PDEM-based stochastic response and reliability analysis of structures

The present paper outlines the probability density evolution method (PDEM), which is capable of capturing probability density function of the responses or performance indices of nonlinear MDOF structural systems. The PDEM is rooted in the principle of preservation of probability. With elaborating the state space description and random event description of the principle, it is found that when we examine the problem completely from the random event description, a generalized density evolution equation can be established. Combining the deterministic dynamic analysis and evolution of densities, the generalized density evolution equation is numerically tractable. The PDEM can be applied and extended to stochastic dynamic response analysis of linear and nonlinear structures, dynamic reliability evaluation and structural system reliability evaluation, etc. The problems open are discussed.