Research Papers: Design Automation

Active Learning Kriging Model Combining With Kernel-Density-Estimation-Based Importance Sampling Method for the Estimation of Low Failure Probability

[+] Author and Article Information
Xufeng Yang

School of Mechanical Engineering,
Southwest Jiaotong University,
Chengdu 610031, China;
The State Key Laboratory of Heavy Duty AC Drive
Electric Locomotive Systems Integration,
Zhuzhou 412001, China
e-mail: xufengyang0322@gmail.com

Yongshou Liu

Department of Engineering Mechanics,
Northwestern Polytechnical University,
Xi'an 710072, China

Caiying Mi

School of Mechanical Engineering,
Southwest Jiaotong University,
Chengdu 610031, China

Xiangjin Wang

AVIC Zhengzhou Aircraft Equipment Co., LTD,
Zhengzhou, 450000, China

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 7, 2017; final manuscript received February 9, 2018; published online March 14, 2018. Assoc. Editor: Xiaoping Du.

J. Mech. Des 140(5), 051402 (Mar 14, 2018) (9 pages) Paper No: MD-17-1610; doi: 10.1115/1.4039339 History: Received September 07, 2017; Revised February 09, 2018

Strategies combining active learning Kriging (ALK) model and Monte Carlo simulation (MCS) method can accurately estimate the failure probability of a performance function with a minimal number of training points. That is because training points are close to the limit state surface and the size of approximation region can be minimized. However, the estimation of a rare event with very low failure probability remains an issue, because purely building the ALK model is time-demanding. This paper is intended to address this issue by researching the fusion of ALK model with kernel-density-estimation (KDE)-based importance sampling (IS) method. Two stages are involved in the proposed strategy. First, ALK model built in an approximation region as small as possible is utilized to recognize the most probable failure region(s) (MPFRs) of the performance function. Consequentially, the priori information for IS are obtained with as few training points as possible. In the second stage, the KDE method is utilized to build an instrumental density function for IS and the ALK model is continually updated by treating the important samples as candidate samples. The proposed method is termed as ALK-KDE-IS. The efficiency and accuracy of ALK-KDE-IS are compared with relevant methods by four complicated numerical examples.

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Grahic Jump Location
Fig. 1

Flowchart of ALK-KDE-IS

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Fig. 2

Comparison of the active learning processes on two-dimensional (2D) example in Sec. 4.1 (case 1): (a) ALK-KDE-IS and (b) metaAK-IS2

Grahic Jump Location
Fig. 6

Active learning process of ALK-KDE-IS solving the example in Sec. 4.3 (case c = 5)

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Fig. 5

Comparison of the active learning processes on 2D example in Sec. 4.2: (a) ALK-KDE-IS and (b) metaAK-IS2

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Fig. 3

Comparison of iPDFs on 2D example in Sec. 4.1 (case 1): (a) the iPDF by KDE, (b) the true optimal iPDF, and (c) the iPDF centered on MPPs

Grahic Jump Location
Fig. 4

Comparison of the active learning processes on 2D example in Sec. 4.1 (case 2): (a) ALK-KDE-IS and (b) metaAK-IS2



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