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Research Papers

A Co-Evolutionary Approach for Design Optimization via Ensembles of Surrogates With Application to Vehicle Crashworthiness

[+] Author and Article Information
Karim Hamza

Mechanical Engineering Department,  University of Michigan, Ann Arbor, MI 48109-2102khamza@umich.edu

Kazuhiro Saitou

Mechanical Engineering Department,  University of Michigan, Ann Arbor, MI 48109-2102kazu@umich.edu

J. Mech. Des 134(1), 011001 (Jan 04, 2012) (10 pages) doi:10.1115/1.4005439 History: Received November 13, 2003; Revised September 24, 2011; Published January 04, 2012; Online January 04, 2012

In many engineering application, where accurate models require lengthy numerical computations, it is a common design practice to perform design of experiments (DOE) and construct surrogate models that provide computationally-inexpensive approximations. Main challenges to that approach are (i) construction of high-fidelity surrogates and (ii) discovery of high performance designs despite the fidelity limitations. An ensemble of surrogates (EOS) is a collection of different surrogates approximating the same process (typically with some form of weighted averaging to get an overall approximation) and has been demonstrated in the literature to often exhibit better performance than any of the individual surrogates. This paper presents a Multi-Scenario Co-evolutionary Genetic Algorithm (MSCGA) for design optimization via EOS. MSCGA simultaneously evolves multiple populations in a multi-objective sense via the predicted performance by the different surrogates within the ensemble. The outputs of the algorithm are solution sets including several designs that are spread over Pareto-optimal space of best-predictions by the surrogates within EOS, as well as best designs as predicted by individual surrogates and the weighted average of the EOS. Studies using analytical test functions show MSCGA to be more likely to discover better performing designs than an individual surrogate or a weighted ensemble. The primary application for MSCGA presented in this paper is that of vehicle structural crashworthiness since it is a typical design application that requires massive computational resources for accurate modeling. Two studies, which include simplified and detailed vehicle models, MSCGA successfully discovers new high performance designs.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Conceptual illustration of design via an EOS

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Figure 2

Results of illustrative example of MSCGA application to the two-objective biquadratic test functions: (a) solution set S1 , (b) solution set S2 , (c) solution set S3 , (d) solution set S4 , (e) solution set Sw , and (f) solution set Su

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Figure 3

Box plots for best obtained solutions in different solution sets for test functions: (a) Branin-Hoo, (b) Camelback, (c) Goldstein-Price, (d) Hartman-3, and (e) Hartman-6

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Figure 4

Box plots for best obtained solutions via different setups of ensembles of surrogate models for the test functions: (a) Branin-Hoo, (b) Camelback, (c) Goldstein-Price, (d) Hartman-3, and (e) Hartman-6

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Figure 5

FE model of front half body of a vehicle subjected to full-lap frontal crash

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Figure 6

Crashworthiness performance of designs generated via DOE and MSCGA

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Figure 7

FE model of a vehicle subjected to frontal crash against an offset deformable barrier

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Figure 8

Crashworthiness performance of designs generated via DOE and MSCGA

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