Safety analysis of structures with probability and evidence theory

Abstract

In safety analysis of structures, classical probabilistic analysis has been a popular approach in engineering. However, it is not always to obtain sufficient information to model all uncertain parameters of structures system by probability theory, especially at early stage of design. Under this circumstance, probability theory (used to model random uncertainty) combined with evidence theory (used to model epistemic uncertainty) may be utilized in safety analysis of structures. This paper proposed a novel method for safety analysis of structures based on probability and evidence theory. Firstly, Bayes conversion method is used as the way for precision of evidence body, and the mean and variance of epistemic uncertain variables is defined. Then epistemic uncertainty variables is transformed to normal random variables by reflection transformation method, and the checking point method (J-C method) is used to solve most probability point and reliability. A numerical example and two engineering examples are given to demonstrate the performance of the proposed method. The results show both precision and computational efficiency of the method is high. Moreover, the proposed method provides basis for reliability-based optimization with the hybrid uncertainties.