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Research Papers

Role of Conservative Moving Least Squares Methods in Reliability Based Design Optimization: A Mathematical Foundation

[+] Author and Article Information
Jongsoo Lee

School of Mechanical Engineering,  Yonsei University, Seoul 120-749, Korea

Chang Yong Song1

Department of Ocean Engineering,  Mokpo National University, Jeonnam 534-729, Koreacysong@mokpo.ac.kr

1

Corresponding author.

J. Mech. Des 133(12), 121005 (Dec 09, 2011) (12 pages) doi:10.1115/1.4005235 History: Received January 14, 2011; Revised September 26, 2011; Published December 09, 2011; Online December 09, 2011

The response surface method (RSM) and the moving least squares method (MLSM) are extensively used due to their computational efficiency in solving reliability based design optimization (RBDO) problems. Since traditional RSM and MLSM are described by second-order polynomials, approximated constraints are sometimes unable to ensure feasibility when highly nonlinear and/or nonconvex constraint functions are approximated in RBDO. We explore the development of a new MLSM based meta-model that ensures the constraint feasibility of an optimal solution in RBDO. A constraint-feasible MLSM (CF-MLSM) is devised to realize feasibility regardless of the multimodality/nonlinearity of the constraint function in all approximation processes as well as the variation of random characteristics in RBDO. The usefulness of the proposed approach is verified by examining a nonlinear function problem and an actively controlled structure problem.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Constraint violation of approximate functions. (b) A deterministic approximate optimal design dDETa that is actually infeasible. (c) A meta-model based RBDO design dRBDOa that is actually infeasible.

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Figure 2

Procedure of CF-MLSM based RBDO

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Figure 3

Deterministic optimum solutions for mathematical problem

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Figure 4

(a) RIA based RBDO solutions for mathematical problem. (b) PMA based RBDO solutions for mathematical problem

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Figure 5

Actively controlled ten-bar planar truss

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Figure 6

RBDO history of design variable, A1

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Figure 7

RBDO history of objective function

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Figure 8

RBDO history of constraint function, G1

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