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Technical Brief

A Study on Computational Efficiency Improvement of Novel SORM Using the Convolution Integration

[+] Author and Article Information
Jeong Woo Park

Korea Advanced Institute of Science and Technology,
291, Daehak-ro, Yuseong-gu,
Daejeon 34141, South Korea
e-mail: parkjw94@kaist.ac.kr

Ikjin Lee

Korea Advanced Institute of Science and Technology,
291, Daehak-ro, Yuseong-gu,
Daejeon 34141, South Korea
e-mail: ikjin.lee@kaist.ac.kr

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 25, 2017; final manuscript received November 14, 2017; published online December 11, 2017. Assoc. Editor: Xiaoping Du.

J. Mech. Des 140(2), 024501 (Dec 11, 2017) (6 pages) Paper No: MD-17-1293; doi: 10.1115/1.4038563 History: Received April 25, 2017; Revised November 14, 2017

This paper proposes to apply the convolution integral method to the novel second-order reliability method (SORM) to further improve its computational efficiency. The novel SORM showed better accuracy in estimating the probability of failure than conventional SORMs by utilizing a linear combination of noncentral or general chi-squared random variables. However, the novel SORM requires significant computational time when integrating the linear combination to calculate the probability of failure. In particular, when the dimension of performance functions is higher than three, the computational time for full integration increases exponentially. To reduce this computational burden for the novel SORM, we propose to obtain the distribution of the linear combination using the convolution and to use the distribution for the probability of failure estimation. Since it converts an N-dimensional full integration into one-dimensional integration, the proposed method is computationally very efficient. Numerical study illustrates that the accuracy of the proposed method is almost the same as the full integral method and Monte Carlo simulation (MCS) with much improved efficiency.

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Figures

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Fig. 1

Comparison of the proposed SORM with existing SORMs

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Fig. 2

Computational time of probability of failure estimation for Eq. (23)

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Fig. 3

PDF of the performance function using the convolution integration

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Fig. 4

Rotating hooped disk subject to angular velocity

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