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Research Papers: Design Automation

High-Dimensional Reliability-Based Design Optimization Involving Highly Nonlinear Constraints and Computationally Expensive Simulations

[+] Author and Article Information
Meng Li

Mem. ASME
Department of Mechanical Engineering,
Iowa State University,
Ames, IA 50011
e-mail: meng@iastate.edu

Mohammadkazem Sadoughi

Mem. ASME
Department of Mechanical Engineering,
Iowa State University,
Ames, IA 50011
e-mail: sadoughi@iastate.edu

Chao Hu

Mem. ASME
Department of Mechanical Engineering and
Department of Electrical and
Computer Engineering,
Iowa State University,
Ames, IA 50011
e-mails: chaohu@iastate.edu;
huchaostu@gmail.com

Zhen Hu

Mem. ASME
Department of Industrial and
Manufacturing Systems Engineering,
University of Michigan-Dearborn,
Dearborn, MI 48128
e-mail: zhennhu@unich.edu

Amin Toghi Eshghi

Mem. ASME
Department of Mechanical Engineering,
University of Maryland,
Baltimore County,
Baltimore, MD 21250
e-mail: amint1@umbc.edu

Soobum Lee

Mem. ASME
Department of Mechanical Engineering,
University of Maryland,
Baltimore County,
Baltimore, MD 21250
e-mail: sblee@umbc.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 16, 2018; final manuscript received October 23, 2018; published online January 11, 2019. Assoc. Editor: Ping Zhu.

J. Mech. Des 141(5), 051402 (Jan 11, 2019) (14 pages) Paper No: MD-18-1456; doi: 10.1115/1.4041917 History: Received June 16, 2018; Revised October 23, 2018

Reliability-based design optimization (RBDO) aims at optimizing the design of an engineered system to minimize the design cost while satisfying reliability requirements. However, it is challenging to perform RBDO under high-dimensional uncertainty due to the often prohibitive computational burden. In this paper, we address this challenge by leveraging a recently developed method for reliability analysis under high-dimensional uncertainty. The method is termed high-dimensional reliability analysis (HDRA). The HDRA method optimally combines the strengths of univariate dimension reduction (UDR) and kriging-based reliability analysis to achieve satisfactory accuracy with an affordable computational cost for HDRA problems. In this paper, we improve the computational efficiency of high-dimensional RBDO by pursuing two new strategies: (i) a two-stage surrogate modeling strategy is adopted to first locate a highly probable region of the optimum design and then locally refine the accuracy of the surrogates in this region; and (ii) newly selected samples are updated for all the constraints during the sequential sampling process in HDRA. The results of two mathematical examples and one real-world engineering example suggest that the proposed HDRA-based RBDO (RBDO-HDRA) method is capable of solving high-dimensional RBDO problems with higher accuracy and comparable efficiency than the UDR-based RBDO (RBDO-UDR) and ordinary kriging-based RBDO (RBDO-kriging) methods.

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Figures

Grahic Jump Location
Fig. 1

Overall flowchart of the HDRA method [11]

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Fig. 2

Effect of adding one sample point at the joint region on the prediction accuracy of two LSFs: (a) true and estimated LSFs without the addition of the point and (b) true and estimated LSFs with the addition of the point

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Fig. 3

Identification of samples in the probable LSF region

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Fig. 4

Overall flowchart of the proposed two-stage surrogate modeling strategy for RBDO

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Fig. 5

(a) Comparison of HDRA surrogate with true function after global stage of sample enrichment and (b) error decay of the global surrogate model

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Fig. 6

(a) Comparison of HDRA surrogate with true function after local stage of sample enrichment and (b) error decay of the local surrogate model

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Fig. 7

Schematics of TPMS-EH in example 3: (a) design variables for TPMS-EH and (b) TPMS-EH encased in the housing

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Fig. 8

Decay of the maximum relative error ε at the first (a) and second (b) stages

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