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Technical Brief

Reliability-Based Design Optimization Concerning Objective Variation Under Mixed Probabilistic and Interval Uncertainties

[+] Author and Article Information
Jianhua Zhou, Min Xu

National Engineering Laboratory for the Automotive
Electronic Control Technology,
Shanghai Jiao Tong University,
Shanghai 200240, China

Mian Li

National Engineering Laboratory for the Automotive
Electronic Control Technology;
University of Michigan-Shanghai Jiao Tong University
Joint Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: mianli@sjtu.edu.cn

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 17, 2016; final manuscript received July 26, 2016; published online September 12, 2016. Assoc. Editor: Zissimos P. Mourelatos.

J. Mech. Des 138(11), 114501 (Sep 12, 2016) (5 pages) Paper No: MD-16-1132; doi: 10.1115/1.4034346 History: Received February 17, 2016; Revised July 26, 2016

Uncertainties, inevitable in nature, can be classified as probability based and interval based uncertainties in terms of its representations. Corresponding optimization strategies have been proposed to deal with these two types of uncertainties. It is more likely that both types of uncertainty can occur in one single problem, and thus, it is trivial to treat all uncertainties the same. A novel formulation for reliability-based design optimization (RBDO) under mixed probability and interval uncertainties is proposed in this paper, in which the objective variation is concerned. Furthermore, it is proposed to efficiently solve the worst-case parameter resulted from the interval uncertainty by utilizing the Utopian solution presented in a single-looped robust optimization (RO) approach where the inner optimization can be solved by matrix operations. The remaining problem can be solved utilizing any existing RBDO method. This work applies the performance measure approach to search for the most probable failure point (MPFP) and sequential quadratic programing (SQP) to solve the entire problem. One engineering example is given to demonstrate the applicability of the proposed approach and to illustrate the necessity to consider the objective robustness under certain circumstances.

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Figures

Grahic Jump Location
Fig. 1

Illustration of Utopian box

Grahic Jump Location
Fig. 2

Determination of worst-case point

Grahic Jump Location
Fig. 3

Determination of the worst-case parameter for the objective

Grahic Jump Location
Fig. 4

Flowchart of the proposed approach

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