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Research Papers: Design Automation

Confidence-Driven Design Optimization Using Gaussian Process Metamodeling With Insufficient Data

[+] Author and Article Information
Mingyang Li

Department of Mechanical
Engineering-Engineering Mechanics,
Michigan Technological University,
Houghton, MI 49931
e-mail: mli7@mtu.edu

Zequn Wang

Department of Mechanical
Engineering-Engineering Mechanics,
Michigan Technological University,
Houghton, MI 49931
e-mail: zequnw@mtu.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 1, 2018; final manuscript received July 20, 2018; published online September 18, 2018. Assoc. Editor: Mian Li.

J. Mech. Des 140(12), 121405 (Sep 18, 2018) (14 pages) Paper No: MD-18-1171; doi: 10.1115/1.4040985 History: Received March 01, 2018; Revised July 20, 2018

To reduce the computational cost, surrogate models have been widely used to replace expensive simulations in design under uncertainty. However, most existing methods may introduce significant errors when the training data is limited. This paper presents a confidence-driven design optimization (CDDO) framework to manage surrogate model uncertainty for probabilistic design optimization. In this study, a confidence-based Gaussian process (GP) modeling technique is developed to handle the surrogate model uncertainty in system performance predictions by taking both the prediction mean and variance into account. With a target confidence level, the confidence-based GP models are used to reduce the probability of underestimating the probability of failure in reliability assessment. In addition, a new sensitivity analysis method is proposed to approximate the sensitivity of the reliability at the target confidence level with respect to design variables, and thus facilitate the CDDO framework. Three case studies are introduced to demonstrate the effectiveness of the proposed approach.

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Figures

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Fig. 2

Confidence-based predictions versus confidence level

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Fig. 1

Four scenarios, (a) and (c) represent type I and II classification errors, respectively

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Fig. 3

Estimated versus origin LSF

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Fig. 4

Estimated probability of failure increases with higher CL (At x = [1.5, 1])

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Fig. 5

Estimation for random outputs at different CL (At x = [1.5, 1])

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Fig. 11

Estimated versus origin LSFs (G1 and G2)

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Fig. 12

Confidence-driven design optimization history of design variables

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Fig. 13

Reliabilities estimation in each design iteration

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Fig. 6

Flowchart of confidence-driven design optimization

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Fig. 7

Estimated versus origin LSFs (G1, G2, and G3)

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Fig. 8

Confidence-driven design optimization history of the two design variables

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Fig. 9

Reliabilities estimation in each design iteration

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Fig. 10

Optimal designs obtained from different methods

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Fig. 14

Optimal designs obtained from different methods

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Fig. 15

Optimal design obtained with sufficient training data

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Fig. 16

Iterative CDDO history for design variables

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Fig. 17

Reliability history for ten probabilistic constraints

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