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Research Papers

First-Order Reliability Method for Structural Reliability Analysis in the Presence of Random and Interval Variables

[+] Author and Article Information
Umberto Alibrandi

Nanyang Technological University, BEARS—Berkeley Education Alliance for Research in Singapore,
1 Create Way, Create Tower, Singapore 138062
e-mails: umbertoalibrandi@ntu.edu.sg; umbertoalibrandi@gmail.com

C. G. Koh

National University of Singapore,
1 Engineering Drive 2, Singapore 117576
e-mail: cgkoh@nus.edu.sg

Manuscript received October 22, 2014; final manuscript received June 17, 2015; published online October 2, 2015. Assoc. Editor: Alba Sofi.

ASME J. Risk Uncertainty Part B 1(4), 041006 (Oct 02, 2015) (10 pages) Paper No: RISK-14-1073; doi: 10.1115/1.4030911 History: Received October 22, 2014; Accepted June 25, 2015; Online October 02, 2015

This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis in the presence of random parameters and interval uncertain parameters. In the proposed formulation, the hybrid problem is reduced to standard reliability problems, where the limit state functions are defined only in terms of the random variables. Monte Carlo simulation (MCS) for hybrid reliability analysis (HRA) is presented, and it is shown that it requires a tremendous computational effort; FORM for HRA is more efficient but still demanding. The computational cost is significantly reduced through a simplified procedure, which gives good approximations of the design points, by requiring only three classical FORMs and one interval analysis (IA), developed herein through an optimization procedure. FORM for HRA and its simplified formulation achieve a much improved efficiency than MCS by several orders of magnitude, and it can thus be applied to real-world engineering problems. Representative examples of stochastic dynamic analysis and performance-based engineering are presented.

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Figures

Grahic Jump Location
Fig. 1

Reliability index of the example in Sec. 3

Grahic Jump Location
Fig. 2

Bounding limit state functions gmin(u)=0 and gmax(u)=0 and FORM solution of the example in Sec. 4 with ϑ∈[0.5,4]

Grahic Jump Location
Fig. 3

Limit states of the example in Sec. 4 using the FORM-based simplified approach with ϑ∈[0.5,4]

Grahic Jump Location
Fig. 4

Limit states of the example in Sec. 4 using the FORM-based simplified approach with ϑ∈[1.575,2.925]

Grahic Jump Location
Fig. 5

Response of an uncertain linear oscillator in terms of (a) reliability index and (b) tail probability; comparison between MCS with 100,000 samples (circle markers) and the FORM-based simplified approach

Grahic Jump Location
Fig. 6

Optimal design using performance-based engineering approach, where the price fluctuation factor is (a) I=1 and (b) modeled as an interval variable I∈[0.5,1.5]; comparison between MCS with 100,000 samples (circle markers) and the FORM-based simplified approach

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