A Design Optimization Method Using Evidence Theory

[+] Author and Article Information
Zissimos P. Mourelatos

Mechanical Engineering Department, Oakland University, Rochester, MI 48309mourelat@oakland.edu

Jun Zhou

Mechanical Engineering Department, Oakland University, Rochester, MI 48309

J. Mech. Des 128(4), 901-908 (Dec 28, 2005) (8 pages) doi:10.1115/1.2204970 History: Received August 02, 2005; Revised December 28, 2005

Early in the engineering design cycle, it is difficult to quantify product reliability or compliance to performance targets due to insufficient data or information to model uncertainties. Probability theory cannot be, therefore, used. Design decisions are usually based on fuzzy information that is vague, imprecise qualitative, linguistic or incomplete. Recently, evidence theory has been proposed to handle uncertainty with limited information as an alternative to probability theory. In this paper, a computationally efficient design optimization method is proposed based on evidence theory, which can handle a mixture of epistemic and random uncertainties. It quickly identifies the vicinity of the optimal point and the active constraints by moving a hyperellipse in the original design space, using a reliability-based design optimization (RBDO) algorithm. Subsequently, a derivative-free optimizer calculates the evidence-based optimum, starting from the close-by RBDO optimum, considering only the identified active constraints. The computational cost is kept low by first moving to the vicinity of the optimum quickly and subsequently using local surrogate models of the active constraints only. Two examples demonstrate the proposed evidence-based design optimization method.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Representative BPA structure for two parameters a and b

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Figure 2

Schematic illustration of focal element contribution to belief and plausibility measures

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Figure 3

Geometrical interpretation of the EBDO algorithm

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Figure 4

A hypothetical two-dimensional BPA structure

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Figure 5

Cantilever beam under vertical and lateral bending

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Figure 6

Thin-walled pressure vessel



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