doi:10.3850/978-981-08-5118-7_053


Interval Estimates of Structural Reliability


Hao Zhang1, Robert L. Mullen2 and Rafi L. Muhanna3

1School of Civil Engineering, University of Sydney, NSW 2006, Australia

2Department of Civil Engineering, Case Western Reserve University, Cleveland, OH 44106, USA

3School of Civil and Environmental Engineering, Georgia Institute of Technology, Savannah, GA 31407, USA

ABSTRACT

This paper demonstrates the feasibility of computing interval estimates of structural reliability when distribution functions of basic random variables have uncertain parameters. The incomplete knowledge regarding the distribution parameters is modeled by interval variables. Relia- bility analysis needs to consider families of distributions whose parameters are within the intervals, leading to an interval estimate of the failure probability. To estimate the interval failure probability, an interval Monte Carlo method has been proposed which combines simulation process with the interval finite element analysis. The authors’ previously developed interval finite element method is utilized to model the ranges of structural responses. The developed method propagates the epistemic uncertainty and aleatory uncertainty separately through the reliability assessment. A planar steel frame example is presented to demonstrate the proposed method.

Keywords: Epistemic uncertainty, Interval analysis, Interval finite element, Monte Carlo simulation, Parameter uncertainty, Probability box, Structural reliability.


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