Research Papers: Design Automation

Reliability Analysis With Monte Carlo Simulation and Dependent Kriging Predictions

[+] Author and Article Information
Zhifu Zhu

Department of Mechanical
and Aerospace Engineering,
Missouri University of Science and Technology,
258A Toomey Hall,
400 West 13th Street,
Rolla, MO 65409-0500
e-mail: zzgc5@mst.edu

Xiaoping Du

Department of Mechanical
and Aerospace Engineering,
Missouri University of Science and Technology,
272 Toomey Hall,
400 West 13th Street,
Rolla, MO 65409-0500
e-mail: dux@mst.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 1, 2015; final manuscript received July 10, 2016; published online September 14, 2016. Assoc. Editor: Nam H. Kim.

J. Mech. Des 138(12), 121403 (Sep 14, 2016) (11 pages) Paper No: MD-15-1741; doi: 10.1115/1.4034219 History: Received November 01, 2015; Revised July 10, 2016

Reliability analysis is time consuming, and high efficiency could be maintained through the integration of the Kriging method and Monte Carlo simulation (MCS). This Kriging-based MCS reduces the computational cost by building a surrogate model to replace the original limit-state function through MCS. The objective of this research is to further improve the efficiency of reliability analysis with a new strategy for building the surrogate model. The major approach used in this research is to refine (update) the surrogate model by accounting for the full information available from the Kriging method. The existing Kriging-based MCS uses only partial information. Higher efficiency is achieved by the following strategies: (1) a new formulation defined by the expectation of the probability of failure at all the MCS sample points, (2) the use of a new learning function to choose training points (TPs). The learning function accounts for dependencies between Kriging predictions at all the MCS samples, thereby resulting in more effective TPs, and (3) the employment of a new convergence criterion. The new method is suitable for highly nonlinear limit-state functions for which the traditional first- and second-order reliability methods (FORM and SORM) are not accurate. Its performance is compared with that of existing Kriging-based MCS method through five examples.

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Fig. 2

Domains of xC, xS, and xF

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Fig. 4

Sample points of DKM

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Fig. 5

Final surrogate model

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Fig. 6

Sample points of IKM

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Fig. 7

A nonlinear oscillator

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Fig. 8

A roof truss structure

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Fig. 13

The curve of ci with respect to Ui

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Fig. 10

A slider–crank mechanism

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Fig. 11

Maximum motion error of [0,2π] s

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Fig. 12

The failure region




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