Advances in probability density evolution analysis of nonlinear stochastic systems

New advances of the Probability Density Evolution Method (PDEM) for nonlinear systems are presented. The path of deriving the generalized density evolution equation by combining the uncoupled physical equation and the random event description of the principle of preservation of probability is firstly outlined. Numerical solving procedure is then delineated. On this basis, new advances, extensions and applications of the PDEM, including the fluctuation of nonlinear structures, response analysis of MDOF structures by the adaption of Q-SPM in the PDEM, time-variant life-cycle reliability and optimal control of civil structures, are discussed or exemplified. Problems to be further studied are pointed out.