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Research Papers

Bayesian Approach for Structural Reliability Analysis and Optimization Using the Kriging Dimension Reduction Method

[+] Author and Article Information
Jooho Choi1

School of Aerospace and Mechanical Engineering, Korea Aerospace University, Goyang-City, Gyeonggi-do, 412-791, Koreajhchoi@kau.ac.kr

Dawn An

School of Aerospace and Mechanical Engineering, Korea Aerospace University, Goyang-City, Gyeonggi-do, 412-791, Koreaskal34@nate.com

Junho Won

School of Aerospace and Mechanical Engineering, Korea Aerospace University, Goyang-City, Gyeonggi-do, 412-791, Koreaopenworldsm@gmail.com

1

Corresponding author.

J. Mech. Des 132(5), 051003 (Apr 29, 2010) (11 pages) doi:10.1115/1.4001377 History: Received July 14, 2009; Revised February 08, 2010; Published April 29, 2010; Online April 29, 2010

An efficient method for a structural reliability analysis is proposed under the Bayesian framework, which can deal with the epistemic uncertainty arising from a limited amount of data. Until recently, conventional reliability analyses dealt mostly with the aleatory uncertainty, which is related to the inherent physical randomness and its statistical properties are completely known. In reality, however, epistemic uncertainties are prevalent, which makes the existing methods less useful. In the Bayesian approach, the probability itself is treated as a random variable of a beta distribution conditional on the provided data, which is determined by conducting a double loop of reliability analyses. The Kriging dimension reduction method is employed to promote efficient implementation of the reliability analysis, which can construct the PDF of the limit state function with favorable accuracy using a small number of analyses. Mathematical examples are used to demonstrate the proposed method. An engineering design problem is also addressed, which is to find an optimum design of a pigtail spring in a vehicle suspension, taking material uncertainty due to limited test data into account.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Reliability analysis procedure

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Figure 2

Bayesian reliability analysis procedure

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Figure 4

PDF and CDF of limit state function g for example 1: (a) PDF and (b) CDF

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Figure 5

PDF and CDF of limit state function g for example 2: (a) PDF and (b) CDF

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Figure 6

PDF of Pg for example 1 when N=20

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Figure 7

PDFs of P[G<0] for example 2 under different numbers of data

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Figure 8

McPherson suspension: (a) simplified diagram, (b) vector of forces acting on the suspension, (c) forces acting on the damper rod, and (d) antiside load

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Figure 9

Variables of the pigtail spring: (a) side view, (b) top view, and (c) bottom view

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Figure 10

Force diagram of the side loads

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Figure 11

Optimum shape of pigtail spring

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Figure 12

PDF of constraint functions of pigtail spring: (a) side load angle β, (b) maximum shear stress τmax, and (c) spring rate k

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Figure 13

PDF of reliability under epistemic uncertainty: (a) maximum shear stress τmax and (b) spring rate k

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Figure 14

Deformation of the pigtail spring for each case: (a) initial model, (b) deterministic optimization model, (c) RBDO model, (d) N=20, Bayesian RBDO model, and (e) N=10, Bayesian RBDO model

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