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Research Papers

Advanced Multi-Objective Robust Optimization Under Interval Uncertainty Using Kriging Model and Support Vector Machine

[+] Author and Article Information
Tingli Xie

The State Key Laboratory of Digital
Manufacturing Equipment and Technology,
School of Mechanical Science and Engineering,
Huazhong University of
Science and Technology,
Wuhan 430074, China
e-mail: xietingli0727@gmail.com

Ping Jiang

Professor
The State Key Laboratory of Digital
Manufacturing Equipment and Technology,
School of Mechanical Science and Engineering,
Huazhong University of
Science and Technology,
Wuhan 430074, China
e-mail: jiangping@hust.edu.cn

Qi Zhou

School of Aerospace Engineering,
Huazhong University of
Science and Technology,
Wuhan 430074, China
e-mail: qizhouhust@gmail.com

Leshi Shu

The State Key Laboratory of Digital
Manufacturing Equipment and Technology,
School of Mechanical Science and Engineering,
Huazhong University of
Science and Technology,
Wuhan 430074, China
e-mail: leshishu@gmail.com

Yahui Zhang

The State Key Laboratory of Digital
Manufacturing Equipment and Technology,
School of Mechanical Science and Engineering,
Huazhong University of
Science and Technology,
Wuhan 430074, China
e-mail: zyhzhangzhang@gmail.com

Xiangzheng Meng

The State Key Laboratory of Digital
Manufacturing Equipment and Technology,
School of Mechanical Science and Engineering,
Huazhong University of
Science and Technology,
Wuhan 430074, China
e-mail: mxz761201@163.com

Hua Wei

School of Mechanical Engineering,
Zhengzhou University,
Zhengzhou 450001, China
e-mail: weihua0319@gmail.com

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received February 5, 2018; final manuscript received June 27, 2018; published online August 6, 2018. Assoc. Editor: Ashok V. Kumar.

J. Comput. Inf. Sci. Eng 18(4), 041012 (Aug 06, 2018) (14 pages) Paper No: JCISE-18-1035; doi: 10.1115/1.4040710 History: Received February 05, 2018; Revised June 27, 2018

There are a large number of real-world engineering design problems that are multi-objective and multiconstrained, having uncertainty in their inputs. Robust optimization is developed to obtain solutions that are optimal and less sensitive to uncertainty. Since most of complex engineering design problems rely on time-consuming simulations, the robust optimization approaches may become computationally intractable. To address this issue, an advanced multi-objective robust optimization approach based on Kriging model and support vector machine (MORO-KS) is proposed in this work. First, the main problem in MORO-KS is iteratively restricted by constraint cuts formed in the subproblem. Second, each objective function is approximated by a Kriging model to predict the response value. Third, a support vector machine (SVM) classifier is constructed to replace all constraint functions classifying design alternatives into two categories: feasible and infeasible. The proposed MORO-KS approach is tested on two numerical examples and the design optimization of a micro-aerial vehicle (MAV) fuselage. Compared with the results obtained from other MORO approaches, the effectiveness and efficiency of the proposed MORO-KS approach are illustrated.

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Figures

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Fig. 1

The framework of MORO-CC approach [12]

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Fig. 2

Flowchart of MORO-KS approach

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Fig. 3

The framework of MORO-KS approach

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Fig. 7

Feasible domain and robust optimal solutions after two iterations for the illustrative example

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Fig. 6

Feasible domain and optimal solutions for the main problem at iteration 1 for the illustrative example

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Fig. 4

Support vector machine classifier of MORO-KS for the illustrative example (Δp=0)

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Fig. 5

Kriging models of MORO-KS for the illustrative example

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Fig. 8

Comparison of MORO-KS with MORO-CC and MORO-SS for the illustrative example

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Fig. 9

Robustness verification for the illustrative example

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Fig. 10

A three-bar truss

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Fig. 11

Support vector machine classifier of MORO-KS for the three-bar truss (ΔA1,Δθ)=(0,0)

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Fig. 12

Kriging models of MORO-KS for the three-bar truss

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Fig. 13

Comparison of MORO-KS with MORO-CC and MORO-SS for the three-bar truss

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Fig. 14

Robustness verification for the three-bar truss

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Fig. 15

Micro-aerial vehicle

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Fig. 16

The geometry of MAV fuselage with general dimension labels

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Fig. 17

Loading and boundary conditions

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Fig. 18

Stress distribution of the fuselage with the rigid link element

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Fig. 19

Comparison of MORO-KS with MORO-SS for MAV fuselage

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Fig. 20

Robustness verification for MAV fuselage

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