A reliability analysis method with multisource uncertainty using saddle-point approximation and convex theory

In practical engineering design, to evaluate and guarantee the high reliability and safety of complex and coupled systems, multidisciplinary reliability analysis (MRA) methods have been received much more attentions. If there are sufficient data of uncertainties to construct the probability distribution of each input variables, the conventional MRA method can tackle this problem. However, both aleatoy and epistemic uncertainties may exist in multidisciplinary systems simultaneously. The uncertainty propagation through coupled subsystems makes multidisciplinary reliability analysis computationally expensive and inaccuracy. This paper proposes a unified method for MRA based on Saddle-point approximation and convex model(UMRA-SC). In this strategy, the probabilistic analysis and convex analysis are decoupled from each other and are performed sequentially, which improves the efficiency of UMRA-SC. The probabilistic analysis is implemented based on the chi-squared distribution and Saddle-point approximation, which improves the accuracy of UMRA-SC. A mathematical example and an engineering application are demonstrated to verify the effectiveness of the proposed method.