TY - JOUR

T1 - Structural reliability analysis on the basis of small samples

T2 - An interval quasi-Monte Carlo method

AU - Zhang, Hao

AU - Dai, Hongzhe

AU - Beer, Michael

AU - Wang, Wei

N1 - Funding Information: This research was supported, in part, by grants from the Australian Research Council (Discovery Project DP110104263 ) and the National Natural Science Foundation of China (Project 10902028 and Project 50978078 ). These supports are gratefully acknowledged. However, the views expressed in this paper are solely those of the authors, and may not represent the positions of the sponsoring organizations. The authors would like to acknowledge the thoughtful suggestions of three anonymous reviewers, which substantially improved the present paper. The authors also acknowledge helpful discussions with Dr. Scott Ferson during the preparation of this paper.

PY - 2013/5

Y1 - 2013/5

N2 - In practice, reliability analysis of structures is often performed on the basis of limited data. Under this circumstance, there are practical difficulties in identifying unique distributions as input for a probabilistic analysis. But the selection of realistic probabilistic input is critical for the quality of the results of the reliability analysis. This problem can be addressed using an entire set of plausible distribution functions rather than one single distribution for random variables based on limited data. The uncertain nature of the available information is then reflected in the probabilistic input. An imprecise probability distribution can be modeled by a probability box, i.e., the bounds of the cumulative distribution function for the random variable. Sampling-based methods have been proposed to perform reliability analysis with probability boxes. However, direct sampling of probability boxes requires a large number of samples. The computational cost can be very high as each simulation involves an interval analysis (a range-finding problem). This study proposes an interval quasi-Monte Carlo simulation methodology to efficiently compute the bounds of structure failure probabilities. The methodology is based on deterministic low-discrepancy sequences, which are distributed more regularly than the (pseudo) random points in direct Monte Carlo simulation. The efficiency and accuracy of the present method is illustrated using two examples. The reliability implications of different approaches for construction of probability boxes are also investigated through the example.

AB - In practice, reliability analysis of structures is often performed on the basis of limited data. Under this circumstance, there are practical difficulties in identifying unique distributions as input for a probabilistic analysis. But the selection of realistic probabilistic input is critical for the quality of the results of the reliability analysis. This problem can be addressed using an entire set of plausible distribution functions rather than one single distribution for random variables based on limited data. The uncertain nature of the available information is then reflected in the probabilistic input. An imprecise probability distribution can be modeled by a probability box, i.e., the bounds of the cumulative distribution function for the random variable. Sampling-based methods have been proposed to perform reliability analysis with probability boxes. However, direct sampling of probability boxes requires a large number of samples. The computational cost can be very high as each simulation involves an interval analysis (a range-finding problem). This study proposes an interval quasi-Monte Carlo simulation methodology to efficiently compute the bounds of structure failure probabilities. The methodology is based on deterministic low-discrepancy sequences, which are distributed more regularly than the (pseudo) random points in direct Monte Carlo simulation. The efficiency and accuracy of the present method is illustrated using two examples. The reliability implications of different approaches for construction of probability boxes are also investigated through the example.

KW - Epistemic uncertainty

KW - Imprecise probability

KW - Low-discrepancy sequence

KW - Probability box

KW - Quasi-Monte Carlo

KW - Structural reliability

UR - http://www.scopus.com/inward/record.url?scp=84876918406&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2012.03.001

DO - 10.1016/j.ymssp.2012.03.001

M3 - Article

AN - SCOPUS:84876918406

VL - 37

SP - 137

EP - 151

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

IS - 1-2

ER -