Research Papers: Design Automation

Design Sensitivity Method for Sampling-Based RBDO With Varying Standard Deviation

[+] Author and Article Information
Hyunkyoo Cho

Department of Mechanical and
Industrial Engineering,
The University of Iowa,
218 Engineering Research Facility,
Iowa City, IA 52242
e-mail: hyunkyoo-cho@uiowa.edu

K. K. Choi

Department of Mechanical and
Industrial Engineering,
The University of Iowa,
2134 SC,
Iowa City, IA 52242
e-mail: kkchoi@engineering.uiowa.edu

Ikjin Lee

Mechanical Engineering Department,
Korea Advanced Institute of Science and
Technology (KAIST),
291 Daehak-ro, Yuseong-gu,
Daejeon 305-701, South Korea
e-mail: ikjin.lee@kaist.ac.kr

David Lamb

6501 E. 11 Mile Road,
Warren, MI 48397
e-mail: david.a.lamb40.civ@mail.mil

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 29, 2015; final manuscript received October 11, 2015; published online November 16, 2015. Assoc. Editor: Xiaoping Du.This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government's contributions.

J. Mech. Des 138(1), 011405 (Nov 16, 2015) (10 pages) Paper No: MD-15-1333; doi: 10.1115/1.4031829 History: Received April 29, 2015; Revised October 11, 2015

Conventional reliability-based design optimization (RBDO) uses the mean of input random variable as its design variable; and the standard deviation (STD) of the random variable is a fixed constant. However, the constant STD may not correctly represent certain RBDO problems well, especially when a specified tolerance of the input random variable is present as a percentage of the mean value. For this kind of design problem, the STD of the input random variable should vary as the corresponding design variable changes. In this paper, a method to calculate the design sensitivity of the probability of failure for RBDO with varying STD is developed. For sampling-based RBDO, which uses Monte Carlo simulation (MCS) for reliability analysis, the design sensitivity of the probability of failure is derived using a first-order score function. The score function contains the effect of the change in the STD in addition to the change in the mean. As copulas are used for the design sensitivity, correlated input random variables also can be used for RBDO with varying STD. Moreover, the design sensitivity can be calculated efficiently during the evaluation of the probability of failure. Using a mathematical example, the accuracy and efficiency of the developed design sensitivity method are verified. The RBDO result for mathematical and physical problems indicates that the developed method provides accurate design sensitivity in the optimization process.

Copyright © 2016 by ASME
Topics: Design , Failure , Probability
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Grahic Jump Location
Fig. 1

Cost function and limit state contours for 2D mathematical example

Grahic Jump Location
Fig. 2

2σ contour of input model at initial design and optimum design: (a) input model A and (b) input model B



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