TY - JOUR

T1 - Computing tight bounds of structural reliability under imprecise probabilistic information

AU - Wang, Cao

AU - Zhang, Hao

AU - Beer, Michael

N1 - Funding Information: This research has been supported by the Faculty of Engineering and IT PhD Research Scholarship (SC1911) from the University of Sydney. This support is gratefully acknowledged. The authors would like to acknowledge the thoughtful suggestions of three anonymous reviewers, which substantially improved the present paper.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - In probabilistic analyses and structural reliability assessments, it is often difficult or infeasible to reliably identify the proper probabilistic models for the uncertain variables due to limited supporting databases, e.g., limited observed samples or physics-based inference. To address this difficulty, a probability-bounding approach can be utilized to model such imprecise probabilistic information, i.e., considering the bounds of the (unknown) distribution function rather than postulating a single, precisely specified distribution function. Consequently, one can only estimate the bounds of the structural reliability instead of a point estimate. Current simulation technologies, however, sacrifice precision of the bound estimate in return for numerical efficiency through numerical simplifications. Hence, they produce overly conservative results in many practical cases. This paper proposes a linear programming-based method to perform reliability assessments subjected to imprecisely known random variables. The method computes the tight bounds of structural failure probability directly without the need of constructing the probability bounds of the input random variables. The method can further be used to construct the best-possible bounds for the distribution function of a random variable with incomplete statistical information.

AB - In probabilistic analyses and structural reliability assessments, it is often difficult or infeasible to reliably identify the proper probabilistic models for the uncertain variables due to limited supporting databases, e.g., limited observed samples or physics-based inference. To address this difficulty, a probability-bounding approach can be utilized to model such imprecise probabilistic information, i.e., considering the bounds of the (unknown) distribution function rather than postulating a single, precisely specified distribution function. Consequently, one can only estimate the bounds of the structural reliability instead of a point estimate. Current simulation technologies, however, sacrifice precision of the bound estimate in return for numerical efficiency through numerical simplifications. Hence, they produce overly conservative results in many practical cases. This paper proposes a linear programming-based method to perform reliability assessments subjected to imprecisely known random variables. The method computes the tight bounds of structural failure probability directly without the need of constructing the probability bounds of the input random variables. The method can further be used to construct the best-possible bounds for the distribution function of a random variable with incomplete statistical information.

KW - Imprecise probability

KW - Interval analysis

KW - Monte Carlo simulation

KW - Probability box

KW - Structural reliability analysis

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=85050677532&partnerID=8YFLogxK

U2 - 10.1016/j.compstruc.2018.07.003

DO - 10.1016/j.compstruc.2018.07.003

M3 - Article

AN - SCOPUS:85050677532

VL - 208

SP - 92

EP - 104

JO - Computers & structures

JF - Computers & structures

SN - 0045-7949

ER -