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Research Papers: Design Automation

An Adaptive Directional Boundary Sampling Method for Efficient Reliability-Based Design Optimization

[+] Author and Article Information
Zeng Meng

School of Civil Engineering,
Hefei University of Technology,
Hefei 230009, China;
Department of Engineering Mechanics,
State Key Laboratory of Structural
Analyses for Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China

Dequan Zhang

State Key Laboratory of Reliability
and Intelligence of Electrical Equipment,
School of Mechanical Engineering,
Hebei University of Technology,
Tianjin 300401, China

Zhaotao Liu

School of Civil Engineering,
Hefei University of Technology,
Hefei 230009, China

Gang Li

Department of Engineering Mechanics,
State Key Laboratory of Structural
Analyses for Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China
e-mail: ligang@dlut.edu.cn

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 5, 2018; final manuscript received July 4, 2018; published online September 18, 2018. Assoc. Editor: Mian Li.

J. Mech. Des 140(12), 121406 (Sep 18, 2018) (12 pages) Paper No: MD-18-1193; doi: 10.1115/1.4040883 History: Received March 05, 2018; Revised July 04, 2018

Due to the nested optimization loop structure and time-demanding computation of structural response, the computational accuracy and cost of reliability-based design optimization (RBDO) have become a challenging issue in engineering application. Kriging-model-based approach is an effective tool to improve the computational efficiency in the practical RBDO problems; however, a larger number of sample points are required for meeting high computational accuracy requirements in traditional methods. In this paper, an adaptive directional boundary sampling (ADBS) method is developed in order to greatly reduce the computational sample points with a reasonable accuracy, in which the sample points are added along the ideal descending direction of objective function. Furthermore, only sample points located near the constraint boundary are mainly selected in the vicinity of the optimum point according to the strategy of multi-objective optimization; thus, substantial number of sample points located in the failure region is neglected, resulting in the improved performance of computational efficiency. Four numerical examples and one engineering application are provided for demonstrating the efficiency and accuracy of the proposed sampling method.

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Figures

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Fig. 1

A sketch of the ADBS criterion

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Fig. 2

A sketch of selecting sampling criterion

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Fig. 3

A flowchart for the ADBS method

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Fig. 4

The three-dimensional diagram of highly nonlinear performance function g1(x) with different bounds

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Fig. 5

Sampling processes of different methods for the example 1: (a) LHS, (b) CBS, (c) LAS, and (d) ADBS

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Fig. 6

The iterative history of Pareto solutions of the proposed ADBS for example 1

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Fig. 7

Sampling processes of different methods for the example 2: (a) LHS, (b) CBS, (c) LAS, and (d) ADBS

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Fig. 8

The iterative history of Pareto solutions of the proposed ADBS for example 2

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Fig. 9

The kinematic sketch of a gear reducer

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Fig. 10

Sampling processes for the example 3: (a) objective function and (b) reliability index

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Fig. 12

Sampling processes for the weld beam: (a) objective function and (b) reliability index

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Fig. 13

The material properties and geometric dimensions of the stiffened shell

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Fig. 14

An eigen-mode shape result of the stiffened shell

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