Reliability Updating Method with Copula-Based Weighted Low-Discrepancy Samplings

Abstract

This study proposes an efficient reliability updating method to quickly estimate the low-level failure probability, Pf, in structural/geotechnical systems, along with the identification of the most probable failure point (MPP). In this method, Sobol’s quasirandom low-discrepancy sequences (LDS) are employed to generate the random samples, and the system reliability updating is conducted based on a weighted low-discrepancy samplings (WLDS) technique. In particular, the updated MPP can be directly captured in x-space according to the probabilistic weighting strategy. Coupled with the copula theory, the implementation framework of the proposed reliability updating method incorporating correlated random variables is thoroughly elaborated. The primary superiority of the proposed reliability updating method with the WLDS technique lies in that the repeated evaluation of costly performance functions is avoided during the updating process. Two illustrative examples show that 2,000 to 20,000 samples are sufficient for estimating and/or updating the probabilistic results of low-level failure probability, Pf, and associated MPP. The proposed method is particularly useful for conducting reliability updating of computationally costly engineering systems in conditions of changing uncertainties such as soil properties, model parameters, and applied structural loadings.