Physically driven full probabilistic uncertainty propagation in complex nonlinear structures

Abstract

The safety and reliability evaluation of complex engineering structures under dynamic loading conditions has long been a challenging problem. The coupling of nonlinearity and randomness in high-dimensional or large-degree-of-freedom stochastic systems is the essential difficulty to be circumvented. To this end, the refined analysis techniques to capture structural behaviors and uncertainty quantification and propagation, seemly irrelevant, are essentially the two sides of a coin. This perspective leads to the thought of physically driven full probabilistic uncertainty propagation in complex nonlinear systems. In this paper, some advances in this framework, in particular the probability density evolution method and its extensions and applications, will be outlined. Problems to be further studied are also discussed.