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Research Papers

A Modified Efficient Global Optimization Algorithm for Maximal Reliability in a Probabilistic Constrained Space

[+] Author and Article Information
Yen-Chih Huang

 National Cheng Kung University, 70101 Tainan, Taiwanyc.huang71@gmail.com

Kuei-Yuan Chan1

 National Cheng Kung University, 70101 Tainan, Taiwanchanky@mail.ncku.edu.tw

1

Corresponding author.

J. Mech. Des 132(6), 061002 (May 20, 2010) (11 pages) doi:10.1115/1.4001532 History: Received August 11, 2009; Revised March 11, 2010; Published May 20, 2010; Online May 20, 2010

Design optimization problems under random uncertainties are commonly formulated with constraints in probabilistic forms. This formulation, also referred to as reliability-based design optimization (RBDO), has gained extensive attention in recent years. Most researchers assume that reliability levels are given based on past experiences or other design considerations without exploring the constrained space. Therefore, inappropriate target reliability levels might be assigned, which either result in a null probabilistic feasible space or performance underestimations. In this research, we investigate the maximal reliability within a probabilistic constrained space using modified efficient global optimization (EGO) algorithm. By constructing and improving Kriging models iteratively, EGO can obtain a global optimum of a possibly disconnected feasible space at high reliability levels. An infill sampling criterion (ISC) is proposed to enforce added samples on the constraint boundaries to improve the accuracy of probabilistic constraint evaluations via Monte Carlo simulations. This limit state ISC is combined with the existing ISC to form a heuristic approach that efficiently improves the Kriging models. For optimization problems with expensive functions and disconnected feasible space, such as the maximal reliability problems in RBDO, the efficiency of the proposed approach in finding the optimum is higher than those of existing gradient-based and direct search methods. Several examples are used to demonstrate the proposed methodology.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Nonconvex feasible domain

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Figure 2

Algorithm flowchart

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Figure 3

Space-filling samples versus random samples

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Figure 4

Samples, the variogram cloud, and the experimental variogram of the example in (a)

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Figure 5

Proposed ISC selection flowchart

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Figure 6

Design progression for the baseball function example

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Figure 7

Design progression of the modified Branin example

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Figure 8

RBDO test problem

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Figure 9

Tuned vibration absorber

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Figure 10

Kriging models of Eq. 27 with increasing infill samples

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Figure 11

Angle bracket design, loading, and results

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