laboratory, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139

1

Corresponding author.

J. Mech. Des 134(10), 100906 (Sep 28, 2012) (10 pages) doi:10.1115/1.4007587 History: Received February 16, 2012; Revised July 26, 2012; Published September 21, 2012; Online September 28, 2012

System complexity is considered a key driver of the inability of current system design practices to at times not recognize performance, cost, and schedule risks as they emerge. We present here a definition of system complexity and a quantitative metric for measuring that complexity based on information theory. We also derive sensitivity indices that indicate the fraction of complexity that can be reduced if more about certain factors of a system can become known. This information can be used as part of a resource allocation procedure aimed at reducing system complexity. Our methods incorporate Gaussian process emulators of expensive computer simulation models and account for both model inadequacy and code uncertainty. We demonstrate our methodology on a candidate design of an infantry fighting vehicle.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Example of Gaussian process emulation with three training points. The dashed line is the mean function of the emulator. The grayed area is the ±2 standard deviation confidence interval for the emulator.

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Figure 2

Bond graph representation of the driveline of the IFV candidate designs (adapted from Ref. [49])

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Figure 3

First 60 s of the simulated terrain used in the estimate of the range of the IFV

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Figure 4

Gaussian process model of a candidate IFV design. The lighter gray surfaces represent the ±2 standard deviation surfaces from the mean surface, which is shown as the darker mesh between the top and bottom surfaces.

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Figure 5

Probability density functions of the range of the IFV. The solid lines represent two distributions that were estimated using two different samples of the Gaussian process emulator. The dashed gray lines are the output distributions from the same two samples of the Gaussian process emulator; however, for these distributions, model inadequacy has been included.

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Figure 6

Sensitivity indices of the four factors that impact the complexity of the IFV design with respect to range. From left to right the indices are for average velocity (AV), usable fuel (UF), code uncertainty (CU), and model inadequacy (MI).

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Figure 7

Sampled distributions and complexity estimates of the range quantity of interest of the two different IFV design options. Design A uses newer technology for the vehicle velocity control and fuel systems, whereas design B uses older technology for both systems.

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Figure 8

Sampled distributions and complexity estimates of the range quantity of interest of design A both before and after activity 1, as well as design B results

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Figure 9

Sampled distributions and complexity estimates of the range quantity of interest of design A both before and after activity 1, as well as design B results

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