A Note on the State-space Separation of the Generalized Density Evolution Equation

摘要

The probability density evolution method (PDEM) is a feasible way to resolve the difficulties of high-dimensional problems in stochastic dynamics of structures.In PDEM, based on the principle of preservation of probability, the generalized density evolution equation (GDEE), which is a state-variable decoupled partial differential equation governing the probability distribution functions of physical quantifies of concern, is derived and solved.From the perspective of probability flux, the present paper aims to discuss why such a separation of state variable is possible, and provides some new insight into n the GDEE for high-dimensional nonlinear systems.The generalized F-discrepancy based procedures of solving GDEE is outlined.A numerical example of a nonlinear structure under earthquake excitation is carried out to verify and validate the accuracy and efficiency of PDEM.