Efficient evaluation of structural reliability under imperfect knowledge about probability distributions

• Published in: Reliability Engineering & System Safety Vol. 175; pp. 160 - 170
• Main Authors: Zhao, Yan-Gang, Li, Pei-Pei, Lu, Zhao-Hui
• Format: Journal Article
• Language: English; Japanese
• Published: Barking Elsevier Ltd 01.07.2018; Elsevier BV
• Subjects: Approximation; Bivariate analysis; Computer applications; Computer simulation; Computing time; Conditional failure probability; Conditional reliability index; Failure; Monte Carlo simulation; Normal distribution; Parameter uncertainties; Parameter uncertainty; Point-estimate method; Probability distribution; Random variables; Reliability analysis; Reliability aspects; Reliability engineering; Risk communication; Standard deviation; Statistical analysis; Structural reliability; Structural reliability; Point-estimate method; Conditional reliability index; Conditional failure probability; Parameter uncertainties
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2018.03.010

•Propose an efficient method for reliability considering parameter uncertainty.•Propose a novel method for quantile of the conditional failure probability.•Provide a complete picture of reliability considering parameter uncertainty.•The efficiency and accuracy of the proposed methods is verified.•Neglecting parameter uncertainty leads to the reliability being overestimated. We investigate the evaluation of structural reliability under imperfect knowledge about the probability distributions of random variables, with emphasis on the uncertainties of the distribution parameters. When these uncertainties are considered, the failure probability becomes a random variable that is referred to as the conditional failure probability. For the sake of transparency in communicating risk, it is necessary to determine not only the mean but also the quantile of the conditional failure probability. A novel method is proposed for estimating the quantile of the conditional failure probability by using the probability distribution of the corresponding conditional reliability index, in which a point-estimate method based on bivariate dimension-reduction integration is first suggested to compute the first three moments (i.e., mean, standard deviation and skewness) of the conditional reliability index. The probability distribution of the conditional reliability index is then approximated by a three-parameter square normal distribution. Numerical studies show that the computational efficiency of the proposed method was well above that of Monte Carlo simulations without loss of accuracy, and also show that neglecting parameter uncertainties will lead to the structural reliability being overestimated. The developed methodology provides a complete picture of structural reliability evaluation under imperfect knowledge about probability distributions.