Hybrid uncertainty propagation and reliability analysis using direct probability integral method and exponential convex model

Uncertainty propagation and reliability evaluation, being the crucial parts of engineering system analysis, play vital roles in safety assessment. How to reasonably consider the complex multisource uncertainty behavior in both static and dynamic systems is paramount to ensuring their safe operation. However, there is a significant lack of research on aleatory and epistemic uncertainties for both static and dynamic systems. To this end, a new hybrid exponential model is proposed by combining probabilistic and non-probabilistic exponential models, which aims to accurately measure the uncertainty propagation and reliability evaluation problem with aleatory and epistemic uncertainties for static and dynamic systems. The proposed hybrid exponential model consists of nested double optimization loops. The outer loop performs a probabilistic analysis based on the direct probability integral method, and the inner loop performs a non-probabilistic computation. Then, a new hybrid exponential probability integral method is developed to effectively perform uncertainty propagation and reliability analysis. Finally, four examples, including two static and two dynamic examples with complex performance functions, are tested. The results indicate that the proposed hybrid exponential model offers a universal tool for uncertainty quantification in static and dynamic systems. Moreover, the hybrid exponential probability integral method can accurately and efficiently obtain the upper and lower bounds of the probability density function and cumulative distribution function.