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Research Papers

Modified Reduced Gradient With Realization Sorting for Hard Equality Constraints in Reliability-Based Design Optimization

[+] Author and Article Information
Chun-Min Ho

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 701, Chinahocm@solab.me.ncku.edu.tw

Kuei-Yuan Chan1

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 701, Chinachanky@mail.ncku.edu.tw

1

Corresponding author.

J. Mech. Des 133(1), 011004 (Dec 29, 2010) (9 pages) doi:10.1115/1.4003036 History: Received April 04, 2010; Revised October 28, 2010; Published December 29, 2010; Online December 29, 2010

In this work, the presence of equality constraints in reliability-based design optimization (RBDO) problems is studied. Relaxation of soft equality constraints in RBDO and its challenges are briefly discussed, while the main focus is on hard equalities that cannot be violated even under uncertainty. Direct elimination of hard equalities to reduce problem dimensions is usually suggested; however, for nonlinear or black-box functions, variable elimination requires expensive root- finding processes or inverse functions that are generally unavailable. We extend the reduced gradient methods in deterministic optimization to handle hard equalities in RBDO. The efficiency and accuracy of the first- and second-order predictions in reduced gradient methods are compared. Results show that the first-order prediction is more efficient when realizations of random variables are available. Gradient-weighted sorting with these random samples is proposed to further improve the solution efficiency of the reduced gradient method. Feasible design realizations subject to hard equality constraints are then available to be implemented with state-of-the-art sampling techniques for RBDO problems. Numerical and engineering examples show the strength and simplicity of the proposed method.

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Figures

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Figure 6

Insulation in a steam pipe

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Figure 5

Flowchart of reduced gradient with realizations sorting in RBDO

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Figure 4

Efficiency of the proposed method compared with FSOLVE from MATLAB

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Figure 3

Reduced gradient concept in two-dimensional space

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Figure 2

Reduced gradient concept in one-dimensional space

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Figure 1

Relaxations of equality constraints

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