An enhanced PDEM-based framework for reliability analysis of structures considering multiple failure modes and limit states

In this paper, an enhanced probability density evolution method (PDEM) framework considering multiple failure modes and limit states is proposed for reliability analysis of structures. Firstly, the PDEM principle and the enhanced mechanism are illustrated, and during the process three typical combination types (i.e., circle, triangle, square ways) are introduced. Secondly, two case studies are given to verify the effectiveness of the enhanced PDEM-based framework and the necessity to consider multiple limit states. The first example is a simply supported beam under two-point concentrated forces with two failure conditions (i.e., shear failure and flexural failure), and the second example is a 3-span-6-story reinforced concrete frame under seismic excitation with three failure conditions (i.e., maximum displacement failure, residual displacement failure and floor acceleration failure). Meanwhile, the Monte Carlo simulation (MCS) is also performed for both examples as a comparison and validation. Thirdly, parametric studies with related to two important aspects in the enhanced PDEM-based framework are primarily performed, including a modified equation of the target variable value via representative points incorporating the influence of individual quantile parameters (e.g., 16%, 50% and 84% quantile), as well as the other potential combination types in the enhanced PDEM-based framework (i.e., more than circle, triangle, square ways). In general, the paper provides a reference to perform the PDEM-based reliability assessment for multiple limit states and multiple failure patterns in the future. The enhanced framework presents less calculation burden and shows comparative calculation accuracy with the MCS. Meanwhile, the enhanced results are generally more conservative and commonly illustrate a lower reliability when compared with the single limit state, which can result in a more comprehensive decision and more robust strategy under the same condition in the practical engineering.