Speakers
Description
In engineering practice, epistemic uncertainty widely exists due to imperfect modeling, simplifications, and limited data. Among these uncertainties, uncertainty in distribution parameters has drawn significant attention. To comprehensively evaluate structural reliability under the distribution parameter uncertainty, often referred to as conditional failure probability, several methods have been proposed. However, these methods have not addressed the reliability evaluation involving correlated random variables. In this study, an explicit calculation formula for the quantile of the conditional failure probability involving correlated random variables is proposed. The proposed method starts by transforming the limit state function with correlated random variables into the standard normal space using orthogonal normal transformation. Subsequently, the first three central moments of the conditional reliability index are calculated through sparse grid quadrature, enabling the derivation of its probability distribution. Finally, an explicit expression for the quantile values of the conditional failure probability is formulated based on the distribution of the conditional reliability index. The effectiveness and accuracy of the proposed method are demonstrated through two illustrative examples, where the results closely match those obtained using Monte Carlo simulations.
References
Li, P.P. Lu, Z.H. and Y.G. Zhao. An effective and efficient method for structural reliability considering the distributional parametric uncertainty, Applied Mathematical Modelling, 106 (2022): 507-523.
Li, P. P. Zhao, Y. G. Dang, C. Broggi, M. Valdebenito, M. A. and Faes, M. G. An efficient Bayesian updating framework for characterizing the posterior failure probability. Mechanical Systems and Signal Processing, 222(2025): 111768.
He, J. Gao, S.B. and J.H. Gong. A sparse grid stochastic collocation method for structural reliability analysis, Structural Safety, 51: 29-34, 2014.
Zhao, Y.G. Weng, Y.Y. and Z. H. Lu. An orthogonal normal transformation of correlated non-normal random variables for structural reliability, Probabilistic Engineering Mechanics, 64 (2021): 103130.
